Finite Element Modelling and Analysis of the Friction Stir Extrusion Process.
Thesis
Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in
the Graduate School of The Ohio State University
By
Chaitanya Karwa
Graduate Program in Mechanical Engineering
The Ohio State University
2019
Thesis Committee
Dr. Rajiv Shivpuri, Advisor
Dr. Prasad Mokashi
1
Copyrighted by
Chaitanya Karwa
2019
2
Abstract
Aluminium and Magnesium are widely used for their light weight and strength in various applications. Over 90% of the energy is used in the production of these metals and 10% for forming, processing etc. Additionally, the demand for these metals is expected to double in the next 30 years. Hence, it is necessary to recycle these metals and develop sustainable machining processes. Friction Stir Extrusion (FSE), the focus of this research, is a process, which holds tremendous potential in solid state recycling and improving the mechanical properties of the finished products. If properly developed, it could lead to products with fine grains improving properties like ductility, corrosion, strength, hardness etc. However, most of the research has been experimental and there is a lack of computational modelling knowledge.
A comprehensive Finite element model has been validated and developed to analyze all the aspects of FSE namely, force, torque, material properties like grain size, state of welding/bonding etc. The effect of varying designs parameters like friction, extrusion ratio, rotation rate, plunging speed has been studied. An attempt has been made to increase the efficiency of the computations by decreasing the computation time by over 50% for results within 20% accuracy. The feasibility of using the ShAPE machine with Aluminium and in
Solid State Recycling processes has been discussed and a new law has been implemented in Forge NxT to analyze the welding between chips in FSE
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Acknowledgements
First, I would like to thank and express my gratitude to Dr. Rajiv Shivpuri for giving me an opportunity to work on an intriguing problem and conduct research under his guidance.
He has not only guided me through complex manufacturing science, plateaus in research but has also been a great mentor, encouraging me through all the difficulties I faced throughout my masters program at The Ohio State University. I would like to sincerely thank Dr. Prasad Mokashi for serving on my committee and helping me build a solid theoretical base for all the analysis in this research. I am grateful for his support and time to guide me on various aspects of the graduate program.
I would like to thank Anudeep Mallarapu and Sumaiya Islam for their constant support and help in various research problems. Last but not the least, I would like to thank my family and friends at The Ohio State university for standing by me throughout my life.
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Vita
2016…………………………………….... B.E.(Hons), Mechanical Engineering,
BITS Pilani, Pilani Campus
2016 to present…………………………… M.S. Mechanical Engineering, The Ohio
State University
Fields of Study
Major Field: Mechanical Engineering
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Table of Contents
Abstract ...... iii Acknowledgements ...... iv Vita ...... v List of Tables ...... viii List of Figures ...... ix Chapter 1: INTRODUCTION...... 1 1.1. Introduction ...... 1 1.2. Extrusion ...... 2 1.3. Material Science review ...... 5 1.4. Recrystallization in Metals ...... 8 1.5. Kinds of Recrystallization...... 11 1.6. Motivation ...... 13 Chapter 2: Friction Stir Processes ...... 16 2.1. Friction Stir Back Extrusion ...... 17 2.2. Friction Stir Consolidation and Processing...... 21 2.3. Friction Stir Forward Extrusion ...... 22 2.4. Summary ...... 23 Chapter 3: Mechanics and Finite Element Method...... 25 3.1. Introduction ...... 25 3.2. Material behavior ...... 26 3.3. Contact and Friction ...... 26 3.4. Heat Transfer ...... 29 Chapter 4: Friction Stir Extrusion Modeling ...... 31 4.1. Previous Modeling efforts...... 31 vi
4.2. Shear Assisted Processing and Extrusion (ShAPE) ...... 33 4.3. Finite Element Modelling ...... 36 4.4. Initial FEM results ...... 42 Chapter 5: Finite Element Analysis ...... 47 5.1. Exploring reduction in Computation time ...... 49 5.2. Material grain size and other results ...... 54 Chapter 6: Effect of process parameters ...... 59 6.1. Plunger Speed ...... 59 6.2. Friction ...... 61 6.3. Extrusion Ratio ...... 63 6.4. Summary ...... 64 Chapter 7: WQI – Welding Quality Index ...... 65 Chapter 8: Summary and Conclusion ...... 69 8.1. Finite element modelling ...... 69 8.2. Analysis on modelling, process parameters ...... 70 8.3. WQI and Future research ...... 72 Bibliography ...... 74
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List of Tables
Table 1: Crystal structure for some metals at room temperature ...... 6
Table 2: SFE of some common alloys and metals at room temperature [5] ...... 12
Table 3: Components in the ShAPE process ...... 35
Table 4: Heat transfer coefficient values for metal-metal contact[20] ...... 37
Table 5: Steady state force and torque values ...... 52
Table 6: Grain size for 200 rpm ...... 57
Table 7: Grain Size for different rotation rates ...... 58
Table 8: Variation of Grain size with plunging speed ...... 61
Table 9: Variation of grain size with friction...... 62
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List of Figures
Figure 1: Extrusion of a blank through a die (Wikipedia) ...... 3
Figure 2: a) Direct extrusion. b) Indirect extrusion [1] ...... 4
Figure 3: Grain/ Grain boundaries for a metal [2] ...... 6
Figure 4: Recrystallization in a metal [3] ...... 8
Figure 5: Kinetics of Recrystallization [3]...... 10
Figure 6: Grain growth behavior for Al 7050 during Friction Stir Processing[4] ...... 11
Figure 7: Comparison of energy inputs[6] ...... 14
Figure 8 : Conventional recycling process[8] ...... 14
Figure 9: Schematic figure of Friction Stir Welding [10]...... 17
Figure 10: Schematic of Friction Stir Back Extrusion ...... 18
Figure 11: FSBE process and results from Hosseini et al[13] ...... 19
Figure 12: Top and Isometric view of the final positions of tracking points for different speeds (increasing from a to c) [15]...... 20
Figure 13: FSC: Process and microstructure[18] ...... 21
Figure 14: ShAPE process[19]...... 23
Figure 15: Coulomb’s law limited to tresca ...... 28
Figure 16: Heat transfer [20]...... 30
Figure 17: Contribution of process parameters toward grain size[26] ...... 31
Figure 18: Microstructure simulation: a) Volume Fraction; b)grain size and c) micro- hardness [27] ...... 32
Figure 19: ShAPE process[19]...... 34 ix
Figure 20: Components of the ShAPE process ...... 34
Figure 21: Force, torque, temperature for ShAPE...... 35
Figure 22: ZK 60 True stress, strain for strain rates(푠 − 1):a)0.001 b)0.01 c) 0.1 d)1 .... 38
Figure 23: Finite element model of the ShAPE process ...... 39
Figure 24: Force from the Finite Element Simulation (ShAPE)...... 43
Figure 25: Torque from the Finite Element Simulation (ShAPE) ...... 43
Figure 26: Force and Torque for Al 6061 – ShAPE ...... 44
Figure 27: Difference in mesh sizes causing noise ...... 45
Figure 28: Velocity Vector plots for FSE at 200 rpm...... 48
Figure 29: Movement of a marking grid and ‘boundary layer’ ...... 48
Figure 30: Force for different rotation rates ...... 51
Figure 31: Torque for different rotation rates ...... 51
Figure 32: Temperature distribution for ShAPE (Aluminium)...... 53
Figure 33: Effective Strain and Strain rate for ShAPE (Aluminium) ...... 53
Figure 34: Rotation velocity and Equivalent stress for ShAPE (Aluminium) ...... 53
Figure 35: Relationship between deformed/initial grain size and Z for Al 6060/6061[29]
...... 55
Figure 36: Point tracking in Extrusion ...... 55
Figure 37: Temperature history ...... 56
Figure 38: Effective Strain history ...... 56
Figure 39: Grain Size vs rpm ...... 58
Figure 40: Variation of force with plunging speed ...... 59
x
Figure 41: Variation of Torque with plunging speed ...... 60
Figure 42: Variation of Force with friction...... 61
Figure 43: Variation of torque with friction ...... 62
Figure 44: Variation of force with extrusion ratio ...... 63
Figure 45: Variation of Torque with extrusion ratio ...... 63
Figure 46: Consolidation of aluminium chips[32] ...... 66
Figure 47: 퐶표푥푖푑푒 and WQI for extrusion ...... 67
Figure 48: 퐶표푥푖푑푒 and WQI for FSE at 50 rpm ...... 68
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Chapter 1: INTRODUCTION
1.1. Overview/ Introduction
This research describes the modelling, analysis and an in depth study of the Friction Stir
Extrusion process. We have tried to tackle and address the knowledge gaps cited by several researchers working in this area. The primary objectives of this thesis have been given below –
Develop a comprehensive Finite Element Model and validate it to study the
following aspects of FSE
o Grain Size and material properties.
o Effect of process parameters on the outgoing product
o Capturing the material flow and physical effect of rotation
Reduce the large computation times(~weeks) encountered in such simulations
Simplify model by taking into account previous research and present a model,
which can give approximate results much quicker to aid the design process.
