Forging Process Design for Risk Reduction Dissertation

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FORGING PROCESS DESIGN FOR RISK REDUCTION

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Yongning Mao, M.S. * * * * *

The Ohio State University 2009

Dissertation Committee: Approved by Professor Rajiv Shivpuri, Adviser Professor Jose M. Castro ______Professor Allen Yi Adviser Industrial and Systems Engineering Graduate Program

ABSTRACT

In this dissertation, forging process design has been investigated with the primary concern on risk reduction. Different forged components have been studied, especially those ones that could cause catastrophic loss if failure occurs. As an effective modeling methodology, finite element analysis is applied extensively in this work. Three examples, titanium compressor disk, superalloy turbine disk, and titanium hip prosthesis, have been discussed to demonstrate this approach.

Discrete defects such as hard alpha anomalies are known to cause disastrous failure if they are present in those stress critical components. In this research, hard-alpha inclusion movement during forging of titanium compressor disk is studied by finite element analysis. By combining the results from Finite Element Method (FEM), regression modeling and Monte Carlo simulation, it is shown that changing the forging path is able to mitigate the failure risk of the components during the service.

The second example goes with a turbine disk made of superalloy IN 718. The effect of forging on microstructure is the main consideration in this study. Microstructure defines

the as-forged disk properties. Considering specific forging conditions, preform has its own effect on the microstructure. Through a sensitivity study it is found that forging temperature and speed have significant influence on the microstructure. In order to choose the processing parameters to optimize the microstructure, the dependence of microstructure on die speed and temperature is thoroughly studied using design of numerical experiments. For various desired goals, optimal solutions are determined.

The narrow processing window of titanium alloy makes the isothermal forging a preferred way to produce forged parts without forging defects. However, the cost of isothermal forging (dies at the same temperature as the workpiece) limits its wide application. In this research, it has been demonstrated that with proper process design, the die temperature can be reduced greatly without violating process window constrictions. Moreover, the computation cost is also reduced by replacing the complex 3-dimensional (3D) shape with its corresponding 2-dimensional (2D) representative cross sections, and a well balanced load distribution has been achieved by proper design of die flashland.

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Dedicated to my family

ACKNOWLEDGMENTS

This dissertation could not have been written without Dr. Rajiv Shivpuri, who not only served as my advisor and provided me financial support, but also encouraged and challenged me throughout my academic program. It is Dr. Shivpuri who guided me to learn knowledge and the methodology to obtain it. The research experience working with

Dr. Shivpuri has helped me to become more professional and be prepared to make more contributions to the future.

I would like to express my sincere appreciation to members of my dissertation committee

Dr. Jose M. Castro and Dr. Allen Yi for their scientific inputs and advices. I would also like to thank members of my candidacy committee, Dr. Gary Kinzel, Dr. Henry Busby, and Dr. Theodore Allen for their valuable comments and suggestions.

Thank also goes to my group members, Dr. Francesco Gagliardi, Dr. Chun Liu, Dr.

Yuanjie Wu, Dr. Xiaomin Cheng, Dr. Meixing Ji, Dr. Wenfeng Zhang, Dr. Jiang Hua, Dr.

Satish Kini, Dr. Sailesh Babu, Dr. Zhiqiang Sheng, Yijun Zhu and Kuldeep Agarwal for their helpful discussions and friendship during my graduate program.

I wish to thank my parents for their unconditional love and endless support throughout my doctoral study. Finally, I would like to express my sincere gratitude to my wife Dr.

Ruomiao Wang for her continuous encouragement, love and never-ending patience.

VITA

May, 1978 Born – Shenyang, China

2000 B.S., Plasticity Engineering, Shanghai Jiao Tong University, Shanghai, China

2000 – 2003 M.S., Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China

2003 – 2009 Graduate Research Associate, Department of Industrial, Welding, and Systems Engineering, The Ohio State University

PUBLICATIONS

Rajiv Shivpuri, Xiaomin Cheng, Yongning Mao. Elasto-plastic pseudo-dynamic numerical model for the design of shot peening process parameters. Materials and Design, in press.

