Hot Tearing and Deformation in Direct-Chill Casting of Aluminum Alloys

Hot tearing and deformation in direct-chill casting of aluminum alloys

Suyitno

Hot tearing and deformation in direct-chill casting of aluminum alloys

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus Prof. dr. ir. J.T. Fokkema, voorzitter van het College voor Promoties, in het openbaar te verdedigen op maandag 30 mei 2005 te 10.30 uur

door

Suyitno

bachelor of engineering in werktuigbouwkunde master of science in materialkunde geboren te Semarang, Indonesia

Dit proefschrift is goedgekeurd door de promotor: Prof. ir. L. Katgerman

Toegevoed promotor: Dr. W.H. Kool

Samenstelling promotiecommissie:

Rector Magnificus, voorzitter Prof. ir. L. Katgerman, Technische Universiteit Delft, promotor Dr. W.H. Kool, Technische Universiteit Delft, toegevoed promotor Prof. dr. R. Boom, Technische Universiteit Delft & CORUS Prof. dr. I.M. Richardson, Technische Universiteit Delft Prof. dr. ir. S. van der Zwaag, Technische Universiteit Delft Prof. dr. A. Mo, SINTEF Materials Technology, Oslo, Norway Dr. ir. R.N. Kieft, CORUS RD&T, Ijmuiden

ISBN 90-9019393-6

All right reserved. No part of the material protected by this copy right notice may be reproduced or utilized in any form or by any means, electronical or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the author.

Table of Contents

Chapter 1...... 1 Introduction...... 1 1.1 Direct-chill casting of aluminum alloys ...... 1 1.2 Hot tearing...... 4 1.3 Outline of this thesis...... 10 Chapter 2...... 15 FEM simulation of mushy zone behavior during direct-chill casting of an Al−4.5%Cu alloy ...... 15 2.1 Introduction...... 16 2.2 Modeling ...... 17 2.3 Experiment ...... 26 2.4 Results...... 27 2.5 Discussion ...... 34 2.6 Conclusions...... 37 Chapter 3...... 41 Hot tearing criteria evaluation for direct-chill casting of an Al−4.5%Cu alloy ...... 41 3.1 Introduction...... 42 3.2 Modeling ...... 43 3.3 Hot Tearing Criteria ...... 45 3.4 Results...... 52 3.5 Discussion ...... 60 3.6 Conclusions...... 67 Chapter 4...... 69 Effects of casting speed and alloy composition on structure formation and hot tearing during direct-chill casting of Al–Cu alloys...... 69 4.1 Introduction...... 70 4.2 Experimental procedure ...... 72 4.3 Computer simulation...... 74 4.4 Results...... 78 4.5 Discussion ...... 90 4.6 Conclusions...... 94 Chapter 5...... 99 Hot tearing study of Al–Cu billets produced by direct-chill casting...... 99 5.1 Introduction...... 100

5.2 Experimental procedure ...... 100 5.3 Results...... 101 5.4 Discussion ...... 110 5.5 Conclusions...... 112 Chapter 6...... 117 Model and simulation for prediction of hot tearing in aluminum alloys...... 117 6.1 Introduction...... 118 6.2 Physical model ...... 119 6.3 Mathematical model...... 121 6.4 Simulation ...... 125 6.5 Results...... 128 6.6 Discussion ...... 141 6.7 Conclusion...... 147 Chapter 7...... 151 Thermal contraction experiment for prediction of ingot distortions...... 151 7.1 Introduction...... 152 7.2 Experimental Procedure ...... 153 7.3 FEM Simulation...... 154 7.4 Results and Discussion...... 155 7.5 Conclusions...... 161 Summary...... 163 Samenvatting ...... 167 Appendix A...... 171 List of Publications ...... 175 Acknowledgment ...... 179 Curriculum Vitae ...... 181

Chapter 1

Introductionα

1.1 Direct-chill casting of aluminum alloys Direct-chill (DC) casting, which was invented independently in the early 1930s [1] and 1940s [2], is a semi-continuous process for producing extrusion billets and rolling slabs. Although the process has been known for a relatively long time, the continuous technological development is still going on. This is due to the demand for more effectiveness and efficiency in this process with improving quality and productivity. Also more critical alloys are cast. Some comprehensive papers reviewing recent developments can be found in refs. [3-5]. The DC casting processes can be classified based on the applied casting orientation and are distinguished between vertical or horizontal direct-chill casting where the slab or billet moves in downward or horizontal direction, respectively.

α Adapted from the paper in: Progress in Materials Science, vol. 49, no. 5, 2004, pp. 629-711

Chapter 1

For casting aluminum billets and slabs, which will be used in wrought alloy applications, DC casting is the standard industrial casting technique. The vertical DC casting process is schematically shown in Fig. 1.1. Casting is performed by pouring the liquid metal from furnace (1) through the launder (2) inside a stationary mold (3) onto a moving bottom block (4), which is stationary in the beginning. The moving bottom block moves downwards and the billet or slab will moves with it. The mold is cooled by water flow that is called primary cooling. At the exit of the mold, the water flow directly impinges on the billet or slab that is called the secondary cooling. Because of the effective cooling, solidification proceeds rather fast. The casting process is stopped when the billet or slab has reached the desired length.

2 3 3

billet

Figure 1.1. Schematic diagram of DC casting apparatus. 1) tilting furnace, 2) launder, 3) hot-top round mold, and 4) bottom block.

2 Introduction

Figure 1.2. Solidification front in DC casting.

The schematic view of the solidification front during DC casting is shown in Fig. 1.2. The solidification front forms a sump which its depth increases with distance from the surface of billet or slab. In the solidification front, three phase regions (solid, mushy and liquid) are developed. The vertical length of the regions is dependent on the casting parameters (i.e. casting speed, water flow rate, alloy composition, dimension of billet or slab). In DC casting, the name “mushy zone” is somewhat misleading, as its top part is actually a slurry, because the newly formed grains are still suspended in the liquid. Only after the temperature has dropped below the coherency temperature, a real mush is formed. Commonly, three stages are known during the casting: start-up, steady state and ending stage. The position of the solidification front, the temperature field and stress and strain fields are the major characteristics in these stages. In the start-up and ending stages, they change with time. The variation of the solidification front, temperature field and stress and strain fields in the start-up phase leads to typical defects such as the formation of hot tears and deformation of the billet or slab.

3 Chapter 1

1.2 Hot tearing

1.2.1 Solidification behavior Unlike pure metals, which solidify at one temperature, alloys transform gradually from liquid to solid over a (wide) temperature interval. During casting there is a considerable time during which the alloy consists of both solid and liquid. The material in this semi-solid state is divided into two classes: slurries and mushes. A slurry is defined as a liquid with suspended solid particles. At some temperature solid grains start to interact with each other and the material develops certain strength. Below this temperature, the material is called a mush, i.e. a solid network with liquid in between. The solid fraction at which this transition occurs varies between 0.25 and 0.6, depending on the morphology of the solid particles. Because of the strongly different mechanical behavior of these different morphologies, slurries are usually described by viscosity-based models and mushes are usually described by deformation-based models [6]. The viscosity-based models start from the liquid side and are modified to take into account the effect of the increasing amount of solid particles. The deformation-based models are based on models for hot working, which are modified to take into account the presence of liquid. The transition from a slurry to a mush remains complicated to model, and a satisfactory model, which describes the behavior for the complete solidification range, is yet to be developed. The solidification process can be divided in four stages, based on the permeability of the solid network [10,13,16,7]: Mass feeding, in which both liquid and solid are free to move; Interdendritic feeding, in which the remaining liquid has to flow through the dendritic network. After the dendrites have formed a solid skeleton, the remaining liquid has to flow through the dendritic network. A pressure gradient may develop across the mushy zone by solidification shrinkage occurring deeper in the mushy zone. However at this stage the permeability of the network is still large enough to prevent pore formation; Interdendritic separation, in which the liquid network becomes fragmented and pore formation or hot tearing may occur. With increasing solid fraction, liquid is isolated in pockets or immobilised by surface tension. When the permeability of the solid network becomes too small for the liquid to flow, further thermal contraction of the solid will cause pore formation or hot tearing; Interdendritic bridging or solid feeding, in which the ingot has developed a considerable strength and solid-state creep compensates further contraction. At the final stage of solidification (fS > 0.9), only isolated liquid pockets remain and the ingot has a considerable strength. Solid-state creep can now only compensate solidification shrinkage and thermal stresses. In the casting practice of alloys one is only familiar with various defects occurring in the final product. One of the main defects is hot tearing (also

4 Introduction mentioned hot cracking, or hot shortness). From many studies [8-16] starting already in the fifties, and reviewed by Novikov [17] and Sigworth [18], it appears that hot tears initiate above the solidus temperature and propagate in the interdendritic liquid film. This result in a bumpy fracture surface covered with a smooth layer of liquid film and sometimes with solid bridges that connect or connected both sides of the crack [15,16,19-25]. During solidification, the liquid flow through the mushy zone decreases until it becomes insufficient to fill initiated cavities so that they can grow further. It is known that a fine grain structure and controlled casting (without large temperature and stress gradients) help to avoid hot cracking. The hot cracking susceptibility depends on the composition of an alloy and their connection is many times established [26]. During the DC casting of billet, the hot tear formation is critical during the start-up phase and at high casting speed in steady state phase. The ramping procedure is commonly applied in the start-up phase for avoiding the hot tear. The hot tear is developed in the center of a billet. An illustration of hot tears in the start- up phase and the steady-state phase due to increasing casting speed are shown in Figs. 1.3 and 1.4, respectively. In the first two stages of solidification, feeding is usually sufficient to avoid any casting defects. It is mainly the “interdendritic separation” stage in which the ingot is vulnerable to pore formation and hot tearing. A large freezing range alloy promotes hot tearing since such an alloys spends a longer time in the vulnerable state in which thin liquid films exist between the dendrites. The liquid film distribution is determined by the dihedral angle θ. With a low dihedral angle, the liquid will tend to spread out over the grain boundary surface, which strongly reduces the dendrite coherency. With a high dihedral angle the liquid will remain as droplets at the triple points so that the solid network holds its strength. Apart from these intrinsic factors, the solidification shrinkage and thermal contraction impose strains and stresses on the solid network, which are required for hot tearing. It is argued that it is mainly the strain and the strain rate, which are critical for hot tearing [9,16]. Stresses do not seem critical as the forces available during solidification are very high compared to the stresses a semi-solid network can resist [16].

5 Chapter 1

Figure 1.3. The hot tear in the start-up phase of 20 cm radius billet. a) radial and b) longitudinal cross section view.

Figure 1.4. The hot tear in the steady state phase of 20 cm radius billet.

6 Introduction

1.2.2 Hot tearing theories A lot of efforts have been devoted to understand the hot tearing phenomenon. The compilation of research in this field has been done by Novikov [17], Sigworth [18] and Eskin et al. [26]. Zheng et al. [27] reviewed the possible causes of hot tearing. Some of the hot tearing mechanisms, suggested in literature, are briefly described below. Novikov and Novik [28] have reported that at low strain rates grain boundary sliding is the main mechanism of deformation of a semi-solid body. The load applied to the semi-solid body will be accommodated by a grain boundary displacement that is lubricated by the liquid film surrounding the grain. Prokhorov [29] proposed a model for deformation of the semi-solid body. If two tangential forces τ1 and τ2 are applied to the semi-solid body in equilibrium, the response of the body manifests itself as grain movement and at some point the grain will touch each other. The liquid covering the grain will circulate to the lowest pressure point. Further deformation will be possible if the surface tension and resistance to liquid flow are sufficient to accommodate the stress imposed. If not, a brittle intergranular fracture or hot tearing will occur. In relation to this theory, Prokhorov postulated that: (1) an increase in film thickness increases the fracture strain, (2) a decrease in grain size increases the fracture strain, (3) any non-uniformity of grain size decreases the fracture strain. Based on this theory, the main measure for hot tearing is the ductility of the semi-solid body. A hot tear will occur if the strain of the body exceeds its ductility. A theory of shrinkage-related brittleness divides the solidification range into two parts. In the upper part the coherent solid-phase network does not exist. Cracks or defects occurring in this stage can be healed by liquid flow. As the solidification progresses and the solid fraction further increases, at a certain stage or a certain solid fraction a coherent network is formed. This stage is considered as the start of linear shrinkage. At the coherence point temperature and below, the shrinkage stress is imposed onto the semi-solid body. Fracture or hot tearing occurs if the shrinkage stress exceeds the rupture stress [30,31]. Pellini [9] suggested a hot tearing theory based on the strain accumulation with the following main features: (1) cracking occurs in a hot spot region, (2) hot tearing is a strain-controlled phenomenon which occurs if the accumulated strain of the hot spot reaches a certain critical value, and (3) the strain accumulated at the hot spot depends on the strain rate and time required for a sample to pass through a the stage where the interdendritic liquid exists as thin layer. The most important factor of hot tearing based on this theory is the total strain at the hot spot region. The total strain is the additive of strain over a period within which the hot spot exists. With taking into account that the highest strain accumulates in the liquid

7 Chapter 1 film, Dodd [32] and Metz and Flemings [33] explain the increase of hot tearing caused by the segregation of a low-melting component from the viewpoint that this addition increases the time of the liquid film existence. Although Pellini mentions a critical value of the accumulated strain, it is not clear whether it is ductility or another entity. The Pellini theory is a basis for a hot tearing criterion proposed by Clyne and Davies [34]. Some authors suggest that not the strain but the strain rate is the critical parameter for hot cracking. The physical explanation of this approach is that the strain rate during solidification is limited by the minimum strain rate at which the material will fracture. Prokhorov [29] is the first who suggested a criterion based on this approach. More recently, a strain-rate based hot tearing criterion is proposed by Rappaz et al. [35]. Yet another approach to the hot tearing phenomenon is the assumption that failure take place at a critical stress. The liquid surrounding the grain is considered as a stress riser of the semi-solid body [36,37]. In this theory, a liquid-filled crack is considered as a possible crack initiation site. The propagation of the crack is determined by the critical stress [37]. The critical stress is mostly determined using the modified Griffith energy balance approach. The modification of the Griffith approach particularly accounts for the effect of plasticity as proposed by Gilman [38] and Orowan [39]. Another approach within the fracture mechanics theory is proposed by Sigworth [18] who considers a possibility of applying a liquid-metal- embrittlement concept to the hot tearing case. There is also a group of hot tearing theories that consider the hindered feeding of the solid phase by the liquid as the main cause of hot tearing. Niyama [40] and Feurer [41] use this approach to derive the hot tearing criterion. Based on this theory, hot tearing will not occur as long as there is no lack of feeding during solidification. Clyne and Davies [13,34,42] give more attention to the time spent in the mushy state. The last stage of solidification is considered as most susceptible to hot tearing. However, during the further decrease of the liquid fraction, bridging between adjacent dendrites is established so that the interdendritic separation is prevented. Based on this models, several hot tearing criteria have been postulated in the past decades. Feurer [12] used the fluid flow through a porous network to calculate the afterfeeding by liquid metal. Hot tears will initiate when this afterfeeding cannot compensate the solidification shrinkage. Clyne and Davies [13] defined a cracking susceptibility coefficient (CSC) as the ratio between the time tV during which the alloy is prone to hot tearing and the time tR during which stress relaxation and afterfeeding can take place. These times are defined as the periods during which the fraction liquid is between 0.1 and 0.01 and between 0.1 and 0.6, respectively. These criteria were combined with a heat flow model describing the

8 Introduction

DC casting process by Katgerman [43]. This enabled the determination of the cracking susceptibility coefficient as a function of the casting parameters. Unfortunately, the above criteria are restricted in their use because they give only a qualitative indication for the hot tearing susceptibility. The ductility of semi-solid non-ferrous (including aluminium) alloys was used as a basis for a hot shortness criterion suggested by Novikov [17]. A characteristic called a “reserve of plasticity in the solidification range” is proposed which is the difference between the average integrated value of the elongation to failure and the linear shrinkage in the brittle (or effective, or vulnerable) temperature range. Prokhorov [29] formulated a mechanical criterion, in which the hot cracking sensitivity is determined by the shrinkage and apparent strain rate in the mush in relation to the fracture strain rate of the mush. In this approach, effects of the surrounding configuration are accounted for by the apparent strain rate. The first two-phase model, which takes into account both fluid flow and deformation of the solid network, is the Rappaz–Drezet–Gremaud (RDG) hot tearing criterion [35]. The RDG criterion is formulated on the basis of afterfeeding, which is limited by the permeability of the mushy zone. At the solidification front the permeability is high but deeper in the mushy zone the permeability is restricted. A pressure drop along the mushy zone exists which is a function of this permeability and the strain rate. If the local pressure becomes lower than a critical pressure, a cavity is initiated. The model is implemented in a thermomechanical model for DC casting by Drezet et al. [44] to predict hot tearing during billet casting. The hot tearing susceptibility is found higher during start-up of the casting and in the centre of the billet, which agrees with general casting practice. A further development of the RDG criterion is carried out by Braccini et al. [45]. They included plastic deformation of the solid phase and a criterion for the growth of a cavity. They base their model on two simplified geometric models, one for a columnar dendritic and one for an equiaxed dendritic structure. Explicit relations are developed for critical strain rates and they indicate that the critical strain rate decreases with increasing solid fraction. Many studies have used tensile testing at semi-solid temperatures to study hot tearing either by in-situ solidification experiments [19-21,7,46-48] or by reheating specimens from room temperature [23,24,37,47,49,50]. Both techniques led to the following general results. In several aluminum alloys it is observed that both strength and ductility strongly decrease from just below the solidus temperature to above solidus temperature, while the fracture surface changes from rough, related to the ductile behavior, to smooth, related to the presence of a liquid film. Further, cracks initiate at micro-pores or molten inclusions and continue along grain boundaries.

9 Chapter 1

1.3 Outline of this thesis This thesis deals with hot cracking during direct-chill casting of aluminum alloys. Issues addressed are the thermomechanical modeling of direct-chill casting, the implementation and evaluation of existing hot tearing criteria, experimental observation the microstructure and hot tearing at various parameters during DC casting, proposing a route for hot tearing prediction and thermal contraction during and after solidification enabling the prediction of ingot distortion. In Chapter 2, the finite element simulation of DC casting is described. The emphasis is put on the mushy zone and close surroundings. The effect of casting speed and start-up conditions on the stresses, strains, depth of sump and length of mush is investigated. The computation described in this chapter will serve as a basis for understanding the computed hot cracking tendencies using various hot tearing criteria that are investigated in the next chapter. In Chapter 3, various hot tearing criteria are implemented and evaluated. Calculations of hot cracking tendency using these criteria are performed at various casting speed and casting conditions. The results are compared and critically examined. In Chapter 4, experimental observation after the direct-chill casting of Al-Cu alloys are reported. The basic aim of this chapter is to analyze the effects of alloy composition and casting speed on structure formation and hot tearing of Al–Cu alloys. The analysis is based on systematic examination of billets of binary Al–(1– 5)% Cu alloys cast at different casting speeds. Experimental results on structure and hot tearing are correlated to computer simulated solidification and hot tearing patterns. Thermomechanical behavior of a solidifying billet is combined with available hot tearing criteria and the results are compared to the experiment. In chapter 5, observation of the hot tear surface and micro-porosity are reported. The aim of this work is to investigate the hot tear surface of Al–Cu alloys with different copper concentrations produced by DC casting. The billets of Al–(1- 4.5%)Cu alloys were cast with a ramping casting speed (i.e. steadily increase followed by a steadily decrease). The microstructure and porosity fraction are examined. The possible interaction between the hot tear and porosity is addressed. In chapter 6, a hot tearing model is derived based on cavity formation when there is insufficient feeding during solidification. The feeding during solidification is incorporated using a transient mass balance equation. The cavity formed becomes a hot tear in case a critical dimension is achieved. The criterion for deciding whether the cavity becomes a hot tear or micro-porosity, which is not found in other models is included. Also, the flow behavior of the semi-solid state has been included in order to model the mechanical response of the semi-solid body.

10 Introduction

In Chapter 7, experimental measurements of linear contraction during and after solidification of an AA5182 alloy are reported. These experimental results are compared to the finite element method (FEM) simulation of thermal contraction. Implementation for the prediction of ingot distortion during the start-up phase of direct-chill casting is also presented.

References [1] Roth, W. (1936) Deutches Reichs patent No. 974203, date of registration 8 August 1936. [2] Ennor, W.T. (1942) US patent No. 2301027, date of registration 3 November 1942. [3] Emley E.F. (1976) International Metals Reviews, Review 206, p. 75. [4] Katgerman, L (1991) Cast Metals, 4, 3, p. 133. [5] Grandfield, J. and McGlade, P.T. (1996) Materials Forum, 20, p. 29. [6] Quaak, C.J. (1996) PhD Thesis, Delft University of Technology, Delft, The Netherlands. [7] Forest, B. and Bercovici, S. (1980) Proc. Conf. Solidification Technology in Foundry and Casthouse, University of Warwick, Coventry, Metals Society, UK, p. 607. [8] Bishop, H.F., Ackerlind, C.G. and Pellini, W.S. (1952) AFS Transactions, 60, p. 818. [9] Pellini, W.S. (1952) Foundry, 80, p. 124. [10] Borland, J.C. (1960) British Welding Journal, 7, p. 508. [11] Metz, S.A. and Flemings, M.C. (1970) AFS Transactions, 78, p. 453. [12] Feurer, U. (1976) Giessereiforschung , 28, p. 75. [13] Clyne T.W. and Davies G.J (1979) Proc. Conference on Solidification and Castings of Metals, Metals Society, London, UK, p. 275. [14] Matsuda, F., Nakagawa, H., Katayama, S. and Arata,Y. (1982) Transaction of Japan Welding Society, 13, p. 41. [15] Rogberg, B. (1983) Scandinavian Journal of Metallurgy, 12, p. 51. [16] Campbell, J. (1991) Castings, Butterworth Heinemann, Oxford, UK. [17] Novikov, I.I. (1966) Goryachelomkost tsvetnykh metallov i splavov (Hot Shortness of Non-Ferrous Metals and Alloys), Moscow: Nauka (in Russian). [18] Sigworth, G.K. (1996) AFS Transactions, 104, p. 1053. [19] Spittle, J.A. and Cushway, A.A. (1983) Metals Technology, 10, p. 6.

11 Chapter 1

[20] Ohm, L. and Engler, S. (1990) Giessereiforschung, 42, 4, p. 149. [21] Nedreberg, M.L. (1991) PhD Thesis, University of Oslo, Oslo, Norway. [22] Boyle, J.P., Mannas, D.A. and Walsh, D.W. (1992) International Symposium on Physical Simulation, eds. D. Ferguson and J. Jacon, Dynamic Systems Inc, Poestenkill, NY, USA, p. 165 [23] Spittle, J.A., Brown, S.G.R., James, J.D. and Evans, R.W. (1997) Proceedings of 7th Intern. Symposium on Physical Simulation, Tsukuba, Japan, p. 81. [24] Van Haaften, W.-M., Kool, W.H. and Katgerman, L. (2000) Continuous Casting, Ed. K. Ehrke and W. Schneider, Wiley-VCH, Germany, p. 239. [25] Farup, I., Drezet J-.M. and Rappaz, M. (2001) Acta Materialia, 49, p. 1261. [26] Eskin, D.G., Suyitno and Katgerman, L. (2004) Progress in Materials Science, 49, 5, p. 629. [27] Zheng, M., Suyitno and Katgerman, L. (2001) Proc. 22nd Risø International Symposium on Materials Science, Edts:Dinesen AR, Eldrup M, Juul Jensen D, Linderoth S, Pedersen TB, Pryds NH, Schrøder Pedersen A, Wert JA, Risø National Laboratory, Denmark, p. 455. [28] Novikov, I.I. and Novik (1963) Doklady Akad. Nauk SSSR, Ser. Fiz., 7, p. 1153. [29] Prokhorov, N.N. (1962) Russian Castings Production, no. 2, p. 172. [30] Lees, D.C.G. (1946) Journal Institute of Metals, 72, p. 343. [31] Korol’kov, A.M. (1963) Casting properties of metals and alloys, Consultants Bureau, New York, USA. [32] Dodd, R.A. (1956) Foundry Trade Journal, p. 321. [33] Metz, S.A. and Flemings, M.C. (1969) AFS Transactions, 77, p. 329. [34] Clyne, T.W. and Davies, G.J (1975) British Foundrymen, 68, p. 238. [35] Rappaz, M., Drezet, J.M. and Gremaud, M. (1999) Metallurgical and Materials Transactions A, 30A, p. 449. [36] Patterson, K. (1953) Giesserei, 40, p. 597. [37] Williams, J.A and Singer, A.R.E. (1968) Journal Institute of Metals, 96, p. 5. [38] Gilman, J.J. (1960) Proceedings Conference of Plasticity; 2nd Symposium on Naval Structural Mechanics, Rhode Island, RI, USA, 1960, p. 43. [39] Orowan, E. (1950) Fatigue and Fracture of Metals, ed. W.M. Murray, Technology Press of MIT, Cambridge, Massachussets, USA, p. 139.

12 Introduction

[40] Niyama, E. (1977) Japan–US Joint Seminar on Solidification of Metals and Alloys, p. 271. [41] Feurer, U. (1977) Quality Control of Engineering Alloys and the Role of Metals Science, Delft University of Technology, p. 131. [42] Clyne, T.W. and Davies, G.J. (1981) British Foundryman, 74, p. 65. [43] Katgerman, L. (1982) Journal of Metals, 34, 20, p. 46. [44] Drezet, J-.M. and Rappaz, M. (2001) Light Metals 2001, ed. J.L. Anjier, TMS, Warrendale, PA, USA, p. 887. [45] Braccini, M., Martin, C.L. and Suery, M. (2000) Modeling of Casting Welding and Advanced Solidification Processes IX, eds. P.R. Sahm, P.N. Hansen, and J.G. Conley, Shaker Verlag, Aachen, p.18. [46] Lankford, W.T. (1972) Metallurgical Transactions, 3, p. 1331. [47] Magnin, B., Maenner, L., Katgerman, L. and Engler, S. (1996) Materials Science Forum, 217–222, p. 1209. [48] Instone, S., StJohn, D. and Grandfield, J. (2000) International Journal of Cast Metals Research, 12, p. 441. [49] Martin, C.L., Favier, D. and Suéry, M. (1999) International Journal of Plasticity, 15, p. 981. [50] Fredriksson, H. and Lehtinen, B. (1979) Proceedings Conference on Solidification and Casting of Metals, University of Sheffield, Sheffield, UK, p. 260.

13 Chapter 1

Chapter 2

FEM simulation of mushy zone behavior during direct- chill casting of an Al−4.5%Cu alloyβ

In this chapter, characteristic parameters such as stresses, strains, sump depth, mushy zone length and temperature fields are calculated through the simulation of the DC casting process for a round billet by using a finite element method. Focus is put on the mushy zone and solid region close to it. In the center of the billet, circumferential stresses and strains (which play a main role in hot cracking) are tensile at temperatures close to the solidus temperature, whereas they are compressive near the surface of the billet. The stresses, strains, depth of sump and length of mushy zone increase with increasing casting speed. They are maximum in the start-up phase and are reduced by applying a ramping procedure in the start- up phase (application of a lower but slowly increasing casting speed during start- up). Stresses, strains, depth of sump and length of mushy zone are highest in the center of the billet for all casting conditions considered.

β Based on the paper in: Metallurgical and Materials Transactions A, vol. 35A, no. 9, 2004, pp. 2917-2926.

Chapter 2

2.1 Introduction Direct-chill (DC) casting is a semi-continuous process for producing extrusion billets and rolling slabs. In this casting process, liquid metal is poured onto a moving bottom block inside a mold. The mold is cooled by water flow that is called primary cooling. At the exit of the mold, water flow directly impinges on the billet or slab, which is called secondary cooling. During the casting process, metal will pass through a mushy state that is critical for the occurrence of some defects such as hot tearing and micro-porosity. The defects are related to the mechanical behavior of the mush, in combination with the feeding possibilities. Understanding of the behavior of the mush during DC casting is not an easy task because of the complex phenomena occurring during the solidification. Modeling of stresses, strains and temperatures during DC casting is generally done by using a finite element method [1-8]. Most researchers were working on the simulation of the thermomechanical behavior of a DC cast slab, and most attention was devoted to the thermomechanical behavior at temperatures lower than the solidus temperature [1-4]. The stresses and strains in the center of a billet at temperatures lower than the solidus temperature are tensile except for the axial strain that is compressive [1,2]. Also the stresses and strains in the center of a slab are found tensile [3,4] Recently, simulation of the thermomechanical behavior of a billet and/or slab at temperatures above the solidus temperature gains significant attention [5- 8]. Several constitutive models of the mushy state are used for simulation of the thermomechanical behavior such as an elastoviscoplastic law [5,6] and Garofalo’s law [7]. All of these models have been fitted to experimental data. In another study [8] solid data are simply extrapolated to temperatures corresponding to the mushy zone up to the coherency point. By applying an elastoviscoplastic law, a tensile circumferential stress in the center of billet and compressive circumferential stress at the billet surface was reported [5,6]. In these studies an increase of the casting speed caused an increase of the principal plastic strain. Another study [7] showed that there is no significant effect of applying Garofalo’s law for the mushy zone on the computed stresses and strains in the a slab, instead of extrapolating the solid data to the mushy range. It is reported [8] that in the start-up phase stresses, strains and strains rates in the mushy zone at 0.95 fraction of solid increase with increasing casting speed. The prediction of the occurrence of defects such as hot tears by using certain criteria requires the computation of the mechanical and physical behavior of the mush. To that purpose, extensive modeling is needed based on thermophysical and thermomechanical data. In this work, the stresses, strains, sump depth, mushy zone length and temperatures fields are calculated through the simulation of the DC

16 FEM simulation of mushy zone behavior during direct-chill casting casting process for a round billet. Focus is put on the mushy zone and its surroundings. The mechanical behavior is explored by means of FEM simulations that include a solidification and constitutive model of the solid and the mushy. The effects of various casting conditions are calculated.

2.2 Modeling

2.2.1 General computation procedure DC casting of a billet, 100 mm radius and 1000 mm length, is simulated. An axi-symmetric model is used in this work. Due to the symmetry, only a half section of the billet and bottom block needs to be modeled. For the simulation, a coupled computation of stress and temperature fields is applied using 4-node rectangular elements with 4 Gaussian integration points. In the simulation, the ingot remains in a stationary position, while the mould and the impingement point of the water flow move upwards with a velocity equal to the casting speed. Continuous feeding of the liquid metal is implemented by activating horizontal layers of elements incrementally. The computational domain is shown in Fig. 2.1. Stresses, strains and temperatures are calculated as a function of position in the billet and time. Equations are solved iteratively using certain time steps. The computation continues until a preset time is reached. In the calculation a solidification model and a constitutive model are used, which are incorporated in the finite element iteration.

17 Chapter 2

z Γ6

mold

Γ3 billet

Γ4

Γ7 Γ5

bottom block Γ2 r

Γ1 Figure 2.1. Computational domain of the DC cast billet. Γ1 - Γ7 correspond with boundary conditions defined in Section 2.2.3. 2.2.2 FEM formulation The FEM model of the billet is derived based on the coupling of the heat flow and mechanical equilibrium equations.