Understand the effect of various inter-dependent process parameters involved in
the process.
Explore the feasibility of using the ShAPE machine for Solid State Recycling by
including laws to predict welding.
The thesis has been divided into 8 chapters, which cover the following aspects- 1
1. Brief overview of all the scientific theories and terminologies, which are necessary to
understand the research. For example, extrusion, recrystallization, recycling etc. have
been discussed. The chapter also includes the motivation for conducting research in
this domain.
2. This chapter includes a literature review of various works, which involve friction stir.
3. The third chapter covers the various models related to materials, friction, contact etc.,
which form the Finite Element Method used for this research. All the models are part
of the software Forge NXT developed by TRANSVALOR.
4. This chapter described the rationale and development of the FE model for the ShAPE
process developed by PNNL.
5. We further analyze the FE model and discuss the results, which are of primary
importance for the process, like grain size, physical effect of rotation, stress/strain etc.
This chapter also describes the procedure adopted to decrease the FE computation time.
6. Effects of various process parameters on the material properties, force, torque etc. have
been discussed in the chapter. We also understand the se
7. A brief discussion on the feasibility of solid state recycling and welding of chips using
the FSE process
8. The summary and important conclusions drawn from this work are included.
1.2. Extrusion
Extrusion is broadly defined as a manufacturing process used to create objects of a fixed cross-sectional profile. Extrusion of metals involves a billet, pushed by a stem at large pressures through a die (of the desired shape) to a certain length. It achieved an important
2 position in the semi-finished product industry in the 20th century [1]. It was mainly used to manufacture wires, tubes, bars and sections in aluminum and copper alloys. In addition, semi-finished products in other materials like stainless steel, steel sections and other metals are produced in small quantities.
Figure 1: Extrusion of a blank through a die (Wikipedia)
There are two important types of extrusions:
i) Direct Extrusion: The stem pushes the billet in a container through a die, which
has the desired shape. The billet and container (stationary) move relative to each
other. Refer Fig. 1
ii) Indirect Extrusion: The stem is hollow and pushes the billet against the
container, which is closed at one end. Hence, the deformed material flows
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through the stem. Therefore, the billet and container do not move relative to
each other. Refer Fig. 1
For the Figure 2 shown below, 1- extrudate, 2-die, 3-billet, 4-dummy block, 5-container,
6-stem, 7-dummy block with die, 8-sealing tool
Figure 2: a) Direct extrusion. b) Indirect extrusion [1]
The billet is under a compressive state during extrusion, which enables large deformations with a minimal risk of cracking. Extrusion ratio is normally defined as the cross section area of billet divided by the cross section area of the extrudate and lies in the range of 10-100 for majority of the processes. In some cases, like the production of nanomaterials, the extrusion ratio can be as high as 1000. The lower the flow stress of the material (stress required for plastic deformation), the easier the extrusion process as less pressure/force is required. The flow stress of metals normally decreases with an increase
4 in the temperature, hence, extrusion if often carried out at high temperatures. For example,
Aluminium – 400-500° C, Copper alloys – 600-900° C, Stainless steels – up to 1250° C etc. Therefore, there are 2 main sub-types of Direct/Indirect extrusion with respect to this research –
i) Cold Extrusion –Although the term cold is relative, it normally refers to
extrusion carried out at around room temperature. A literature search also
revealed that extrusion is carried out at cryogenic temperatures for some special
applications (fibers). Cold extrusion could be used to produce parts with high
strength due to strain hardening, better surface finish and accuracy. However,
the process requires higher pressures and stronger tools than hot extrusion.
ii) Hot Extrusion – As the name implies, hot extrusion is carried out at higher
temperatures making it easier to extrude because of the low flow stress. The
surface finish and accuracy is not as good as cold extrusion, while the tools do
not have to be as strong.
1.3. Material Science review
a) Grains
Metals have a crystalline structure. The crystalline nature ensures that metals have strong bonds and are packed as closely as possible. Crystals are made of smaller units, namely unit cells. Different metals have different kinds of crystal structures and unit cells.
Some common types of cells/crystal structure are Hexagonal Close Packing (HCP), Face
Centered Cubic (FCC), Body Centered Cubic (BCC) etc. Unit cells might determine some 5 properties of metals – FCC implies more ductility than BCC or HCP [2]. Crystal Structures for some metals has been shown below
Table 1: Crystal structure for some metals at room temperature
Metal Crystal Structure
Aluminum FCC
Magnesium HCP
Iron BCC
Lead FCC
As a melted metal begins to solidify, atoms pack together to form a crystal lattice. As more atoms get added to the crystals, they increase in size forming a solid made up of many small crystals, called grains. These grains grow and meet (impinge) other grains at grain boundaries. All the grains could have different sizes and orientation as shown in the figure below
Figure 3: Grain/ Grain boundaries for a metal [2]
6 b) Hall-Petch relationship
Plastic deformation arises from the movement of dislocations in metals. Grain boundaries oppose the dislocation movement and the number of dislocations in a grain have an effect on how dislocations move. Therefore, the grain size directly affects the movement of dislocations and the yield strength (onset of plastic deformation) of the metal.
For example, heat treatment is carried out after manufacturing processes to change the grain size and alter the behavior of the metal.
When a force is applied to a metal, the existing and new dislocations move through a crystal lattice until they encounter a grain boundary. As the movement of dislocations increases, they start piling up and are unable to move past a boundary. Dislocations generate repulsive stress fields at the grain boundaries and reduce the energy barrier for diffusion across the boundaries, allowing deformation in the metal. Hence, more the number of grain boundaries, more the piling up of dislocations, which increases the applied stress necessary to move dislocation across boundaries. Higher applied stress implies higher yield strength; hence, there is an inverse relationship between the grain size and the yield strength. This relationship is known as the Hall Petch relationship
푘 Δ휏 훼 푑푥
Where 푑 is the grain size, 푘 푎푛푑 푥 are material specific constants.
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1.4. Recrystallization in Metals
A process wherein a new set of defect free grains nucleate and grow until they replace the original deformed grains is called Recrystallization. Recrystallization normally has side effects like reduction in strength and hardness in a metal with an increase in the ductility.
Hence, it is used as processing step in manufacturing processes to soften metals, increase ductility and control the grain structure of the final product. [3]
i. Stages of Recrystallization
Figure 4: Recrystallization in a metal [3]
The above figure shows the recrystallization process in a typical metal. The various stages in Recrystallization have been explained below –
a) Initial grain structure – The part (a) in the figure above shows the initial grain structure
of the metal before recrystallization. b) Nucleation – The difference in the stored internal energy between strained and
unstrained regions leads to nucleation and formation of new grains. The new grains
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take form of small nuclei and grow subsequently through short-range diffusion. The
part (b) of the above figure shows the formations of small nuclei in the metal. c) Impingement – The newly formed grains start growing until they encounter neighbor
grains, which are also growing. The part (c) show the grain structure as the grains
impinge each other. d) Grain growth – After recrystallization, the newly formed grains begin to grow. If the
growth continues for a long time, the number of grains start decreasing and the size of
grains increases. Adjacent grains might start coalescing to form bigger grains if they
share a lower energy boundary between them. The part (d) in the figure above shows
the growth of grains and increas4e in their size after their formation in part (c).
Therefore, controlling the amount of time the metal undergoes recrystallization is necessary to obtain the desired material and grain properties.
ii. Laws of Recrystallization [3] a) Thermal activation – The rate of growth and formation (nucleation) of grains depends
on the processing temperature. b) Critical Temperature – A minimum temperature is required for the new grains to form
and initiate atomic mechanisms. This temperature decreases with time. c) Critical Deformation – The deformation in the material must be enough to provide
energy for nuclei formation and growth. d) Deformation vs Critical Temperature – The critical temperature decreases if the amount
of deformation is high. This is due to the store energy provided by the deformation.
9 e) Initial grain size – More the initial grain size, fewer grain boundaries in the material.
As nucleation starts at boundaries, this reduces the rate and increases the
recrystallization temperature. f) Effect of Deformation – Upon increase in deformation and decrease in temperature, the
rate of nucleation increases faster than the growth, refining the grain structure of the
material.
Hence, it is necessary to strike the right balance between the temperature and deformation to achieve the desired grain size. iii. Kinetics of Recrystallization
The figure below shows the kinetic of recrystallization and how the growth varies with respect to time.
Figure 5: Kinetics of Recrystallization [3]
The above figure broadly shows the pattern followed during recrystallization. Although, the process is not strictly followed, it represents the best approximation for the 10 recrystallization process. 푡0 represents the initla nucleation period where new nuclei are formed; this is followed by a period of constant growth in the size of the newly formed nuclei.
Figure 6: Grain growth behavior for Al 7050 during Friction Stir Processing[4]
1.5. Kinds of Recrystallization
Majority of metals undergoing hot deformation encounter Dynamic recrystallization
(DRX). Many important factors like thermo-mechanical processing (TMP) conditions, stacking fault energy (SFE) and chemistry of the materials affects the Dynamic recrystallization [5]. DRX is further divided into Discrete Dynamic Recrystallization
(DDRX), Continuous Dynamic Recrystallization (CDRX) and the most recent geometric dynamic recrystallization (GDRX). We will not cover GDRX as a part of this thesis and additional information can be found in the paper by Huang et.al. DDRX and CDRX are explained text following the Table below –
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Table 2: SFE of some common alloys and metals at room temperature [5]
−ퟐ −ퟐ Metal 휸푺푭푬(풎푱풎 ) Metal 휸푺푭푬(풎푱풎 )
Aluminum 166 Zinc 140
Copper 78 Magnesium 125
Silver 22 Zirconium 240
Gold 45 Stainless Steel 21
a) Discrete Dynamic Recrystallization (DDRX) – This type of recrystallization usually
occurs in materials with medium or lower SFE, which are undergoing hot deformation.
A low SFE enables easier formation of stacking faults, which reduced the cross slip or
climb. When the recovery is not fast enough to annihilate dislocations, nuclei start
forming after the dislocation density reached a critical condition. The nucleation of new
strain-free grains and their growth in regions of a large number of dislocations upon
the application of plastic strain results in DDRX. A critical strain (휀푐푟) is to be reached
before DDRX can start. This critical strain decreases as the Zener Holloman parameter
decreases. The Zener Holloman parameter combines the effects of strain and
temperature in a single parameter. The stress-strain response of the material shows
single or multiple peaks depending on the initial grain size, strain rate and temperature. b) Continuous Dynamic Recrystallization (CDRX) – CDRX usually occurs in high SFE
metals/alloys where the cross slip or climb of dislocations is easier, for example,
aluminum, magnesium etc. In CDRX, sub-grains with low angle grain boundaries
(LAGB) are formed from dislocations. As more plastic deformation occurs, the LAGB 12
turn into High Angle Grain Boundaries (HAGB) and the sub-grain wall are
immobilized leading to new grain formation. The stress increases with the strain and
reaches a steady state at large strains. A decrease in the temperature leads to an increase
in the stress. Al and Mg curves show a single peak while Steel does not show any clear
peak.
1.6. Motivation
Combining the effects of recrystallization and its implications as shown by the Hall
Petch relationship with a mass production process like Extrusion can lead to immense improvement in the quality of products. As stated in the sections above, high strain/shear plays an important role in refining the grain size of materials. Several processes have been developed to exploit this property and are broadly known as Severe Plastic Deformation
(SPD) processes. A major part of this work will focus on one such SPD process, called
Friction Stir Extrusion. The process inculcates the high shear encountered in the Friction
Stir Welding process with Extrusion leading to a product with better ductility, strength than normal extrusion. This process has been discussed in detail in the next chapter.
SPD has extensive applications in recycling of metals. Recycling of metals like aluminum, magnesium, copper etc. only requires 0.05-0.3 times the energy required to extract the metal from ores[6]. The figure below shows the energy required for recycling vs extraction from ores.
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Figure 7: Comparison of energy inputs[6]
The use of Aluminum along with various light metals has increased substantially in the past decade. The conventional process for recycling Aluminum has been shown in the figure below. During this process, more than 46% of the metal is lost in various processes leading to a highly inefficient process [7].
Figure 8 : Conventional recycling process[8]
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In case of direct recycling of Aluminum by SPD processes, 95% of the metal is recovered. Gronostajski et al have concluded that the direct recycling of Aluminum can lead to savings of 40% in materials, 26-31% in energy and 16-60% in labor. Additionally, during direct recycling, the emission of toxic gases generated from combustion of oils sticking to chips does not occur. As the energy consumption is reduced, it decreases the emission of greenhouse gases produced as a byproduct of electricity. Therefore, SPD processes have several advantages over the conventional recycling process.
The next chapter discusses the various types of SPD processes used in solid state recycling, grain refinement and improvement on material properties. The research in this thesis focuses on Friction Stir Extrusion (FSE), which has been used extensively to recycle and refine various metals. Modeling the FSE process can be very difficult owing to the high rates of tool rotations, complicated heat transfer and long computation times. An effort has been made to simplify the numerical modelling in the FSE process and predict the material properties via simulations, hence avoiding costly experiments.
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Chapter 2: Friction Stir Processes
Metal forming processes in which a large plastic strain is introduced into a bulk material in order to create ultra-fine grained materials are called Severe Plastic
Deformation processes [9].
This chapter specifically discusses SPD processes, which involve a rotational tool/friction stir and are used for processing or recycling metals. The numerical modelling for these processes is similar, as it is very difficult to model discrete chips undergoing such a complicated process. Since the focus of this research is to explore the Finite element modelling of such processes, it is critical to understand the previous experimental/modelling work.
The inspiration for Friction Stir Extrusion was drawn from the Friction Stir Welding
(FSW) process. The Welding Institute (Thomas et al.) patented the FSE process, which follows the same principles as FSW. FSW uses a non-consumable rotating tool, which is inserted between two edges of the sheets/plates to be joined and moved in the direction of the edge. The tool produces heat because of friction and plasticizes the material around it, making it soft. The rotating motion leads to the mixing of the material in the 2 plates/sheets and a joint is formed in ‘solid state’ [10].
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Figure 9: Schematic figure of Friction Stir Welding [10]
The intense plastic deformation encountered in the FSW process leads to the development of texture within the stirred zone, recrystallization and formation of fine and equiaxed grains [11]. The fine grains and refined microstructure improve the mechanical properties of the weld.
2.1. Friction Stir Back Extrusion
Some early work on the feasibility and grain structure in Friction Stir (Back) Extrusion was done by Abu-Farah[12]. A rotating stirring tool was plunged in a cylindrical billet at a certain axial and rotational speed. This pushed the material from the Billet against the axial motion of the rotating tool and formed a tube as shown in the figure below. The material used was AA6063-T52 aluminium alloy, and H13 tool steel was used for the plunger. The preliminary results showed a stir zone and grain size refinement was observed in the microstructure of the starting material. Following this preliminary study, several researchers have studies different configurations of the FSE process and varied various
17 process parameters like the heating/cooling, rotations rate, die design etc. The modelling of this process has been discussed in detail in a later chapter.
Figure 10: Schematic of Friction Stir Back Extrusion
Friction stir back extrusion has been used extensively as a solid state recycling process to convert metal chips into wires by eliminating the conventional melting process. Hosseini et al. studied the process parameters, which affect the quality of wires produced by the FSE process. It was observed that either too high or too low rotation speeds could cause hot or cold cracks respectively. There is an optimum range for the rotational speed for the production of wires without cracks (around 400 rpm).Also, an increase in the defects, such as inclusions, was observed upon the increase the axial speed of the die [13]. The process and results obtained are shown below 18
Figure 11: FSBE process and results from Hosseini et al[13]
Buffa et al. also produced rods from FSBE process using AZ31 magnesium alloy. They studied the effects of extrusion ratio and variable rotation on the quality of the rod. Similar to the results obtained by Hosseini et al., defects and fractures were observed for too low or too high speeds. They also found that the best recycled rod had a tensile strength of upto
80% of the parent material. Sharifzadeh et al. varied the process parameters for FSBE using
Magnesium chips and studied the tribological behavior and the corrosion resistance of the produced wires. They observed a fine homogenous microstructure and wires of good quality. The friction coefficient of the wire was lower than the base material and the wear resistance was enhanced. They further conclude that the fine grain structure is a potential reason for the improved corrosion resistance in the wires[14].
Baffari et al. also varied process parameters and concluded that a complicated interplay between parameters governs the quality of the outgoing rod (AZ31). Additionally, they
19 tried to understand the process mechanics by using a copper marker to understand the path of a material point. They observed that helical material flow occurs as shown in the figure below [15].
Figure 12: Top and Isometric view of the final positions of tracking points for
different speeds (increasing from a to c) [15].
Baffari et al. also explored the production of a Al-SiC metal matrix composite using FSBE process for aluminum chips and SiC powder [16]. In yet another publication, they discuss the major issues and difficulties encountered in the FSBE process. They stress the need of a continuous process to make FSE a commercially viable process and increase its impact
[17].