Finite element equation of the heat flow equations For the non-stationary condition, the thermal balance equation is written as:

k q ∂T ∇T + v = ( 2.1 ) c p ρ c p ρ ∂t

where T is the temperature, k is the thermal conductivity, qv is the heat source, cp is the specific heat, ρ is the density, and t is the time. In case of solidification, the heat source is the latent heat released during the solidification. The boundary conditions imposed to the thermal balance equation are:

T = Tc ( 2.2a )

∂T k = q ( 2.2b ) ∂n c

18 FEM simulation of mushy zone behavior during direct-chill casting

∂T k = α ()T − T ( 2.2c ) ∂n c f where Tc is the temperature of the body surface, qc is the heat flux normal to the body surface, αc is the heat convection coefficient and Tf is the temperature of the liquid. S is the total surface of the body. The finite element formula is obtained by applying the Galerkin method [9] to Eq.2.1 with the boundary conditions Eqs. 2.2a-c and assuming that the temperature T in the element can be approximated by the temperature vector {T}e on the nodes by an interpolation function [H] as

T = []H {}T e , and [G] is the matrix of the gradient operator [N];

[]K I {T}+ []C {T&}= {}F ( 2.3 ) where:

T T T ∂ [K I ]= ∑ ∫ [][]G k G dV + ∑ ∫ []H α c []H dS − ∑ ∫ []H k []H dS e V e S e S ∂n

( 2.4 )

T []C = ∑ ∫ [H ]ρc p [H ]dV ( 2.5 ) e V

T T T ( 2.6 ) {}F = ∑ ∫ []H qv dV − ∑ ∫ [H ] qc dS − ∑ ∫ [H ] α cT f dS e V e S e S

The following notations are used here: [KI] is the global heat capacity matrix, [C] is the global conductivity matrix and {F} is the global load vector. Various time-integration schemes are available for solving Eq. 2.3. The computed temperature is used for updating the temperature dependent material properties and computing thermal stresses in the mechanical computation.

Finite element equation of the mechanical equilibrium equations The statement of virtual work is as follows:

T T T ∫δε ij σ ij dV − ∫δui fi dV − ∫δui ti dΓ = 0 ( 2.7 ) V V Γ

19 Chapter 2

where σij is the internal stress tensor, fi are the components of externally applied forces per unit volume, ti are the components of the applied surface traction per unit length acting on the boundary Γ, δui are the components of the virtual displacement vector, δεij is the strain tensor corresponding to the virtual displacement, and V is the volume element. The additive decomposition for the rate of the strain tensor in a thermo- elasto-viscoplastic deformation in a solid body has the form:

e T vp ε&ij = ε&ij + ε&ij + ε&ij ( 2.8 )

e T whereε&ij are the components of the elastic strain rate tensor,ε&ij are the components vp of the thermal strain rate tensor andε&ij are the components of the viscoplastic strain rate tensor. The linear elastic deformations rate are related to the stress rates as follows:

e ε&ij = Eijklσ& kl ( 2.9 )

where Eijkl denote the material coefficients that are defined by Young’s modulus and Poisson’s ratio. The thermal strain rate tensor is a function of the temperature variation and reads:

T ε&ij = α ijT& ( 2.10 )

whereα ij is the linear thermal expansion tensor component. The viscoplastic strain rate tensor is formulated as follows:

vp  ϕ f ()σ ,T T ≤ T sol ε&ij =  ( 2.11 ) ϕ f ()σ , f S ,T T 〉 T sol

0 σ ≤ σ Y ϕ =  1 σ 〉σ Y

20 FEM simulation of mushy zone behavior during direct-chill casting

where σ is the effective stress determined by the constitutive models, σ Y is the yield stress and Tsol is solidus temperature. Separate constitutive models are applied for the solid region and the semi-solid region as described in Section 2.2.5. Spatial discretization of the mechanical balance equation is done by adopting a purely displacement-based formulation [9]. In the spatial discretization, the incremental displacement vector {∆u} and the incremental strain vector {∆ε} can be related using the strain displacement matrix [B], and interpolated by the nodal displacement vector in the form:

{}∆u = []N {}∆u e ( 2.12 )

{}∆ε = []B {}∆u e ( 2.13 )

The discrete forms of the mechanical balance equations are:

[]K {}{}∆u = ∆L ( 2.14 ) where:

[K ]= ∑ ∫ [][][]B T D B dV ( 2.15 ) e V

T T T vp {}{∆L = ∆L1 }+ ∑ ∫ []B [D]{∆ε }dV + ∑ ∫ [B] [D]{∆ε }dV ( 2.16 ) e V e V where [K] is the incremental stiffness matrix, {∆L} is the total force increment vector, {∆L1} is the external force increment, [D] is the elastic stress-strain matrix, {∆εT} is the thermal strain increment vector, and {∆εvp} is the elasto-viscoplastic strain increment vector. The unknown quantity i.e. the deformation increment {∆u}, can be solved by using Eq. 2.14. A full Newton-Raphson algorithm is applied to treat the set of non-linear algebraic equations that arise after discretization of the non-linear continuum equations. The computation is started with given boundary conditions, initial conditions and a given time step. Eqs. 2.3 and 2.14 are solved iteratively and when values converge for a certain time step, they are then used as initial values for the next time step. The computation continues until the preset time is reached.

21 Chapter 2

2.2.3 Boundary conditions Different boundary conditions are applied to the different boundaries Γ of the billet (Fig. 2.1). At the bottom, Γ1, it is assumed that the convective heat transfer to the environment is constant, and that the position z is constant. At the interface of billet and bottom block, Γ2, the heat transfer is determined by conditions of either contact, non-contact (open gap) or water intrusion, between billet and bottom block. These conditions depend on the gap distance and correspond with different values of the heat transfer coefficient. The values of the heat transfer coefficients depend on temperature (contact and water intrusion situation) or gap distance (non-contact situation). At boundary condition Γ2, the z position of the bottom block is fixed but the billet can freely move in axial and radial direction.

The boundary condition, Γ3, corresponds with either contact or non-contact between billet and mould, and it uses similar criteria and values as for the boundary conditions at Γ2. The billet may freely move in the negative radial direction. The boundary condition Γ3 moves in axial direction with the casting speed. Boundary conditions related to secondary cooling (water flow) are defined in two regions: water impingement zone, Γ4 and downstream zone, Γ5. With the boundary conditions Γ4 and Γ5, the billet may move freely in radial and axial direction.

At boundary condition Γ6 temperature is constant (casting temperature) and the boundary moves in axial direction with the casting speed. At the boundary Γ7 heat flux is zero, due to the axial symmetry. All boundary condition data are summarized in Table 2.1. In this table the following parameters are defined: hbc is the heat transfer coefficient from bottom to the surrounding, htc htnc and htwi are the heat transfer coefficients between bottom block and billet for contact, non-contact and water intrusion situation respectively, hmc and hnc are the heat transfer coefficients of mold and billet interface in contact and non-contact situations respectively, q is heat transferred, A is area, Qw is water flow rate, Tbulk is temperature of cooling water, Tsat is saturation temperature i.e. the temperature where the water will boil off the surface of the billet, and Vc is the casting speed. Values for htc, htnc and htwi are summarized in Tables 2.2-2.4.

22 FEM simulation of mushy zone behavior during direct-chill casting

Table 2.1. Data of boundary conditions for simulation. 2 Γ1 h = hbc hbc: 50 W/m K [10] o z = constant Tsurroundings: 20 C

Γ2 if −5 h ,h and h [10]  htc d t < 10 m tc tnc twi  if −5 −3 see Tables 2.2-2.4 h = htnc 10 m < d t < 10 m h if −3  twi d t > 10 m

zbottom block = constant 2 Γ3 −5 hmc: 1500W/m K [10] hmc if dt < 10 m h =  htnc: see Table 2.2 h if −5 o  tnc dt ≥ 10 m Tmold: 100 C

Tmold = constant

z = Vct Γ q [11] 4 = 27300 T – 1273088.915 A if T < 120 o q = 94252.48 T – 9240434.453 A if 120 oC ≤ T < 150 oC q = 12259.18 T – 3058560.867 A if T ≥ 150 oC

z = Vct

Γ5 q 1/3 Qw: 150 l/min [11] =(-167000+cTbar)(Qw/60000) ∆T + o A Tbulk: 10 C o 3 Tsat: 90 C 100(∆Tx) 2 c = -21.2035Qw + 1.1508Qw + 62794

Tbar = ( T + Tbulk)/2

∆T = T + Tbulk

∆Tx = T + Tsat z = Vct o Γ Tin: 700 C 6 T = Tin

z = Vct

23 Chapter 2

q = 0 A

Γ7 q = 0 A

Table 2.2. Heat transfer coefficient in contact situation. o 2 T ( C) htc (W/m K) 0 1000 200 1000 500 1000 600 1000 680 1500 700 1500 800 1500

Table 2.3. Heat transfer coefficient in non-contact situation. 2 Gap (m) htnc (W/m K) 0.000 450 0.015 300

Table 2.4. Heat transfer coefficient during water intrusion. o 2 T ( C) htwi (W/m K) 0 1000 100 1000 150 2000 200 3000 400 1000 600 400 700 400

24 FEM simulation of mushy zone behavior during direct-chill casting

2.2.4 Materials data An Al–4.5%Cu billet was simulated. The material of the bottom block was taken as AA6063. Temperature dependent data for thermal conductivity, specific heat, thermal expansion coefficient and Youngs’ modulus were taken from literature [12-15]. 2.2.5 Solidification and constitutive model The simulation uses a solidification model, which accounts for back- diffusion [16]. The fraction of liquid fl is given by: ∗  1−2αs k  1  T −T  k−1  f =  m  ( 2.17 ) l ∗  T −T   1− 2α s k  m l     with

* 1 1 1 α =α s [1− exp(− )]− exp(− ) ( 2.18 ) αs 2 2αs

where Tm is melting temperature of the pure metal, T is temperature, k is partition * coefficient, αs is back diffusion coefficient and α s is modified dimensionless solid state back-diffusion parameter. For the constitutive model of the solid metal, plastic deformation is described by a viscoplastic equation [5].

u n σ = K()()ε& p + ε& po ε p + ε po ( 2.19 ) where σ is true stress (MPa); K is stress at a strain and strain rate of unity (MPa); ε is strain rate (s-1); ε is a small constant plastic strain rate (10-4 s-1); ε is & p & po p -2 plastic strain; ε po is a small constant plastic strain (10 ); u is strain rate sensitivity coefficient; n is strain hardening coefficient. The parameters K, u and n in this equation were fitted to the experimental data described in ref. [5]. They are temperature dependent. The bottom block is assumed to be rigid, so its thermomechanical behavior is not calculated. For the constitutive equation of the mush we use the following expression:

 mQ  m σ = σ o exp()αf s exp ()ε& ( 2.20 )  RT 

25 Chapter 2 where Q is the activation energy which is given by the solid phase deformation behaviour, m is the strain rate sensivity coefficient, R is the gas constant, σ o and α are material constants and ε& is the strain rate. The values for Q, σo, α and m were fitted from experimental data [17] and were Q: 160 kJ/mol; σ o : 4.5 Pa; α: 10.2 and m: 0.26. 2.2.6 Computation Computations were performed for both the start-up phase and the steady state phase. For the start-up phase, four casting conditions denoted 1 to 4 were applied in the computation to calculate the stresses, strains, depth of sump and length of mush as a function of the axial position. The casting modes are shown in Fig. 2.2. The stresses, strains, depth of sump and length of mush were also calculated at a distance of 750 mm from the beginning of the billet, which were considered representative for the steady state phase. The casting speeds selected were constant and equal to 120, 150 and 180 mm/min. Here, the stresses, strains, depth of sump and length of mush were calculated as a function of the radial position in the billet.

160

150

140

130

120

110

100 Casting speed (mm/min)

80 0 100 200 300 400 500 600 Length of billet (mm)

Figure 2.2. The casting modes applied for simulation of the start-up phase of DC casting. Casting conditions: () 1, () 2, (∆) 3 and (x) 4.

2.3 Experiment Although this chapter concentrates on modeling only, one validation experiment was carried out. A billet of an Al−4.5 %Cu alloy was hot top cast in a

26 FEM simulation of mushy zone behavior during direct-chill casting

DC casting pit, situated in our laboratory, under the following conditions: casting speed was 120 mm/min, melt temperature at the launder was 700 oC, and water flow rate was 118 l/min. Billet diameter was 20 cm and billet length was 150 cm. A temperature measurement was performed as a function of time a radial distance of 90 mm. A chromel-alumel thermocouple was used, connected to an acquisition data system. The thermocouple was inserted in the molten metal during steady state casting, fixed at a certain length of the billet and frozen in during solidification.

2.4 Results

2.4.1 General overview of stresses and strains in DC casting

Axial (σzz), radial (σrr) and circumferential (σθθ) stresses during steady state casting are shown in Fig. 2.3, together with the solidus (551.2 oC) and liquidus (654.1 oC) lines, at a casting speed of 120 mm/min. It is seen that stresses develop in the mushy zone in the vicinity of the solidus. It is found that for solid material far from the mushy zone the axial stress is negative (compressive) close to the edge of the billet and positive (tensile) in the center of the billet (Fig. 2.3a). The radial stress is tensile at all positions (Fig. 2.3b). The circumferential stress is compressive close to the edge and tensile in the center of billet (Fig. 2.3c). The stress state in the mushy zone is tensile in the vicinity of the solidus line.

Axial (εzz), radial (εrr) and circumferential (εθθ) viscoplastic strains during steady state casting are shown in Fig. 2.4 for the same casting speed. It is found that for the solid material far from the mushy zone, in contrast with the axial stress, the axial viscoplastic strain is positive (tensile) close to the edge of the billet and negative (compressive) in the center of the billet (Fig. 2.4a). The radial viscoplastic strain is tensile for all locations in the billet (Fig. 2.4b). The circumferential viscoplastic strain is compressive near the edge of the billet and tensile in the center of the billet (Fig. 2.4c). The radial and circumferential viscoplastic strains in the mushy state are tensile in the vicinity of the solidus. The axial viscoplastic strain in the mushy state is compressive.

27 Chapter 2

CL CL CL

551.2 551.2 551.2

a. b. c. Figure 2.3. Axial (a), radial (b) and circumferential (c) stresses (MPa) during steady state casting. Solidus (654.1 oC) and liquidus (551.2 oC) are indicated. Casting speed: 120 mm/min. CL denotes billet center.

28 FEM simulation of mushy zone behavior during direct-chill casting

CL CL CL

551.2

551.2 551.2

- -

0 0

. .

0 0

0.000

0 0

3 9

0 0

0 0 0

0 0

. .

. 1

0 0

. . .

. .

2 0 0 0

0 0

0 0 0

0 0

3 0 6 6 3

a. b. c. Figure 2.4. Axial (a), radial (b) and circumferential (c) strains during steady state casting in MPa. Solidus (654.1) and liquidus (551.2) are indicated. Casting speed: 120 mm/min. CL denotes billet center.

2.4.2 Time evolution of temperature and stresses Fig. 2.5 shows the calculated temperatures at 0, 50, 70 and 90 mm distance from the center of the billet as a function of time, during steady state casting with a casting speed 120 mm/min. The characteristic times, corresponding with the mushy state are 22 s (0 mm), 19 s (50 mm), 13 s (70 mm) and 10 s (90 mm), which correspond with mush lengths of approximately 44, 38, 26 and 20 mm, respectively. It is clear that cooling is more effective near the edge of the billet (curve 5) than in the center of the billet (curve 1). In the figure, also the experimental data of the temperature evolution at a radial distance of 90 mm are given. It is found that the computed result is in excellent agreement with the experimental result. In Fig. 2.6 the time evolution of the axial, radial and circumferential stresses are given both at the center and at a radial distance of 90 mm. Conditions are identical to those of Fig. 2.5. In the center, radial and circumferential stresses are

29 Chapter 2 identical. It can be seen that stresses develop during solidification and further cooling till at a temperature of approximately 200 oC stresses become constant. In the center all stresses are tensile over the whole solid region. In the region close to the edge of billet, situation is more complicated. There, the axial and circumferential stresses are tensile at the mushy zone boundary and become compressive at certain distances. The radial stress is tensile over the whole solid region.

800 200

1 700 150 2,3

600 100 C) o 500 1 2 50 400 5 3 0 300

4 (MPa) Stress -50 Temperature ( Temperature 200 5 4 6 100 -100

0 -150 0 50 100 150 200 0 50 100 150 200 Time (s) Time (s)

Figure 2.5. Time evolution of the Figure 2.6. Time evolution of the stress. temperature. Casting speed: 120 mm/min. Casting speed: 120 mm/min. Steady state. Steady state. Calculated temperatures at 1) axial, 2) radial and 3) circumferential radial distance of 1) 0 mm, 2) 50 mm, 3) stress at the center of the billet, and 4) 70 mm and 5) 90 mm and measured axial, 5) radial and 6) circumferential temperature at radial distance of 4) 90 mm. stress at radial distance of 90 mm.

2.4.3 Development of stresses and strains in and near the mush Fig. 2.7 shows the circumferential stress and circumferential viscoplastic strain for temperatures, which correspond to the mushy state or to the solid region close to the mush, for various locations of the mush. In general these stresses and strains are tensile. At 50 mm from the bottom, which corresponds with the start-up phase of billet casting, stress and strain are highest. They become lower at larger distance from the bottom, when a steady state condition is reached. Near the edge of the billet, stress and strain become lower than in the center of the billet. Fig. 2.8 presents the circumferential stress and circumferential viscoplastic strain during the start-up phase for the various casting modes applied (see Section 2.2.6). The results show that stresses and strains become lower in the order (of casting modes) 3, 1, 4 and 2, which is the same order as found in Fig. 2.2 at 50 mm

30 FEM simulation of mushy zone behavior during direct-chill casting for the momentary casting speed. Clearly casting speed and the start-up conditions influence the stress and strain. The ramping procedure in the start-up phase will reduce the stress and strain. The effect of casting speed on the circumferential stress and viscoplastic strain during steady state casting is shown in Fig. 2.9. The figure clearly shows that an increasing casting speed results in an increase of stress and strain in the mush. The circumferential stress and circumferential viscoplastic strain at solidus temperature are shown in Fig. 2.10, for the center of the billet during the start-up phase. The stresses and strains increase to a maximum at about 50 mm and 40 mm respectively, and then decrease till the steady state value is reached (casting conditions 1, 3) or decrease and then increase again till the steady state value is reached (casting conditions 2, 4). Steady state values are reached at about 140 mm for casting conditions 1 and 3, and at about 390 mm for casting conditions 2 and 4.

30 0.012

25 0.010

20 0.008 1 1 15 0.006 2 2 10 0.004

3 3 5 0.002

Tsol Tsol 0.000 Circumferential stress (MPa) 0 Tliq Tliq Circumferential viscoplastic strain viscoplastic Circumferential -5 -0.002 500 520 540 560 580 600 620 640 660 500 520 540 560 580 600 620 640 660 Temperature (oC) Temperature (oC)

a. b. Figure 2.7. Circumferential stress (a) and circumferential viscoplastic strain (b) in and near the mush. 1) center of the billet at 50 mm from the bottom, 2) center of the billet at steady state and 3) at radial distance of 90 mm at steady state. Casting speed: 120 mm/min.

31 Chapter 2

30 0.012

3 3 25 1 0.010 1 4 4 20 0.008 2 2 15 0.006

10 Tsol Tliq 0.004

5 0.002 Tsol Tliq

0 Circumferential (MPa) stress 0.000

-5 strain viscoplastic Cirrcumferential -0.002 500 520 540 560 580 600 620 640 660 500 520 540 560 580 600 620 640 660 o Temperature ( C) Temperature (oC)

a. b. Figure 2.8. Circumferential stress (a) and circumferential viscoplastic strain (b) in the center of the billet at a distance of 50 mm from the bottom for different start-up casting conditions. Conditions 1-4: see Fig. 2.2.

30 0.012

25 0.010

0.008 20 3 2

1 0.006 3 15 1 2

0.004 10

0.002 5 Tsol Tliq Tsol Tliq

0.000

Circumferential (MPa) stress 0 Circumferential viscoplastic strain -0.002 -5 500 520 540 560 580 600 620 640 660 500 520 540 560 580 600 620 640 660 Temperature (oC) Temperature (oC)

a. b. Figure 2.9. Circumferential stress (a) and circumferential viscoplastic strain (b) in the center of the billet. Steady state. Casting speed is 1) 120 mm/min, 2) 150 mm/min and 3) 180 mm/min.

32 FEM simulation of mushy zone behavior during direct-chill casting

25 0.010

20 0.008

3 15 0.006 4 3 1 2 4 10 0.004 1 2

5 0.002 Circumferential stress (MPa) Circumferential viscoplasticstrain

0 0.000 0 50 100 150 200 250 300 350 400 450 0 50 100 150 200 250 300 350 400 450 Distance from bottom (mm) Distance from bottom (mm)

a. b. Figure 2.10. Circumferential stresses (a) and circumferential viscoplastic strain (b) at solidus temperature as a function of distance from the bottom of the billet for different start-up casting conditions. Casting condition 1-4: see Fig. 2.2.

2.4.4 Mush dimension Fig. 2.11 shows the evolution of the depth of sump, defined by the distance between the location of the solidus and the melt level, and the length of the mushy zone during the start-up phase for the various casting conditions applied (see Section 2.2.6). The results show that the depth of sump and the length of the mushy zone increase to a maximum at about 80 s and then decrease somewhat (casting conditions 1, 3) or decrease somewhat and increase again (casting conditions 2, 4). Steady state is obtained for condition 1 at 145 s (135 mm), 2 at 240 s (385 mm), 3 at 165 s (150 mm) and 4 at 215 s (400 mm). Comparing condition 1 with 3 it is seen that for the higher casting speed steady state is attained after a slightly longer time, and consequently after a longer cast length. Use of ramping delays the time and increase the length for which steady state is reached. The effect of casting speed during steady state on the depth of sump and the length of the mushy zone is presented in Fig. 2.12. In the center of the billet, depth of sump and length of mushy zone are higher than near the edge of the billet. Depth of sump and length of mushy zone increase with increasing casting speed.

33 Chapter 2

200 80

180 70 160 3 60 140 3 4 1 50 4 120 1 2 100 40 2

80 30 60 20 Depth of sump (mm) sump of Depth 40

20 mushy zoneof (mm) Length 10

0 0 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Time (s) Time (s)

a. b. Figure 2.11. Depth of sump (a) and length of mushy zone (b) in the center of billet as a function of time for different start-up casting conditions as defined in Fig. 2.2.

200 80

180 70 160 3 3 60 140 2 2 120 50 1 1 100 40

80 30 60

Depth of sump(mm) of Depth 20 40 Length of mushy zone (mm) mushy of Length 20 10

0 0 0 20406080100 0 20406080100 Distance from center (mm) Distance from center (mm)

a. b. Figure 2.12. Depth of sump (a) and length of mushy zone (b) as a function of radial distance. Steady state. Casting speed: (1) 120 mm/min, (2) 150 mm/min and (3) 180 mm/min.

2.5 Discussion

2.5.1 Stresses and strains during steady state casting Stresses and strains developed in DC cast billets or slabs have been reported by others [1-8]. In general these stresses and strains were calculated using a FEM approach and using certain constitutive models for the solid and/or semi-solid

34 FEM simulation of mushy zone behavior during direct-chill casting metal. However, papers dealing with stresses and strains in round billets are limited [1,2,5,6,8] and they only report on the solid part of the billet. In addition to this, the present paper also reports on stresses and strains in the mush. This study not only uses a constitutive model for the solid state, but also incorporates a constitutive model for the mush. This not only provides data for the mush itself, but it will also influence the results in the solid part. Fracture during solidification of a DC cast billet is characterized by a granular fracture that has a tendency to be brittle [18,19]. In case of brittle fracture, one- directional stress/strain is more important than the three-directional stress/strain. For a billet, axial, radial and circumferential stresses and strains are then the principal stress and strain components in assessing the tendency for fracture and its direction. In general, hot tears in a billet initiated in the mush are found in the center of the billet and have a star-like shape [20-22], which shows that the crack grows in radial directions. Under such conditions, circumferential tensile stresses and strains are determining factors for the hot tear development in the billet. Therefore, this study concentrates on the circumferential stresses and strains, developing in the region around the solidus temperature. In this study it is found that local stresses and strains in the region around the solidus temperature are tensile in the center of billet for all stress/strain components except for the axial strain, which is compressive in the mush. This is in agreement with the results reported in refs. [1,2,5,6]. The stress evolution in the center and near the surface of the billet, as depicted in Fig. 2.6 is also supported by refs. [5] and [6]. In some cases, an axial tensile stress is found with an axial compressive strain. This is also reported in ref. [1], where this phenomenon is attributed to the consequence of a large compressive axial viscoplastic strain rate near the solidification front. Although the present general findings and trends are supported qualitatively [1,2,5,6,8], quoted values of the various stress/strain components are generally different since they strongly depend on the constitutive material model and on the boundary conditions applied. The value of such a comparison is however limited since none of the simulations in literature could be validated so far with experimental data. The material model we used consists of a model for the solid and a model for the semi-solid. Using this approach, a better description of stresses and strains in and near the mush should be found. Validating the temperature evolution as a function of time for a particular position (see Fig. 2.5), excellent agreement is found which strongly indicates that the right boundary conditions were applied in this study. Close to the edge of the billet circumferential stress and strains components are highest and tensile, but the circumferential stress and strain are considerably

35 Chapter 2 lower near the edge than in the center of the billet. Therefore hot tears will preferably develop in the billet center. As a function of time or distance from the mush, stresses and strains develop till a constant value is reached. The time at which they reach the constant value corresponds with a temperature of 200 oC. At this temperature materials parameters K, u and n have become constant as a function of temperature. 2.5.2 Effect of casting rate during steady state casting Stresses, strains, depth of sump and length of mushy zone all increase with increasing casting speed. This is confirmed for stresses [2], for strains [5], for depth of sump [23] and for the length of the mushy zone [24]. A higher sump depth and mushy zone length arise from the lower cooling efficiency per unit billet length at higher casting rate. A higher casting rate will lead to higher strain rates, which give rise to increasing stresses and strains (see Eqs. 2.19 and 2.20). Due to the higher stresses and strains, hot tearing will be promoted by a higher casting speed, which is experimentally confirmed [23]. The mushy zone length found for a casting speed of 120 mm/min is 45 mm in the billet center and 25 mm near the billet edge. Comparable distances are reported elsewhere [24] but for a different alloy and casting speed and for slab instead of billet. Mushy zone length at the billet surface is slightly higher than near the edge (see Fig. 2.12b) due to the specific cooling conditions at the surface/mold interface. Due to the existence of a gap opening in the mold before the secondary cooling stage begins, the cooling at the billet surface is temporarily diminished. This phenomenon is reported elsewhere [25]. 2.5.3 Start-up phase and effect of ramping It is observed that stresses, strains and mushy dimensions have become independent of the cast length (i.e. steady state is reached) at ~140 mm billet length for a casting speed of 120 mm/min. and at ~390 mm billet length for a casting speed of 150 mm/min. When a ramping procedure is applied, steady state is reached within some shorter distance, measured from the location in the billet corresponding with the end of ramping. Of course the total distance measured from the bottom block will be larger in case of ramping. During the start-up phase, circumferential stress and strain are higher than during steady state casting. This is confirmed in ref. [8], where it is found that stresses reach a maximum value in the start-up phase and then decrease to a steady state value. During the start-up phase, sump depth and length of mushy zone increase, reach a maximum and decrease to the steady state value. Similar behavior

36 FEM simulation of mushy zone behavior during direct-chill casting is also reported in ref. [8]. It is recognized that during the start-up phase the formation of hot tears is promoted [8,22,26]. Lowering the casting rate during the start-up phase such as for instance by applying a ramping procedure will suppress the initiation of hot cracks [26,27]. By the ramping procedures applied here stresses, strains, sump depth and mushy zone length are indeed reduced during start-up. It is suggested [26,27] that sump depth is a criterion for hot tear development and that it can be reduced by applying a ramping procedure or using specific starting block material and shape. It is found that the ramping procedures extend the start-up phase (both time and cast length). Once steady state is reached, stresses, strains, sump depth and mushy zone length are determined by the steady state casting speed, and are not influenced by the previous ramping procedure.

2.6 Conclusions From the FEM simulation of direct-chill casting of an Al-4.5%Cu alloy, it is concluded that: 1. The stress and strain states are tensile in the center of billet and compressive in the surface of billet in region around the solidus temperature. 2. Stresses and strains in the mushy zone increase with increasing casting speed and they are maximum in the start-up phase which are reduced by applying a ramping procedure in the start-up phase. 3. The depth of sump and length of mushy zone increase for increasing casting speed and they are maximum in the start-up phase and will become lower by applying a ramping procedure in the start-up phase. 4. Stresses, strains, depth of sump and length of mushy zone are highest in the center of billet for all casting conditions.

References [1] Fjaer, H. and Mo, A.(1990) Metallurgical and Materials Transactions A, 21A, p. 1049. [2] Fjaer, H. and Mo, A.(1990) Light Metals 1990, ed. C.M. Bickert, TMS, Warrendale, PA, p. 945. [3] Hannart, B., Cialti, F. and Schalkwijk, R.V. (1994) Light Metals 1994, ed. U. Mannweiler, TMS, Warrendale, PA, p. 879. [4] Drezet, J.-M., Rappaz, M. and Krähenbuhl, Y. (1995) Light Metals 1995, ed. J. Evans, TMS, Warrendale, PA, p. 941.

37 Chapter 2

[5] Magnin, B., Maenner, L., Katgerman, L. and Engler, S. (1996) Materials Science Forum, 217-222, p. 1209. [6] Magnin, B., Katgerman, L. and Hannart, B. (1995) Modeling of Casting Welding and Advanced Solidification Processes VII, eds. M. Cross and J. Campbell, TMS, Warrendale, PA, p.303. [7] Giron, A., Chu, M.G. and Yu, H. (2000) Light Metals 2000, ed. R.D. Peterson, TMS, Warrendale, PA, p. 579. [8] M’Hamdi, M., Benum, S., Mortensen, D., Fjaer, H.G., and Drezet J.-M. (2003) Metallurgical and Materials Transaction A, 34A, p. 1941. [9] Sluzalec, A. (1992) Introduction to Nonlinear Thermomechanics: Theory and Finite Element Solutions, Springer-Verlag, Germany. [10] Suyitno, Katgerman L. and Burghardt, A. (2002) Proceedings of ASME Heat Transfer Division, 5, p. 147. [11] Zuidema (Jr.), J., Katgerman, L., Opstelten, I.J. and Rabenberg, J.M. (2001) Light Metals 2001, ed. J.L. Anjier, TMS, Warrendale, PA, p. 873. [12] Touloukian, Y.S. and Buyco, E.H. (1970) Thermophysical Properties of Matter; Volume 4 Specific Heat; Metallic Elements and Alloys, IFI/Plenum Press, New York– Washington, USA. [13] Taylor, R.E., Groot, H., Goerz, T. Ferrier, J. and Taylor D.L. (1998) High Temperature-High Pressure, 30, p. 269. [14] Brammer, J.A. and Percival, C.M. (1970) Experimental Mechanics, 10, p.245. [15] Van Haaften, W.M. (1997) Thermophysical Properties of Certain Al Alloys, Internal Report, Delft University of Technology, The Netherlands. [16] Kurz, W. and Fisher, D.J. (1992) Fundamentals of Solidification, Trans- Tech Publications, Aedermannsdorf, Switzerland. [17] Braccini, M., Martin, C.L. and Suery, M. (2000) Modeling of Casting Welding and Advanced Solidification Processes IX, eds. P.R. Sahm, P.N. Hansen, and J.G. Conley, Shaker Verlag, Aachen, p.18. [18] Van Haaften W.M, Kool W.H. and Katgerman, L. (2003) Journal of Materials Engineering and Performance, 11, p. 537. [19] Sigworth, G.K. (1996) AFS Transactions, 104, p. 1053. [20] Drezet, J.-M. and Rappaz, M. (2001) Light Metals 2001, ed. J.L. Anjier, TMS, Warrendale, PA, p. 887. [21] Farup, I. and Mo, A. (2000) Metallurgical and Materials Transactions A, 31A, p. 1461.