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2.2. Friction Stir Consolidation and Processing
Friction Stir Consolidation (FSC) is a manufacturing process, which could be used to consolidate metal hips, powder, scrap etc. into a solid block for further processing. Early experiments by Tang et al. showed the feasibility of the FSC process where finely divided powder or metals wastes were consolidated in one step using simple equipment. Li et al. manufactured solids discs from AA 6061 aluminum alloy chips by FSC. They conducted
Design of Experiments to quantify the effect of process parameters like rotation speed, force and the processing time. They observed a bowl like recrystallized zone in the disc where, the chips had completely consolidated [18].
Figure 13: FSC: Process and microstructure[18]
They observed a significant reduction in the voids after the compaction and consolidation of chips and a relative density close to one. There is dead metal zone as observed in the metal extrusion process where the consolidation/recrystallization does not occur. The
21 fraction of the consolidated material can be increases by processing for longer times. The fully consolidated region never reaches the maximum radial zone even after a long processing time.
2.3. Friction Stir Forward Extrusion
Although many products have been manufactured using indirect friction stir extrusion, it has some disadvantages. In addition to the high extrusion ratio required, the length of the plunger limits the length of the product extruded in indirect extrusion. Compared to FSBE, very few researchers have explored the Direct Friction Stir Extrusion/Friction Stir Forward
Extrusion. Whalen et al. have used FSFE to manufacture magnesium tubes used in automobile parts [19]. They used the ZK60 magnesium alloy hollow billet with a chilled mandrel and an extrusion die with scrolls to increase friction. It is called as Shear Assisted
Processing and Extrusion (ShAPE). In the SHAPE process, the container and mandrel are one single part, and billet ids inserted in the part. The billet is rotated with the container/mandrel and pushed against the extrusion die to form a thin ZK60 tube.
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Figure 14: ShAPE process[19]
They embedded thermocouples in the die to measure the temperature reached during the process. Due to the heating of the material and hence softening, the force requires is 10 times lesser than conventional magnesium extrusion with same dimensions [19]. However, the plunger speed is very low compared to conventional extrusion process and hence is not entirely ready to be commercialized. This process is used to show the Finite element modelling nuances and optimization in this thesis.
2.4. Summary
To summarize the experimental efforts, the feasibility of FSE has been proven by many researchers by manufacturing rods, wires, cylinders etc. primarily using Aluminium and
Magnesium alloys. These processes have shown that Friction Stir could be used for grain refinement and consolidation in extrusion, consolidation etc. However, each process has a different range of optimum parameters to manufacture a sound product. The understanding 23 of basic parameters like temperature, grain size and stress/strain, which is currently lacking, can be developed by modelling the experiments correctly. Hence, we develop a FE model as a part of this research. The next section describes all the important physical laws following which we discuss the previous modelling efforts and discuss the new model.
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Chapter 3: Mechanics and Finite Element Method
3.1. Introduction
The Finite Element Analysis in this thesis uses Forge NxT – a software for simulation of hot and cold forming processes, by TRANSVALOR. The initial setup is done on the pre-processor, which is followed by thermomechanical calculations using the solver. All the laws/ data used in this section are taken from the Forge Manual published by
TRANSVALOR with the software [20]. Two important laws/assumptions used by Forge
NxT are –
Norton-Hoff law is for viscoplastic behavior to simulate plastic deformation in hot
forging.
Elastoplastic and elastoviscoplastic behavior to simulate elastic and plastic
deformation in warm and cold forging.
The Finite element formulation uses mechanical and thermal equilibrium equations. The geometry is discretized using triangular elements in 2D (3 nodes), while tetrahedral elements are used in 3D (4 nodes). Parallel computation can also be used with the 3D solver so that it can partition the computation over several processors by allocating different portions of the mesh. This decreases the computation time significantly allowing the user to use fine mesh near important regions to improve the precision.
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3.2. Material behavior
The stress tensor is found as a function of the strain undergone by the material. The most common laws have been discussed below –
Linear elastic – Stress tensor depends on small deformations(strain tensor)
𝜎 = 푆(휖)
Viscoplastic – Stress tensor is dependent on strain rate, strain and other internal parameters. For example – 𝜎 = 푆(휖̇, 휖,̅ . . )
Elastoplastic or elastic-viscoplastic – Derivative of stress is a function of the strain rate tensor 푑𝜎 = Σ(휖̇, 휖,̅ 𝜎. . ) 푑푡
3.3. Contact and Friction a) Contact
Unilateral contact is used in this research. The contact at an interface is called unilateral contact when the node can attach (compressive interface) or detach (tensile interface) itself from the surface of the die. It has two conditions, compression stress condition and non- penetration condition for attachment
𝜎푛 ≤ 0
(푣 − 푣푑푖푒). 푛 = ∆푣. 푛 ≤ 0
26
The ∆푣 represents the relative sliding velocity vector, 푛 is the normal vector and 𝜎푛 denotes the normal stress at the interface.
There are two special contact conditions available with software – Bilateral Sticking and
Bilateral Sliding. For the bilateral condition, the nodes in contact with the billet cannot detach from the surface of the die. Therefore, bilateral sliding means the nodes can move along the surface of the die, while bilateral sticking implies the nodes are fixed to die’s surface.
A ‘no contact law’ condition if we do not want two solid to interact with each other. The two parts with such a condition do not interact with each other. For example, in the extrusion process the plunger could be a little longer than the diameter of the container, which ensures that the material does not flow in the gap between them. b) Friction
The contact at the interface and the relative motion also causes a shear stress/friction 휏
(tangential to the interface). The value of this friction is generally define by the following law –
휏 = −휇(Δ푣, 𝜎푛)Δ푣
Where 휇 is an arbitrary function of the sliding velocity, normal stress etc.
There are three friction models available with the software –
1) Coulomb friction – Coulomb’s law define the shear stress due to friction as a function
of the co-efficient of friction and the normal pressure/ pressure at the interface.
휏 = 휇𝜎푛
27
Where 휇 is the co-efficient of friction and 𝜎푛 is the normal stress.
2) Tresca Friction – During metal forming processes, the normal stress can reach high
values. These values could be multiple times the yield strength of the metal. Hence,
Coulomb friction may not be valid, as the shear stress due to friction cannot exceed the
shear strength of the material. The friction according to Tresca’s law is a function of
the coefficient of friction and the equivalent stress
푚̅𝜎̅ 휏 = √3
Where, 푚̅ is the friction coefficient and 𝜎̅ is the equivalent stress/flow stress of the material
A combine law is often used as the best approximation as shown below –
Figure 15: Coulomb’s law limited to tresca
28
3.4. Heat Transfer
The general heat transfer for a material is represented by the following equation subject to boundary conditions –
훿푇 𝜌푐 = 푑푖푣(푘𝑔푟푎푑(푇)) + 푊̇ 훿푡
In the above equation, 𝜌 is the density, 푐 is the specific heat capacity and 푘h is the thermal conductivity. The plastic strain that dissipates in the form of heat is represented by 푊̇ which for a material obeying the Norton Hoff law would be as follows –
푊̇ = 휂퐾√3휖̇̅푚+1
Where, 휂 is the strain efficiency and is characteristic to a material. It defines the part of the power dissipated by crystal sliding and actually transforming to heat.
Interactive Heat Transfer
Various laws govern the heat exchange between the die and the billet for the thermomechanical computation. Conduction, convection, radiation, transfer due to friction are the important modes of hear transfer/generation.
Radiation – Radiation causes heat transfer at the boundaries of the material. The heat flux due to radiation is given as –
4 4 휙푟 = 𝜎푠휖(푇 − 푇0 ) where, 휖 is the emissivity of the material in a specific environment, 𝜎푠 is the Stefan’s constant, 푇0 is the temperature of the external environment and 푇 is the temperature of the region’s boundary.
29
Conduction and Convection – Both these modes are involved at the boundary in the form of the following flux –
휙푐 = ℎ(푇 − 푇표) where, ℎ is the coefficient of transfer,푇 is the temperature of the region’s boundary and 푇표 is the temperature of the external environment.
Friction –The power dissipated due to friction is shared by the two bodies in contact with each other and can act as a flux for each body. The effusivities of the respective bodies determine the heat flux for every body.
푏1 휙푓푟 = 휏푓푟푉푔 푏1 + 푏2
Where, 푉푔 is the sliding velocity and 휏푓푟 is the shear friction. The effusivities are computed by the following equation –
푏 = √푘𝜌푐
The diagram below shows the overall heat transfer phenomenon for a body
Figure 16: Heat transfer [20] 30
Chapter 4: Friction Stir Extrusion Modeling
4.1. Previous Modeling efforts
The simulation of Friction Stir Welding (FSW) follows various approaches. Baffari et al have summarized the various methods used in FSW simulation [21]. The following strategies have been used to model FSW – Eulerian Solid Mechanics[22], Lagrangian solid mechanics [23], ALE [24] and CFD [25] . Inspiration can be drawn from all the above approaches to simulate the FSE process. Surprisingly, limited literature is available regarding the modeling of the FSE process. Ansari et al. conducted process optimization studies using the Taguchi method on backward FSE using magnesium alloy chips[26].