38 FEM simulation of mushy zone behavior during direct-chill casting

[22] Nagaumi, H. and Umeda, T. (2003) Journal of Light Metals, 2, p. 161. [23] Commet, B., Delaire, P., Rabenberg, J. and Storm, J. (2003) Light Metals 2003, ed. P.N. Crepeau, TMS, Warrendale, PA, p. 711. [24] Drezet, J.-M., Rappaz, M., Carrupt, B. and Plata, M. (1995) Metallurgical and Materials Transactions B, 26B, p. 821. [25] Buxmann, K (1981) Heat and Mass Transfer in Metallurgical Systems, eds. D.B. Spalding and N.H. Afgan, Hemisphere Publishing Corporation, Washington, USA. [26] Schneider, W. and Jensen, E.K. (1990) Light Metals 1990, ed. C.M. Bickert, TMS, Warrendale, PA, p. 931. [27] Jensen, E.K. and Schneider, W. (1990) Light Metals 1990, ed. C.M. Bickert, TMS, Warrendale, PA, p. 937.

39 Chapter 2

Chapter 3

Hot tearing criteria evaluation for direct-chill casting of an Al−4.5%Cu alloyχ

Predicting the occurrence of hot tears in the direct-chill casting of aluminum alloys by numerical simulation is a crucial step for avoiding such defects. In this study, eight hot tearing criteria proposed in literature, have been implemented and evaluated in a similar finite element simulation as performed in Chapter 2. These criteria were based on limitations of feeding, mechanical ductility or both. It is concluded that six criteria give a higher cracking sensitivity for a higher casting velocity and that five criteria give a higher cracking sensitivity for the center location of the billet. This is considered in qualitative accordance with casting practice. Seven criteria indicate that use of a ramping procedure has no significant effect. However, in industrial practice this is a common procedure, needed for avoiding hot cracking. Based on this only one criterion is in qualitative accordance with casting practice, but since it predicts fracture under conditions used in casting practice, it fails to predict the hot tearing occurrence during DC casting quantitatively.

χ Based on the paper in: Metallurgical and Materials Transactions A, 36A, 2005 (in press).

Chapter 3

3.1 Introduction A hot tear is a fracture formed during solidification due to shrinkage and hindered contraction and lack of feeding, and initiates in the mushy zone. Because of the complex mechanisms acting during the solidification of metals, the prediction of the hot tearing phenomenon is not an easy task. The complex nature of mushy properties gives additional difficulties to apply in a model. Several mechanisms of hot tearing have recently been reviewed [1]. Various criteria which might enable the prediction of hot tears have been proposed [2-10]. These criteria can be classified into those based on non-mechanical aspects such as feeding behavior [2-4] those based only on mechanical aspects [5-7], and those which combine these features [8-,9,10]. Three criteria [2-4] based only on non-mechanical aspects are proposed by Feurer, Clyne and Davies’ and Katgerman. Feurer’s criterion calculates the maximum feeding rate in relation to the shrinkage rate in the vulnerable temperature range, whereas Clyne and Davies’ criterion is based on the simpler approach of time spent in the vulnerable temperature range. Katgerman’s criterion combines both approaches. Also three criteria [5-7] based only on mechanical aspects are proposed by Novikov, Prokhorov, and Magnin et al.. All these mechanical criteria introduce an experimentally determined fracture strain which is compared with the thermal contraction and plastic strain (Prokhorov), the thermal contraction strain only (Novikov), and the plastic strain only (Magnin et al.). These six criteria [2-7] are the oldest criteria proposed in literature and are rather simple in formulation so that they are easily implemented in finite element method (FEM) simulations. The other criteria combining both mechanical and non-mechanical aspects [8-10] are proposed recently and include several parameters, which are complex in formulation and implementation in FEM simulations. In the RDG model [8], the pressure drop in the mush is introduced as the main factor for hot tear development. The pressure drop is equal to the difference of the metallostatic pressure and the local pressure in the mush and depends on the location in the mush. A hot tear will develop if the local pressure in the mush becomes lower than a critical pressure for cavity formation (i.e. if the pressure drop becomes sufficiently high). However, in the model a constant, externally applied strain rate is used and not a local strain rate. An extension of this model is proposed [9], in which the strain rate is determined from the rheological properties of the mush. Further, the concept is introduced that the formation of a cavity will not automatically lead to a growing crack, and a criterion is developed for crack growth. Recently, a model is proposed by us that should be able to predict both hot tearing and the development of micro-porosity [10]. It uses the concept of cavity

42 Hot tearing criteria evaluation for direct-chill casting of an Al−4.5%Cu alloy formation under influence of strain rate [8], counterbalanced by the effect of afterfeeding [2]. If the cavity diameter will remain smaller than a certain critical diameter, micro-porosity is formed and if the cavity diameter will exceed the critical diameter, a crack will develop. The model has not yet been coupled with a FEM simulation. The application of these criteria in DC casting is still limited. Clyne and Davies’, and Katgerman’s criteria are applied for predicting the hot cracking tendency in the start-up phase of DC casting [11]. Hot cracking sensitivity obtained with the Clyne and Davies’ criterion is not affected by the casting speed, but depends on the position in the billet, whereas the sensitivity obtained using Katgerman’s criterion increases with the casting speed. The strain-based criterion (Magnin et al.) is used for the prediction of hot tearing of an Al-4.5%Cu alloy during DC casting [7,12]. It states that cracking will occur if the circumferential [7] or maximum principal [12] plastic strain at solidus temperature exceeds the experimentally determined rupture strain of the materials at a temperature close to the solidus. It is concluded that hot cracking is more likely at higher casting speeds. Implementation of the RDG’s criterion in a FEM simulation for DC casting has been reported [13-15]. The pressure drop is highest in the center of the billet and increases with casting speed [13]. However, some reports [14,15] show that the pressure drop has little relation with the measured crack length measured for various start-up conditions. In some other approach, which did not make use of a specific hot tearing criterion, a one dimensional FEM simulation is performed for DC casting [16-18]. Stresses and pressures in the mush are simulated for the center of the billet and it is stated that their values are a measure for the occurrence of hot tears. A hot tearing criterion was neither formulated nor applied. In the present study, we evaluate numerically eight hot tearing criteria [2-9]. These criteria are implemented in a FEM simulation of DC casting. The hot cracking sensitivity is evaluated for both the start-up phase and the steady state phase and for various casting conditions and casting speeds. It is an extension of an earlier, more limited study, reported elsewhere [19].

3.2 Modeling The computation procedure is similar to that in [18]. Simulation is performed on DC casting of an Al−4.5%Cu billet, 100 mm radius and 1000 mm length. An axis-symmetric model is used and due to the symmetry, only a half section of the billet and bottom block needs to be modeled. For the simulation, a coupled computation of the stress and the temperature fields is applied using 4- node rectangular elements with 4 Gaussian integration points.

43 Chapter 3

In the simulation, the ingot remains in a stationary position, while the mould and the impingement point of the water flow move upwards with a velocity equal to the casting speed. Continuous feeding of liquid metal is implemented by activating horizontal layers of elements incrementally. The computational domain and the boundary conditions applied are given in detail in [18] as well as the solidification model and the constitutive model used. After every time step the hot cracking susceptibility is computed at every node. In general, the schemes for implementation of the hot tearing criteria are shown in Fig. 3.1.

casting process parameters casting process parameters

FEM FEM solidification and constitutive T, t model solidification model

T, ∆T, t, ∆t,σ,ε fl hot tearing criterion hot tearing criterion

HCS HCS

Fiure 3.1. The general schemes in the computation of the hot cracking susceptibility. Left: non-mechanical criteria; right: mechanical criteria including RDG.

The non-mechanical criteria use a FEM simulation to solve the thermal balance equation. The temperature fields (T) obtained using the method are used as input for a solidification model to compute the liquid fraction (fl) during solidification. Input parameters for the non-mechanical criteria and the calculation of the hot cracking susceptibility are the liquid fraction, the depth of sump and the time (t). The mechanical criteria including the RDG’s criterion use a solidification model and a constitutive model to compute the stress and strain fields (σ, ε) as a function of temperature. The models are incorporated in the FEM iteration which is not the case for the non-mechanical criteria. Input parameters for the mechanical criteria and the calculation of the hot cracking susceptibility are the stress and strain fields calculated. The hot cracking susceptibility calculated by the RDG’s criterion is computed by using the strain rate, depth of sump and length of mush as input. The implementation of the eight hot tearing criteria in the computation will be described in the next Section. Computation is performed for two regions in the

44 Hot tearing criteria evaluation for direct-chill casting of an Al−4.5%Cu alloy billet. The first region is from 0 to 400 mm distance from the beginning of the billet (start-up phase). Four casting conditions denoted 1 to 4 are applied in the computation to calculate the hot tearing tendency as a function of the axial position. The casting modes are shown in Fig. 3.2. The second region is at a distance of 750 mm from the beginning of the billet (steady state phase). The casting speeds selected were constant and equal to 120, 150 and 180 mm/min. Here, the hot tearing tendency is calculated as a function of the radial position in the billet.

160

150

140

130

120

110

100 Casting speed (mm/min) 90

80 0 50 100 150 200 250 300 350 400 450 Distance from bottom (mm)

Figure 3.2. The casting modes applied for simulation of the start-up phase of DC casting. Casting conditions: () 1, (~) 2, (∆) 3 and (x) 4.

3.3 Hot Tearing Criteria

3.3.1 Feurer’s criterion Feurer’s theory of hot tearing [2] is a non-mechanical criterion that focuses on the feeding and shrinkage during solidification. This approach considers that hot tearing occurs due to the lack of feeding, which is related to the difficulties of fluid flow through the mushy zone as a permeable medium in competition with solidification shrinkage. Feurer considers two terms, SPV and SRG, indicating maximum volumetric flow rate (feeding term) through a dendritic network and

45 Chapter 3 volumetric solidification shrinkage, respectively. Feurer's criterion states that hot tearing is possible if

SPV < SRG ( 3.1 )

The maximum volumetric flow rate per unit volume through a dendritic network is formulated as follows:

f 2λ2 P SPV = l 2 s ( 3.2 ) 24πc3ηL2

PS = PO + PM − PC ( 3.3 )

PM = ρgh ( 3.4 )

ρ = ρl f l + ρ s f s ( 3.5 )

4γ SL PC = ( 3.6 ) λ2

where fl is volume fraction liquid, λ2 is secondary dendrite arm spacing, Ps is effective feeding pressure, L is length of porous network that is determined as the distance between the locations at coherency and solidus temperature, c is tortuosity constant of the dendritic network, η is viscosity of the liquid phase, γSL is solid liquid interfacial energy, ρ is average density of the mush, g is gravity constant, h is distance to the melt surface, ρl and ρs are densities of liquid and solid, respectively, fl and fs are volume fractions liquid and solid in the dendritic network, respectively, and PO, PM and PC are atmospheric, metallostatic and capillary pressure respectively. The volumetric solidification shrinkage is caused by the density difference between solid and liquid phase, and the shrinkage velocity is given by

46 Hot tearing criteria evaluation for direct-chill casting of an Al−4.5%Cu alloy

 ∂ lnV  1 ∂ρ SRG =   = − ( 3.7 )  ∂t  ρ ∂t where V is a volume element of the solidifying mush with constant mass and t is time. The data used for the computation are shown in Table 3.1. The hot cracking susceptibility based on Feurer’s criterion is expressed in that value of liquid fraction fL for which SPV is equal to SRV. Table 3.1. Data used for the computation applying Feurer’s, RDG’s and Braccini’s criteria.

Symbol Value Unit 3 ρl 2480 kg/m 3 ρs 2790 kg/m

λ2 10 µm c 4.6

η=ηL 0.0013 Pa.s

γSL 0.84 N/m c fs 0.98 e =fL.λ µm θ 6o λ 60 µm -2 σlv 0.914 J.m l 300 µm a 0

3.3.2 Clyne and Davies’ criterion The hot tearing criterion proposed by Clyne and Davies [3] is based on the assumption of Feurer [2] that in the last stage of freezing, it is difficult for the liquid to move freely so that the strains developed during this stage cannot be accommodated by mass and liquid feeding. They consider this last stage as the most susceptible to hot tearing. The cracking susceptibility coefficient is defined by the ratio of the vulnerable time period, where hot tearing may develop, tV, and time available for the stress-relief process, where mass feeding and liquid feeding occur, tR. The cracking susceptibility coefficient HCS reads

47 Chapter 3

t t − t HCS = V = 0.99 0.9 ( 3.8 ) tR t0.9 − t0.4

where t0.99 is the time when the volume fraction of solid, fs, is 0.99, t0.9 is the time when fs is 0.9 and t0.4 is the time when fs is 0.4. 3.3.3 Katgerman’s criterion In a model of Katgerman [4] he combines the theoretical considerations of Clyne and Davies [3] and Feurer [2]. The model defines the hot tearing index, HCS, as follows:

t − t HCS = 0.99 cr ( 3.9 ) tcr − tcoh

where t0.99 is the time when the volume fraction of solid, fs, is 0.99, tcoh is the time when fs is at the coherency point and tcr is the time when feeding becomes inadequate. Time tcr is determined using Feurer’s criterion and is the time for which SPV = SRG. 3.3.4 Prokhorov’s criterion Prokhorov [5] formulated a mechanical criterion, in which the hot cracking sensitivity is determined by the shrinkage and apparent strain rate in the mush in relation to the fracture strain rate of the mush. In this approach, effects of the surrounding configuration are accounted for by the apparent strain rate. It is assumed that during solidification, alloys pass through a low-ductility temperature range that is called the brittle temperature range, BTR. The brittle temperature range is from the coherence temperature till the solidus temperature. The minimum fracture strain in this range is called Dmin. Now, the difference between Dmin and the sum of the linear free shrinkage, ∆εfree, and the apparent strain, ∆εapp, is considered in the brittle temperature range.

The reserve of hot tearing strain, ∆εres, is the minimum value in this interval and is written

∆ε res = min(Dmin − ∆ε free − ∆ε app ) ( 3.10 )

48 Hot tearing criteria evaluation for direct-chill casting of an Al−4.5%Cu alloy

∆ε Dmin − (∆ε free + ∆ε app ) res = ( 3.11 ) BTR BTR

∆ε Since ε& = T& where ε& is strain rate and T& is cooling rate, Eq. 3.11 BTR results in

ε&res = ε&min − ε& free − ε&app ( 3.12 )

A hot tear will form in the solidified body if ε&res ≤ 0, or

ε&min ≤ ε& free + ε&app ( 3.13 )

The criterion is used for both a qualitative and a quantitative prediction of hot tearing. Eq. 3.13 is used quantitatively, whether a hot tear will form or not. However, Eq. 3.13 is very sensitive to the constitutive behavior of the mush, which is in general not precisely known. Therefore, often Eq. 3.12 is used for a more qualitative prediction, in which the hot tearing susceptibility is considered to be −1 given by the inverse of the reserve strain rate ε&res .

The strain rates ε& free andε&app are determined from the FEM analysis. In −1 the calculation, the inverse reserve strain rate ε&res is set to 10000 when ε&res ≤ 0.

The value of Dmin of Al–4.5%Cu was taken from [20]. 3.3.5 Novikov’s criterion The mechanical criterion of Novikov [6,20] considers the hot cracking sensitivity determined by shrinkage strains in the mush in relation to the fracture strain of the mush. He neglects the apparent strain which is used in Prokhorov’s criterion [5]. He proposes a “reserve of plasticity“ pr in the solidification range which is the integrated difference between the elongation to failure, εfr, and the linear shrinkage, εsh. Integration is performed from the coherency temperature till the solidus temperature, which interval he calls the brittle (or effective) -1 temperature range, ∆Tbr. The hot tearing susceptibility is then given by pr where pr is given by

49 Chapter 3

1 Tsol p = ()ε − ε dT ( 3.14 ) r ∆T ∫ fr sh br Tcoh

where Tcoh is the coherency temperature and Tsol is the solidus temperature. To determine the hot cracking susceptibility, the strain due to linear shrinkage was computed with the FEM in the semi-solid region. The fracture strain in the semi- solid region is taken from experimental data for Al–4.5%Cu [20]. 3.3.6 Strain-based criterion. The criterion proposed by Magnin et al. [7] is based on the strain experienced during solidification in relation to the fracture strain in the last stage of solidification. The hot cracking sensitivity, HCS, is taken as the quotient of the circumferential plastic strain, εθθ, at solidus temperature and the experimentally determined fracture strain, εfr, close to the solidus temperature. Thus, the sensitivity is taken as

ε HCS = θθ ( 3.15 ) ε fr

If HCS is higher than one, a crack will develop. Therefore, the model can be used to predict hot tearing both qualitatively and quantitatively. In the present calculation εθθ was obtained from FEM simulations, such as described in [18] and

εfr was obtained from ref. [12] and was taken equal to 0.0018. 3.3.7 RDG (Rappaz-Drezet-Gremaud) criterion In the RDG hot tearing criterion [8], the depression pressure, ∆p , over the mush reads:

∆p = ∆psh + ∆pmec − ρgh ( 3.16 )

where ∆psh and ∆pmec are the pressure drop contributions in the mush associated with the solidification shrinkage and the deformation induced fluid flow, respectively, ρ is density, g is gravitation constant and h is distance below the melt level.

50 Hot tearing criteria evaluation for direct-chill casting of an Al−4.5%Cu alloy

The pressure drop contributions in the mush associated with the solidification shrinkage and deformation induced fluid flow are computed as follows:

180µ∆T  (1+ β )Bε∆T  ∆p + ∆p = v βA + & ( 3.17 ) sh mec 2  T  Gλ2  G 

1 Tmf f 2 dT 1 Tmf f 2 .F (T ) 1 T A = s ; B = s s dT ; F ()T = f dT ∆T ∫ 2 ∆T ∫ 3 s ∆T ∫ s Tend ()1− f s Tend ()1 − f s Tend

( 3.18 ) where µ is dynamic viscosity of the liquid phase, T is temperature, G is thermal gradient, λ2 is dendrite arm spacing, vT is casting velocity, β is solidification shrinkage factor, ε& is viscoplastic strain rate, fs is volume fraction of solid, Tend is temperature at which bridging of the dendrite arms between grains occurs and Tmf is mass feeding temperature. The depression pressure ∆p is a measure for the hot cracking sensitivity. A criterion for hot cracking is introduced [8] by introduction of a critical depression pressure ∆pc (taken equal to 2 kPa [13]). The hot tear will form if ∆p> ∆pc. 3.3.8 Criterion of Braccini et al. In the criterion of Braccini et al. [9] the strain rate for the crack initiation and propagation reads:

1 2 m  e λ − a −PC PM  e 2κ P ε C = 1−  3  + C ( 3.19 ) &     2  l  λ  K()T , f s  l ()λ − a ηL

4cosθσ P = lv C e

PM = ρgh

ρ = ρl f l + ρ s f s 2 e 1.3 κ = ()1− f ()f C − f 32 S S S

51 Chapter 3

C where ε& is critical strain rate for hot tearing, e is liquid film thickness, l is gauge length, λ is half grain size, a is length of the tear, PC is cavitation pressure, PM is metallostatic pressure, K is a constitutive parameter that is a function of temperature T and fraction of solid fS, m is strain rate sensitivity, κ is permeability of the mushy zone, ηL is viscosity of the liquid, h is distance below the melt level C and f S is solid fraction at which the liquid network becomes disconnected. The data used for the computation are shown in Table 3.1. The critical strain C rate for hot tearing,ε& is a measure for the hot cracking sensitivity.

3.4 Results

3.4.1 Hot cracking susceptibility during the start-up phase Figs. 3.3-3.5 show the hot cracking susceptibilities computed using the eight criteria as a function of distance from the bottom of the billet. The results are obtained for the center of the billet and for the four casting conditions, given in Fig. 3.2. Hot cracking susceptibilities computed using Feurer’s criterion (Fig. 3.3a) show a relatively low value at the contact area of the bottom block and an increasing susceptibility with increasing distance. A constant value is reached at about 60 mm distance (casting condition 1) or 110 mm distance (casting condition 3). The same constant value is reached at larger distance for casting conditions 2 and 4. The susceptibility shows a relatively high value for casting conditions 3 and 4, which correspond with the highest casting rate. In contrast to these results, hot cracking susceptibilities computed using Clyne and Davies’ criterion show a high sensitivity at the contact area with the bottom block and a rapidly (within 25 mm) decreasing sensitivity with increasing distance, which then reaches a nearly constant value. There is no influence of the various casting conditions. Hot cracking susceptibilities computed using Katgerman’s criterion show that close to the bottom block, the susceptibility is relatively low and then increases till a distance of about 60 mm. Then the susceptibility increases slightly further with distance. Similar to Feurer’s criterion, the highest susceptibility is found with casting conditions 3 and 4. Hot cracking susceptibilities computed using Prokhorov’s criterion (Fig. −1 3.4a) show that the inverse reserve strain rate ε&res always becomes higher than the set value of 10000 and therefore that hot tears develop for all casting conditions. They start to develop at a distance of about 30 mm. At larger distance the cracking sensitivity becomes considerably reduced for casting conditions 1 and 2, which

52 Hot tearing criteria evaluation for direct-chill casting of an Al−4.5%Cu alloy may imply that a developed crack will stop with further growth. For casting conditions 3 and 4 the hot cracking sensitivity will remain high. Hot cracking susceptibilities computed using Novikov’s criterion show that the susceptibilities are hardly dependent on the distance from the bottom block and are also similar for all casting conditions. Hot cracking susceptibilities computed using the strain-based criterion of Magnin et al. show that in the first 30 mm the susceptibility increases till a maximum value. After that it decreases and reaches a constant value at some distance from the bottom block. A ramping procedure reduces the hot cracking susceptibility but the final hot cracking susceptibility obtained is only influenced by the steady state casting speed. Since the strain-based criterion implies that a hot tear will develop when the hot cracking susceptibility is higher than one, indeed a hot tear will develop at a distance of ~3 mm from the bottom block for all casting conditions. Hot cracking susceptibilities computed using the RDG’s criterion (Fig. 3.5a) show that in the first 20 mm the susceptibility is low and that it increases till a maximum value. Then it decreases and reaches a constant value at some distance from the bottom block. A ramping procedure reduces the hot cracking susceptibility but the final hot cracking susceptibility obtained is only influenced by the steady state casting speed. In principle, a ramping procedure might prevent cracking since there exists a window of ∆p values (between maximum sensitivity and steady state sensitivity) which will not reached if ramping is applied. Since the RDG’s criterion implies that a hot tear will develop when the depression pressure is higher than 2 kPa, hot tears will develop at a distance of ~20 mm from the bottom block for all casting conditions. Use of a ramping procedure will not prevent this. The hot cracking susceptibility calculated using the criterion Braccini et al. (Fig. 3.5b) shows that it increases in the first 20 mm. Then it slightly decreases and reaches a constant value. A ramping procedure somewhat reduces the hot cracking susceptibility but the hot cracking susceptibility finally obtained is only influenced by the steady state casting speed.

53 Chapter 3

0.30 a) 0.25

0.20 L f 0.15

0.10

0.05

0.00 0 100 200 300 400 5.0 Distance from bottom (mm) b)

4.0

3.0 HCS 2.0

1.0

0.0 0 100 200 300 400 1.80 Distance from bottom (mm) c)

1.50

1.20

0.90 HCS

0.60

0.30

0.00 0 100 200 300 400 Distance from bottom (mm)

Figure 3.3. Hot cracking susceptibility based on the criteria of Feurer (a), Clyne and Davies (b) and Katgerman (c) at the center of the billet as a function of distance from bottom block. Casting conditions: () 1, (~) 2, (∆) 3 and (x) 4.

54 Hot tearing criteria evaluation for direct-chill casting of an Al−4.5%Cu alloy

12000 a) 10000

8000

6000

4000

2000

0 0 100 200 300 400 300 Distance from bottom (mm) b)

250

200 -1

r 150 P

100

0 0 100 200 300 400 5.0 Distance from bottom (mm) c)

4.0

3.0 HCS 2.0

1.0

0.0 0 100 200 300 400 Distance from bottom (mm)

Figure 3.4. Hot cracking susceptibility based on the criteria of Prokhorov (a), Novikov (b) and Magnin et al. (c) at the center of the billet as a function of distance from bottom block. Casting conditions: () 1, (~) 2, (∆) 3 and (x) 4.

55 Chapter 3

1.0 a)

0.8

0.6 P (MPa) 0.4 ∆

0.2

0.0 0 100 200 300 400 0.0004 Distance from bottom (mm) b)

0.0003

0.0002

0.0001

0 0 100 200 300 400 Distance from bottom (mm)

Figure 3.5. Hot cracking susceptibility based on the criteria of RDG (a) and Braccini et al. (b) at the center of the billet as a function of distance from bottom block. Casting conditions: () 1, (~) 2, (∆) 3 and (x) 4.

3.4.2 Hot cracking susceptibility during the steady state phase The hot cracking susceptibilities are calculated using the eight criteria for a position at 750 mm distance from the bottom block. At such distance steady state condition in DC casting is reached [18]. The susceptibilities are calculated as a function of radial position in the billet and the results of the computation are shown in Figs. 3.6-3.8. The hot cracking susceptibilities using Feurer’s criterion (Fig. 3.6a) show that the susceptibility is highest in the center of the billet and lowest at the edge of

56 Hot tearing criteria evaluation for direct-chill casting of an Al−4.5%Cu alloy the billet. Susceptibility increases with increasing casting speed. The hot cracking susceptibilities computed using Clyne and Davies’ criterion show that for a casting speed of 120 mm/min susceptibility is highest at the edge of the billet and is also high about halfway between center and edge of the billet. For a casting speed of 180 mm/min, susceptibility is highest about halfway between center and edge. Susceptibility at the edge decreases strongly with increasing casting speed whereas susceptibility halfway between center and edge hardly changes. The susceptibilities calculated using Katgerman’s criterion show similar features as those found with Feurer’s criterion. The hot cracking susceptibilities based on Prokhorov’s criterion (Fig. 3.7a) show that for casting rates 180 mm/min and 150 mm/min hot tears indeed appear −1 since the inverse reserve strain rate ε&res becomes higher than 10000. The center of billet is the location where this condition will be first fulfilled. For the casting speeds of 120 mm/min, the hot cracking susceptibility is such that the condition for fracture is not attained. The hot cracking susceptibilities using Novikov’s criterion show that for all casting speeds the susceptibilities are about equal and independent of the radial distance. The hot cracking susceptibility based on the strain-based criterion of Magnin et al. shows that for all casting speeds a hot tear will develop in or near the center of the billet. Tendency for cracking increases with higher casting speed. At the surface of the billet the susceptibilities are somewhat higher than those at the subsurface but they do not exceed the value of one, so hot tears will not develop at the surface. The hot cracking susceptibilities based on the RDG’s criterion (Fig. 3.8a) show that the susceptibility is highest in the center of the billet and lowest at the edge of the billet. Susceptibility increases with increasing casting speed. A hot tear will develop in or near the center of the billet for all casting conditions. The hot cracking susceptibility calculated using the criterion of Braccini et al. (Fig. 3.8b) shows that the strain rate is highest in the center of the billet and lowest at the edge of the billet. Increasing casting speed leads to an increase of the critical strain rate.

57 Chapter 3

0.35 a) 0.30

0.25

0.20 L f 0.15

0.10

0.05

0.00 0 20406080100 1.1 Distance from center (mm) b) 1.0

0.9

0.8

0.7 HCS 0.6

0.5

0.4

0.3 0 20406080100 2.5 Distance from center (mm) c)

2.0

1.5 HCS 1.0

0.5

0.0 020406080100 Distance from center (mm)

Figure 3.6. Hot cracking susceptibility based on the criterion of Feurer (a), Clyne and Davies (b) and Katgerman (c) as a function of distance from the billet center. Casting speed: () 120 mm/min, (~) 150 mm/min and (∆) 180 mm/min.

58 Hot tearing criteria evaluation for direct-chill casting of an Al−4.5%Cu alloy

12000 a) 10000

8000

6000

4000

2000

0 0 20406080100 300 Distance from center (mm) b) 250

200 -1

r 150 P

100

0 0 20 40 60 80 100 5.0 Distance from center (mm) c)

4.0

3.0 HCS 2.0

1.0

0.0 0 20406080100 Distance from center (mm)

Figure 3.7. Hot cracking susceptibility based on the criteria of Prokhorov (a), Novikov (b) and Magnin et al. (c) as a function of distance from the billet center. Casting speed: () 120 mm/min, (~) 150 mm/min and (∆) 180 mm/min.

59 Chapter 3

2.0 a) 1.6

1.2 P (MPa) 0.8 ∆

0.4

0.0 0 20406080100 0.0004 Distance from center (mm) b)

0.0003

0.0002

0.0001

0 0 20406080100 Distance from center (mm)

Figure 3.8. Hot cracking susceptibility based on the criteria of RDG (a) and Braccini et al. (b) as a function of distance from the billet center. Casting speed: () 120 mm/min, (~) 150 mm/min and (∆) 180 mm/min.

3.5 Discussion The mechanism of hot tearing is complex, because hot tears initiate in the mushy zone and mushy properties are complex. On one hand, mechanical aspects play a role such as strength and ductility of the mush, and strain and strain rates imposed by solidification shrinkage, on the other hand the permeability of the mush is of importance since feeding may heal the deformed structure. In all these aspects, the morphology of the mush plays a key role.