They determined that the rotation of the die is the most important factor for the soundness of a joint. A proper combination of process parameters gives a product (wire) with higher strength and better material properties.
Figure 17: Contribution of process parameters toward grain size[26] 31
Behnagh et al. studied the metallurgy of magnesium by conducting a 2D analysis for the process – Backward FSE of magnesium chips [27]. They modeled the material grain size evolution using the dynamic recrystallization (DRX) kinetics. However, they did not include the effect of the severe plastic deformation in the calculation.
Figure 18: Microstructure simulation: a) Volume Fraction; b)grain size and c)
micro-hardness [27]
A CFD model was used to visualize the material flow in the process by Zhang et al
[22]. Baffari et al. created a 3D FEM model to calculate the Zener-Holloman parameter and hence predict the grain size. They used DEFORM to model the backward FSE process with a rotation rate of 900 rpm for magnesium alloys [21]. Although all these efforts have given correct results in specific areas, no single model solves all the major problems together. Some areas of concerns are as follows –
32
Large computation times for 3D simulations. In addition, a 2D axisymmetric
simulation cannot include the effect of rotation.
Conversion of rotation to heat flux is not entirely correct as it neglects the velocity
of the billet in the boundary layer, which is in contact with the die.
The effect of temperature changes on grain size of the outgoing material have not
been captured.
The effect of process parameters and constants like friction, rotation speed, plunger
speed etc. on the material properties, force, torque etc. is not studied
comprehensively.
We have attempted to touch upon all the above issues and come up with a simplified modeling approach to simulate the FSE process faster and extract all the necessary information required to design the process effectively. For the purpose of this research, a forward FSE process conducted by the Pacific Northwest National Laboratory has been used as a benchmark. We first identify a Finite Element model, which matches the results from the experiments, and then conduct numerical studies using Al 6061 to tackle all the above problems.
4.2. Shear Assisted Processing and Extrusion (ShAPE)
Section 2.3 briefly describes the ShAPE process. This research highlights the need of a forward FSE process to manufacture parts with long lengths and uniform grain size. There is significant grain growth along the walls of wires/tubes manufactured using FSBE process. The length of the plunger limits the length of the wires/tubes. Hence, Whalen et
33 al. developed a forward FSE process and successfully improved the material properties of the outgoing product. The figures below shows the concept and components used.
Figure 19: ShAPE process[19]
Figure 20: Components of the ShAPE process 34
As shown in Fig 19, the billet is rotated and pushed against the extrusion die, which has spiral scrolls to guide the material and increase the area/coefficient of friction. The process successfully extruded a 30 cm tube (length) without any structural defects. The ram speed was 3.81mm/min while the rotation speed was 250 rpm. The table below describes the dimensions, materials etc. for all the components
Table 3: Components in the ShAPE process
Component Material Dimensions
Billet ZK60A-T5 OD = 88.8mm, ID = 47.9mm, Length = 113mm
Container/Mandrel ANSI 8620 steel mandrel OD= 47.8mm, Container ID= 88.9mm
Extrusion Die H13 tool steel ID= 50.8mm
The force, torque and temperature for the process are shown in the figure below
Figure 21: Force, torque, temperature for ShAPE. 35
The research describes the experiments and the results, which show significant grain refinement along with increase in elongation. However, the UTS decreases by 15% because of texture development. The authors suggest that texture development is dominant over strengthening due to grain refinement. A grain size of about 3.8휇푚 is observed for the tube. Further optimization of the process and heat treatment could lead to better mechanical properties. It is expensive to conduct experiments, identify the optimal values, and predict the grain size. Given the complex nature of the process, developing a Finite
Element model is essential to virtually experiment with different process parameters. The next section describes the development of a FEA model.
4.3. Finite Element Modelling
All the above components except the billet are modeled as rigid bodies to reduce the computation time. Since they are rigid bodies, only the boundary conditions at the interface with the billet have to be specified. A surface mesh is used to model the components. A specific temperature and heat transfer co-efficient is assigned to all the components after considering the experimental results and the values used in literature. Tresca’s law has been used to compute the friction, as high forces are encountered at interfaces in forming processes and the friction cannot exceed the flow stress of the material. Generally, the heat transfer coefficient is a function of temperature and pressure at the interface, but can be assumed to be constant according to the approximate values below-
36
Table 4: Heat transfer coefficient values for metal-metal contact[20]
Contact With Pressure Without Pressure
(푾풎−ퟐ푲−ퟏ) (푾풎−ퟐ푲−ퟏ)
Perfect contact 10000 -
Part Die contact 4000 1000
Contact with oxide coating 500 200
The magnesium alloy used in the ShAPE process is ZK60. Upon extensive literature review, we did not find a constitutive law, which predicted the material’s behavior precisely. A constitutive law determines how the material behaves under different conditions, like temperature, strain, strain rate etc. and is important in FE calculations.
Forge Nxt offers a functionality to enter the ‘point-to-point’ data for a material, which does not behave/adapt any standard law (Hansel Spittel, Norton Hoff etc.). Yun-Bin et al. have modeled the behavior of ZK60 and predicted a constitutive law, which cannot be accommodated in Forge. Hence, the point-to-point data from their research was used to model the behavior of the material. The figure below show the stress-strain behavior –
37
Figure 22: ZK 60 True stress, strain for strain rates(푠−1):a)0.001 b)0.01 c) 0.1 d)1
38
Figure 23: Finite element model of the ShAPE process
39
The figures above show the meshing and geometry of the FE model. The dimensions are assigned such that the dies intersect and there are no gaps, to ensure the material does not flow between them. Since the dies are assumed to be rigid bodies with only surface properties, the intersection between them does not cause a computational problem. The friction and the heat transfer co-efficient for the parts given below is with respect to the billet.
a) Plunger
Nodes Elements Temperature(Celsius) h(푾풎−ퟐ푲−ퟏ) Friction
768 1532 20 20000 1
The plunger (and billet) should ideally move down with a velocity of 0.0653 cm/sec, rotating with a speed of 200 rpm. However, instead of rotating the plunger and billet together, the extrusion die is rotated and moves upwards. We hypothesize that both the configurations represent the same physical behavior. This has been showed to be true in the following sections. Hence, the plunger does not have any velocity and hold the billet at the interface. The temperature of the plunger is close to room temperature as we assume the effect of the heat due to rotation is not realized at the plunger. b) Container
Nodes Elements Temperature(Celsius) h(푾풎−ퟐ푲−ퟏ) Friction
3872 7740 150 10000 0
40
The container is rigid body without any movement and ensures the billet deforms only in the direction of extrusion. The surface of the container is assumed to be frictionless as it minimal effect on the billet, force and torque. The heat transfer coefficient is 10000
푊푚−2퐾−1 as discussed in the beginning of this section. c) Extrusion Die
Nodes Elements Temperature(Celsius) h(푾풎−ퟐ푲−ퟏ) Friction
4281 8562 500 20000 0.35
The extrusion die rotates with an angular velocity of 200 rpm and moves towards the billet with a velocity of 0.0653 cm/sec. Meshing the die correctly is critical for the simulation to converge. The area where the maximum deformation happens has smaller elements to avoid convergence issues. The die also has a fillet and a slight taper i.e. the height decreases from the circumference to the center to guide the material and tackle convergence issues.
The heat transfer coefficient with the die is the highest as the billet shares a high pressure interface and we account for the area of scrolls in the original design by increasing the h. d) Mandrel
Nodes Elements Temperature(Celsius) h(푾풎−ퟐ푲−ퟏ) Friction
3387 6770 300 10000 0
The mandrel does not have any motion and ensures the outgoing pipe is hollow. The heat transfer coefficient, like the container, is the typical value for metal-metal contact. The surface of the container is assumed to be frictionless as it minimal effect on the billet, force
41 and torque. The temperature of the mandrel, which is not measured experimentally. was chosen after conducting multiple simulations and identifying the one which gives the correct output (force, torque) as per the experiments. e) Billet
Nodes Elements Temperature(Celsius) h(푾풎−ퟐ푲−ퟏ) Friction
5859 24070 20 - -
The meshing for the billet is perhaps the most critical factor in determining the convergence of the solution. The size of the elements is small in the area close to the extrusion die, as there is frequent change in the physical configuration due to the high value of rotation. The size of elements is smallest in the area near the mandrel and the die, as that region encounters the maximum deformation. Constant re-meshing is required in the high deformation area to ensure convergence due to high variation in physical properties. We start with the room temperature as described in the FSE process and the billet heats up with time.
4.4. Initial FEM results
The force and torque observed in the FE simulation have been shown in the figures below
42
Force 12
10
8
6
4 Force (Tonnes) Force
2
0 0 5 10 15 20 Time (Sec)
Figure 24: Force from the Finite Element Simulation (ShAPE)
Torque (Nm) 1000 900 800 700 600 500
400 Torque 300 200 100 0 -100 0 5 10 15 20 Time(sec)
Figure 25: Torque from the Finite Element Simulation (ShAPE)
As observed in the figures above, the approximate steady state values of Force and Torque are 40 kN and 600 Nm respectively. The experimental values from Fig 21 are close to these values, which is a validation of our model and the values of the physical parameters used.
43
However, a major discontinuity is observed in the data at around the 10th second in the above figures. Upon conducting subsequent simulations with different parameters, it was concluded that the point-to-point extrapolation was not smooth, to accurately predict the
FE results, even though the steady state values are close. Hence, it was decided to conduct further research with the same model using an Aluminum alloy – Al 6061 that has a defined constitutive law in Forge NxT. The Hansel Spittel constitutive law and constants for AL
6061 are as follows –
Where, A=352.387, m1= -0.00454, m2=0.06604, m3=0.13165, m4=0.00241
Additionally, we can also investigate the grain size and the bonding in the material because of the previous research on Al 6061.
The same calculations were done using Al 6061 and the results are shown below. These results act as a benchmark for all the further analysis regarding optimization of the computation, grain size calculation etc.
Force Torque 100 90 1400 80 1200 70 1000 60 50 800 40 600
30 Torque Torque (Nm) Force (Tonne) Force 400 20 10 200 0 0 0 50 100 0 20 40 60 80 100 Time(sec) Time(sec)
Figure 26: Force and Torque for Al 6061 – ShAPE 44
As observed in the graphs above, the force required for the extrusion is significantly higher for Aluminum compared to the ZK 60 alloy. The next section discusses all the other results in detail, research towards decreasing the computational time, physical properties, grain sizes etc. Before analyzing the FE results in detail, the challenges encountered in developing this model have been given below –
Mesh – Several schemes for meshing were tried out to identify remeshing periods,
criterion and the effect of mesh size on the outputs – Force and Torque. The mesh needs
to be particularly small in the extrudate to capture the variation across the thickness of
the tube. A minor change in the meshing can cause difference in the outgoing product
and the output as shown below –
Figure 27: Difference in mesh sizes causing noise
45
Also, if we were to change the nature of meshing in the dies from surface (rigid) to volume, it would drastically increase the computation time, due to the excess time required to calculate the physical properties of the dies. This was not tried for the ShAPE process due to time constraints.
Rotation rate – The high rotation rate implies constant change in the position of billet.
This increases the chances of re-meshing because of constant deformation thus
increasing the time of computation. This challenge is one of the major motivations to
decrease the computation time.
Process Parameters and Others- Most of the process parameters in this model do not
affect the computation time. However, if we were to change the properties such as
friction at the frictionless interfaces in the current model, that would increase the
computation time.
46
Chapter 5: Finite Element Analysis
The original experiment was conducted by rotating the billet and pushing it against the die, while in the previous simulations, the die rotates and is pushed into the billet. Upon the finite element analysis of both these configurations, same results (forces and torques) are obtained. However, the simulation time differs significantly – rotating the die and pushing it is computationally less expensive than rotating the billet. This can be attributed to the constant change in positions of the elements in the billet for the latter configuration, which changes the stiffness matrix in the FE solver continuously, making it difficult to solve. Specifically, the simulation with the rotating die is approximately 20 % – 30 % faster. Rotating the billet at 200 rpm took 5.5 days (132 hours) to compute while rotating the die takes around 4.4 days (106 hours) to compute.
As mentioned in Section 4.1, previous efforts in modelling FSE have considered the effect of rotation in terms of a heat flux. However, this may not be entirely correct as the physical properties of the material close to the die change because of the rotation. We observed a ‘boundary layer’ in the FE simulations where the metal has a certain velocity, synonymous to fluids but with the opposite behavior. The figures below show the velocity vector plots for the simulation, deformation of a planar section and point tracking figures.
A boundary layer wherein the metal has a lateral velocity can be seen in Fig 28. Fig 27 also
47 shows the velocity of the material in a thin layer before the extrusion supporting the claim of a boundary layer with a finite velocity.
Figure 28: Velocity Vector plots for FSE at 200 rpm.
Figure 29: Movement of a marking grid and ‘boundary layer’
48
5.1. Exploring reduction in Computation time
As mentioned before, researchers have approximately predicted the force, material properties assuming the effect of rotation as heat. We hypothesize that a similar reduction in modelling is possible where we can break the effect of rotation in two components – heat and shear due to the following reasons -
The force due to friction is limited and cannot exceed flow stress of the material.
Therefore, once the maximum value is attained, the force due to friction cannot
cause the billet to rotate faster
We observed the existence of a ‘boundary layer’ too, which implied the effect of
rotation.
Simulations with varying rotation rates were carried out to understand the effect of rotation on the billet. The change in the rotation is compensated by the increase in heat transfer to the billet from the extrusion die. This is primarily done by increasing the static temperature of the extrusion die. To compensate for the decreased rotation, we consider the decrease in energy transferred by friction and use a fraction of that energy as per the effusivities of aluminium and steel (die) as an input in the billet. This ensures that the temperature distribution across the billet is the same across all simulations. The increase in temperature for the die is calculated as follows –
Heat into the billet must be constant.
Heat = Conventional modes + Heat due to friction
As we decrease the rpm, we need to compensate for the decrease in heat due to deformation.
49
Let T0 and r0 be the initial temperature and rpm of the die.
Let Tiand ribe the new variables. ri is known.
Ho = Hi
h A (Tbillet − To) + qo = h A (Tbillet − Ti) + qi
h A (Ti − To) = qi − qo
b1 Heat flux into billet generated due to friction is represented by ϕfr = τfrVg b1 + b2 b1, b2 are effusivities of the billet and die repectively and are fixed for all variations .
Hence, let ϕfr = CτfrVg, where C is a constant and τfr is the shear force
∴ h A (Ti − To) = qi − qo = ΣCτfrVo − ΣCτfrVi = C(Torqueoωo − Torqueiωo)
In the above equation, except 푇푖 all the other factors are known, hence we can find the new temperature of the die.
* We choose to ignore the energy due to deformation as it is a very small fraction compared to the other forms of energy (shown by Zhang et al.) [28]
We first analyze the input parameters i.e. Force and torque, which can be predicted from the simulations and then move on to other properties. Simulations were conducted for
10, 30, 50,100 and 200 rpm to capture the variation as shown below. A few simulations crashed before completion, but reached steady state, which is sufficient for our analysis.
50
Force 100 90 10 rpm 80 70 30 rpm 60 50 rpm 50
Tonne 200 rpm 40 30 100 rpm 20 10 0 0 20 40 60 80 100 120 140 Time (sec)
Figure 30: Force for different rotation rates
Torque 1200
1000
800 10 rpm
600 30 rpm Nm 50 rpm 400 200 rpm
200 100 rpm
0 0 20 40 60 80 100 120 140 Time (sec)
Figure 31: Torque for different rotation rates
51
As observed in the figures above, the force predicted in simplified simulations is higher than the actual force while the torque is lower than the actual value. As we increase the rpm, the difference in the simplified values and actual values decreases, implying more precision. The table below summarizes the steady state values observed in the graphs above along with the computation times required for the simulations.
Table 5: Steady state force and torque values
RPM Temp- die(ºC) Force(Ton) % diff Torque(Nm) % diff Time (days) 10 rpm 640 62 44.19 880 20.00 0.40 30 rpm 625 58 34.88 910 17.27 0.80 50 rpm 610 55 27.91 950 13.64 1.20 100 rpm 585 50 16.28 1050 4.55 2.20 200 rpm 500 43 0.00 1100 0.00 >4
The computation time decreases rapidly as the rotation rate decreases. We can predict the values within 20% accuracy at lesser than half the maximum computation time.
The precision in the prediction of torque is more than that of the force. We try to understand the physical effect of simplifying the computation in the next section. Various properties like the strain, strain rate, grain size, temperature etc. and their effects are studied in the next section. Figures below describe the temperature distribution, strain, stresses etc. encountered in the process. We can note the high temperature close to the die (Fig 31), the high strain/strain rate near the deformation area (Fig 32), equivalent stress and the velocity distribution (Fig 33). The extruded tube has a rotational velocity while the billet does not rotate, which implies the effect of the shear during deformation.