60 Hot tearing criteria evaluation for direct-chill casting of an Al−4.5%Cu alloy

In the phase change from liquid to solid, there are some stages in which the morphology of the mush changes gradually. Basically four stages are known. The first stage is the initial part of solidification where the nucleated crystals freely float and the macroscopic behavior is close to the liquid behavior. In the second stage, the nuclei are close and tend to attach to each other to form a porous network. In this stage, the solidification shrinkage strain is easily counteracted by liquid flow and solid arrangement. In the third stage, the deformation of the solidified body caused by the solidification shrinkage and external strains is not fully counteracted by liquid flow and solid movement. In this stage, solidification defects, such as hot tears and porosity are usually initiated. In the fourth stage, the grains are strongly interconnected so that deformation of the solidified body will not result in further defects. 3.5.1 Non-mechanical criteria The non-mechanical criteria put emphasis on the feeding properties in the mush and assume that the second and third stage of the solidification play the main role in the formation of a hot tear. Feurer [2] considers that the transition from second to third stage is important for determining whether hot tears may initiate or not. He neglects the other stages in deriving the hot tearing criteria. The transition point is strongly dependent on the feeding pressure, length of porous network, volume fraction of liquid, dendrite arm spacing, tortuosity constant, viscosity of liquid, and density of solid and liquid and Feurer takes these parameters into account. Clyne and Davies [3] also consider that the transition from the second to the third stage corresponds with the region where a hot tear may initiate, but they include the other transitions also in their expression of the hot tearing criterion. However, Clyne and Davies propose constant values of the fraction liquid for the transition limits and neglect the influence of other parameters. Consequently, the formulation of the Clyne and Davies’ criterion is simple, and it only needs an expression for the relation between time, temperature and solid fraction, such as given by Scheil or lever rule. Their relation might be too simple, since it only depends on cooling rate but ignores effects of feeding pressure, length of porous network, volume fraction of liquid, dendrite arm spacing, tortuosity constant, viscosity of liquid, and different density of solid and liquid. Katgerman [4] uses the Clyne and Davies’ expression but he used for the transition of the first to second stage the coherency temperature, and for the transition from the second to third stage the expressions of Feurer. The results using Feurer’s criterion show that the highest hot cracking sensitivity is in the billet center, at least at steady state, and that the sensitivity increases with casting speed (Fig. 3.6). The sensitivity increases with distance from the bottom block till a constant level is reached (Fig. 3.3). The constant level is

61 Chapter 3 reached at a distance of about 60 mm (casting condition 1) and 110 mm (casting condition 3), whereas steady state casting is attained at 120-140 mm and 140-160 mm, respectively [18]. Apparently, the constant (and maximum) sensitivity is already attained during the start-up phase. For distances lower than 50 mm, the sensitivity for cracking is hardly dependent on casting speed and therefore if cracking will occur in this region, it cannot be prevented by starting at a lower speed. After a distance of 50-75 mm from the bottom block, an effect of casting rate is clearly visible and the sensitivity for cracking increases for the higher rate. However, ramping does not affect the maximum sensitivity which means that the use of a ramping procedure will not prevent cracking. It will only affect the distance from the bottom block where fracture will initiate. Therefore, we conclude that in case of Feurer’s criterion the use of ramping has no sense. Regarding the results of Clyne and Davies the highest sensitivity is at about halfway the radial distance (Fig. 3.6) and at the bottom of the billet (Fig. 3.3). The high value at the bottom block, which is not dependent on the casting rate, implies that, if cracking occurs, it will immediately start at the beginning. We conclude that in the case of Clyne and Davies’ criterion the use of ramping has no sense either. The results, obtained using Katgerman’s criterion are, at least qualitatively, similar to those of Feurer and the conclusions are identical to those stated above with Feurer. The different results calculated using Feurer’s and Katgerman’s criteria on one hand and Clyne and Davies’ criterion on the other hand can be understood considering Eq. 3.2. During the start-up phase of DC casting the effective feeding 2 pressure Ps and length of porous network L will be small but the ratio Ps/L will be high, and the feeding flow will be more effective than at larger distances from the bottom block. Therefore, the condition of Eq. 3.1 will be met at a relatively low liquid fraction. This is reflected in the results obtained with Feurer and Katgerman. In the formulation of the Clyne and Davies’ criterion a constant critical liquid fraction (0.1) is set, independent of the local properties of the mush. Near the bottom block it underestimates the possibility of feeding in comparison with Feurer, since the critical fraction of liquid with Feurer is ~0.03 (Fig. 3.3). At steady state it overestimates the possibility of feeding in comparison with Feurer, since the critical fraction of liquid with Feurer ranges from ~0.15 to ~0.25 for the casting rates considered. The same considerations also apply when understanding the different behavior as a function of radial distance (Fig. 3.6). In the billet center feeding pressure and sump depth are relatively high and near the billet edge relatively low, enabling relatively good feeding near the billet edge and less feeding in the billet center. Therefore, cracking sensitivity decreases with radial distance as is shown in Figs. 3.6a and 3.6c. Using the Clyne and Davies’ criterion however, feeding flow is

62 Hot tearing criteria evaluation for direct-chill casting of an Al−4.5%Cu alloy overestimated in the billet center and underestimated near the billet edge, which leads to the result shown in Fig. 3.6b. 3.5.2 Mechanical criteria The mechanical criteria emphasize the importance of the strengths and strains developed in the third and fourth stage of the solidification. They do not account for fluid flow and healing of the structure under the influence of feeding. A fracture is initiated when local strains or strain rates surpass the ability of the mush to deform without fracturing. The consideration of Prokhorov is based on the effect of strain rate. The criterion of Prokhorov accounts for the thermal contraction strain and the local plastic deformation under the influence of the surrounding, and considers these for each temperature during solidification. The constitutive material data of the mush and ductility data of the mush as a function of temperature are needed for the computation using the criterion. Novikov considers the effect of only the thermal contraction strain on whether a hot tear will initiate or not and accounts for only the integrated value of the strain, where integration is from coherency temperature to solidus temperature. The approach of Novikov neglects several issues but is simpler and much less dependent on material data. The strain-based criterion of Magnin et al. compares the circumferential strain at solidus temperature and the fracture strain at a temperature close to the solidus. This approach is a simplification of Prokhorov’s criterion that uses all data from coherency to solidus temperature. The results obtained using Prokhorov’s criterion show that for all casting conditions a hot tear will form. Hot tears develop at short distance from the bottom block (~30 mm). The most sensitive area is in the billet center, so hot tears are expected to initiate there. The possibility exists that for the lower velocities cracks will stop growing after a certain distance from the bottom block. Comparing Figs. 3.4 and 3.7, it is clear that ramping will not prevent the formation of hot tears. Regarding the result obtained with Novikov’s criterion, cracking tendency is not dependent on either casting rate or position in the billet. A ramping procedure will not reduce the possibility of hot cracking. The result obtained using the strain- based criterion of Magnin et al. shows that for all casting conditions a hot tear will develop and that although the hot cracking sensitivity depends on casting rate and use of ramping, use of a ramping procedure does not prevent cracking. Some of these results can be understood from the assumptions made in the criteria. At all locations in the billet, thermal contraction strains depend on temperature but are always compressive, whereas at the cooled, outer surface of the billet, circumferential viscoplastic strains are compressive in the first part of the solidification but become tensile in the last part of the solidification [18]. The

63 Chapter 3 circumferential viscoplastic strains are lower at the surface than at other locations [18]. Under those conditions the cracking sensitivity is relatively low close to the bottom block and at the edge of the billet, and is high at the center of the billet, which is reflected in the results obtained with Prokhorov’s criterion and also with the strain-based criterion of Magnin et al. Novikov neglects the local plastic strain and therefore the total strain is equal to the thermal contraction strain and is always compressive. The thermal contraction strain is independent of the solidification conditions and the position in the billet, which leads to the results obtained by Novikov’s criterion. 3.5.3 Combined mechanical and non-mechanical criteria In the present calculation, the RDG’s criterion is applied in the calculation of the depression pressure in the mush using the local, computed strain rate. Both solidification shrinkage and deformation induced fluid flow are taken into account. The result obtained using the RDG’s criterion shows that for all casting conditions a hot tear will develop. The same is found by the authors [13] for casting condition similar to those used here and a less critical alloy (AA6063). The result obtained using the RDG’s criterion also shows that although the hot cracking sensitivity depends on casting rate and use of ramping, applying a ramping procedure does not prevent cracking. The overall behavior of the sensitivity resembles that of the strain-based criterion of Magnin et al. However, the effect of casting speed is more pronounced with the RDG’s criterion. This can be understood since for a lower casting speed both the development of strain is lower and the afterfeeding is stronger, leading to a relatively lower sensitivity for the lower strain rates. The hot cracking sensitivity calculated using the criterion of Braccini et al. shows comparable characteristics as found with the RDG criterion. The sensitivity increases with casting rate, but not so pronounced as with the RDG criterion. In case a crack will be formed, it will form already in the first 30 mm from the bottom block and a ramping procedure will not prevent its formation. 3.5.4 Evaluation of the various criteria Casting practice shows that in general hot tears are easier formed with a higher casting speed and that they develop in the center of a billet with a star-like form [16,21,22]. During casting a ramping procedure is used for the alloy and casting conditions considered here, which prevents cracking. The ramping procedures in the simulation resemble those used in practice. Further for the conditions and alloy selected hot cracking is not expected. Table 3.2 summarizes the results obtained for the eight criteria. If the criteria are used quantitatively, it is seen that none of the criteria is able to predict all observations. If the criteria are used qualitatively –considering that constitutive and

64 Hot tearing criteria evaluation for direct-chill casting of an Al−4.5%Cu alloy fracture data of the mushy zone are not well known- only the RDG’s criterion might be of value. When we compare our results with literature data on simulation of DC casting, it is seen that our observations A and C with the Clyne and Davies’ criterion are confirmed by [11], our observation A with the strain-based criterion is confirmed by [7,12] and our observations A and B with the RDG’s criterion are confirmed by [13-15]. In contrast our observations A and C with Katgerman’s criterion are different from those quoted in [11]. We attribute this discrepancy to the simplification that for the critical time a value is used, corresponding to a fraction of solid of 0.90 [11], whereas a value should be used which is dependent on mush dimension, dendrite arm spacing and hydrostatic pressure (see Eq. 3.2). The RDG’s criterion, formulated in [8] is based on several assumptions. During solidification, growth is columnar dendritic and thermal gradient and solidification rate are taken constant. Further, when a cavity is formed, it will lead to a crack. The possibility that cavities will lead to porosity, and not always to a crack is not included. Several of these limitations are tried to overcome in the criterion of Braccini et al. [9]. However, our calculations do not show a significant effect on the predicted hot tearing tendency. In fact in the criterion of Braccini et al. the metallostatic pressure which depends on the depth of sump is the dominant parameter. Further improvement for the hot tear prediction should involve an approach which is proposed in ref. [10]. This approaches should lead to better predictions whether hot cracks will be formed during actual casting.

65 Chapter 3

Table 3.2. Summary of the results. Observations during casting practice are included.

66 Hot tearing criteria evaluation for direct-chill casting of an Al−4.5%Cu alloy

3.6 Conclusions Eight hot tearing criteria have been implemented in a FEM simulation of the DC casting process and evaluated. It is concluded that 1. Six criteria (Feurer, Katgerman, Prokhorov, strain-based, RDG and Braccini et al.) indicate a higher cracking sensitivity for higher casting velocity, which is considered in accordance with casting practice. Two criteria (Clyne and Davies, Novikov) show different results in this. 2. Five criteria (Feurer, Katgerman, Prokhorov, RDG and Braccini et al.) indicate a higher sensitivity in the billet center, which is considered in accordance with casting practice. Two criteria (Clyne and Davies, Novikov) show different results in this. 3. All criteria except RDG indicate that use of a ramping procedure (lower casting speed during start-up phase) has no sense, which is considered not in accordance with casting practice. 4. None of the eight criteria is able to correctly predict whether hot tear during DC casting will occur. The greatest potential has the RDG’s criterion when used on a qualitative base.

References [1] Eskin, D.G., Suyitno and Katgerman, L. (2004) Progress in Materials Science, 49, p. 629. [2] Feurer, U. (1977) Quality Control of Engineering Alloys and the Role of Metals Science, Delft University of Technology, Delft, p. 131. [3] Clyne, T.W. and Davies, G.J. (1979) Proc. Conference on Solidification and Castings of Metals, Metals Society, London, p. 275. [4] Katgerman, L. (1982) Journal of Metals, 34, 2, p. 46. [5] Prokhorov, N.N. (1962) Russian Castings Production, 2, p. 172. [6] Novikov, I.I. (1966) Goryachelomkost tsvetnykh metallov i splavov (Hot Shortness of Non-Ferrous Metals and Alloys), Moscow: Nauka. (in Russian). [7] Magnin, B., Katgerman, L. and Hannart, B. (1995) Modeling of Casting Welding and Advanced Solidification Processes VII, eds. M. Cross and J. Campbell, TMS, Warrendale, PA, p. 303. [8] Rappaz, M., Drezet, J.M. and Gremaud, M. (1999) Metallurgical and Materials Transactions A, 30A, p. 449.

67 Chapter 3

[9] Braccini, M., Martin, C.L. and Suery, M. (2000) Modeling of Casting Welding and Advanced Solidification Processes IX, eds. P.R. Sahm, P.N. Hansen, and J.G. Conley, Shaker Verlag, Aachen, p.18. [10] Suyitno, Kool, W.H. and Katgerman, L. (2002) Materials Science Forum, 396-402, p. 179. [11] Nedreberg, M.L. (1991) Ph.D. Thesis, University of Oslo, Oslo, Norway. [12] Magnin, B., Maenner, L., Katgerman, L. and Engler, S. (1996) Materials Science Forum, 217-222, p. 1209. [13] Drezet, J.-M. and Rappaz, M. (2001) Light Metals 2001, ed. J.L. Anjier, TMS, Warrendale, PA, p. 887. [14] Drezet, J.-M., M’Hamdi, M., Benum, S., Mortensen, D. and Fjaer, H. (2002) Materials Science Forum, 396-402, p. 59. [15] M’Hamdi, M., Benum, S., Mortensen, D., Fjaer, H.G. and Drezet J.-M. (2003) Metallurgical and Materials Transactions A, 34A, 9 p. 1941. [16] Farup, I. and Mo, A. (2000) Metallurgical and Materials Transactions A, 31A, p. 1461. [17] M’Hamdi, M., Mo, A. and Martin, C.L. (2002) Metallurgical and Materials Transactions A, 33A, p. 2081. [18] Suyitno, Kool, W.H. and Katgerman, L. (2004) Metallurgical and Materials Transactions A, 35A, p. 2917. [19] Suyitno, Kool, W.H. and Katgerman, L. (2003) Light Metals 2003, ed. P.N. Crepeau, TMS, Warrendale, PA, p. 753. [20] Navikov, I.I. and Grushko, O.E. (1995) Materials Science and Technology, 11, p. 926. [21] Commet, B., Delaire, P., Rabenberg, J. and Storm, J. (2003) Light Metals 2003, ed. P.N. Crepeau, TMS, Warrendale, PA, p. 711. [22] Nagaumi, H. and Umeda, T. (2003) Journal of Light Metals, 2, p. 161.

Chapter 4

Effects of casting speed and alloy composition on structure formation and hot tearing during direct-chill casting of Al–Cu alloysδ

Effects of casting speed and alloys composition on structure formation and hot tearing during direct chill casting of 200 mm round billets from binary Al–Cu alloys are studied. It is experimentally shown that the grain structure, including the occurrence of coarse grains in the central part of the billet, is strongly affected by the casting speed and composition, while the dendritic arm spacing is mainly dependent on the casting speed. The hot cracking pattern reveals that the hot tearing susceptibility is high in the range of low-copper alloys (1–1.5%) and at high casting speeds (180–200 mm/min). The amount of non-equilibrium eutectics is minimum in the center of the billet and at lower concentrations of copper, which corresponds with the location as well as the compositional range of maximum hot tearing sensitivity. Structure formation and hot cracking could be correlated to computational results on the dimensions of the solidification region in the billet. Several hot tearing criteria earlier evaluated in Chapter 3 are again evaluated for a varying (constant increase or decrease) casting speed such as used in these experiments. It is shown that hot tearing criteria that account for the dynamics of the process, e.g. strain rate, actual stress–strain situation, feeding rate, melt flow, can be successfully used for the qualitative prediction of hot tearing in these experiments.

δ Based on the paper in: Metallurgical and Materials Transactions A, vol. 35A, no. 11, 2004, pp. 3551-3562.

Chapter 4

4.1 Introduction During direct-chill (DC) casting, alloy composition and casting parameters are critical for the formation of solidification defects such as hot tearing, micro/macro-porosity and macrosegregation [1]. These defects can be present to some extent in any ingot and billet. Their occurrence effects the productivity in the case of hot tear and macro-porosity, and to a great extent mechanical properties and performance of cast material in the case of micro-porosity and macrosegregation. Under those circumstances, a possibility to predict casting defects, in particular hot tears, for different alloy compositions and process parameters is crucial. It is already known that there is a clear correlation between alloy composition and hot tear tendency in binary and more complex aluminum alloys [2–4]. The most vivid example is a so-called ‘lambda’ curve that shows the maximum hot tearing susceptibility for a certain compositional range and can be reproduced for different alloying systems. It is also known that casting parameters play an important role in occurrence of casting defects [1,5–7]. The most important casting parameter that affects hot tearing is the casting speed [5,7,8]. Water flow rate and casting temperature have much less impact [7]. The optimum casting speed is a compromise between productivity, alloy composition, billet size, and quality (structure and defects). Casting speed and other process parameters, i.e. casting temperature and water flow rate are also known to affect the structure formation during solidification. This is because of their influence on cooling conditions, melt flow and geometry of liquid and semi-liquid parts of the billet [1,5–9]. The increase in casting speed results in proportional deepening of the liquid sump, increasing of the mushy zone thickness, and overall acceleration of solidification [5]. The solidification rate (the normal velocity of the solidification front) is maximum in the center and on the periphery of a billet. In these sections, the effect of an increased casting speed on the solidification rate is mostly pronounced [5]. Another kinetic parameter of solidification is the cooling rate that characterizes the local solidification time. Higher cooling rates produce finer microstructure with smaller dendritic arm spacing (DAS) [10] and less and finer porosity [11]. The distribution of solidification and structure parameters across the horizontal section of a billet is another important feature. Due to the peculiar way in which solidification occurs during DC casting, each point of a horizontal slice is formed under different conditions [1]. Cooling rate is affected by the casting speed unevenly across the billet section. The fastest cooling and, hence finest DAS is found in the region

70 Effect of casting speed and alloy composition on structure formation and hot tearing corresponding to the area where cooling water impinges on the surface of the billet [9]. In the billet cross-section, this place is at a certain distance from the surface. From that point inward the cooling rate decreases. The dendritic arms are coarser in the center of the billet and in the region where the air-gap is formed. The grain size distribution across the billet depends on the type of grain morphology. In pure alloys the subsurface region exhibits fine equiaxed grains, further inside the billet columnar grains grow to give place to coarser equiaxed grains in the center. In the case of grain refined or equiaxed structures, the general distribution of grain sizes is similar to that of dendritic arm spacing. Pores have a general tendency to increase in size and quantity towards the center of the billet, their amount and distribution being a function of dissolved hydrogen, alloy composition, cooling rate, mushy zone dimensions, and microstructure [5,11]. Casting practice shows that structure refinement and homogeneity decrease the vulnerability of an alloy to hot tearing [2,5]. It is logical to suggest that the effects of casting parameters on structure formation and hot tearing are correlated. Prediction of hot tearing probability through some criteria is already suggested elsewhere [2,3,12–18]. However, the application of these criteria to DC casting is limited. The efforts in prediction of hot tearing during DC casting are streaming in two directions: (1) modeling of the thermomechanical behavior during solidification [19,20] and (2) formulation of hot tearing criteria and their implementation in numerical simulations [15,16,21–23]. The first approach uses constitutive equations to describe thermomechanical behavior of solidifying material and then correlates the computed stress or/and strain to the hot tearing tendency. In this case, the tendency to hot tearing increases with the increasing stress or/and strain. The second approach is concentrated on relationships between properties of the material, process parameters and solidification parameters. Through a ratio of these parameters a hot tearing criterion (hot tearing susceptibility) is formulated that shows the probability of crack occurrence under particular conditions. The advantage of the first methodology is the physical description of the phenomenon, which however requires accurate formulation of solidification physics and the knowledge of thermophysical and rheological parameters that are not readily available. The second approach is easier in practical application but sometimes lacks physical background that makes it difficult to apply it under variable conditions. The combination of these two methods looks like a promising way to follow. The aim of this paper is to analyze the effects of alloy composition and casting speed on structure formation and hot tearing of Al–Cu alloys. The analysis is based on systematic examination of billets of binary Al–(1–5)% Cu alloys cast at different casting speeds. Experimental results on structure and hot tearing are

71 Chapter 4 correlated to computer simulated solidification and hot tearing patterns. Thermomechanical behavior of a solidifying billet is combined with available hot tearing criteria and the results are compared to the experiment.

4.2 Experimental procedure Round billets were cast in a pilot DC casting installation at the Delft University of Technology. The DC caster consists of an electrical resistance tilting furnace (up to 200 kg of liquid aluminum); a flexible trough and a launder that make up a delivery system; a hot-top round (∅200 mm) mold fitted into a water box; a hydraulic movement mechanism for an ingot (a maximum length of 1800 mm); a displacement sensor for measuring the casting length and speed; a submersible water pump and a system of pipes and valves enabling the water flow rates from 60 to 300 l/min; and a melt level laser sensor controlling the melt level in the launder and the furnace tilt. The process parameters such as melt temperature, water flow rate, casting speed, and melt level in the launder are controlled and recorded by a personal computer equipped with National Instruments data acquisition cards and software. The operation is semi-automatic, with a manual start-up phase and a fully automatic steady-state casting. A unique feature of the set-up is a possibility to change process parameters during a single drop. Each casting trial started with rapid ramping to a casting speed of 100 mm/min. After producing 100 to 200 mm of casting length at this casting speed, the casting speed was slowly ramped up to 200 mm/min and then down to 100 mm/min. The water flow rate was maintained constant at 150 l/min, if not mentioned otherwise. Casting temperature was in the range 715–720 oC for all casting trials. Figure 4.1 shows an example of a process chart.

72 Effect of casting speed and alloy composition on structure formation and hot tearing

Casting speed, mm/min 200

Water flow rate, l/min 150

100

50 Casting parameter

0 0 200 400 600 Billet length, mm

Figure 4.1. Example of a process chart

Table 4.1. Chemical composition of tested alloys as determined by spectrum analysis

Alloy no. Cu, % Fe, % Si, % Other impurities, total % 1 1.03 0.16 0.04 0.04 2 1.98 0.18 0.06 0.03 3 2.93 0.19 0.10 0.04 4 4.49 0.19 0.06 0.03

Several models Al–Cu alloys with compositions given in Table 4.1 were tested. Alloys were prepared using 99.7% pure aluminum and an Al-48% Cu master alloy. The purity was chosen to be close to that of commercial alloys. No grain refiners were added, the concentration of Ti being less than 0.01%. Cast billets were sawed in horizontal sections corresponding to different casting speeds. The sections were then cut to smaller samples, as shown in Fig. 4.2, which were ground, polished, etched or oxidized and examined in optical microscope. In addition, samples were cut at the very edge of the billet in order to examine the subsurface structure. Polished and carefully cleaned in an ultrasonic bath samples were used for studying crack propagation. A 20% NaOH solution and a Nital cleaning agent were used for macroetching. An 0.5% water solution of HF or a Keller etchant were used for revealing microstructure. Grain structure was studied under cross-polarized light using samples oxidized at 20 VDC in a 3%

73 Chapter 4

HBF4 water solution. Structure parameters such as dendritic arm spacing and grain size were measured on photographs using the random linear intercept technique. Statistical analysis of the results was performed. Dendritic arm spacing was determined accurate to 5 rel.%; grain size, to 10 rel.%, volume fractions of eutectic and coarse grains, to 10 rel.%. In order to study the occurrence of hot cracks and to quantify their appearance, billets were sawed in horizontal sections reflecting different casting speeds and in the vertical center-plane of the billet. These large sections were cut and polished, and the hot crack susceptibility (HCS) was quantified as the area affected by cracks in the horizontal cross-section (Acrack) divided by the area of the billet cross-section (Atotal) as shown in Fig. 4.2b. The measured structure and crack parameters are presented in this paper in a form of three-dimensional plots. Each plot is constructed by triangulation with linear interpolation of experimental data that forms at least 4 × 8 data points grid.

a b Figure 4.2. A scheme of cutting samples (a) and a scheme of crack quantification

Acrack/Atotal (b)

4.3 Computer simulation

4.3.1 Model A DC cast billet 200 mm in diameter and 900 mm in length was simulated. Due to the symmetrical shape, an axis-symmetric model was used in this work. A coupled computation of stress and temperature fields was applied using 4-node

74 Effect of casting speed and alloy composition on structure formation and hot tearing rectangular elements with 4 Gaussian integration points. In the simulation, the ingot remained in a stationary position while the mold and the impingement point of water moved upwards with a velocity equal to the casting speed. Layers activation in accordance with filling time and casting speed was used for simulating the continuous feeding of the liquid metal. The computational domain is shown in Fig. 4.3.

z Ω7

mold

Ω4

TLiq

Ω5

TSol

billet Ω1 Ω Ω6

Ω3

bottom block r

Ω2 Figure 4.3. Computational domain and boundary conditions of the DC cast billet.

A FEM model of the billet was derived based on coupling heat flow and mechanical equilibrium equations. A full Newton–Raphson algorithm was applied to treat the set of non-linear algebraic equations that arose after discretization of non-linear continuum equations [24]. The computation started with given boundary conditions, initial conditions and a given time step. Thermal and mechanical fields were solved iteratively and when values converged for a certain time step, they were then used as initial values for the next time step. The computation continued until the preset time was reached. In the computation, a solidification model and a constitutive model were incorporated in the finite element iteration. The solidification model that accounted for back diffusion [25] was applied:

75 Chapter 4

∗  1−2α s k  k −1 1  Tm − T   fl =    ( 4.1 ) ∗  T − T  1 − 2α s k  m l    

with * 1 1 1 α s = α s [1− exp(− )]− exp(− ) α s 2 2αs

where fl is the volume fraction of liquid, Tm is the melting temperature of pure base metal, Tl is the liquidus temperature, T is the temperature, k is the partition * coefficient, αs is the back-diffusion coefficient, and α s is the modified dimensionless solid state back-diffusion parameter. No melt flow in the liquid part of a billet has been taken into account. A constitutive model to represent the viscoplastic behavior of semi-solid or solid material was described by the following equation [16]:

m n σ = K()()ε& p + ε& po ε p + ε po ( 4.2 ) where σ is the true stress (MPa), K is the stress at unity strain and unity strain rate (MPa), ε is the strain rate (s–1), ε is a small constant plastic strain rate (10–4 s– & p & po 1 –2 ), ε p is plastic strain, ε po is a small constant plastic strain (10 ), m is the strain rate sensitivity coefficient, and n is the strain hardening coefficient.

4.3.2 Boundary Conditions Boundary conditions applied to the computational domain Ω of the billet are given in Table 4.2 and shown in Fig. 4.3.

76 Effect of casting speed and alloy composition on structure formation and hot tearing

Table 4.2. Boundary conditions applied in numerical simulation of DC casting

Notation in Fig. 4.3 Boundary condition Ω1 Heat flux is zero due to the axial symmetry. Ω2 Convective heat transfer to the environment is constant. Position z is constant [26]. Ω3 Heat transfer is determined by conditions of either contact, non-contact (open gap) or water intrusion between the billet and the bottom block. Position z of the bottom block is fixed but the billet can freely move in axial and radial direction [26]. Ω4 Heat transfer is determined by conditions of either contact or non-contact between the billet and the mold [26]. Ω5 Water impingement zone [27]. Ω6 Downstream zone [27]. Ω7 Temperature is constant and equal to the casting temperature. The boundary moves in axial direction with the casting speed.

4.3.3 Materials data Thermophysical properties of an Al–4.5%Cu alloy (billet) and an AA6063 alloy (bottom block), such as thermal conductivity, specific heat, thermal expansion coefficient and Young’s modulus were taken from literature as temperature dependent characteristics [28–32]. The temperature dependent parameters K, m and n of Eq. 4.2 are fitted to the experimental data from ref. [16]. 4.3.4 Computation of hot cracking susceptibility Hot-tearing criteria are reviewed in detail elsewhere [4]. Three mechanical criteria by Novikov, Prokhorov, and Manin et al. [2,12,16] (based on the ratio between material ductility and thermal contraction in the solidification range), three non-mechanical criteria by Clyne and Davies [3] (time spent in the vulnerable temperature range), Feurer [14] (restricted feeding in the vulnerable temperature range) and Katgerman [15] (restricted feeding and time spent in the vulnerable temperature range), and combination mechanical and mechanical by Rappaz- Drezet-Gremaud (RDG) [17] were evaluated for hot tearing prediction. The output

77 Chapter 4 of the finite element model was used as an input for the hot tearing criteria. The procedure is reported in more detail elsewhere [25]. 4.3.5 Validation experiments In order to validate computer simulations of the process, temperature measurements were performed in various locations of the billet during casting. K- thermocouples with open tips (0.15 mm thick wires) were placed using special support in the center of the billet and in three locations at the periphery, 5, 9 and 16 mm from the surface. These thermocouples moved with the billet (starting in the liquid part) and were eventually frozen into solid metal. Additionally, temperature measurements were performed in the launder and in the center of the liquid bath of an ingot. Good agreement was found between calculated and experimentally measured temperatures. The sump depth was probed by a steel rod connected to a digital length meter.

4.4 Results

4.4.1 Distribution of structure parameters across the billet section Alloys 2–4 with a concentration of copper above 2% show equiaxed structure throughout the entire billet cross-section. However, alloy 1 containing about 1% copper has a zone (though narrow) of columnar grains at the periphery of the billet, Fig. 4.4a. These grains are obviously larger than equiaxed grains found elsewhere in the billet as shown in Fig. 4.5a, b. Individual columnar grains were observed in alloy 2. Distribution of structure parameters across the billet is a function of composition and casting speed as illustrated in Figs. 4.5 and 4.6. Generally structure coarsens towards the center of the billet, with a region of finest structure at the billet surface and at about 15–20 mm from the surface. The amount of nonequilibrium Al–Cu eutectics tend to slightly decrease in the central part of the billet. The characteristic feature of macrostructure is the appearance of “coarse” grains in the central part of a billet. These grains have thicker branches and larger dendritic arm spacing, sometimes with a rim of fine dendritic arm spacing at the periphery of the grain. Figure 4.4b shows a vivid example of such a structure.

78 Effect of casting speed and alloy composition on structure formation and hot tearing

a b Figure 4.4. Structures of an Al–1.03% Cu alloy: (a) macrostructure at the periphery of the billet (surface on the right-hand side) and (b) grain structure in the center of the billet with “coarse” grains.

4.4.2 Effect of casting speed and composition on structure Figs. 4.5 and 4.6 demonstrate the effects of casting speed and copper concentration on the distribution of grain size and dendritic arm spacing across the billet diameter. Increasing casting speed results in some refinement of grains and their internal structure, the diametral distribution being only slightly affected. The most interesting feature is the vanishing grain coarsening in the central part of the billet (compare Figs 4.5a and 4.5b). Enrichment of alloys in copper above 2% results in prominent grain refinement but has virtually no effect on the dendritic arm spacing. Figs. 4.7 and 4.8 show the influence of casting speed and composition on the amount of nonequilibrium eutectics and “coarse” grains. There is a general tendency of increasing the amount of nonequilibrium eutectics and coarse grains with increasing copper concentration. At copper concentrations less than 2% the amount of eutectics increases with the casting speed, this dependence being opposite at larger concentrations of copper. An interesting observation is that the central part of the billet shows less nonequilibrium eutectics than the periphery, this tendency being mostly pronounced at low concentrations of copper. Coarse grains are concentrated in the central part of the billet and their fraction considerably grows with the casting speed (compare Figs. 4.8a and 4.8b).

79 Chapter 4

b. Figure 4.5. Effects of casting speed (a, 100 mm/min and b, 200 mm/min) and copper concentration on the distribution of grain size, larger grains at the periphery in low- copper alloys reflect the zone of columnar grains in DC cast round billets.

80 Effect of casting speed and alloy composition on structure formation and hot tearing

b. Figure 4.6. Effects of casting speed (a, 100 mm/min and b, 200 mm/min) and copper concentration on the dendritic arm spacing in DC cast round billets.