52
Figure 32: Temperature distribution for ShAPE (Aluminium)
Figure 33: Effective Strain and Strain rate for ShAPE (Aluminium)
Figure 34: Rotation velocity and Equivalent stress for ShAPE (Aluminium)
53
5.2. Material grain size and other results
As described in the Introduction, Aluminum follows the CDRX mechanism for recrystallization owing to its high stacking fault energy. Gerlich et al. used Zener-
Holloman parameter to predict the microstructure in friction spot welds for Al 5074 and Al
6061 alloys [29]. The Zener Holloman parameter is defined as follows –
푄 푍 = 휖̇ exp ( ) 푅푇
They have summarized that the Zener-Holloman parameter and the subgrain diameter are related by the following equation –
푑−1 = 푎 + 푏 푙표𝑔(푍)
However, this relationship is valid for Al 5XXX alloys like Al 5754 and Al 5083.
Researchers have validated this equation against experimental results. For Al 6XXX alloys, the initial subgrain diameter influence the above relationship between Z and the subgrain diameter. Hence, they rewrite the equation as –
푑 log ( ) = 푎2 + 푏2log (푍) 퐷0
Where, 퐷0 is the initial subgrain diameter. Gerlich et al. referred to older experiments comparing the relationship between the grain size and Z and came up with the values of
푎2 = 1.75, 푏2 = −0.244 and Q= 156 푘푗/푚표푙 . The figure below shows the comparision of the equation with previous experiments for Al 6060 and 6061 alloys.
54
Figure 35: Relationship between deformed/initial grain size and Z for Al
6060/6061[29]
Wan et. al have used the same relationship with point tracking method to predict the grain growth in Friction Stir Welding for AA 6082[30]. They used the strain, strain rate and temperature histories for various points in the FEA model for their calculations.
Considering the above research studies, we use a similar relationship to calculate grain sizes for our study using point tracking.
Figure 36: Point tracking in Extrusion 55
As shown in the figure above, random points were selected on/in various parts of the tube and the histories of properties for these points was extracted. The figures below show the histories of Temperature and Effective Strain for five different point/sensors.
Temperature (C)
600
500
400
300
200
100
0 0 20 40 60 80 100 Time Temp1 Temp2 Temp3 Temp4 Temp5
Figure 37: Temperature history
Effective Strain 40 35 30 25 20 15 10 5 0 0 20 40 60 80 100 Time
Strain1 Strain2 Strain3 Strain4 Strain5
Figure 38: Effective Strain history
56
The effective strain history is used to calculate the average strain rate for each sensor and the corresponding highest temperature is used to calculate the grain size as per the equation above. The table below shows the grain sizes for each of these points assuming as initial grain diameter of 200 휇푚. We get an average value of 3.15 휇푚.
Table 6: Grain size for 200 rpm
Sensor Strain rate Temperature Grain Size(휇푚)
1 0.43 480 3.24
2 0.2 480 3.90
3 0.33 465 3.04
4 0.23 455 3.05
5 0.43 450 2.52
It is interesting to note the effect of temperature and strain rate on the grain size. Comparing sensor 1 and 2, at the same temperature and half the strain rate, the grain size only increases by 20%. On the other hand, if we compare sensors 1 and 5 with the same strain rate, an increase in temperature of 30℃ causes the grain size to increase by 30 %. Hence, the relative effect of temperature on the grain size is more significant than the strain rate.
Similar to the calculation of force and torque, we also calculate the variation of grain size with simplified modelling. The table below includes the average grain size from all sensors for different rpms.
57
Table 7: Grain Size for different rotation rates
RPM 10 30 50 100 200
Grain Size 4.79 4.49 4.12 3.5 3.15
Grain Size 6.00
5.00 m) - 4.00
3.00
2.00 Grain Grain Size(micro 1.00
0.00 0 50 100 150 200 250 Rotation rate (rpm)
Figure 39: Grain Size vs rpm
As observed in the figure above the precision of the calculation increases significantly as the rotation rate increases. The following conclusions can be drawn from the FEA results
It is possible to reduce the computation time by more than 50% using simplified
modelling and get results within 20% accuracy.
Temperature is the most significant factor in determining the grain size of the
material.
58
Chapter 6: Effect of process parameters
In this chapter, we discuss the effect of various process parameters in the Friction Stir
Extrusion process. This understanding will enable the understanding of how each parameter changes material properties, machine requirements etc. As reduced models give approximates results in lesser time, we study the effect of process parameters at a rotation speed of 50 rpm. We expect a FSE process at higher rpms to follow the same trends, as in case of a reduced model.
6.1. Plunger Speed
The plunging speed affects the material properties as well as the other process parameters.
The effect on increasing/decreasing the plunging speed on force/ torque is shown in the figures below
Force- Plunger speed(mm/s) 100 90 80 70 60 50 40 30 20 10 0 0 20 40 60 80 100 120 0.06 0.13 0.22
Figure 40: Variation of force with plunging speed 59
Torque- Plunger speed 1200
1000
800
600
400
200
0 0 20 40 60 80 100 120 0.06 0.13 0.22
Figure 41: Variation of Torque with plunging speed
As observed in the above figures the force and torque both increase upon increase in plunging speed. Increasing the plunging speed implies lesser heating of the material undergoing extrusion. This leads to a lower overall temperature due to frictional heating and hence the flow stress is higher causing the force and torque to increase. We can observe a maximum value of the force in the Fig 39 for the fastest plunging speed before the steady state. This is typically observed in FSE processes due to the initial time in heating up the billet to an optimal temperature. For the ShAPE process, the extrusion speed is lower than most commercial standards. The grain size is also affected by the plunging speed by two main effects -
Reduction in effective strain as the time encountered under shear stress (from the
die) decreases.
Reduction in temperature as described above.
Both the effects work against each other and the following results are obtained
60
Table 8: Variation of Grain size with plunging speed
Speed(cm/s) 0.065 0.13 0.22
Grain Size(휇푚) 4.13 3.83 3.53
Hence, the effect of reduction in temperature dominates the change in grain size.
6.2. Friction
The effect of changing the friction between the extrusion die and billet has been studied in this section. Increase in friction implies increase in heat generation (temperature) and shear force on the billet. The figures below the show the effect on Force and Torque
Force (Tonne) 80 70 60 50 40 30 20 10 0 0 20 40 60 80 100 120 Time 0.2 0.3 0.4
Figure 42: Variation of Force with friction
The force decreases upon increase in friction, possibly due to the increased temperature of the billet.
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Torque(Nm) 1600 1400 1200 1000 800 600 400 200 0 0 20 40 60 80 100 120 Time 0.2 0.3 0.4
Figure 43: Variation of torque with friction
Torque is observed to be directly proportional to the friction coefficient for the above simulations. However, this might not be true always as the flow stress could drop further as the temperature increases, which would affect the torque directly. The effect on grain size is described below
Table 9: Variation of grain size with friction
Friction 0.2 0.3 0.4
Grain Size(휇푚) 3.82 4.12 4.05
As observed above, there is no conclusive trend upon changing the friction coefficient. It is suggested to simulate the process for different friction conditions/friction to find the optimal value according to the constraints of the machine and required material properties.
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6.3. Extrusion Ratio
This section describes the change in process parameters and material properties with change in the extrusion ratio. The extrusion ratio was changed by changing the dimensions of the extrusion die. The figures below describe the force and torque
Force(Tonne) 100 90 80 70 60 50 40 30 20 10 0 0 20 40 60 80 100 120 140 Time 12 19 24
Figure 44: Variation of force with extrusion ratio
Torque(Nm) 1200
1000
800
600
400
200
0 0 20 40 60 80 100 120 140 Time 12 19 24
Figure 45: Variation of Torque with extrusion ratio 63
As observed in the figures above, the force and torque increase upon increase in extrusion ratio. Theoretically, the extrusion force is directly proportional to the natural logarithm of the extrusion ratio. This is validated by the results above. Extrusion ratio is known to have an effect on the grain size due to the change in strain imparted. The grain size is included below
Ratio 12 19 24
Thickness of tube 2.32 mm 1.45 mm 1.15 mm
Grain Size(휇푚) 3.7 3.9 3.6
Strain Rate (Avg) 0.15 0.16 0.2
Temperature(Avg) 463 470 471
The grain size was expected to decrease with increase in extrusion ratio due to the higher strain/strain rate. However, the results from the simulation do not conform to the hypothesis. Although the strain rate follows a predictable trend, the variation in temperature is puzzling. Hence, it is recommended to carry out thorough simulations before designing the machine for different extrusion ratios.