81 Chapter 4

b. Figure 4.7. Effects of casting speed (a, 100 mm/min and b, 200 mm/min) and copper concentration on the distribution of nonequilibrium Al–Cu eutectics in DC cast round billets.

82 Effect of casting speed and alloy composition on structure formation and hot tearing

Figure 4.8. Effects of casting speed (a, 100 mm/min and b, 200 mm/min) and copper concentration on the distribution of coarse grains in DC cast round billets.

83 Chapter 4

4.4.3 Effect of casting speed and composition on hot cracking Hot cracks were observed in alloys 1–3 from Table 4.1. Cracks appeared in the central part of the billet and have a typical spider-type shape in the billet cross- section as shown in Fig. 4.9. In most cases cracks look like spread from the center in radial directions. The dependence of hot cracking susceptibility on the casting speed and copper concentration in the billets cast according to the experimental procedure (as illustrated in Fig. 4.1) is shown in Fig. 4.10. Hot cracking strongly depends on the casting speed with the threshold casting speed for the initiation of crack being higher than the casting speed required to stop (heal) cracking. The concentration dependence of hot tearing shows the existence of the compositional range of maximum hot cracking susceptibility, between 0.5 and 1.5% Cu. It should be noted that no hot tearing at any given casting speed (up to 220 mm/min) was observed in alloys that contained more than 4% Cu (we studied alloys containing up to 5.6% Cu).

Figure 4.9. General hot cracking pattern observed in an Al–Cu billet cast according to the scheme shown in Fig. 4.1 (bottom of the billet on the left). 4.4.4 Results of computer simulations The effect of copper concentration and casting speed on the vertical distance between the liquidus and solidus (solidification region) in the billet is shown in Fig. 4.11. In the simulation, a non-equilibrium binary phase diagram is used with the equilibrium liquidus and the non-equilibrium solidus, the latter was taken as a temperature of the binary eutectics, 548 oC. The transition region becomes wider with the increasing casting speed and decreasing copper concentration.

84 Effect of casting speed and alloy composition on structure formation and hot tearing

b . -10 -11 -12 -13 -14 -15 -16 -17 -18 Casting speed down, cm/min -19 -2020 19 18 17 16 15 14 13

Casting speed up, cm/min 12 11 10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Cu, % Figure 4.10. Effects of casting speed (experimental diagram in Fig. 4.1) and copper concentration on hot cracking (HCS) in Al–Cu alloys: (a) a 3D plot and (b) contour lines of equal HCS.

85 Chapter 4

b Figure 4.11. Distance between liquidus and solidus as a function of billet cross-section and copper concentration at two casting speeds: (a) 100 mm/min and (b) 200 mm/min.

86 Effect of casting speed and alloy composition on structure formation and hot tearing

Another observation is that the transition region tends to narrow in the central part of the billet. This feature becomes more pronounced at larger casting speed and copper concentration. Hot tearing is a failure of semi-solid material under stresses and strains that occur in the billet, and when there is not enough liquid to fill the gap between solid crystals that are pulled apart by these stresses. Numerical simulation demonstrates that the tensile stresses and strains in the billet are concentrated in its central part, start to appear already in the mushy zone, and strongly increase with increasing the casting speed as demonstrated in Fig. 4.12 for strains (the patter for stresses looks similar). The next step is to implement hot tearing criteria in the FEM model of thermomechanical behavior of a billet during DC casting. The hot cracking tendency at different casting speeds are computed using six hot tearing criteria available in literature and described briefly in Introduction. The results are shown in Fig. 4.13. The casting speed in the simulation is constant at 100 mm/min for first 100 mm of length, then linearly increased till 200 mm/min at 350 mm of length. After a short period of keeping a constant casting speed (200 mm/min for 50 mm) the casting speed is linearly decreased till 100 mm/min at 550 mm, and then constant till the end of casting. These conditions correspond well to the conditions of our experiments as described in Fig. 4.1. The probability of hot cracking increases with casting speed and with the distance from the surface of the billet when criteria by Feurer, Katgerman, Prokhorov, Magnin or RDG are applied. The criterion of Clyne and Davies is not responding to the change of the casting speed and the criterion of Novikov gives only slight indication of hot cracking in the central part of the billet at a high casting speed. The numerical simulation also shows that the casting speed required to initiate the hot tear is larger than the casting speed at which the hot crack is healed.

87 Chapter 4

a. b. Figure 4.12. Distribution of strain in an Al–4.5% Cu billet cast at 100 mm/min (a) and 200 mm/min (b). Only half of the billet is shown, center of the billet is on the right.

88 Effect of casting speed and alloy composition on structure formation and hot tearing

n 1.0 i

/ 0.9 t

m 0.8 a

C 0.7 m 200 0.5 0.4 0.3 0.2 0.1 100 0.0

Length of billet

Feurer CL Clyne & Davies CL Katgerman CL Prokhorov CL Novikov CL Magnin et al. CL RDG CL

Figure 4.13. Hot cracking susceptibility normalized to the highest value as determined in the vertical cross-section of an Al–4.5% Cu billet (only half of a billet is shown; CL denotes the centerline of the billet) computed using different hot tearing criteria for a varying casting speed. The darker the shape is the more the hot cracking probability.

89 Chapter 4

4.5 Discussion

4.5.1 Evolution of structure The observed effects of casting speed and copper concentration on the distribution of structure parameters (grain size and dendritic arm spacing) in the horizontal section of a billet are in good agreement with previously reported results [1,5,7,9]. The very surface of the billet comprises fine grains formed during the first contact of the melt with the water-cooled mold, Figs. 4.4a and 4.5. The zone of coarser structure at some 10 mm from the surface reflects the cooling conditions in the air-gap zone, when the solid shell detaches from the mold surface as a result of thermal contraction and the heat extraction considerably deteriorates. Further towards the center of the billet, the structure is refined as shown in Fig. 4.5, this zone being formed under conditions of direct cooling of the billet surface with water. And the structure – especially the dendritic arm spacing that is particularly sensitive to cooling conditions – tends to coarsen in the central part of the billet due to slower cooling. The internal grain structure characterized by dendritic arms spacing remains virtually the same irrespective of the copper concentration, being only responsive to the changed cooling conditions. This can be explained in terms of the unique relation that the dendritic arm spacing has to the cooling rate or local solidification time [10]. On the contrary, the grain structure is strongly affected by the composition. At low concentrations of copper, grains are considerably larger, and the zone of columnar grains is observed at the periphery of a billet. The columnar to equiaxed transition (CET) is known to be controlled by constitutional undercooling that is created by local enrichment of the melt in solute elements with corresponding decrease in the apparent solidification temperature [10,33]. Higher solute concentrations facilitate the constitutional undercooling and the CET, with total suppression of columnar grains in high-copper alloys as illustrated in Fig. 4.5a, b. In addition, the “solidification distance” or the vertical dimension of the solidification region in the billet is larger in low-copper alloys, which is a result of greater difference between the liquidus and eutectic temperatures in these alloys. Hence, the grains have longer time for the growth. Ramping up of the casting speed causes general structure refinement and produces a more uniform grain structure. The comparison of graphs in Figs. 4.6a and 4.6b, and Fig. 4.11 suggests that there is a general correlation between diametral distribution of the dendritic arm spacing and the distance between liquidus and solidus isotherms in a billet. The larger the “solidification distance”, the thicker the dendrite branches. This relationship can be interpreted in terms of the solidification time – the larger the solidification range, the longer the solidification time and the coarser the dendrite branches. On the other hand, the

90 Effect of casting speed and alloy composition on structure formation and hot tearing distance between liquidus and solidus grows with increasing casting speed, while the dendritic arm spacing becomes finer. That means that the dimension of the solidification region is not the only factor that influences the structure formation. It is important to note that with increasing casting speed, a unit volume of the billet passes the solidification region faster, and that effect can completely overrun the enlargement of the “solidification distance” as we showed in our previous paper [6]. The solidification rate may be yet another factor. The solidification rate or the normal velocity of the solidification front is related to the casting speed as Vsol = Vcasrcosϕ [5], where ϕ is the angle between the normal to the solidification front and the billet vertical axis. The solidification rate is maximum at the periphery and in the center of a billet. Therefore, the acceleration of casting may result in structure refinement because of the general acceleration of solidification, despite the fact that the geometrical dimensions of the transition region increase. The calculation shows that there is a local narrowing of the solidification region in the central part of the billet (Fig. 4.11), which may be indicative of higher solidification rates. The appearance of coarse grains in the central part of DC cast billets is a phenomenon frequently observed in casting practice [1]. The origins of these grains may be argued. In literature [1,5] several hypotheses are suggested, including (1) the formation of these grains on the open surface of the melt or on a distribution bag, or on a hot top with subsequent separation and transporting by melt flow or due to gravity and (2) the fragmentation of dendrites at the solidification front as a result of local remelting or mechanical forces with detachment of fragments and transporting of them by melt flow. Both mechanisms are possible. A flow pattern existing in round billets during DC casting involves quite strong currents along the liquidus isotherm towards the center of a billet [34]. The maximum of these currents are at approximately 2/3 of billet radius, measuring from the center. These currents further develop into a recirculation zone in the central part of the billet. As a result, fragments of dendritic grains nucleated in the part with strong melt currents can be easily detached. These fragments act as nucleation sites for aluminum solid solution, grow in the melt volume ahead of the solidification front under very small undercooling and are dragged to the central part of the billet (that explains the larger dendritic arm spacing). Subsequently, these grains are captured by the solidification front, being forced down by currents or sedimenting under gravity, and finish solidifying at higher undercooling or cooling rate (resulting in frequently observed finer dendrite branches at the grain periphery). In addition to that, we suggested earlier [6] that at least some grains found in the central part of the billet were nucleated at its periphery and then transported to the center, growing as they travel. As a result, the structure of the central part of the billet shows a spread in apparent cooling rates and, hence in

91 Chapter 4 dendritic arm spacings. Therefore, the third mechanism of coarse grains formation is a longer growth due to their trajectory within the slurry zone. The observed dependence of the number of coarse grains on the casting speed (Figs. 4.8a and 4.8b) is in good agreement with the widening of the solidification region upon casting acceleration (Fig. 4.11) due to the obvious reason – a larger slurry region provides more time and opportunity to transfer (and grow) grains from the periphery to the center. On the other hand, the number of coarse grains tends to increase with the copper concentration (Figs. 4.8a and 4.8b). That may seem to contradict the previous statement as the “solidification distance” shortens with increasing copper (Fig. 4.11). However, the enrichment of the melt with the solute (i.e. copper) and the corresponding undercooling [35] facilitate the nucleation of more grains ahead of the continuous solidification front and, therefore increase the probability of transporting these grains by melt currents to the central part of the billet. 4.5.2 Hot cracking Our results on the effects of casting speed and composition on hot tearing, though original in representation, agree well with the previously reported patterns as reviewed elsewhere [4]. There are three issues to be addressed further. Firstly, the compositional dependence of hot tearing with the maximum cracking in a certain low-alloyed range. This can be explained in terms of a thicker mushy zone (region with hindered feeding or low permeability), less residual liquid available for feeding (represented by the amount of nonequilibrium eutectics in Figs. 4.7a and 4.7b), more time spent in the vulnerable temperature range [3], and larger deformations induced by thermal contraction [2,36]. Secondly, the strong dependence of hot cracking on the casting speed. This phenomenon is well documented [8,15,17,37]. The main causes of stresses and strains in the solidifying billet are thermal gradients. The difference in temperatures between the surface and the center of the billet results not only in different stages of solidification that occur there, but also in the build-up of stresses due to the fact that the thermal contraction of the mushy zone is restricted by the resistance of the already solidified outer part of the billet. Thermal gradients increase with the casting speed to the same proportion as the depth of the sump increases. Higher stresses and strains may promote the occurrence of hot tears if the ductility of the semi-solid material is not sufficient to accommodate these strains. Interesting fact that the maximum of hot tearing corresponds to a casting speed lower than the maximum one, at the deceleration stage of casting (Fig. 4.10), agrees well with the results reported elsewhere [37] that the change of sump profile with increasing casting speed occurs with some delay due to the thermal inertia. So the maximum hot cracking corresponds to the deepest sump (which reflects

92 Effect of casting speed and alloy composition on structure formation and hot tearing maximum thermal gradients), rather than to the casting speed proper. Our results also show that the casting speed required to initiate the hot tear is higher than the casting speed required for crack healing (Fig. 4.10). This is in good agreement with the reported experimental data [8,37]. And thirdly, the concentration of hot cracks in the central part of the billet as can be clearly seen in Fig. 4.9. Hot tears occur in the central part of DC cast billets because the stresses and strains are concentrated there as demonstrated in Fig. 4.12. However, the stress–strain situation is a necessary but not sufficient condition for the appearance of hot cracks. The feeding of the solidifying material with the melt should be inadequate for compensation of the solidification shrinkage and thermal contraction [3,4,17]. Hence, the amount of the liquid available at the crucial stage of solidification, when the semi-solid material is most vulnerable and the hot cracking susceptibility is high, is extremely important [3,15]. Figs. 4.7a and 4.7b clearly demonstrates that the amount of eutectics (last liquid to solidify) is decreasing towards the center of the billet, this tendency being more pronounced at higher casting speeds and at lower copper concentrations. This observation fits well into the mechanism of hot tearing, proving that the amount of the available liquid at the end of solidification is lower in the most critical part of the billet and in the most crack-sensitive compositional range. Hot tearing criteria can be very useful in qualitative assessment of vulnerability of a billet made from a certain alloy and cast under certain casting conditions. Results given in Fig. 4.13 show that non-mechanical (Feurer [14] and Katgerman [15]), mechanical (Prokhorov [12] and Magnin et al. [16]) and combination of non-mechanical and mechanical (RDG[17]) criteria can successfully predict the distribution of hot tears and the hot-cracking sensitivity to the casting speed. At the same time, other criteria cannot foresee the occurrence of hot cracks and its dependence on the casting speed (criteria by Novikov [2,13] and Clyne and Davies [3]). All working criteria take into account dynamics of direct chill casting. Feurer has incorporated the flow rate and the shrinkage velocity in his criterion. Katgerman combines the criteria by Clyne and Davies and by Feurer, thereby adding dynamics to the approach of Clyne and Davies. Feurer’s and Katgerman’s criteria are sensitive to the casting speed because they include casting-speed dependent length of the mush and depth of the sump (pressure) in the formulation. The mechanical criteria of Prokhorov and Magnin et al. are able to reproduce the hot-tearing behavior during DC casting due to incorporation of plastic/viscoplastic deformation that is influenced by the casting speed. RDG’s criterion uses viscoplastic strain rate for the same purpose. Novikov’s and Clyne and Davies’ criteria fail to predict hot-tearing behavior during DC casting. This might be due to the fact that the parameters for the

93 Chapter 4 formulation of these criteria are static and do not change with changing casting conditions. Novikov uses the integral ratio between thermal contraction and ductility in the solidification range, the thermal contraction being a substitute for the actual plastic deformation during solidification. Although the thermal contraction and ductility in the solidification range are dependent on process parameters, only few data are available on these relationships. The formulation of thermal contraction in terms of the structure and process parameters may make the Novikov criteria working. Clyne and Davies use in their criterion the ratio between the time spent by an alloy in the vulnerable solidification range (between 90 and 99% solid) and the time available for the stress relaxation and melt feeding (between 40 and 90% solid). Although, the critical temperatures are affected by casting parameters, Clyne and Davies take them as a ratio of prescribed values, which make their criterion not responsive to the varying casting speed. However, it is worth to mention that these criteria are successfully used to forecast the hot tearing susceptibility of casting alloys and the compositional dependence of hot cracking susceptibility [2,3].

4.6 Conclusions The conclusions that can be drawn from this work are: 1. Experiments are performed on direct-chill casting of round billets (200 mm in diameter) from binary Al–Cu alloys. During casting the casting speed is automatically ramped up from 100 to 200 mm/min and then down to 100 mm/min. Four alloys containing 1 to 4.5% Cu are tested. The results of structure examination are correlated to the casting speed and chemical composition as well as to the dimensions of solidification region in the billet. 2. The grain size strongly varies across the billet cross-section and depends on the casting speed and chemical composition. Most coarse structure is observed at low concentrations of copper (< 2%) and low casting speeds. The dendritic arm spacing is influenced by the casting speed and the position in the billet, being virtually unaffected by the chemical composition. The amount of nonequilibrium eutectics strongly depends on the position in the billet, casting speed and chemical composition, being minimum in the central part of the billet and at low concentrations of copper. The number of coarse grains that are concentrated in the center of the billet is found to increase with the casting speed and concentration of copper. 3. Numerical simulations show that the solidification region in the billet (distance between liquidus and solidus) enlarges from the periphery to the

94 Effect of casting speed and alloy composition on structure formation and hot tearing

center of the billet, with increasing the casting speed, and with decreasing the copper concentration. 4. The results on structure formation are explained in terms of the conditions of nucleation (enrichment of melt in solute, constitutional undercooling), growth (dimensions of solidification range, cooling rate, solidification rate) and transport of solid phase within the slurry zone. 5. Hot tears are shown to occur in the central part of the billet, their quantity being maximum at high casting speeds and low copper concentrations. These results are correlated to the results of numerical simulation (strain analysis) and structure examination (actual hot tears and amount of nonequilibrium eutectics). Several hot tearing criteria were implemented into a finite element model of direct-chill casting and tested against the practice. It is shown that criteria that account for the dynamics of the process can be successfully used for qualitative prediction of hot tearing during DC casting.

References [1] Emley E.F. (1976) International Metals Reviews, 206, p. 75. [2] Novikov, I.I. (1966) Goryachelomkost tsvetnykh metallov i splavov (Hot Shortness of Non-Ferrous Metals and Alloys), Moscow: Nauka. (in Russian). [3] Clyne, T.W. and Davies, G.J. (1979) Proceedings Conference on Solidification and Castings of Metals, Metals Society, London, p. 275. [4] Eskin, D.G., Suyitno and Katgerman, L. (2004) Progress in Materials Science, 49, p. 629. [5] Livanov, V.A., Gabidullin, R.M. and Shepilov, V.S. (1977) Nepreryvnoe lit’e alyuminievykh splavov (DC Casting of Aluminum Alloys), Metallurgiya, Moscow. [6] Eskin, D.G., Zuidema (Jr.), J., Savran, V.I. and Katgerman L. (2004) Materials Science and Engineering A, 384, p. 232. [7] Nagaumi, H, Aoki, K., Komatsu, K. and Hagizawa, N. (2000) Materials Science Forum, 331–337, p. 173. [8] M’Hamdi, M., Kieft, R., Mortensen, D., Mo, A. and Rabenberg, J. (2002) Aluminium, 78, p. 847. [9] Buxmann, K. and Gold, E. (1982) Journal of Metals, 4, p. 28. [10] Flemings, M.C. (1974) Solidification Processing, McGraw-Hill, New York, USA.

95 Chapter 4

[11] Nagaumi, H. (2001) Science and Technology Advanced Materials, 2, p. 49. [12] Prokhorov, N.N. (1962) Russian Castings Production, 2, p. 172. [13] Navikov, I.I. and Grushko, O.E. (1995) Materials Science and Technology, 11, p. 926. [14] Feurer, U. (1977) Quality Control of Engineering Alloys and the Role of Metals Science, Delft University of Technology, Delft, p. 131. [15] Katgerman, L. (1982) Journal of Metals, 34, 2, p. 46. [16] Magnin, B., Katgerman, L., and Hannart, B. (1995) Modeling of Casting Welding and Advanced Solidification Processes VII, eds. M. Cross and J. Campbell, TMS, Warrendale, PA, p. 303. [17] Rappaz, M., Drezet, J.M. and Gremaud, M. (1999) Metallurgical and Materials Transactions A, 30A, p. 449. [18] Suyitno, Kool, W.H. and Katgerman, L. (2002) Materials Science Forum, 396-402, p.179. [19] Braccini, M., Martin, C.L. and Suery, M. (2000) Modeling of Casting Welding and Advanced Solidification Processes IX, eds. P.R. Sahm, P.N. Hansen, and J.G. Conley, Shaker Verlag, Aachen, p.18. [20] Farup, I. and Mo, A. (2000) Metallurgical and Materials Transactions A, 31A, p. 1461. [21] M’Hamdi, M., Mo, A. and Martin, C.L. (2002) Metallurgical and Materials Transactions A, 33A, p. 2081. [22] Nedreberg, M.L. (1991) Ph.D. Thesis, University of Oslo, Oslo, Norway [23] Drezet, J.-M. and Rappaz, M. (2001) Light Metals 2001, ed. J.L. Anjier, TMS, Warrendale, PA, p. 887. [24] MSC.Marc, Theory and User Information, Volume A, 2000. [25] Suyitno, Kool, W.H. and Katgerman, L. (2003) Light Metals 2003, ed. P.N. Crepeau, TMS, Warrendale, PA, p. 753. [26] Suyitno, Katgerman, L. and Burghardt, A. (2002) Proceedings of the ASME Heat Transfer Division – 2002, eds. T. Bayazitoglu and H.S. Cameron, The American Society of Mechanical Engineers, New York, 5, p. 147. [27] Zuidema (Jr.), J., Katgerman, L., Opstelten, I.J. and Rabenberg, J.M. (2001) Light Metals 2001, ed. J.L. Anjier, TMS, Warrendale, PA, p. 873. [28] Touloukian, Y.S., and Buyco, E.H. (1970) Thermophysical Properties of Matter; Volume 4 Specific Heat; Metallic Elements and Alloys, IFI/Plenum Press, New York– Washington, USA.

96 Effect of casting speed and alloy composition on structure formation and hot tearing

[29] Taylor, R.E., Groot, H., Goerz, T., Ferrier, J. and Taylor, D.L. (1998) High Temperature-High Pressure, 30, 3, p.269. [30] Overfelt, R.A., Bakhtiyarov, S.I. and Taylor, R.E. (2002) High Temperature-High Pressure, 34, p. 401. [31] Brammer, J.A. and Percival, C.M. (1970) Experimental Mechanics, 10, 6, p. 245. [32] Van Haaften, W.M. (1997) Thermophysical Properties of Certain Al Alloys, Internal Report, Delft University of Technology, Delft. [33] Hutt, J. and StJohn, D. (1998) International Journal Cast Metals Research, 11, p. 13. [34] Venneker, B.C.H. and Katgerman, L. (2002) Journal of Light Metals, 2, p.149. [35] Bäckerud, L., Król, E. and Tamminen, J. (1986) Solidification Characteristics of Aluminium Alloys. Vol. 1: Wrought Alloys, Skanaluminium/ Universitetsforlaget AS, Oslo. [36] Eskin, D.G., Suyitno, Mooney, J. and Katgerman, L. (2004) Metallurgical and Materials Transactions A, 35A, p. 1325. [37] Commet, B., Delaire, P., Rabenberg, J. and Stoorm, J. (2003) Light Metals 2003, ed. P.N. Crepeau, Warrendale, TMS, p. 711.

97 Chapter 4

Chapter 5

Hot tearing study of Al–Cu billets produced by direct- chill castingε

In this chapter, hot cracking in Al–(1-4.5%)Cu direct-chill cast billet is investigated. The hot tear surfaces of the DC cast billets with different composition were observed in a SEM. Measurements on the porosity fraction are also reported. It was found that a decrease of the copper concentration from 3 to 1 % causes a decrease of the amount of eutectic observed on the hot tear surface. Special features are observed on the hot tear surface of an Al−1%Cu alloy in which the hot tear dominantly propagates through the bridged grain boundaries. A solute-rich (eutectic) path along grain boundaries ahead of the hot-crack tip was observed in billets with hot tears, which could be an evidence of crack healing. The porosity is maximum in the center of the billet. Higher casting speed leads to increasing porosity.

ε This chapter is submitted for publication in: Materials Science and Engineering A, 2005.

Chapter 5

5.1 Introduction The solidification defects such as porosity and hot tear are known in the direct-chill (DC) cast billet for a long time. Their occurrence determines the productivity in the case of hot tear and porosity, and to a great extent mechanical properties and performance of cast material in the case of porosity. A few mechanisms of hot tearing are already suggested [1]. Macroscopically, the hot tear formation is caused by the inability of the material to withstand the existing stress or strain in the solidification range [2-7]. On the microscopic level, there are two approaches suggested. The first approach is that the hot tear formation is caused by the lack of feeding to counteract shrinkage [8,9], and due to the shrinkage and deformation [10]. The second approach is that failure happens at a critical stress. The liquid surrounding the grain is considered as a stress riser of the semi-solid body [11,12]. In this theory, a cavity formed in the stress riser is considered as a crack initiator. The propagation of the crack initiator is determined by the critical stress [12]. Porosity in casting can be classified based on the size (micro-porosity and macro-porosity) and on the cause (shrinkage porosity and gas porosity). Two mechanism of porosity formation are known [13-18]. The shrinkage porosity is caused by the lack of melt feeding to compensate the solidification shrinkage. The gas porosity is caused by gas segregation due to the fact that the solubility of gas in the solid metal is far less than that in the liquid metal. The porosity is characterized by irregular shape and round shape for the shrinkage and the gas porosity, respectively [18]. In reality, these two types of porosity mixed together. Although liquid feeding and shrinkage play a role in porosity and hot tear formation, the relation between these two defects is still not clear. In fact, an attempt to describe the porosity and hot tear as consecutive processes is reported in ref. [19]. The description is applied for deriving the model of hot tear prediction, which leads to the formation of either porosity or hot tear. The aim of this work is to investigate the hot tear surface of Al–Cu alloys with different copper concentration produced by DC casting. The billets of Al–(1- 4.5%)Cu alloys were cast with a ramping casting speed. The microstructure and porosity fraction are examined. The possible interaction between the hot tear and porosity is addressed.

5.2 Experimental procedure Billets 195 mm in diameter and up to 1800 mm in length were produced in a pilot scale direct-chill caster in Delft University of Technology. The caster is equipped with a tilting electrical furnace of 200 kg capacity for melting alloys; a

100 Hot tearing study of Al−Cu billet produced by direct-chill casting flexible closed launder for transferring melt to a permanent launder; a permanent ceramic launder; a 200-mm hot-top round mold; a laser melt-level control coupled with the furnace; and a PC-based process monitoring and control unit. Melt and cooling water temperatures, water-flow rate, casting speed, melt level and billet length are the controlled parameters.

Table 5.1. Conditions used during DC casting. Alloy Al−1%Cu Al−2%Cu Al−3%Cu Al−4.5%Cu Composition, wt% 1.03%Cu, 1.98%Cu, 3.03%Cu, 4.49%Cu, 0.16%Fe, 0.18%Fe, 0.20%Fe, 0.19%Fe, %Zn, 0.01%Zn, 0.13%Zn, 0.02%Zn, 0.04%Si 0.06%Si 0.09%Si 0.06%Si Melt temperature 728 oC 728 oC 728 oC 728 oC in furnace Water flow rate 150 l/min 150 l/min 150 l/min 150 l/min

Billets of Al−Cu alloys were cast under the conditions shown in Table 5.1. Casting speed was a variable with a gradual ramping up and down in the range of 100 to 200 mm/min, ramping rate being ~1 mm/min/s. The hot tear surfaces selected from the billets are investigated by scanning electron microscopy (SEM). The location of the samples is in the center of the billets and corresponds to a casting speed of 200 mm/min. Specimens for metallographic analysis were taken along the axial and radial cross sections of the billet. The specimens were prepared by grinding, polishing and electro-oxidizing in a 3% solution of fluoboric acid in water.

5.3 Results

5.3.1 Hot tear surface Hot tears were observed under given casting conditions only in the alloy contained 1−3 % Cu (see Fig. 4.10). The hot tear surfaces of the Al−(1-3)%Cu alloys in the center of the billet corresponding to a casting speed 200 mm/min are shown in Figs. 5.1-5.3. The fracture surface is smoother at a higher copper concentration, with regions of eutectics. The existence of liquid film at the surface is clearly shown at a high copper concentration. The fracture in the alloys containing 2-3 % Cu is obviously intergranular. At a copper concentration 1%, the fracture surface is dominated by bridged grain boundaries. In this case, the fracture surface shows feature of brittle and, possibly, transgranular failure.

101 Chapter 5

Possibly brittle fracture

Figure 5.1. SEM images on the hot tear surface of Al−1% Cu alloy.

102 Hot tearing study of Al−Cu billet produced by direct-chill casting

Bridging

Eutectics

Figure 5.2. SEM images on the hot tear surface of Al−2% Cu alloy.

103 Chapter 5

Eutectics

Figure 5.3. SEM images on the hot tear surface of Al−3% Cu alloy.

104 Hot tearing study of Al−Cu billet produced by direct-chill casting

5.3.2 Microstructure around the hot tear tip A micrograph in Fig. 5.4 shows the place in the billet where the macro-crack stops. One can seen a solute-rich (eutectic) path along several grain boundaries as a continuation of the hot crack, which could be an evidence of fluid flow in the dendritic network and (probably) crack healing (Fig. 5.4a). Furthermore, the eutectic path close to the crack tip contains micro-pores that could be the initiators for the crack (Fig. 5.4b). These pores are retained till the end of solidification. In the solute rich region, the pore is filled eutectic (Fig. 5.4c) or remains a cavity (Fig. 5.4d).

105 Chapter 5

c) a)

Figure 5.4. Hot tear tip region and micro-pore along the grain boundary in front of the crack tip in an Al−3%Cu alloy. The black arrow denotes the solute-rich path.

106 Hot tearing study of Al−Cu billet produced by direct-chill casting

5.3.3 Porosity The relation of copper concentration, position in the billet and porosity at the three casting speed is shown in Fig. 5.5. The porosity decreases with increasing distance from the center of the billet and the highest fraction of porosity is observed around the center of the billet. The porosity tends to increase with copper concentration and reaches a maximum at a certain copper concentration. The porosity increases significantly with increasing casting speed from 100 mm/min to 160 mm/min, and then it slightly decreases at casting speed (200 mm/min). At a high casting speed and around the center of the billet, the porosity is irregular shape and is distributed along the solute-rich grain boundaries (Fig. 5.6). At a low casting speed, the observed porosity is rounded. 5.3.4 Microstructure The structure of Al−(1-3)%Cu alloy in the center of the billet is shown in Fig. 5.7 in which the grain size increases with decreasing copper concentration. Fig. 5.8 shows the dendritic structure of Al−3%Cu at casting speed of 100 mm/min (a, b, c) and 200 mm/min (c, d, e). The structure consists of equiaxed grain in which the dendritic arm spacing (DAS) increases with the distance from the surface of billet. A mixture of coarse and fine dendrites is observed in the center of the billet at a high casting speed (200 mm/min).

107 Chapter 5

Figure 5.5. Effects of casting speed (a: 100 mm/min b: 160 mm/min and c: 200 mm/min) and copper concentration on the distribution of porosity in DC cast round billets.

108 Hot tearing study of Al−Cu billet produced by direct-chill casting

Figure 5.6. Porosity of an Al–3 % Cu alloy at casting speed 200 mm/min at the center of the billet.

a. b. c. Figure 5.7. Microstructure of Al−Cu billets in the as-cast condition for casting speed 200 mm/min and in the center of billet. (a) Al−1%Cu, (b) Al−2%Cu and (c) Al−3%Cu.

109 Chapter 5

a. b. c.

d. e. f. Figure 5.8. Dendritic structure of an Al−3%Cu alloy billet in the as-cast condition. Casting speed: 100 mm/min (a), (b) and (c) from the surface to the center, 200 mm/min (d), (e) and (f) from the surface to the center.

5.4 Discussion It has been established that binary aluminum alloys has a certain concentration that has a highest susceptibility for hot tear (see Fig. 4.10). Increasing alloy concentration higher than the highest susceptibility concentration will certainly decrease the susceptibility. In the aluminum-copper system, the maximum susceptibility is found at copper concentration about 1 % [1,20]. The observed hot tear surfaces in the billets of Al−Cu alloys containing 2 and 3 % Cu are in accordance with the previously reported results for commercial alloys [21-

110 Hot tearing study of Al−Cu billet produced by direct-chill casting

26] in term of liquid film covering the fracture surface and visible dendrites on the fracture surface. The solid bridging, which is clearly seen at a copper concentration of 2 % (Fig. 5.2), has been also reported in several papers, though not for fracture surface [21,23,26]. Apparently, the hot tear propagates either through the fully liquid film, or through the liquid film and solid bridges. This first mechanism will result in the smooth hot tear surface and the second one will result in the hot tear surface with fractured solid bridges. The bridged grain boundary is dependent on the alloying content, tending to decrease with increasing solute concentration (Al−(1-5)%Cu and Al−(1-5)%Sn) [27]. It can be understood from the increasing eutectic fraction in the last stage of solidification. The eutectic liquid is the last available liquid that solidifies. This is proved by the existence of solute-rich grain boundaries in the center of billet. The eutectic liquid feeding will avoid the formation of cavity due to the shrinkage, deformation due to gradient temperature, and gas release. All of those indicate, first: the important role of liquid feeding in the last stage of solidification for reducing the hot tear development, and second: the bridged grain boundary will not reduce the hot tear propagation. Special feature is observed on the hot tear surface of an Al−1% Cu alloy (Fig. 5.1). At this copper concentration, the amount of eutectic liquid is low and due to low permeability of the system, it cannot flow in a long path to counteract the shrinkage and deformation. Another fact, at such low copper concentration the bridged grain boundary is considerable [27]. The hot tear propagation may occur through the bridged grain boundaries. The hot tear initiator might be formed in the last liquid that is isolated in certain sites, e.g. triple-junctions, due to the interrupted liquid network. Any stresses can be transmitted through the dendritic network. However, the liquid pocket becomes narrow so that stress concentrates in this site. From the liquid-metals-embitterment point of view [28], the surface energy for the propagation of crack/pore filled with liquid through grain boundary is smallest than the other possibility of propagation. This will enhance further crack propagation in 1% copper concentration. The porosity is a common feature in the solidified structure. It is caused by solidification shrinkage and hydrogen saturation [29]. Shrinkage and/or gas precipitation are the driving forces for the initiation of pores, and the same forces act for continuing the pore growth to a macroscopic size [30]. The porosity reaches maximum in the center of billet, and it inversely correlates with hot tear fraction [31,32]. The inverse relation of porosity and hot tear length (compare Fig. 5.5 and ref. [20]) is attributed to the closely related mechanisms of both defects. The porosity is the initiator for either a further slow growth to a larger size and/or a further fast development to become the hot tear (Fig. 5.4). The cavity relaxed due

111 Chapter 5 to the stress release by the hot tear formation. The hot tear length is longer at a low copper concentration (1 %) billet than that at a high copper concentration (3 %) billet. At copper concentration more than ~3.5 %, the porosity decrease slightly with increasing copper concentration. The decrease is due to a better feeding at high copper concentration. The better feeding is also reflected in the hot tear that is not developed at copper concentration higher than 3.5 %. The increase of casting speed causes an increase of porosity at casting speed of 160 mm/min and somewhat decrease at casting speed of 200 mm/min. The increase of casting speed leads to the increasing possibility of the hot tear formation. The decrease of porosity at casting speed of 200 mm/min is also due to the relaxation of the porosity by hot tear formation. A transition state between hot tear and no hot tear in billet is reported previously [33,34]. The transition is known by the formation of a micro-pore at the grain boundary. It reflects the possibility of the hot tear to be initiated by pore formation. A comprehensive explanation on the effect of casting speed and copper concentration on the structure formation is reported in ref. [20]. The decrease of grain size with copper concentration is attributed to the “solidification distance” or the vertical dimension of the solidification region that is larger in low-copper alloys, which is a result of greater difference between the liquidus and eutectic temperatures in these alloys [20]. Hence, the grains have longer time for the growth. The effect of location in the billet, which shows a mixture of coarse and fine grains in the center of billet cast at high casting speed, is attributed to the movement of nuclei with fluid flow. The increase of casting speed leads to a deeper sump and longer solidification path. Because of that, the coarse grains form by either the nuclei initiated in the periphery that grow and flow to the center or the nuclei initiated in the center of the billet that detache and flow circularly up and down [20].

5.5 Conclusions The observation of the microstructure, porosity and hot tear surface of Al−Cu billet as in dependence on the casting speed and copper concentration leads to conclusion the following: 1. Decreasing the copper concentration from 3 to 1 % causes a decrease of eutectic amount observed on the hot tear surface.

112 Hot tearing study of Al−Cu billet produced by direct-chill casting

2. Special features are observed on the hot tear surface of an Al−1%Cu alloy. The hot tear appears to predominantly propagate through the bridged grain boundary. 3. A solute-rich (eutectic) path along grain boundaries ahead of the hot-crack tip was observed in billets with hot tears. This could be an evidence of crack healing. 4. The porosity is maximum in the center of billet

References [1] Eskin, D.G., Suyitno and Katgerman, L. (2004) Progress in Materials Science, 49, p. 629. [2] Pellini,W.S. (1952) Foundry, 80, p. 124. [3] Novikov, I.I. (1966) Goryachelomkost tsvetnykh metallov i splavov (Hot Shortness of Non-Ferrous Metals and Alloys), Moscow: Nauka. (in Russian). [4] Novikov, I.I. and Grushko, O.E. (1995) Materials Science and Technology, 11, p. 926. [5] Prokhorov, N.N. (1962) Russian Castings Production, 2, p. 172. [6] Magnin, B., Katgerman, L., and Hannart, B. (1995) Modeling of Casting Welding and Advanced Solidification Processes VII, eds. M. Cross and J. Campbell, TMS, Warrendale, PA, p. 303. [7] Magnin, B., Maenner, L., Katgerman, L. and Engler, S. (1996) Materials Science Forum, 217-222, p. 1209. [8] Feurer, U. (1977) Quality Control of Engineering Alloys and the Role of Metals Science, Delft University of Technology, Netherlands, p. 131. [9] Niyama E. (1977) Japan–US joint seminar on solidification of metals and alloys. Tokyo: Japan Society for Promotion of Science, p. 271. [10] Rappaz, M., Drezet, J.M. and Gremaud, M. (1999) Metallurgical and Materials Transactions A, 30A, p. 449. [11] Petterson, K. (1953) Giesserei, 40, p. 597. [12] Williams, J.A. and Singer, A.R.E. (1968) Journal Institute of Metals, 96, p. 5. [13] Campbell J. (1991) Castings. Butterworth-Heinemann, Oxford, UK. [14] Piwonka, T.S. and Fleemings, M.C. (1966) AIME Metallurgical Society Transactions, 236, p. 1157.

113 Chapter 5

[15] Shivkumar, S., Apelian, D. and Zou, J. (1990) AFS Transactions, 98, 178, p. 897. [16] Kubo, K. and Pelke, R.D. (1985) Metallurgical Transactions, 16B, p. 359. [17] Poirier, D.R., Yeum, K. and Maples, A.L. (1987) Metallurgical Transactions, 18A, p. 1979. [18] Lee, P.D., Chirazi, A. and See, A. (2001) Journal of Light Metals, 1, p. 15. [19] Suyitno, Kool, W.H. and Katgerman, L. (2002) Materials Science Forum, 396-402, p. 179. [20] Suyitno, Eskin, D.G., Savran, V.I. and Katgerman, L. (2004) Metallurgical and Materials Transactions A, 35A, p. 3551. [21] Instone, S. (1999) PhD thesis, University of Queensland, Australia. [22] Nedreberg, M.L. (1991) Ph.D. Thesis, University of Oslo, Oslo, Norway. [23] Van Haaften, W.M. (2001) PhD Thesis, Delft University of Technology, Delft, The Netherlands. [24] Dickhaus, C.H., Ohm, L. and Engler, S. (1994) AFS Transactions, 101, p. 677. [25] Han, Q., Viswanathan, S., Spainhower, D.L. and Das, S.K. (2001) Metallurgical and Materials Transactions A, 32A, p. 2908. [26] Spittle, J.A., Brown, S.G.R., James, J.D. and Evans, R.W. (1997) Proceedings of 7th International Symposium on Physical Simulation of Casting, Hot rolling and Welding, National Research Institute for Metals, Tsukuba, Japan, p. 81. [27] Ju, Y. (2004) Ph.D Thesis, Norwegian University of Science and Technology, Trondheim, Norway. [28] Rostoker, W., McCaughey, J.M. and Markus, H. (1960) Embrittlement by Liquid Metals, Reinhold Publishing Corp., New York, USA. [29] Sabau, A.S. and Visvanathan, S. (2002) Metallurgical and Materials Transactions B, 33B, p. 243. [30] Gupta, A.K., Saxena, B.K., Tiwari, S.N. and Malhotra, S.L. (1992) Journal of Materials Science, 27, p. 853. [31] Nagaumi, H. (2001) Science and Technology of Advanced Materials, 2, p. 49. [32] Lee, P.D., Atwood, R.C., Dashwood, R.J. and Nagaumi, H. (2002) Materials Science and Engineering A, 328, p. 213.

114 Hot tearing study of Al−Cu billet produced by direct-chill casting

[33] Ohara, K., Kurino, S., Toyoshima, M. and Wakasaki, O. (1996) Proceedings of the 4th Inernational Conference on Aluminum Alloys, Atlanta, Georgia. p. 122. [34] Savran, V.I. (2004) MSc. Thesis, Delft University of Technology, The Netherlands.

115 Chapter 5

116

Chapter 6

Model and simulation for prediction of hot tearing in aluminum alloysφ

Shrinkage, imposed strain rate and (lack of) feeding are considered as the main factors which determine cavity formation and/or the formation of hot tears. A hot tearing model is proposed which will combine a macroscopic description of the DC casting process and a microscopic model. The micro-model predicts whether porosity will form or a hot tear will develop. Results for an Al-4.5%Cu alloy are presented as a function of constant strain rate and cooling rate. Also, incorporation of the model in a FEM simulation of the DC casting process is reported. The model shows features, well-known from literature such as increasing hot tearing sensitivity with increasing deformation rate, cooling rate and grain size. Similar trends are found for the porosity formation as well. The model also predicts a beneficial effect of applying a ramping procedure during the start-up phase, which is an improvement in comparison with earlier findings obtained with alternative models. However, a rigorous test of the model with data obtained from industrial practice was outside the scope of this thesis.

φ This chapter is submitted for publication in: Acta Materialia, 2005.

Chapter 6

6.1 Introduction Hot tears are cracks that initiated in the mushy zone. These cracks are characterized by intergranular fracture and a smooth fracture surface due to the existence of a liquid phase in the interdendritic region during cracking [1]. Hot tearing is one of the crucial problems encountered during the direct-chill (DC) casting process. Their occurrence determines the productivity during the process. These solidification defects are already known for a long time, but quantitative prediction of their occurrence is still underdeveloped. Quantitative prediction of hot tearing is not easy, because of the complex interplay between macroscopic and microscopic phenomena. Prediction of hot tearing during DC casting is based on two steps, namely modeling of the thermomechanical behavior during solidification [2-4] and implementing of hot tearing criteria in the thermomechanical modeling [5-10]. The first step uses constitutive equations to describe the thermomechanical modeling to calculate stresses and strains in the billet. Computed stresses and/or strains indicate the hot tearing tendency. In the second step the results of the first step are used as input in a hot tearing criterion. Several mechanisms of hot tearing have recently been reviewed [1]. Various criteria which might enable the prediction of hot tears have been proposed [11-18]. These criteria can be classified into those based on non-mechanical aspects such as feeding behavior [11-13] those based only on mechanical aspects [14-16], and those which combine these features [17,18]. In general, the solidification processes proceed in four steps which reflect the morphological development and interaction [10], namely: (1) the nucleated crystals freely float and the macroscopic behavior is close to the liquid behavior, (2) the nuclei are close and tend to attach to each other to form a porous network and the solidification shrinkage strain is easily counteracted by liquid flow and solid arrangement (3) the deformation of the solidified body caused by the solidification shrinkage and external strains is not fully counteracted by liquid flow and solid movement so that solidification defects, such as hot tears and porosity are usually initiated, and (4) the grains are strongly interconnected so that deformation of the solidified body will not result in further defects. Approaches based on non-mechanical criteria [11-13] put emphasis on the feeding properties in the mush and assume that the second and third stage of the solidification play the main role in the formation of a hot tear. In contrast, the mechanical criteria [14-16] emphasize the importance of the strengths and strains developed in the third and fourth stage of the solidification. Some approaches [17,18] combine these mechanical and non-mechanical method for the prediction of hot tearing.

118 Model and simulation for prediction of hot tearing in aluminum alloys

A comprehensive evaluation of existing hot tearing criteria for direct-chill casting of aluminum billets is reported in refs. [8-10]. In the assessment of various criteria for hot tearing, it is found that the RDG criterion [17], which combines mechanical and feeding conditions had the greatest potential with respect to the other criteria but it did not predict cracking for practical conditions where cracking will not occur [10]. Therefore in this study, a hot tearing model is derived based on cavity formation when there is insufficient feeding during solidification. The feeding during solidification is incorporated using a transient mass balance equation. The flow behavior of the semi-solid state has been included in order to model the mechanical response of the semi-solid body. The cavity formed becomes a hot tear in case a critical dimension is achieved, else porosity will result. The possibility of the formation of micro-porosity is not found for other models. The proposed model is applied in two types of simulation. First, the porosity growth, the hot cracking sensitivity and the developed stress in the mush are calculated as a function of several parameters using as constant parameters strain rate and cooling rate. Second, the proposed model is incorporated in FEM simulation of DC casting an Al−4.5% Cu billet. The hot cracking sensitivities are calculated as a function of several parameters, and are compared with those from the RDG criterion [17].

6.2 Physical model Solidification is initiated by the formation of nuclei that grow to form a dendritic structure. In the model it is assumed that the microstructure is equiaxed. The floating grains grow, coarsen and reach the coherency point where the dendrites touch each other. Cavities are formed at triple junctions between the grains. At and beyond the coherency point, stresses can be transmitted through the dendritic network. At the coherency point, the volume difference due to the thermal shrinkage and imposed deformation can be filled with liquid metal. During further solidification, the liquid network becomes interrupted and liquid pockets become isolated. Permeability becomes low and the dendritic network becomes strong. Liquid flow and afterfeeding of the volume difference becomes suppressed. During complete solidification there are three possibilities. The first is that liquid flow and afterfeeding (or even solid diffusion after complete solidification) are sufficient to counteract thermal shrinkage and imposed deformation and therefore, that cavities are not formed and a fully dense microstructure is found. The second is that liquid flow and afterfeeding are insufficient to counteract thermal shrinkage and imposed deformation and therefore, that cavities are formed, leading to a microstructure containing porosity. The third is that the cavity

119 Chapter 6 dimension reaches a critical value, which leads to the formation of a hot crack. The critical cavity dimension which leads to crack is determined by using Griffith’s approach [19,20] considering that local conditions are brittle. Experimental observations indicate that hot tears are generally found in the center of billet and with star-like form (visible in the billet cross section) [2,9,21]. This means that stresses and strains in the billet cross section are dominant. To simplify the complex three-dimensional conditions of solidification during casting, it therefore is assumed that stress, strain and strain rates imposed by the mush are acting in the plane normal to the casting direction. Feeding takes place in the casting direction. The stress, strain and strain rate are calculated by a finite element method (FEM). The feeding behavior is represented by Feurer’s approach that is derived from Darcy’s law.

T,ε&,T&

f no solidification s constitutive T < Tcoh model model yes fs Shrinkage Shrinkage + Feeding rate (fe) σ rate (fr) deformation -permeability rate (fr) -hydrostatic pressure

fr > |fe | fr < |fe|

fr − fe ≥ ζ crit fr − fe < ζ crit

cavity

Griffith model

hot tearing micro-porosity no micro-porosity

Figure 6.1. Schematic representation of the model; fr: shrinkage+deformation rate, fe: feeding rate.

120 Model and simulation for prediction of hot tearing in aluminum alloys

6.3 Mathematical model The model which enables the prediction of the formation of micro-porosity or hot tears during direct-chill casting consists of a micro-model, accounting for local mechanical and feeding properties of the mush, coupled with a macro-model of the direct-chill casting process (for instance by FEM simulation). The proposed model is illustrated in detail in Fig. 6.1. The input data for the model provided by the macro-model are temperature (T), cooling rate (T& ) and strain rate ( ε& ). The solidification model links temperature with solid/liquid fraction, needed in the constitutive model of the mush and in the feeding model. The contribution of feeding, |fe|, is compared with the local strain rate, fr, resulting from shrinkage and deformation. Above the coherency temperature only a shrinkage term contributes to fr, and fr will be smaller than |fe|. Below the coherency temperature deformation forces will contribute to fr. If at any moment during the solidification |fe| becomes smaller than fr, and the different between both is higher than a critical value, a cavity is formed. In case the diameter of the cavity exceeds a critical diameter determined by Griffith’s model, the cavity will result in a hot tear. In the Griffith’s model, the critical diameter depends on the stress in the mush. The stress, σ, follows from the constitutive model. Based on this, three possibilities arise: dense microstructure without micro-porosity, formation of micro-porosity or formation of hot tears. 6.3.1 Solidification model

In the solidification model, the liquid fraction, fl, as a function of temperature is determined using the following equation [22]:

∗  1−2αs k  1  T −T  k−1  f =  m  and l ∗  T −T   1− 2α s k  m l    

* 1 1 1 α s = α s [1− exp(− )]− exp(− ) ( 6.1 ) α s 2 2αs

where Tm is melting temperature of the pure metal, Tl is liquidus temperature, T is * temperature, k is partition coefficient, αs is back diffusion coefficient and α s is modified dimensionless solid state back-diffusion parameter.

121 Chapter 6

6.3.2 Constitutive model of the mush The stress developed in the mush is computed using a constitutive model which will depend on solid fraction, strain rate and temperature. Here we will use the following expression [18]:

 mQ  m σ = σ o exp()βf s exp ()ε& ( 6.2 )  RT  where Q is the activation energy which is given by the solid phase deformation behaviour, m is the strain rate sensivity coefficient, R is the gas constant, σ o and β are material constants and ε& is the strain rate. 6.3.3 Shrinkage, deformation and feeding terms A transient mass conservation equation is applied to a three-dimensional element in the solidifying billet of which a complete derivation is shown in Appendix A. It reads

ρ s ∂f v  ρ s  ∂f l  ρ s  = − −1 +  ε& + fe ( 6.3 ) ρl ∂t  ρl  ∂t  ρl  whereε& and fe are strain rate and feeding rate respectively, fs, fl and fv are solid, liquid and cavity fraction, respectively, and ρs and ρl are the densities of solid and liquid, respectively. The contribution of shrinkage and deformation, fr, reads

 ρ S  ∂f l  ρ S  fr = − −1 +  ε& ( 6.4 )  ρl  ∂t  ρl 

The feeding term, fe, is based on the interdendritic flow in a mush, which uses Carman-Kozeny approximation [23,24], and reads as follows:

P fe = fe = K s ( 6.5 ) ηL2

122 Model and simulation for prediction of hot tearing in aluminum alloys

λ2 ()1 − f 3 K = s ( 6.6 ) 2 180 f s

Ps = Po + Pm − Pc ( 6.7 )

4γ P = s ( 6.8 ) c λ where K is permeability, λ is secondary dendritic arm spacing, η is the viscosity of the liquid phase, L is the length of the porous network, γs is solid-liquid interfacial energy, Ps is effective feeding pressure and Po, Pm and Pc are atmospheric, metallostatic and capillary pressure, respectively. In the model λ and Pc are independent of temperature. L is taken as the length of mush from the coherency till the end of solidification. For the feeding term |fe| only the z direction (casting direction) is taken into account. Under compressive conditions, Ps is negative, resulting in a negative value of fe. 6.3.4 Cavity growth If fr < |fe| (Eqs. 6.4 and 6.5), feeding will be sufficient and the actual volumetric flow rate per unit volume will be equal to the shrinkage and deformation rate. If fr > |fe|, feeding will be insufficient and a cavity will form and grow if fr − fe ≥ ζ crit , where ζ crit is a term describing the nucleation of the cavity.

ζ crit can be expressed in a critical pressure (Pcrit) for cavity nucleation as follows: P ζ = K crit ( 6.9 ) crit ηL2

The value of the critical depression pressure has to be determined from experimental data. A value 2 kPa such as used in ref. [5] will result in a small value ofζ crit . Therefore in this calculation ζ crit is taken equal to zero and it is assumed that fr − fe is always equal to the cavity volume.

If the condition for the formation of a cavity is fulfilled, parameter ∂fv ∂t is a measure for cavity growth. The fraction, fv, and the diameter, d, of the cavity are determined by

123 Chapter 6

t ∂f f = v dt ( 6.10 ) v ∫ ∂t tliq

1  3  3 d =  fvVchar  ( 6.11 )  2π 

3 Vchar = Cd g ( 6.12 )

where tliq is the time corresponding with the start of solidification, Vchar is the characteristic volume of the local geometry (cavity and grains), and dg is the diameter of the grain. C is a packing parameter accounting for the packing of the 8 grains. It is equal to 2 2 for face-centered cubic and for body-centered cubic 3 3 packing. In Griffith’s approach [19,20], the relation between the critical cavity length, acrit and the stress σ in the mush for the cavity to propagate as crack is expressed in Eq. 6.13.

E acrit = 4γ s ( 6.13 ) πσ 2 where γe is surface tension of the liquid metal and E is Young's modulus of the mush. The stress in the mush is given by Eq. 6.2. To account for the irregularity of the cavity shape, a constant, C1, is introduced:

a = C1d ( 6.14 ) which relates the longest cavity length with the diameter of a spherical cavity. Cl is larger than or equal to 1. From Eqs. 6.11, 6.12 and 6.14, a is calculated. If a ≥ acrit, a crack will develop. 6.3.5 Hot cracking sensitivity The hot cracking susceptibility is defined by:

124 Model and simulation for prediction of hot tearing in aluminum alloys

a HCS = crit ( 6.15 ) a

Used qualitatively, this definition means an increasing susceptibility for hot cracking with increasing value. Used quantitatively, it means that, if the hot cracking sensitivity is higher than one, a hot tear will develop.

6.4 Simulation

6.4.1 Simulation with constant parameters A part of the calculations in the model was performed for constant ε& , T& , -5 -3 -1 and L where the strain rates ε& were varied from 10 -10 s , the cooling rates T& were varied from 0.1-10 K/s and L was taken 0.1 m. Simulation was done for an Al−4.5%Cu alloy. The parameters used in the calculation are given in Table 6.1. Further it is assumed that the deformation was only in the cross section of the billet.

Table 6.1. Parameters used in the calculations and the appropriate references Parameter Value Unit Ref.

αs 0.01 [17] k 0.14 [22] Tm 933 K [25] σo 4.5 Pa [18] m 0.26 [18] α 10.2 [18] Q 160 kJ/mol [18] E 40 MPa [18,26] 2 γs 0.84 J/m [25] 3 ρS 2790 kg/m [25] 3 ρl 2480 kg/m [25] λ 8.10-5 m η 0.0013 Pa.s [25] -4 dg 5.10 m C1 1 C 2 2

125 Chapter 6

6.4.2 Simulation with FEM modeling of DC casting billet Another part of the calculations in the model was performed after incorporating the model in an FEM code. DC casting of an Al−4.5%Cu alloy billet, 100 mm radius and 1000 mm length, is simulated. Computation procedure is similar to that, performed in [4]. An axis-symmetric model is used in this work. Due to the symmetry, only a half section of the billet and bottom block needs to be modeled. For the simulation, a coupled computation of the stress and the temperature fields is applied using 4-node rectangular elements with 4 Gaussian integration points. In the simulation, the ingot remains in a stationary position, while the mould and the impingement point of the water flow move upwards with a velocity equal to the casting speed. Continuous feeding of liquid metal is implemented by activating horizontal layers of elements incrementally. The computational domain is shown in Fig. 6.2. After every time step the hot cracking susceptibility is computed at every node. Computation is performed for two phases in the billet. The first phase is from 0 to 400 mm distance from the beginning of the billet (start-up phase). Four casting conditions denoted 1 to 4 are applied in the computation to calculate the hot tearing tendency as a function of the axial position. The casting modes are shown in Fig. 6.3. The second region is at a distance of 750 mm from the beginning of the billet (steady state phase). The casting speeds selected were constant and equal to 120, 150 and 180 mm/min. Here, the hot tearing tendency is calculated as a function of the radial position in the billet. Most of the parameters used in the incorporation with FEM modeling of DC casting a billet are also given in Table 6.1. However, three parameters were adjusted and are given in Table 6.2. This adjustment parameters were taken from experimental data [9].

Table 6.2. Modified parameters used in the calculations of DC casting. Parameter Value Unit Ref. E 10 GPa λ 1.10-5 m [9] -4 dg 3.10 m [9]

126 Model and simulation for prediction of hot tearing in aluminum alloys

z Γ6

mold

Γ3 billet

Γ4

Γ7 Γ5

bottom block Γ2 r

Γ1 Figure 6.2. Computational domain of the DC cast billet. Γ1 - Γ7 correspond with boundary conditions defined in Section 3.2.3 or [4].

160

150

140

130

120

110

100 Casting speed (mm/min) 90

80 0 50 100 150 200 250 300 350 400 450 Distance from bottom (mm)

Figure 6.3. The casting modes applied for simulation of the start-up phase of DC casting. Casting conditions: () 1, (~) 2, (∆) 3 and (x) 4.

127 Chapter 6

6.5 Results

6.5.1 Simulation with constant parameters In the simulation studies with constant strain rate, cooling rate and length of porous network the main emphasis was on the calculation of feeding rate or mechanical parameters as a function of solid fraction.

6.5.1.1 Cavity growth In section 6.3, the quantities |fe| and fr, which are the volume fraction per unit time fed by liquid flow and the volume fraction per unit time related to shrinkage and imposed deformation, respectively, were introduced. Fig. 6.4 shows the value of |fe| and fr as a function of the solid fraction for various strain rates and cooling rates. The value of fr becomes lower at high solid fractions, since the shrinkage term is dominant and ∂fl ∂T decreases with increasing solid fraction. The value of fr increases with increasing strain rate or cooling rate according to Eq. 6.4. The value of |fe| decreases as a function of solid fraction since feeding becomes more difficult at higher solid fractions. For the effect of strain rate or cooling rate on |fe| microstructural parameters are the most influential factor for the value of |fe|. Since in this calculation these parameters are kept constant there is no effect of strain rate or cooling rate on |fe|. The intersection points of the |fe| and fr curves, indicated in the figure, give the solid fractions at which the growth of cavities will begin. It is seen that growth occurs earlier (i.e. at lower fractions of solid) for higher strain rates and cooling rates. This is evident since the amount of volume per unit time, which should be feeded, increses with higher strain rates and cooling rates.

6.5.1.2 Porosity and hot tearing Figs. 6.5 and 6.6 present both the stress developed in the mush as a function of solid fraction (calculated from Eq. 6.2) and the critical stress in the Griffith’s approach, i.e. the stress calculated from Eq. 6.13 for a cavity with length a calculated from Eq. 6.14. In the figure also the hot cracking susceptibility is given (Eq. 6.15). Developed stress and hot cracking susceptibility increase for increasing solid fraction and strain rate. Hot cracking susceptibility increases for increasing cooling rate. The intersection points of the developed stress and the critical stress for cavity growth mark the transition from development of micro- porosity to the initiation of hot tearing. Fig. 6.7 shows the cavity fraction, fv, as a function of solid fraction for the various strain rates and cooling rates. Cavities are initiated at the solid fraction where fv starts to deviate from zero. These points correspond with the intersection

128 Model and simulation for prediction of hot tearing in aluminum alloys points found in Fig. 6.4 and indicate the begin of the formation of porosity. Also the intersection points, found in Figs. 6.5 and 6.6 are indicated in Fig. 6.7. They are connected by a dashed line, that indicates the fraction solid values where hot cracks are formed. Lowering the strain rate or cooling rate will increase the solid fraction at which hot tears start to develop. At certain strain rates the hot tear will not develop.

129 Chapter 6

0.020

|fe|

0.015 )

-1 6

0.010

|fe|or fr (s 5

0.005

4 3 2 1 0.000 0.50 0.60 0.70 0.80 0.90 1.00 fs

0.020

|fe|

0.015 ) -1 4

fr(S 0.010 or

|fe| |fe| 3

0.005

2 1 0.000 0.50 0.60 0.70 0.80 0.90 1.00

b. Figure 6.4. Parameters fr (1-6) and |fe| versus solid fraction. (a) the effect of strain rate at cooling rates of 1 K/s; strain rates: (1) 10-5 s-1, (2) 10-4 s-1, (3) 5.10-4 s-1, (4) 10-3 s-1, (5) 5.10-3 s-1, (6) 10-2 s-1; (b) the effect of cooling rate for strain rate of 5.10-4 s-1; cooling rates: (1) 0.1 K/s, (2) 1 K/s, (3) 5 K/s, (4) 10 K/s. |fe| is independent of strain rate or cooling rate.

130 Model and simulation for prediction of hot tearing in aluminum alloys

1.0 1 2

3 0.8 4

) 0.6 5 MPa

σ ( σ 0.4

0.2

5' 4' 3' 2' 1' 0.0 0.80 0.85 0.90 0.95 1.00

2.0

1.8

1.6

1.4

1.2

1.0 HCS 0.8 5 0.6 4 3 2 1 0.4

0.2

0.0 0.80 0.85 0.90 0.95 1.00

b. Figure 6.5. Developed stress and critical stress (a) and hot cracking susceptibility (b) versus solid fraction for various strain rates; cooling rate: 1 K/s. Developed stress (1’- 5’); critical stress and HCS (1-5). Strain rates: (1) 10-5 s-1, (2) 10-4 s-1, (3) 5.10-4 s-1, (4) 10-3 s-1, (5) 5.10-3 s-1.

131 Chapter 6

1.0

0.8 2 1 3 0.6 4 (MPa)

σ 0.4

0.2 1',2',3',4'

0.0 0.80 0.85 0.90 0.95 1.00

2.0

1.8

1.6

1.4

1.2

1.0 HCS 0.8

0.6

0.4

0.2 43 21

0.0 0.80 0.85 0.90 0.95 1.00

b. Figure 6.6. Developed stress and critical stress (a) and hot cracking susceptibility (b) versus solid fraction for various cooling rates; strain rate: 5.10-4 s-1. Developed stress (1’-4’); critical stress and HCS (1-4). Cooling rates: (1) 0.1 K/s, (2) 1 K/s, (3) 5 K/s, (4) 10 K/s.