6.4. Summary
Summarizing the relative effect of the above parameters on force, torque and grain size, the following can be concluded (the numbers show the average difference in the result caused by varying the parameters according to the values in the sections above)
Force: Plunging Speed (20%) > Extrusion ratio (10%) > Friction (< 5%)
Torque: Friction (50%) > Plunging Speed (25%) > Extrusion Ratio (< 5%)
Grain Size: Plunging Speed > Friction > Extrusion Ratio (No conclusive numbers)
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Chapter 7: WQI – Welding Quality Index
The machine used for ShAPE could have potential applications in recycling of Aluminum chips. In this section, we explore how design changes could affect the quality/bonding in the outgoing material. Aluminium chips are normally covered with a layer of oxides, which hinder the direct bonding of chips. These oxide layers need to be broken for welding between two chips. Mohamed et al. found that the oxide layers did not contribute to solid state pressure welding[31]. Breakage of oxide layers caused by plastic flow of the material is necessary for welding. Wan et al. have proposed two possible ways for the consolidation of chips[32]. Shear deformation leads to oxide breakage, which enables direct contact between pure metal surfaces resulting in interface bonding. This shear stress must exceed a critical value to ensure fracture.
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Figure 46: Consolidation of aluminium chips[32]
Wan et al. summarize the 3 main theoretical models used to understand the quality of bonding between chips a) Gronostajski et al. concluded that the quality of welding depends on the normal stresses
acting on fresh surfaces of the chips. A large tensile strain with the largest principal
compression stress is required to reach a critical value which determines joining of
chips[7] b) To predict the quality of boding in chips, Plata and Piwnik proposed a pressure-time
criterion. They used the criterion to predict the solid state welding in porthole extrusion. c) Guley et al. have proposed a criterion called the Boundary Quality Index (BQI). The
BQI is directly proportional to the mean stress and inversely proportional to the flow
stress.
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푑푖푒 푒푥푖푡 푃푖푗 퐵푄퐼 = Σ표푥푖푑푒 푏푟표푘푒푛 > 푐표푛푠푡푎푛푡 𝜎푖푗
The bonding begins after the BQI exceeds the constant value and ends when the chips flow out of the die. Mallarapu has written a new user law called ‘Chip Welding’ in Forge NxT to analyze this effect. It is directly based on the work of Guley et al and the following parameters are calculated
퐶표푥푖푑푒 = 휏푚푎푥/휏푐푟푖푡푖푐푎푙 푝 푊푄퐼 = Σ푑푖푒 푒푥푖푡 Δ푙 표푥푖푑푒 푏푟표푘푒푛 𝜎
Where, p is the pressure, 𝜎 is the flow stress and Δ퐿 is the length travelled by the material.
The oxide layer is assumed to be broken when 퐶표푥푖푑푒 exceeds 1. To understand how the
FSE process can aid in the solid state recycling, we computed the WQI for only extrusion and then FSE with different friction factors. The results are included below –
Figure 47: 퐶표푥푖푑푒 and WQI for extrusion
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Figure 48: 퐶표푥푖푑푒 and WQI for FSE at 50 rpm
As observed in Figures 46 and 47, the values of WQI is higher for FSE (36) when compared to conventional extrusion (31). This validates the hypothesis of better welding between chips in FSE. Computations showed that the welding quality increases with increase in the friction between the die and billet. However, this might not be beneficial for the grain size as the temperature might increase. Hence, this addition to the FE model will help in determining the optimum conditions for recycling using FSE.
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Chapter 8: Summary and Conclusion
The work presented in this thesis provides a comprehensive guide to model the Friction
Stir Extrusion process and tackles important issues like computation time, grain size prediction, feasibility in solid state recycling processes and effects of process parameters.
Significant work has been done to model the FSW process, but limited literature is available for the Friction Stir Extrusion process. Through this research, we have developed a FE model for the FSE process, which can be used iteratively to design the machine. Forge
NxT has been used for all computations because of its ability to simulate forming processes faster than typical FE packages. The following section includes the summary and major findings from the research –
8.1. Finite element modelling
Most of the previous studies rely on experiments to understand the FSE process. Several researchers have studied the Friction Stir Backward extrusion process and integrity of wires/tubes produced. All the experiments found out an optimum range for the production of sound products. While efforts have been made to develop 2D, CFD and other simplified models, there is lack of literature on full 3D FEM modelling of the process. This lack of comprehensive knowledge has inhibited fast research and process scalability [15]. Baffari et al. also recently (2017) noted the significant knowledge gap in the previous research for material flow analysis, defect prediction, metallurgical properties of the outgoing product
69 etc. We have attempted to fill this gap by developing a comprehensive FE model capable of solving all the above issues. As forward/direct extrusion commercially more viable process than backward extrusion, we selected the ShAPE process. The ShAPE process has not been modelled or optimized by PNNL. The important conclusions and challenges faced have been mentioned below -
The steady state values from the FE model for force, torque, temperature etc. were
validated against the experimental results from previous research for ZK 60.
A constitutive law for ZK60 could not be found. However, discrete data from
previous experiments was used in the FE model as point-to-point curves. Although
the results (force, torque) agreed with experiments, there were several
discontinuities, possibly due to the discrete material data.
Al 6061 is extensively used in automobiles and has similar applications as ZK60,
we developed a FEM model with the aluminium alloy. Owing to the well-defined
constitutive law, we obtained continuous results, which could be used in future
design and research with the ShAPE process.
8.2. Analysis on modelling, process parameters
Several researchers have cited long computation times as a major problem in simulating
FSE. On the other hand, many researchers have managed to approximately predict the results of the process using reduced modelling. They ignore the physical effect of ‘stir’ and assume the die as a heat source due to the friction between the die and the billet. Upon further analysis, we observed the existence of a boundary layer, where the rotation of the die cause the billet to rotate. Since, majority of the recrystallization would occur in this
70 area, it would not be fully correct to ignore the rotation. We explored the feasibility of reducing the rotation and compensating the reduction by heat. Although this does not exactly represent the system, it leads to a huge reduction in the computations with reasonable results. All the important values like Force, Torque, Grain size etc. can be computed with 20% accuracy with a reduction of up to 70% in computation time. Models for rpms of 10, 30, 50,100 and 200 have been computed for comparison. The variation in the torque is particularly low compared to other parameters. We conclude that this modelling approach is feasible on the design process as it gives approximate results in a fraction of the computation time. We also note that temperature is the most significant factor to affect the grain size.
Past research has only focused on varying one/two process parameters in a FSE machine like rotation rate, plunging speed, extrusion ratio etc. It is not feasible to modify the machine, die, billet to test all the effects. With this research, we present the effects of varying important process parameters
Plunger Speed – The plunger speed determines if the force/torque will exceed the
steady state value. A high plunging speed may cause the force/torque to have an initial
peak and would be an important factor in design. The grain size decreases upon increase
in plunging speed, primarily because of the lower temperature.
Friction – Friction between the die and billet can be varied by changing the material or
including scrolls in the die. The plunging force decreases upon increase in friction
while the torque increases. Although no conclusive trend was observed on the grain
size, it is observed that the grain size increases as 휇 is increased over 0.2.
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Extrusion Ratio – Extrusion ratio increases the force and torque required for FSE. The
grain size also increases upon increase in the extrusion ratio. Although. The strain rate
increases, increase in temperature causes the grain size to increase. Previous research
has already suggested that if the extrusion ratio is low, the grain size distribution along
the radial distance varies. However, for the ShAPE process the difference is miniscule.
Though all the above effects would hold in general, it is important to note that the results have been obtained for the ShAPE process by varying parameters around the original values. The above results are in agreement with previous experimental research by Ansari et al. for the FSBE process.[26]. Through these computations, we cannot analyze the presence of defects, cracks, voids etc., which influence the quality of the outgoing product.
Hence, experiments must be conducted for complete understanding.
8.3. WQI and Future research
The ShAPE machine could be used for solid state recycling of aluminium/magnesium chips in the future. To that end, we have implemented a new user law called ‘Chip Welding’ in Forge NxT, which can predict the quality of bonding in chips using a solid billet. We compare the effects of changing friction between the die and billet on the welding quality as an illustration. It is interesting to note that even though the welding is better upon increase in friction, it won’t necessarily produce excellent material properties because of the high heat generated. Thus, an additional processing step would be required to make to recycled product commercially viable.
The following problems could be explored in the future considering this work -
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The comprehensive FE model could be used to optimize the process and produce
products according to the required grain size, machining constraints etc.
Further experimentation with ZK 60 along with the FE predictions can lead to the
development of a grain size law for ZK60 as researchers have done for Aluminium.
A huge improvement is possible if temperature of the billet is controlled. Cryogenic
extrusion or extrusion with a cold billet can lead to excellent material properties
and the model can be used for predictions.
Solid State recycling of chips.
Electricity aided extrusion or ‘Spark Plasma Extrusion’ can be integrated in the
ShAPE machine for solid state recycling. This integration could lead to continuous
process capable of converting chips into a finished product
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