132 Model and simulation for prediction of hot tearing in aluminum alloys

0.10

0.08

0.06 5 v f

0.04

0.02

3 2 0.00 1 0.75 0.80 0.85 0.90 0.95 1.00

0.10

0.08

0.06 v f

0.04

0.02 4 3 2 1 0.00 0.75 0.80 0.85 0.90 0.95 1.00

b. Figure 6.7. Cavity fraction versus fraction solid. Dashed curve indicates start of tear development. (a) the effect of strain rate at cooling rate of 1 K/s; strains rates: (1) 10-5 s-1, (2) 10-4 s-1, (3) 5.10-4 s-1, (4) 10-3 s-1, (5) 5.10-3 s-1; (b) the effect of cooling rate for strain rate of 5.10-4 s-1; cooling rates: (1) 0.1 K/s, (2) 1 K/s, (3) 5 K/s, (4) 10 K/s.

133 Chapter 6

In Fig. 6.8 the boundaries of three regions are given as a function of strain rate and solid fraction for cooling rates 1 K/s or 5 K/s. In region A, ∂f v ∂t equals zero or negative and consequently no micro-porosity or hot tears are developed. In region B, ∂f v ∂t is positive but a is smaller than acrit. Only micro-porosity will develop. Region C where a is larger than acrit marks the conditions for which hot tearing will occur. The beginning of the formation of porosity or hot cracks increases with strain rate and cooling rate.

6.5.1.3 The effect of grain size and packing parameter The effect of grain size on the developed stress in the mush and the critical stress is shown in Fig. 6.9. It is found that a smaller size reduces the developed stress (and hot tearing tendency) and that below a certain grain size, a hot tear will not develop. In Fig. 6.10, the effect of packing parameter on the developed stress in the mush and the critical stress is shown. The packing parameter hardly influences the stress or the location of the intersection points.

134 Model and simulation for prediction of hot tearing in aluminum alloys

1.0E-02

C 1.0E-03 B

1.0E-04 A )

-1 1.0E-05 (s . ε 1.0E-06

1.0E-07

1.0E-08 0.70 0.75 0.80 0.85 0.90 0.95 1.00

1.0E-02

1.0E-03 C

B 1.0E-04

A )

-1 1.0E-05 . (s ε 1.0E-06

1.0E-07

1.0E-08 0.70 0.75 0.80 0.85 0.90 0.95 1.00

b. Figure 6.8. The three regions A, B and C which give the conditions of strain rate and solid fraction for which micro-porosity is absent (A), for which micro-porosity develops but hot tears do not form (B) and for which hot tears are formed (C). Cooling rate: (a) 1 K/s; (b) 5 K/s.

135 Chapter 6

2.0

1.8

1.6

1.4 4 1.2

1.0 (MPa) 3

σ 0.8

0.6 2 1 0.4

0.2 1',2',3',4'

0.0 0.80 0.85 0.90 0.95 1.00

Figure 6.9. Effect of grain size on the developed stress in the mush (1’-4’) and the critical stress (1-4). Strain rate: 10-4 s-1. Grain diameter: (1,1’) 600 µm, (2,2’) 300 µm, (3,3’) 100 µm, (4,4’) 30 µm.

2.0

1.8

1.6

1.4

1.2

1 1.0 2 (MPa) 3

σ 0.8

0.6

0.4

0.2 1',2',3' 0.0 0.80 0.85 0.90 0.95 1.00

Figure 6.10. Effect of packing parameter on the developed stress in the mush (1’-3’) and the critical stress (1-3). Strain rate: 10-4 s-1. Packing parameter: (1,1’) 2.83, (2,2’) 2.34, (3,3’) 1.85.

136 Model and simulation for prediction of hot tearing in aluminum alloys

6.5.2 Incorporation in FEM simulation of DC casting billet In the simulation studies of the DC casting of a billet the emphasis was on the calculation of the hot cracking susceptibility as a function of various parameters. Here a similar approach was taken as in an earlier study, assessing several hot tearing criteria in literature [10].

6.5.2.1 Start-up phase Fig. 6.11 shows the hot tearing susceptibility for the various casting conditions during start-up. The susceptibility is maximum at about 70 mm from the bottom of billet. Using a ramping procedure reduces the susceptibility, although it does not influence its steady state value. Hot cracking sensitivity is higher for the higher casting rate. Since the HCS value is smaller than 1, hot tear will not form. In Fig. 6.12, the development during solidification of the hot cracking susceptibility at the 50 mm from the bottom of the billet is shown. The susceptibility increases with the solid fraction. A hot crack will not form.

0.30

0.25 3

0.20

4 0.15 HCS

0.10

0.05 2

0.00 0 100 200 300 400 Distance from bottom (mm)

Figure 6.11. Hot cracking susceptibility as a function of distance from the bottom for the four casting conditions.

137 Chapter 6

0.30

0.25

0.20 3

0.15 1 HCS 4 0.10 2

0.05

0.00 0.95 0.96 0.97 0.98 0.99 1.00 fs

Figure 6.12. The hot cracking susceptibility in the last stage of solidification at 50 mm from the bottom.

6.5.2.2 Steady state phase Susceptibilities are considered steady state at 750 mm from the bottom of the billet.The effect of casting speed on the hot cracking susceptibility in steady state is shown in Fig. 6.13 as a function of the distance from the center of the billet. The susceptibilities increase with increasing casting speed and are maximum in the center of billet. At a distance of about 70 mm and higher from the center the susceptibility is close to zero. Also for a casting speed of 180 mm/s susceptibility will be lower than one and a hot crack will not form. The development of the susceptibility during solidification is shown in Fig. 6.14. Values of the susceptibility start to deviate from zero level at a certain fraction solid which is dependent on the casting speed. The higher the casting speed the lower the solid fraction for which the value deviates from zero.

138 Model and simulation for prediction of hot tearing in aluminum alloys

0.50

0.45

0.40 3 0.35

0.30

0.25 2 HCS 0.20

0.15

0.10 1

0.05

0.00 0 20406080100 Distance from center (mm)

Figure 6.13. Hot cracking susceptibility as a function of distance from the center of the billet. Casting speed: 1) 120 mm/min, 2) 150 mm/min and 3) 180 mm/min.

Since the Youngs modulus at semi-solid temperature is not well known, the effect of Youngs modulus on the hot cracking susceptibility is shown in Fig. 6.15. A higher Youngs modulus will reduce the hot cracking susceptibility. The effect of grain size on the hot cracking susceptibility is shown in Fig. 6.16. An increasing grain size will result in an increasing hot cracking susceptibility, which is relevant for the center of the billet.

139 Chapter 6

0.50

0.45

0.40

0.35 3 0.30

0.25 HCS 0.20 2

0.15

0.10 1 0.05

0.00 0.9 0.92 0.94 0.96 0.98 1

Figure 6.14. The hot cracking susceptibility development during the last stage of solidification at casting speed: 1) 120 mm/min, 2) 150 mm/min and 3) 180 mm/min.

2.0

1.8

1.6 3

1.4

1.2

1.0 HCS 0.8

0.6 2 0.4

0.2 1 0.0 0.95 0.96 0.97 0.98 0.99 1.00

Figure 6.15. The hot cracking susceptibility development during the last stage of solidification at Youngs modulus: 1) 10 GPa, 2) 1 GPa and 3) 0.1 GPa. Center of billet. Casting speed 120 mm/min.

140 Model and simulation for prediction of hot tearing in aluminum alloys

0.15

0.12

0.09

HCS 2 0.06

0.03 1

0.00 0 20406080100 Distance from center (mm)

Figure 6.16. The hot cracking susceptibility as a function of the distance from the center, grain size: 1) 100 µm, 2) 300 µm and 3) 500 µm. Casting speed 120 mm/min.

6.6 Discussion

6.6.1 Assumptions in the presented model In an assessment study [10] of various criteria for hot cracking, which were integrated in a FEM simulation and applied to DC casting, it is found that the RDG criterion [17], which combines aspects of mechanical as well as feeding conditions had the greatest potential but did predict cracking for practical conditions where cracking will not occur. In the present model several approaches and assumptions differ from those in the RDG model. In both models the basic equation is that of mass conservation, but in the RDG approach it is taken steady state whereas in the present approach it is transient, allowing for the formation of a cavity volume. RDG considers in the mass balance equation the strain rate, whereas in the present model the equation is strain based. In RDG feeding follows the shrinkage and gives rise to a pressure drop, which may become critical. In the RDG approach a crack is formed if the pressure drop becomes so high that the pressure in the liquid of the mush becomes lower than a critical pressure for cavity formation. For such a case a cavity will form which always gives rise to the formation of a hot tear. In the present approach a cavity will grow if the volume which can be fed per unit time becomes smaller than the volume change due to shrinkage and deformation. A cavity will lead to porosity and only when its size will surpass a critical size a crack will be formed.

141 Chapter 6

Considering the mush as brittle, the critical size is determined from the Griffith approach [19] and depends on the stress in the mush. It becomes smaller for higher stresses. Other differences are that RDG considers a columnar solidification structure, whereas the present model assumes an equiaxed structure, such as commonly found in DC cast billets and that RDG is essentially a 2D approach whereas the present model is in principle 3D. 6.6.2 Observations with the constant parameter simulations As Fig. 6.8 demonstrates, the formation of porosity and/or hot cracks is promoted by higher strain rates and by higher cooling rates. These observations are in line with those found by other authors [17,26]. The observation that smaller grain sizes reduce the tendency for porosity or hot tearing (see Fig. 6.9) is confirmed by [27-29] and is supported by the beneficial effect of the addition of grain refiners. Fig. 6.8 indicates that during the last stage of solidification porosity is always formed. The model not only indicates whether porosity will be found but also predicts the amount of porosity. Stresses in the mush at which hot tears are formed (see Figs. 6.5, 6.6, 6.9 and 6.10) are in the range of 0.1–2 MPa. These values are in agreement with the fracture stresses found in tensile tests of semi- solid aluminum alloys [30-32]. The hot tearing sensitivities as presented in Figs. 6.5a and 6.6b also indicate increasing sensitivity for increasing strain rate or increasing cooling rate. For all strain rates and cooling rates applied here, the HCS value becomes higher than one, which means that hot cracking will take place. However, some parameters, for instance Youngs modulus used in these calculations are rather uncertain and have a big influence on the HCS value (see also Section 6.1.4). For Youngs modulus we did use in these calculations the only value known to us [18,26] but we believe that a higher value might be more realistic, that predicts that cracks are not formed for some of the strain rate and cooling rate parameters, which is more in agreement with industrial practice. 6.6.3 Observations with the DC cast simulations Incorporation of the model into a FEM simulation leads to comparable results as obtained with the simulations with constant parameters. Hot cracking susceptibility increases with the casting speed and is maximum in the center of the billet. It is higher for larger grain size. The FEM simulation also shows (see Fig. 6.11) that the susceptibility at about 80 mm from the bottom is highest and that it reduces when casting speed is lowered. It means that application of a ramping procedure during the start-up phase has significance.

142 Model and simulation for prediction of hot tearing in aluminum alloys

In Figs. 6.17 and 6.18 the hot cracking susceptibilities obtained in this study are compared with the depression pressures (which are a measure for hot cracking susceptibility), obtained in an earlier study [10] with the RDG model [17]. Conditions used in the simulation were identical. It is seen that shapes of the corresponding curves are rather similar, so in qualitative sense there is not much difference between the predictions between the RDG model and the present model. In the RDG model depression pressures exceeding a critical value will lead to the formation of a hot crack. As critical value a value of 2 kPa is given [5]. The depression pressures in Figs. 6.17 and Fig. 6.18 are considerably higher and will therefore always lead to the formation of a hot crack. In the present model HCS values lower than one will not lead to the formation of a hot crack and it is seen that for the conditions simulated here a hot crack will not be formed. In [10] we assessed several hot cracking criteria on their predictive capability of four major observations in industrial experience. In table 6.3 a similar assessment is done with the present model. It is seen that the predictive capability of the present model is excellent on these four issues. A full quantitative assessment should require detailed casting trials and possible adjustment of some parameters in the model, which will be further addressed in the next Section.

143 Chapter 6

0.30

0.25 3

0.20

4 0.15 HCS

0.10

0.05 2

0.00 0 100 200 300 400 Distance from bottom (mm)

1.0

0.8

3 0.6 (MPa)

P 0.4 ∆ 4

0.2 1 2 0.0 0 100 200 300 400 Distance from bottom (mm)

b. Figure 6.17. Hot cracking susceptibility (a) and depression pressure (b) [10] as a function of distance from the bottom for the four casting conditions.

144 Model and simulation for prediction of hot tearing in aluminum alloys

0.50

0.45

0.40 3 0.35

0.30

0.25 2 HCS 0.20

0.15

0.10 1

0.05

0.00 0 20406080100 Distance from center (mm)

2.0

1.8

1.6

1.4

1.2

1.0 3 (MPa) P

∆ 0.8

0.6 2 0.4

0.2 1 0.0 0 20406080100 Distance from center (mm)

b. Figure 6.18. Hot cracking susceptibility (a) and depression pressure (b) [10] as a function of distance from the center of the billet. Casting speed: 1) 120 mm/min, 2) 150 mm/min and 3) 180 mm/min.

145 Chapter 6

Table 6.3 Predictive capability of the model on four major observations. Observation Practice Prediction A Increasing sensitivity for yes yes higher casting speed B Highest sensitivity in yes yes billet centre C Ramping might have yes yes positive effect D Crack will be formed no no

6.6.4 Present limitations Validation of the model should take place in direct comparison with actual casting trials. In such validation some model parameters are more critical or less known than others. Let us assume, as has been done in this study, a constant strain rate and a constant cooling rate. For the calculation of the fraction solid where porosity starts to appear, we set |fe| equal to fr and using Eqs. 6.4-6.8 we derive the following equation:

ηL2 f 2  ρ  ∂f ∂T  ρ   2 2 l  s  l  s  Kλ ()1 − f s = 1 −  +  ε&k  (6.16 )  4γ s   ρl  ∂T ∂t  ρl    Po + Pm −   λ 

The expression at the left hand side is related to the amount of porosity found after casting (in case hot tears are absent). At the right hand side parameters

L and ∂fl ∂T are well known or can easily be determined. Parameter 4.γs/λ is relatively small, compared with P0 + Pm so its influence on the porosity is relatively low. At the left hand side, the permeability of the mush K is a critical parameter in determining when porosity starts to form and the final amount obtained. However, the value of K is relatively uncertain and also difficult to determine. Therefore, regarding porosity the permeability is the main parameter under consideration for possible adjustment in a validation experiment. For the determination when a hot crack starts to appear we derive the following equation from Eqs. 6.11-6.14:

1 3 4γ E 1  2π  3  f =  s    (6.17 ) v πσ 2 C d 3C  1 g   

146 Model and simulation for prediction of hot tearing in aluminum alloys

If fv is smaller than the right hand side term, a hot tear will not be formed, whereas if fv is higher, a hot tear will form. The various parameters at the right hand side are dg, which can be experimentally determined and, C, C1, γs, E and 2 1/3 stress σ in mush. The parameter combination (γs.E/σ .C1.C ) is dominant in the formation of hot cracks and is therefore the main expression under consideration for possible adjustment in a validation experiment. The most unknown parameter is assumed Youngs modulus E, which is difficult to determine because of the low strength and high brittleness of the mush. Literature data on Youngs modulus of a mush are scarce. The value in the study with the constant parameters is taken from [18,26]. The value taken in the simulation with DC casting is higher in order to be more in agreement with the results in actual casting experiments.

6.7 Conclusion A model is proposed for prediction of the formation of micro-porosity and hot tears during DC casting. It assumes that volume changes during solidification, resulting from the mechanical conditions should be fed by liquid. If feeding is insufficient, a cavity volume is formed. A new element in the model is that formation of a cavity leads to micro-porosity and that if its size exceeds a certain critical size, a hot crack will form. The mush is considered brittle and therefore the critical size is derived from fracture mechanics. The model shows features, well- known from literature such as increasing susceptibility for micro-porosity formation and hot tearing with increasing deformation rate, increasing cooling rate (i.e. increasing casting speed) and increasing grain size. The model also indicates a higher sensitivity in the billet center. After incorporating this model in a FEM simulation for DC casting billet, this observations are not only confirmed, but it is also found that application of a ramping procedure during the start-up phase might give a beneficial effect. As such, the present model improves the results, found in an earlier assessment study based on criteria, known from literature. Further, in this study key parameters are identified of which the values are rather uncertain and which may therefore act as fitting parameters in a validation study.

References [1] Eskin, D.G., Suyitno and Katgerman, L. (2004) Progress in Materials Science, 49, p. 629. [2] Farup, I. and Mo, A. (2000) Metallurgical and Materials Transactions A, 31A, p. 1461. [3] M’Hamdi, M., Mo, A. and Martin, C.L. (2002) Metallurgical and Materials Transactions A, 33A, p. 2081.

147 Chapter 6

[4] Suyitno, Kool, W.H. and Katgerman, L. (2004) Metallurgical and Materials Transactions A, 35A, p. 2917. [5] Drezet, J.M. and Rappaz, M. (2001) Light Metals 2001, ed. Anjier JL, TMS, Warrendale, PA, p. 887. [6] Drezet, J.M., M’Hamdi, M., Benum, S., Mortensen, D. and Fjaer, H. (2002) Materials Science Forum, 396-402, p. 59. [7] M’Hamdi, M., Benum, S., Mortensen, D., Fjaer, H. and Drezet, J.M. (2003) Metallurgical and Materials Transactions A, 34A, p. 1941. [8] Suyitno, Kool, W.H. and Katgerman, L. (2003) Light Metals 2003, ed. P.N. Crepeau PN, TMS, Warrendale, PA, p. 753. [9] Suyitno, Eskin, D.G., Savran, V.I. and Katgerman, L. (2004) Metallurgical and Materials Transactions A., 35 A, p. 3551. [10] Suyitno, Kool, W.H. and Katgerman, L. (2005) accepted for publication in Metallurgical and Materials Transactions A. [11] Feurer, U. (1977) Quality Control of Engineering Alloys and the Role of Metals Science, Delft University of Technology, Delft, The Netherlands, p. 131. [12] Clyne, T.W. and Davies, G.J. (1981) British Foundryman, 74, p. 65. [13] Katgerman, L. (1982) Journal of Metals, 34, 2, p. 46. [14] Prokhorov, N.N. (1962) Russian Castings Production, 2, p. 172. [15] Novikov, I.I. (1966) Goryachelomkost tsvetnykh metallov i splavov (Hot Shortness of Non-Ferrous Metals and Alloys), Moscow: Nauka. (in Russian). [16] Magnin, B., Katgerman, L. and Hannart, B. (1995) Modeling of Casting Welding and Advanced Solidification Processes VII, eds. M. Cross and J. Campbell, TMS, Warrendale, PA, p. 303. [17] Rappaz, M., Drezet, J.-M. and Gremaud, M. (1999) Metallurgical and Materials Transactions A, 30A, p. 449. [18] Braccini, M., Martin, C.L. and Suery, M. (2000) Modelling of Casting Welding and Advanced Solidification Processes IX, eds. P.R. Sahm, P.N. Hansen, and J.G. Conley, Shaker Verlag, Aachen, Germany, p. 18. [19] Griffith, A.A. (1920) Phillosophical Transactions Royal Society London, A 221, p. 163. [20] Griffith, A.A. (1924) Proceedings of the First International Congress for Applied Mechanics, eds. C.B. Biezeno and J.M. Burgers, Waltman, Delft, The Netherlands, p. 55.

148 Model and simulation for prediction of hot tearing in aluminum alloys

[21] Commet, B., Delaire, P., Rabenberg, J. and Storm, J. (2003) Light Metals 2003, ed. P.N. Crepeau, TMS, Warrendale, PA, p. 711. [22] Kurz, W. and Fisher, D.J. (1992) Fundamentals of Solidification, Trans- Tech Publications, Switzerland. [23] Piwonka, T.S. and Flemings, M.C. (1966) Transactions AIME, 236, p. 1157. [24] Kubo, K. and Pehlke, R.D. (1985) Metallurgical Transactions B, 16B, p. 359. [25] Touloukian, Y.S. and Buyco, E.H. (1970) Thermophysical Properties of Matter; Volume 4 Specific Heat; Metallic Elements and Alloys, IFI/Plenum New York – Washington, USA. [26] Suéry, M., Martin, C.L., Braccini, M. and Bréchet, Y. (2001) Advanced Engineering Materials, 3, 8, p. 589. [27] Campbell, J. (1992) Castings, Butterworth, UK. [28] Pellini, W.S. (1952) Foundry, 80, p. 124. [29] Clyne, T.W. and Davies, G.J. (1979) Solidification and Casting of Metals, Metals Society, p. 275. [30] Ackermann, P. and Kurz, W. (1985) Materials Science Engineering, 75, p. 79. [31] Van Haaften, W.M., Kool, W.H. and Katgerman, L., (2000) Material Science Forum, 331-337, p.265. [32] Wisniewski, P. (1990) PhD Thesis, University of Pittsburgh, USA.

149 Chapter 6

150

Chapter 7

Thermal contraction experiment for prediction of ingot distortionsγ

Shape distortions and hot cracking during casting are strongly related to thermal contraction during and after solidification. The understanding of this phenomenon is crucial in designing defect-free cast products and in numerical simulation of their thermomechanical behavior. This chapter presents the results of experimental and numerical simulation work on the thermal contraction during and after solidification of a commercial AA5182 alloy are presented. In the specially developed experimental set-up, the contraction is measured simultaneously with the temperature while the material solidifies and cools down in the solid state. An elasto-viscoplastic constitutive model fitted to the experimental data is used in finite element simulations of the contraction process. The implementation of thermal contraction data for ingot distortion during the start-up phase of casting is also included. The results show that the contraction starts at a certain temperature in the non-equilibrium solidification range, close to the non-equilibrium solidus. Good agreement is found between simulation and experimental results.

γ Based on the paper in: (1) Metallurgical and Materials Transactions A, vol. 35A, no. 4, 2004, pp.1325-1335, and (2) Key Engineering Materials, 2005 (in press).

Chapter 7

7.1 Introduction During direct-chill (DC) casting, defects such as shape distortion (butt-curl, butt-swell, pull-in), hot cracking, and porosity have been recognized. All of them are related to the shrinkage/contraction phenomenon during solidification. A number of theories have been proposed to explain defect formation. Butt-curl is one of the shape distortion defects frequently occurring during the start-up of DC casting. This phenomenon involves bending upwards of the ends of the shell solidified against the bottom block. This bending is caused by excessive thermal stresses due to high cooling rates resulting from water impingement on the ingot surface. The occurrence of butt curl impairs the stability of the ingot on the starting block, and is therefore a potential safety hazard. Besides that, the partial loss of contact between the ingot and the bottom block temporarily reduces the heat transfer with possible shell re-melting and allows the intrusion of water between the ingot and the bottom block. In the worst case, the butt curl can graduate to ingot cracks. Upon solidification, a metallic alloy passes through the solidification range that can be conditionally divided into two parts: semi-liquid (slurry) and semi-solid (mush) zones. Both are distinguished by the physical characteristics, i.e. material has good fluidity and no strength in the semi-liquid zone, while it has poor fluidity and some strength in the semi-solid region [1-3]. Enlargement of semi-liquid temperature range is very useful in reducing solidification defects such as hot cracking and porosity. In this case, good slurry fluidity will prevent the formation of solidification defects that are mostly caused by the lack of feeding. Besides that, due to the narrowing of the semi-solid temperature range the accumulated contraction stress will be lower, which may reduce hot cracking. There are three terms usually used for characterizing shrinkage or contraction: solidification shrinkage, thermal contraction and linear contraction. The solidification shrinkage refers to the volumetric shrinkage due to the liquid- solid phase transformation. The thermal contraction refers to the volumetric contraction of the solid phase. The linear contraction refers to one-dimensional thermal contraction during and after solidification [3,4]. Finite element method (FEM) simulation is used as a tool for reducing or avoiding defect formation in relation to process parameters. The mechanism of deformation during and after solidification has to be understood in order to gain a comprehensive approach in modeling. The contraction behavior during and after solidification is a crucial property for the input of the modeling. The existing method for implementing the contraction behavior is by using the coefficient of thermal expansion (CTE) data at solid state that is extrapolated till coherency temperature. This estimation is improved in this work by using the thermal

152 Thermal contraction experiment for prediction of ingot distortions contraction data that will provide the thermal contraction coefficient and thermal contraction onset during solidification. Experimental measurements of linear contraction during and after solidification of an AA5182 alloy are reported in this paper. These experimental results are compared to the finite element method (FEM) simulation of thermal contraction. Implementation for the prediction of ingot distortion during the start- up phase of direct-chill casting is also presented.

7.2 Experimental Procedure A contraction test apparatus is schematically shown in Fig. 7.1. The set-up consists of an open mould with a special T-shaped cavity on one side and a movable wall on the other side, a water-cooled bronze base, a linear displacement sensor (LVDT) attached to the moving wall, a thermocouple for temperature measurement, and a personal computer for data acquisition. The dimensions of the mould gauge cavity are 25 × 25 mm in cross-section and 100 mm in length, which is identical to dimensions used in earlier work [3] and is based on the original work of Novikov [4]. The experiment is described in more detail elsewhere [3]. The displacement of the movable wall and the temperature in the centre of the sample at 1 mm from the mould bottom are recorded simultaneously.

movable wall

sample

mould

Figure 7.1. Schematic view of the mould and the sample used in experiments

The chemical compositions of tested alloy in wt % is Mg: 3.6, Mn: 0.16, Si: 0.21, Fe: 0.26, Ti: 0.02 and Al: balance. The material is melted in a graphite crucible in an electrical furnace, the pouring temperature being 700 oC.

153 Chapter 7

The linear contraction upon solidification is determined as follows [3]:

l s + ∆l exp − l f ε s = ×100% ( 7.1 ) l s where l s is the initial length of the cavity, l f is the length of the sample at the solidus temperature, and ∆l exp is the pre-shrinkage expansion. The thermal contraction after solidification is determined according to the ASTM standard for thermal expansion coefficient [5]:

( − ) 1 ∆ α = l 2 l1 l1 = l ( 7.2 ) T2 − T1 l1 ∆T where l1 and l 2 are the lengths of the sample at temperatures T1 and T2, respectively.

7.3 FEM Simulation A fully three-dimensional model is used in this work. Due to the symmetry, only a half of the sample for thermal contraction sample and a quarter of the ingot for ingot distortion need to be modeled. A coupled computation of stress and temperature field is applied for simulation, using 8-node brick elements with 8 Gaussian integration points. 7.3.1 Boundary conditions of thermal contraction. The heat transfer between sample and mould is specified for two cases: contact and non- contact. The heat transfer coefficient in the contact situation is defined as a function of temperature, and in the non-contact situation as a function of gap distance. 7.3.2 Boundary conditions of ingot distortion. The boundary conditions and the detail of procedure is found elsewhere [6].

7.3.3 Thermo-physical and thermomechanical properties. All thermo-physical properties applied in this simulation are taken from ref. [7] unless indicated otherwise. Some properties (thermal conductivity, specific heat, and Youngs’ modulus) are implemented as functions of temperature, while

154 Thermal contraction experiment for prediction of ingot distortions the other properties are kept constant. The thermal contraction coefficient and the temperature of contraction onset are taken from our measurements. Plastic deformation at subsolidus temperatures is described by a modified Ludwik model:

σ = K()ε + ε m (ε + ε )n &p &po p po ( 7.3 ) where σ is the true stress (MPa); K is the stress at a strain and strain rate of unity -1 -4 (MPa); ε& is the strain rate (s ); ε& is a small constant plastic strain rate (10 p po -1 -2 s ); ε p is the plastic strain; ε po is a small constant plastic strain (10 ); m is the strain rate sensitivity coefficient; n is the strain hardening coefficient. The parameters K, m and n in this equation are fitted to the experimental data from ref. [8]. The following expression is used as the constitutive equation of the mush:

 mQ  m σ = σ o exp()α f s exp ()ε& ( 7.4 )  RT  where Q is the activation energy given by the solid phase deformation behaviour, m is the strain rate sensivity coefficient, R is the gas constant, σ o and α are the material constants and ε& is the strain rate. The values for Q, σo, α and m are fitted to the experimental data [8].

7.4 Results and Discussion

7.4.1 Experimental results Fig. 7.2 shows the grain structure of AA5182 alloy in the center of the sample at a distance of 2 mm from the bottom (see Fig. 7.1). The material comprises equiaxed dendritic grains with an average grain size of 160 µm.

155 Chapter 7

700

600 132

T 500 solidus C) o

400

300

200 Temperature ( Temperature

100

0 0 20406080100120140 Time (s) Figure 7.2. Optical micrograph of Figure 7.3. Measured temperature at 1 mm grain structure in the centre of the (1), 8 mm (2) and 15 mm (3) from the sample at a distance of 2 mm from the bottom of sample. bottom.

Cooling curves at three different heights of the centre of the sample are shown in Fig. 7.3. At temperatures higher than the solidus, these curves are clearly different, although the solidus temperature is reached at approximately the same time. The vertical temperature gradient in the centre of the sample becomes very low below the solidus. That makes this technique suitable for measuring the thermal contraction coefficient at sub-solidus temperatures. The measured contraction is shown in Fig. 7.4. First, an expansion is observed that is typical of aluminium alloys [3,9]. This pre-shrinkage expansion is caused by gas evolution and pressure drop over the mushy zone [10]. At a temperature of 530 oC, the contraction is started. In the beginning, the contraction proceeds with acceleration on decreasing temperature. Later, the contraction occurs linearly till room temperature. The accelerated contraction is primarily due to the combination of solidification shrinkage and thermal contraction of the solid shell. In this temperature range (500–530 oC) the thermal contraction coefficient is higher (26 × 10-6 K–1) than at sub-solidus temperatures (300–500 oC) when it becomes equal to 24.6 × 10-6 K–1.

156 Thermal contraction experiment for prediction of ingot distortions

0.10 700

-0.10 600

-0.30 500

C) 2 o 1 -0.50 400

-0.70 300

Contraction (mm) -0.90 Temperature ( Temperature 200

-1.10 100

-1.30 0 0 100 200 300 400 500 600 700 0 50 100 150 200 250 o Temperature ( C) Time (s)

Figure 7.4. Linear contraction of AA5182 Figure 7.5. Measured (1) and calculated (2) temperature in the centre of sample.

7.4.2 Numerical simulation results Calculated and experimental cooling curves agree well as shown in Fig. 7.5. Computed temperature dependence of linear contraction correlates adequately to experimental results as can be seen in Fig. 7.6. However, the simulations fail to reproduce the pre shrinkage expansion, which needs further insight in the expansion mechanism. Distributions of temperature, contraction and strain at partially and fully solid samples are shown in Figs. 7.7 and 7.8, respectively. In Fig. 7.8a, the temperature of the solid shell is around 513 oC (solidus temperature). The contraction gradient in the longitudinal (x) direction is not uniform due to the combination of solidification shrinkage and thermal contraction of the solid phase (Fig. 7.7b). In Fig. 7.8, the whole sample is solid (Fig. 7.8a), and the contraction gradient is now uniform (Fig. 7.8b) as the entire sample undergoes isotropic thermal contraction. The longitudinal strains show compression in all sections (Figs.7.7c and 7.8c) because of the contraction.

157 Chapter 7

0.1

0.0

-0.1 1

2 -0.2 3 Contraction (mm)

-0.3

-0.4 400 500 600 700 Temperature (oC)

Figure 7.6. Calculated (1) and measured (2,3) contraction of AA5182.

The results of the simulation are in accordance with the experimental results – the contraction starts at a temperature above the solidus and the contraction coefficient changes at solidus temperature. The implementation of the thermal contraction phenomenon in the numerical simulation of solidification process is crucial in prediction of deformation-related defects such as butt curl, pull-in, butt swell and hot cracking.

158 Thermal contraction experiment for prediction of ingot distortions

5 5 5 1 2 5 3 1 4 3 8 0 535

Meter 0 53 1.340e-05 B. 524 9.969e-06 18 6.539e-06 5 Z 513 3.109e-06 Y -3.214e-07 X -3.751e-06 -7.181e-06 -1.061e-05 -1.404e-05 -1.747e-05 -2.090e-05 C.

-1.312e-04 -2.576e-04 -3.840e-04 -5.104e-04 -6.368e-04 -7.632e-04 -8.896e-04 -1.016e-03 -1.142e-03 -1.269e-03 -1.395e-03

Figure 7.7. Calculated temperature, white color represent temperature lower than 513 oC, (a), accumulated contraction in longitudinal direction with respect to the axes origin (b) and accumulated strain in longitudinal direction (c) after 20 sec.

159 Chapter 7

Meter 2.577e-05 B. 1.322e-05

6.654e-07 Z

-1.189e-05 Y -2.444e-05 -3.699e-05 X -4.954e-05 -6.210e-05 -7.465e-05 -8.720e-05 -9.975e-05 C.

-1.751e-03 -1.838e-03 -1.925e-03 -2.012e-03 -2.099e-03 -2.186e-03 -2.273e-03 -2.360e-03 -2.447e-03 -2.534e-03 -2.621e-03

Figure 7.8. Calculated temperature, white color represent temperature lower than 513 oC, (a), accumulated contraction in longitudinal direction with respect to the axes origin (b) and accumulated strain in longitudinal direction (c) after 30 sec.

The predicted butt-curls are shown in Fig. 7.9, in which the butt-curl computed using the tabular coefficient of thermal expansion [11] does not differ significantly from the value calculated using the experimentally determined

160 Thermal contraction experiment for prediction of ingot distortions coefficient of thermal contraction. Despite the observed complex behavior of TCC [9], the suggested technique can be used as a relatively simple means for the estimation of the real contraction coefficient at subsolidus temperature, especially in cases when it is unknown.

Butt curl(mm) 10

0 0 100 200 300 400 500 600 700 Time (s)

Figure 7.9. Butt curl simulated for a casting speed of 55 mm/min using thermal expansion coefficients based on Ref. 11 (O) and determined in this work by contraction experiment (∆).

7.5 Conclusions From the experimental measurements and numerical simulations of thermal contraction of AA5182 alloy, it can be concluded that: 1. The contraction starts at a certain temperature within the solidification range; it is non-uniform above the solidus and uniform below the solidus. 2. Numerical simulations that take into account the temperature of contraction onset and the transition from semi-solid to solid contraction behaviour are in good agreement with the experimental data.

References [1] Campbell, J. (1991) Castings, Butterworth Heinemann, Oxford, UK. [2] Kim, J.H., Choi, J.W., Choi, J.P., Lee, C.H. and Yoon, E.P. (2000) Journal Materials Science Letters, 19, p.1395.

161 Chapter 7

[3] Eskin, D.G., Zuidema (Jr.), J. and Katgerman, L. (2002) International Journal Cast Metals Research, 14, p. 217. [4] Novikov, I.I. (1966) Goryachelomkost tsvetnykh metallov i splavov (Hot Shortness of Non-Ferrous Metals and Alloys), Moscow: Nauka. (in Russian). [5] James, J.D., Spittle, J.A., Brown, S.G.R. and Evans, R.W. (2001) Measurement Science and Technology, 12, p. 1. [6] Suyitno, Katgerman, L. and Burghardt, A. (2002) Proceedings of ASME Heat Transfer Division, 5, p. 147. [7] Van Haaften, W.M. (1997) Thermophysical Properties of Certain Al Alloys, Internal Report, Delft University of Technology, The Netherlands. [8] Van Haaften, W.M. (2001) PhD Thesis, Delft University of Technology, Delft, The Netherlands. [9] Eskin, D.G., Suyitno, Mooney, J. and Katgerman, L., (2003) Metallurgical and Materials Transactions A, 35A, p. 1325. [10] Korolkov, G.A. and Kuznetsov, G.M. (1990) Soviet Castings Technology, 6, p. 1. [11] ASM Handbook (1997) Properties and Selection: Nonferrous Alloys and Special Purpose Materials, ASM International.

162 Summary

Summary This thesis deals with hot cracking during direct-chill (DC) casting of aluminum alloys. Issues addressed are the thermomechanical modeling of direct- chill casting, the implementation and evaluation of existing hot tearing criteria, the experimental observation of microstructure and hot tearing for various parameters during DC casting, the proposal of a model for the prediction of hot tearing and the determination of the thermal contraction during and after solidification which enables the prediction of ingot distortion. The content of the thesis is as follows: In Chapter 2 characteristic parameters such as stresses, strains, sump depth, mushy zone length and temperature fields are calculated through the simulation of the DC casting process for a round billet by using a finite element method. Focus is put on the mushy zone and solid region close to it. In the center of the billet, circumferential stresses and strains (which play a main role in hot cracking) are tensile at temperatures close to the solidus temperature, whereas they are compressive near the surface of the billet. The stresses, strains, depth of sump and length of mushy zone increase with increasing casting speed. They are maximum in the start-up phase and are reduced by applying a ramping procedure in the start- up phase (application of a lower but slowly increasing casting speed during start- up). Stresses, strains, depth of sump and length of mushy zone are highest in the center of the billet for all casting conditions considered. In Chapter 3 eight hot tearing criteria proposed in literature, have been implemented and evaluated in a similar finite element simulation as performed in Chapter 2. These criteria were based on limitations of feeding, mechanical ductility or both. It is concluded that six criteria give a higher cracking sensitivity for a higher casting velocity and that five criteria give a higher cracking sensitivity for the center location of the billet. This is considered in qualitative accordance with casting practice. Seven criteria indicate that use of a ramping procedure has no significant effect. However, in industrial practice this is a common procedure, needed for avoiding hot cracking. Based on this only one criterion is in qualitative accordance with casting practice, but since it predicts fracture under conditions used in casting practice, it fails to predict the hot tearing occurrence during DC casting quantitatively. Therefore the development of a new or modified hot tearing criterion is needed (Chapter 6). In Chapter 4 effects of casting speed and alloys composition on structure formation and hot tearing during direct chill casting of 200 mm round billets from binary Al–Cu alloys are studied. It is experimentally shown that the grain structure, including the occurrence of coarse grains in the central part of the billet, is strongly

Summary affected by the casting speed and composition, while the dendritic arm spacing is mainly dependent on the casting speed. The hot cracking pattern reveals that the hot tearing susceptibility is high in the range of low-copper alloys (1–1.5%) and at high casting speeds (180–200 mm/min). The amount of non-equilibrium eutectics is minimum in the center of the billet and at lower concentrations of copper, which corresponds with the location as well as the compositional range of maximum hot tearing sensitivity. Structure formation and hot cracking could be correlated to computational results on the dimensions of the solidification region in the billet. Several hot tearing criteria earlier evaluated in Chapter 3 are again evaluated for a varying (constant increase or decrease) casting speed such as used in these experiments. It is shown that hot tearing criteria that account for the dynamics of the process, e.g. strain rate, actual stress–strain situation, feeding rate, melt flow, can be successfully used for the qualitative prediction of hot tearing in these experiments. In Chapter 5 hot cracking in Al–(1-4.5%)Cu direct-chill cast billet is investigated. The hot tear surfaces of the DC cast billets with different composition were observed in a SEM. Measurements on the porosity fraction are also reported. It was found that a decrease of the copper concentration from 3 to 1 % causes a decrease of the amount of eutectic observed on the hot tear surface. Special features are observed on the hot tear surface of an Al−1%Cu alloy in which the hot tear dominantly propagates through the bridged grain boundaries. A solute-rich (eutectic) path along grain boundaries ahead of the hot-crack tip was observed in billets with hot tears, which could be an evidence of crack healing. The porosity is maximum in the center of the billet. Higher casting speed leads to increasing porosity. In Chapter 6 shrinkage, imposed strain rate and (lack of) feeding are considered as the main factors which determine cavity formation and/or the formation of hot tears. A hot tearing model is proposed which will combine a macroscopic description of the DC casting process and a microscopic model. The micro-model predicts whether porosity will form or a hot tear will develop. Results for an Al-4.5%Cu alloy are presented as a function of constant strain rate and cooling rate. Also, incorporation of the model in a FEM simulation of the DC casting process is reported. The model shows features, well-known from literature such as increasing hot tearing sensitivity with increasing deformation rate, cooling rate and grain size. Similar trends are found for the porosity formation as well. The model also predicts a beneficial effect of applying a ramping procedure during the start-up phase, which is an improvement in comparison with earlier findings obtained with alternative models. However, a rigorous test of the model with data obtained from industrial practice was outside the scope of this thesis.

164 Summary

In Chapter 7 the results of experimental and numerical simulation work on the thermal contraction during and after solidification of a commercial AA5182 alloy are presented. In the specially developed experimental set-up, the contraction is measured simultaneously with the temperature while the material solidifies and cools down in the solid state. An elasto-viscoplastic constitutive model fitted to the experimental data is used in finite element simulations of the contraction process. The implementation of thermal contraction data for ingot distortion during the start-up phase of casting is also included. The results show that the contraction starts at a certain temperature in the non-equilibrium solidification range, close to the non-equilibrium solidus. Good agreement is found between simulation and experimental results.

165 Summary

166 Samenvatting

Samenvatting In dit proefschrift wordt de gevoeligheid voor warmscheuren beschreven tijdens het semi-continu gieten van aluminium legeringen. Zaken die aan de orde komen zijn de thermomechanische modellering van het semi-continu gietproces, de integratie hiervan met uit de literatuur bekende criteria voor het ontstaan van warmscheuren, de waarneming van de microstructuur en van warmscheuren bij experimenten gedaan bij verschillende proces parameters, een voorstel voor een nieuw criterium om warmscheuren te voorspellen en het bepalen van de thermische contractie tijdens en na stollen, wat het mogelijk maakt vervorming van de gegoten paal te voorspellen. De inhoud van het proefschrift is als volgt: In hoofdstuk 2 worden karakteristieke parameters als spanning, rek, lengte van vloeibaar en gedeeltelijk gestold aluminium en temperatuur berekend via computersimulatie van het semi-continu gietproces voor een gietpaal, gebruik makend van een eindige elementenmethode. Speciale aandacht is gericht op het gedeeltelijk gestolde gebied en het nabij gelegen vaste gebied. In het centrum van de paal staan de spanningen en rekken, relevant voor warmscheuren, onder trek bij temperaturen overeenkomend met het eind van het stoltraject; nabij het oppervlak van het gietstuk staan deze onder druk. Spanning, rek en lengte van vloeibaar en gedeeltelijk gestold aluminium nemen toe bij toenemende gietsnelheid. Zij zijn maximaal in de beginfase van het gietproces en worden lager als in deze beginfase "ramping" wordt toepast, d.w.z. dat het gietproces begonnen wordt met een lagere, langzaam toenemende gietsnelheid. Spanning, rek en lengte van vloeibaar en gedeeltelijk gestold aluminium zijn het hoogst in het centrum van het gietstuk bij alle onderzochte proces parameters. In hoofdstuk 3 zijn acht criteria voor het optreden van warmscheuren, bekend uit de literatuur, verwerkt in de eindige elementen berekening van hoofdstuk 2 en de resultaten geevalueerd. Uitgangspunten van deze criteria waren onvoldoende navoeding, onvoldoende taaiheid of een combinatie van beide. De conclusie is dat zes criteria resulteren in een hogere gevoeligheid voor warmscheuren bij hogere gietsnelheid en dat vijf resulteren in een hogere gevoeligheid in het centrale gebied van de gietpaal. Dit is kwalitatief in overeenstemming met praktijkervaringen. Zeven criteria laten zien dat toepassing van "ramping" geen effect heeft, terwijl in de praktijk dit een standaard procedure is om warmscheuren te vermijden. Dit leidt tot de conclusie dat slechts één criterium in kwalitatief in overeenstemming is met de praktijk. Echter, dit criterium voorspelt het optreden van warmscheuren onder standaard omstandigheden in de praktijk, zodat een kwantitatieve voorspelling met de bestaande kriteria niet

167 Samenvatting mogelijk blijkt. Daarom is de ontwikkeling van een nieuw of aangepast criterium noodzakelijk (hoofdstuk 6). In hoofdstuk 4 zijn effecten van gietsnelheid en legeringssamenstelling op de vorming van microstructuur en warmscheuren bestudeerd na semi-continu gieten van een gietpaal, 200 mm diameter; diverse binaire Al-Cu legeringen werden hierbij toegepast. De korrelstructuur, en met name ook de aanwezigheid van grove korrels in het centrum van de paal, worden sterk beinvloed door de gietsnelheid en de legeringssamenstelling. De dendrietarm afstand blijkt vooral afhankelijk van de gietsnelheid alleen. Het patroon van warmscheuren laat zien dat de gevoeligheid maximaal is voor de lagere Cu concentraties (1-1.5%) en de hogere gietsnelheden (180-200 mm/min.). De hoeveelheid niet-evenwicht eutecticum is minimaal midden in de gietpaal en bij lagere Cu concentraties, wat overeenkomt met plaats en Cu concentraties waarvoor de gevoeligheid voor warmscheuren het hoogst is. De microstructuur en het warmscheuren konden gecorreleerd worden met de afmetingen van het stollingsgebied die uit de simulaties volgden. Een aantal criteria, eerder geevalueerd in hoofdstuk 3, is wederom geevalueerd bij een varierende (constante toename en afname) gietsnelheid zoals bij deze experimenten toegepast. De criteria die rekening houden met de dynamica van het proces (reksnelheid, feitelijke spanning en rek, navoeding) kunnen met succes worden gebruikt bij een kwalitatieve voorspelling. De conclusies ondersteunen die, getrokken in hoofdstuk 3. In hoofdstuk 5 is het optreden van warmscheuren in binaire Al-Cu (1-4.5%) semi-continu gegoten palen onderzocht. Het oppervlak van de scheuren werd onderzocht in de raster electronenmicroscoop. Tevens werd de hoeveelheid porositeit gemeten. Afname van de Cu concentratie van 3% naar 1% leidt tot een afname van de hoeveelheid eutecticum aan het scheuroppervlak. Speciale kenmerken werden waargenomen aan het scheuroppervlak van een Al-1% Cu legering waarbij de scheur zich hoofdzakelijk uitbreidt langs de korrelgrenzen, die onderling nog op sommige plaatsen verbonden bleven. Een potentieel scheurpad dat veel Cu-rijk eutecticum voor de scheurtip uit bevatte, is waargenomen hetgeen suggereert dat een scheur geheeld kan worden. Porositeit is maximaal midden in de gietpaal. Een hogere gietsnelheid leidt tot een hogere porositeit. In hoofdstuk 6 worden slink, opgelegde reksnelheid en onvoldoende navoeding beschouwd als de belangrijkste factoren die holtevorming en/of de vorming van warmscheuren bepalen. Een warmscheurmodel wordt geintroduceerd dat de macroscopische beschrijving van het semi-continu gietproces koppelt aan een microscopisch model. Het microscopisch model voorspelt of porositeit zal ontstaan of dat een warmscheur zich zal ontwikkelen. Resultaten van dit microscopische model voor een Al-4.5Cu legering worden gepresenteerd als

168 Samenvatting functie van een constant gehouden reksnelheid en afkoelsnelheid. Ook worden resultaten vermeld na integratie van dit model in een eindige elementen berekening. Het model laat resultaten zien, die ook bekend zijn vanuit de literatuur, zoals een toenemende gevoeligheid voor warmscheuren met een toenemende deformatiesnelheid, afkoelsnelheid en korrelgrootte. Vergelijkbare trends worden gevonden voor de hoeveelheid porositeit. Het model laat ook zien dat toepassing van "ramping" gedurende de opstartfase een gunstig effect heeft, wat dus een verbetering is t.o.v. de in hoofdstuk 3 onderzochte modellen/criteria. Echter, een rigoureuze test van het model aan de hand van experimentele data uit de industriele praktijk viel buiten de scope van dit proefschrift. In hoofdstuk 7 worden de resultaten gepresenteerd van experimenten en simulaties betreffende de thermische contractie tijdens en na stolling van een commerciele AA5182 legering. In een speciaal daartoe ontwikkelde opstelling is de mate van contractie gemeten als functie van de temperatuur. Een constitutief model, gebaseerd op een elasto-viscoplastische benadering, is gefit aan de experimentele data en is vervolgens gebruikt in eindige elementen berekeningen met betrekking tot contractie in een gietpaal. Tevens wordt de vervorming van de gietpaal tijdens de opstart fase berekend. De resultaten laten zien dat contractie begint bij een bepaalde temperatuur in het (niet-evenwichts) stollingstraject, die dicht ligt bij de niet-evenwichts solidustemperatuur. Een goede overeenstemming tussen berekening en experiment is daarbij gevonden.

169 Samenvatting

170 Appendix

Appendix A The derivation of three-phase (solid-liquid-cavity) model for hot tearing model uses the conservation of mass equation based upon the general framework for the volume averaged conservation equation as presented in ref. [1].

∂()f ρ s s + ∇.()f ρ v = Γ ( A1 ) ∂t s s s

∂()f ρ l l + ∇.()f ρ v = −Γ ( A2 ) ∂t l l l fn = volume fraction of phase n (n=s , l and v for solid, liquid and cavity), ρk denotes mass density, vk velocity, and Γ the interfacial mass transfer due to phase change. Add Eqs. A1 and A2: mass conservation equation for two-phase (solid- liquid) system:

∂()f ρ ∂()f ρ s s + l l + ∇.()()f ρ v + ∇. f ρ v = 0 ( A3 ) ∂t ∂t s s s l l l

∂()f ρ ∂ρ ∂f s s = f s + ρ s ( A4a ) ∂t s ∂t s ∂t

∂()f ρ ∂ρ ∂f l l = f l + ρ l ( A4b ) ∂t l ∂t l ∂t

∂ ∂ ∂ ∇.()f ρ v = ()f ρ v + ()f ρ v + ()f ρ v ( A5a ) s s s ∂x s s x,s ∂y s s y,s ∂z s s z,s

∂ ∂ ∂ ()f ρ v = ρ ()f v + f v ()ρ ( A5b ) ∂x s s x,s s ∂x s x,s s x,s ∂x s

∂ ∂ ∂ ()f ρ v = ρ ()f v + f v ()ρ ( A5c ) ∂y s s y,s s ∂y s y,s s y,s ∂y s

171 Appendix

∂ ∂ ∂ ()f ρ v = ρ ()f v + f v ()ρ ( A5d) ∂z s s z,s s ∂z s z,s s z,s ∂z s

∂ ∂ ∂ ∇.()f ρ v = ()f ρ v + ()f ρ v + ()f ρ v ( A5e ) l l l ∂x l l x,l ∂y l l y,l ∂z l l z,l

∂ ∂ ∂ ()f ρ v = ρ ()f v + f v ()ρ ( A5f ) ∂x l l x,l l ∂x l x,l l x,l ∂x l

∂ ∂ ∂ ()f ρ v = ρ ()f v + f v ()ρ ( A5g ) ∂y l l y,l l ∂y l y,l l y,l ∂y l

∂ ∂ ∂ ()f ρ v = ρ ()f v + f v ()ρ ( A5h ) ∂z l l z,l l ∂z l z,l l z,l ∂z l

Substitute Eqs. ( A4a, A4b, A5a-A5h) to Eq. A3:

∂ρ ∂f ∂ρ ∂f ∂ ∂ f s + ρ s + f l + ρ l + ρ ()f v + f v ()ρ + s ∂t s ∂t l ∂t l ∂t s ∂x s x,s s x,s ∂x s ∂ ∂ ∂ ∂ ρ ()f v + f v ()ρ + ρ ()f v + f v ()ρ + s ∂y s y,s s y,s ∂y s s ∂z s z,s s z,s ∂z s

∂ ∂ ∂ ∂ ρ ()f v + f v ()ρ + ρ ()f v + f v ()ρ + l ∂x l x,l l x,l ∂x l l ∂y l y,l l y,l ∂y l ∂ ∂ ρ ()f v + f v ()ρ = 0 l ∂z l z,l l z,l ∂z l ( A6 )

1 = fl + f s + fv ( A7 )

f s = 1− fl − fv ( A8 )

∂f ∂f ∂f s = − l − v ( A9 ) ∂t ∂t ∂t

Substitute Eqs. (A9) to Eq. (A6) and then divide by ρl:

172 Appendix

f ∂ρ ρ ∂f ρ ∂f f ∂ρ ∂f ρ ∂ s s − s l − s v + l l + l + s ()f v + ρ ∂t ρ ∂t ρ ∂t ρ ∂t ∂t ρ ∂x s x,s l l l l l f s v x,s ∂ ρ s ∂ f s v y,s ∂ ()ρ s + ()f s v y,s + ()ρ s + ρ l ∂x ρ l ∂y ρ l ∂y

ρ s ∂ f s vz,s ∂ ∂ ()f s vz,s + ()ρ s + ()f l vx,l + ρl ∂z ρl ∂z ∂x

f l vx,l ∂ ∂ fl v y,l ∂ ()ρl + ()fl v y,l + ()ρl + ρl ∂x ∂y ρl ∂y

∂ fl vz,l ∂ ()f l vz,l + ()ρl = 0 ( A10 ) ∂z ρl ∂z

Assumed ρl and ρs are constant.

ρ ∂f ρ ∂f ∂f ρ ∂ ρ ∂ − s l − s v + l + s ()f v + s ()f v + ρ ∂t ρ ∂t ∂t ρ ∂x s x,s ρ ∂y s y,s l l l l ( A11 ) ρ s ∂ ∂ ∂ ∂ ()f s v z,s + ()f l v x,l + ()f l v y,l + ()f l v z,l = 0 ρ l ∂z ∂x ∂y ∂z

ε& is strain rate, fe is feeding rate.

ρ s ∂f v  ρ s  ∂f l ρ s = − −1 + ε& + fe ( A12) ρ l ∂t  ρl  ∂t ρ l

[1] Ni, J., Beckermann, C. (1991) Metallurgical Transactions B, 22B, p.349.

173

List of publications

List of Publications Journal 1. Suyitno, W.H. Kool, L. Katgerman, Micro-mechanical model of hot tearing in DC casting, Materials Science Forum, vol. 396-402, 2002, pp. 179-184. 2. Suyitno, L. Katgerman, A. Burghardt, Determination of boundary conditions during the start-up of DC casting, Proceedings ASME Heat Transfer Division, vol. 5, 2002, pp. 147-154. 3. D.G. Eskin, Suyitno, J. Mooney and L. Katgerman, Contraction of aluminum alloys during and after solidification, Metallurgical and Materials Transactions A, 35A, 2004, pp.1325-1335. 4. Suyitno, W.H. Kool, L. Katgerman, Finite Element Method simulation of mushy zone behavior during direct-chill casting of an Al−4.5%Cu alloy, Metallurgical and Materials Transactions A, 35A, 2004, pp. 2917-2926. 5. D.G. Eskin, Suyitno and L. Katgerman, Mechanical properties of aluminum alloys in the semi-solid state and hot tearing criteria, Progress in Materials Science, 49, 5, 2004, pp. 629-711. 6. Suyitno, D.G. Eskin, V.I. Savran, L. Katgerman, Effect of composition and casting speed on structure formation and hot tearing during direct-chill casting of Al−Cu alloys, Metallurgical and Materials Transactions A, 35A, 2004, pp. 3551-3562. 7. Suyitno, W.H. Kool, L. Katgerman, Hot tearing criteria evaluation for direct-chill casting of an Al−4.5%Cu alloy, Metallurgical and Materials Transactions A, 36A, 2005 (in press). 8. Suyitno, D.G. Eskin, L. Katgerman, Thermal contraction of AA5182 for prediction of ingot distortion, accepted for publication in Key Engineering Materials, 2005 (in press). 9. Suyitno, D.G. Eskin, L. Katgerman, Hot tearing study of Al−Cu alloys billet produced by direct-chill casting, submitted for publication in Materials Science and Engineering A, 2005. 10. Suyitno, W.H. Kool, L. Katgerman, Integrated approach for prediction of hot tearing in aluminum alloys, Part 1: Model description, submitted for publication in Acta Materiallia, 2005. 11. Suyitno, W.H. Kool, L. Katgerman, Integrated approach for prediction of hot tearing in aluminum alloys, Part 2: application for direct-chill billet, submitted for publication Acta Materiallia, 2005.

175 List of publications

Conference Proceedings 1. M. Zheng, Suyitno, L. Katgerman, On the transport phenomena and hot tearing criteria in DC casting of aluminium alloys, Proceedings of the 22nd Riso International Symposium on Materials Science, Eds. A.R. Dinesen et al., 3-7 September, Roskilde, Denmark, 2001, pp. 455-460. 2. M. Zheng, Suyitno, W.M. Van Haaften, L. Katgerman, On the plastic flow behavior of aluminium alloys in the mushy zone, Advances in the Metallurgy of Aluminum Alloys: Proceedings of the James T. Staley Honorary Symposium on Aluminum Alloys, Ed. M. Tiryakioglu, ASM International, OH, USA, 2001, pp. 378-384. 3. Suyitno, W.H. Kool, L. Katgerman, Micro-mechanical model of hot tearing in DC casting, Proceedings of 8th International Conference of Aluminum Alloys, Cambridge, UK, Ed. P.J. Gregson and S. Harris, Trans Tech Publications Ltd, Switzerland, 2002, pp. 179-184. 4. Suyitno, W.H. Kool and L. Katgerman, A finite element prediction of deformations in aluminium alloy slab during DC casting, Proceeding of ISSM2002, Berlin, Germany, Ed. B.H. Iswanto and M. Gozan, 2002, p.386- 390. 5. Suyitno, W.H. Kool, L. Katgerman, Evaluation of mechanical and non- mechanical hot tearing criteria for DC casting of an aluminum alloy, Light Metals 2003, San Diego, CA, Ed. P.N. Crepeau, TMS, Warrendale, PA, USA, 2003, pp. 753-758. 6. L. Katgerman, D.G. Eskin, B.C.H. Venneker, J. Zuidema (Jr.), and Suyitno, Experimental description and process simulation of DC casting of aluminum alloys, Aluminium Cast House Technology, Proceedings of the 8th Australasian Conference, Brisbane, Australia, Ed. P.R. Whiteley, TMS, Warrendale, PA, USA, 2003, pp. 243-257. 7. Suyitno, E.N. Straatsma and L. Katgerman, Modeling of single-roll strip casting of Al-1%Mn alloy: Correlation of strip thickness, solidification zone length and puddle shape, Multiphase Phenomena and CFD Modeling and Simulation in Materials Processing, Charlotte, NC, Eds. L. Nastac and B.Q. Li, TMS, Warrendale, PA, USA, 2004, pp. 325-334. 8. Suyitno, D. Eskin and L. Katgerman, Effect of casting speed on structure formation and hot tearing during direct-chill casting of Al−Cu alloys, Solidification Processes and Microstructure: A Symposium in Honor of Prof. W. Kurz, Charlotte, NC, Eds. M. Rappaz, C. Beckermann and R. Trivedi, TMS, Warrendale, PA, USA, 2004, pp. 47-52.

176 List of publications

9. Suyitno, D.G. Eskin, L. Katgerman, Thermal contraction of AA5182 and AA5083: experiment and simulation, Proceedings of 9th International Conference of Aluminum Alloys, Brisbane, Australia, Eds. J.F. Nie, A.J. Morton and B.C. Muddle, 2004, pp. 1309-1315. 10. Suyitno, D.G. Eskin, L. Katgerman, Microstructure and hot tearing of Al−Cu alloys billet produced by direct-chill casting, Aluminium Cast House Technology 2005, Melbourne, Australia, Eds. J. Taylor, I. Bainbridge and J. Grandfield, 2005 (submitted). 11. Suyitno, D.G. Eskin, L. Katgerman, Hot tearing study of Al−Cu alloys billet produced by direct-chill casting, Continues Casting of Non-ferrous Metals, Neu-Ulm, Germany, 2005 (submitted).

177 List of publications

178 Acknowledgement

Acknowledgment

This research was carried out as part of the strategic research program of the Netherlands Institute for Metals Research (NIMR) on the “Experimental description and process simulation of direct-chill (DC) casting of aluminum alloys” project number MP 97014. This research was conducted in a team with regular contact with CORUS RD&T. I am greatly indebted to my promotor, Prof. L. Katgerman who has provided me an opportunity to do a Ph.D work. His guidance, support and encouragement are tremendous for me. I am also greatly indebted to my daily supervisor, Dr. W.H. Kool who has provided me critical comment, inspiration and correction on the content of my thesis. Special thank is for Dr. D.G. Eskin who has shared his depth knowledge of aluminum alloys. In this regard, I wish particularly to mention the useful contribution of the project meeting members: Dr. Rene Kieft and Dr. W. Bounder from CORUS RD&T, Dr. B.C.H. Venneker and Ir. J. Zuidema Jr. from NIMR. I would like to thank to Dr. A. Burghardt from CORUS RD&T for introducing me with thermomechanical modeling of direct-chill casting, V.I. Savran M.Sc. for performing a microstructure analysis, Dr. V. Svetchnikov from High Resolution Electron Microscopy Group and Ir. P.T.G. Koenis from BOAL B.V. for helping with Scanning Electron Microscopy. I like to thank W.O. Dijkstra for being my roommate in office and Simon Peter for helping with English language. Also thanks go to Jan van Etten, Sjaak Jansen and Jan Boomsma for their time for helping during experiment. Furthermore, I must express my gratitude to all members of Light Metals Processing (LMP) group who provide good atmosphere for working. The support from Indonesian community in Delft is gratefully acknowledged.

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180 Curriculum Vitae

Curriculum Vitae

Suyitno (born November 3th, 1970 in Semarang, Indonesia) finished high school in SMA 1 Ungaran in 1990. He obtained a B.Eng. degree from Mechanical Engineering Department, Gadjah Mada University, Indonesia, in 1995. Since 1995 he was employed as Junior Lecturer in the Department. His M.Sc. degree was obtained from Materials Science and Engineering Department, Delft University of Technology, The Netherlands, in 2000. During the Masters Study, He worked on the “Parametric Study of Single-Roll Strip Casting of Aluminum Alloys”. Since December 2000 he becomes Junior Researcher in the Material Science and Engineering Department, Delft University of Technology, The Netherlands. During the last four years of his PhD research he worked on Project of “Experimental Description and Process Simulation of Direct–Chill Casting Process of Aluminum Alloys”. This research was set up as a strategic research project by the Netherlands Institute for Metals Research (NIMR) in collaboration with CORUS RD&T, Ijmuiden, the Netherlands. His tasks and responsibilities have included: (1) Performing numerical predictions for deformation and hot tearing of aluminium alloys during the direct–chill casting process. (2) Involvement in experiments of direct-chill casting studying the effects of various parameters and compositions with respect to microstructure and hot tearing susceptibility. (3) Performing experiments on the contraction of aluminum alloys during and after solidification. (4) Performing experiment on the thermomechanical properties of aluminum alloys at semi-solid state. (5) Involvement in educational activities e.g. co-supervising master students, supervising a practical course on the evaluation of mechanical properties. This thesis contains the results of his research since December 2000-December 2004.

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