FIELDS OF STUDY

Major Field: Industrial and Systems Engineering

Minor Fields: Operations Research and Design Optimization

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TABLE OF CONTENTS

ABSTRACT...... ii ACKNOWLEDGMENTS ...... v VITA ...... vii LIST OF FIGURES ...... xii LIST OF TABLES ...... xvi CHAPTER 1 INTRODUCTION ...... 1 1.1 Forging processes...... 1 1.1.1 Applications of forged parts...... 2 1.1.2 Classification of forging processes ...... 3 1.2 Tooling and process design issues...... 5 1.3 Risk and forging ...... 8 1.4 Objective and outline ...... 14 CHAPTER 2 BACKGROUND AND LITERATURE REVIEW...... 17 2.1 Preform design in forging process...... 18 2.1.1 Backward finite element simulation ...... 18 2.1.2 Sensitivity analysis approach...... 23 2.1.3 Other approaches ...... 27 2.2 Property control in titanium forging...... 29 2.2.1 Metallurgy of conventional titanium alloys...... 30 2.2.2 Hot working of titanium alloys...... 32 2.2.3 Related work on forging of titanium alloys ...... 38 2.3 Property control in superalloys forging...... 46 2.3.1 Metallurgy of superalloys ...... 47 2.3.2 Melt-related defects in superalloys ...... 48 viii

2.3.3 Forging of superalloys ...... 53 CHAPTER 3 APPROACH AND METHODOLOGY...... 58 3.1 Finite element method...... 58 3.1.1 Rigid-plastic FEM...... 60 3.1.2 Metal forming modeling using viscoplastic approach...... 62 3.1.3 Applications in forging ...... 63 3.2 Design of experiments and response surface methods...... 65 3.3 Monte Carlo simulation...... 70 CHAPTER 4 EFFECT OF FORGING PATH ON MICROFEATURE LOCATION IN COMPRESSOR DISK FORGING...... 72 4.1 Introduction to hard alpha inclusion...... 72 4.2 Multi-body simulation modeling...... 75 4.2.1 Constitutive equations and friction ...... 75 4.2.2 Spatial and time discretization...... 77 4.2.3 Discrete contact treatment...... 78 4.2.4 Finite element formulation...... 79 4.3 Titanium forging modeling with hard alpha inclusion...... 80 4.3.1 3D modeling of hard alpha in forging...... 81 4.3.2 Simplification of 3D modeling to 2D modeling ...... 94 4.4 Risk mitigation by changing forging paths ...... 95 4.4.1 Forging path selection and constraints...... 97 4.4.2 Numerical simulations to build regression models...... 100 4.4.3 Stochastic simulations for risk evaluation ...... 103 4.4.4 Further investigation on other possible paths ...... 109 4.5 Summary and conclusions...... 112 CHAPTER 5 MICROSTRUCTURE CONTROL IN TURBINE DISK FORGING ...... 114 5.1 Modeling microstructure in hot working ...... 114 ix

5.1.1 Microstructure evolution during forging ...... 114 5.1.2 Microstructure modeling of superalloys ...... 115 5.1.3 Microstructure model validation for IN 718...... 119 5.2 Effects of forging path design on microstructure of disk forging ...... 120 5.2.1 Various forging path designs...... 121 5.2.2 Risk associated with microstructure ...... 123 5.2.3 Microstructure comparison for different forging paths...... 125 5.3 Effects of forging parameters on microstructure of disk forging...... 131 5.3.1 Different combinations of temperature and die speed ...... 131 5.3.2 Analysis of simulation results...... 132 5.3.3 Optimization of forging parameters for various objectives ...... 139 5.4 Summary and conclusions...... 144 CHAPTER 6 APPLICATION TO TITANIUM HIP IMPLANT FORGING ...... 146 6.1 Introduction ...... 146 6.2 Problem definition and constraints...... 150 6.3 Methodology and Procedure ...... 152 6.3.1 Material modeling...... 152 4.3.2 Thermal data ...... 153 4.3.3 Material instability...... 153 6.3.4 Geometry simplification ...... 155 6.3.5 Process variables...... 157 6.4 Results and Discussion...... 159 6.4.1 Simulation results...... 159 6.4.2 Relation to risk...... 172 6.5 Summary and conclusions...... 172 CHAPTER 7 CONCLUSIONS AND FUTURE WORK ...... 174

7.1 Summary and conclusions...... 174 7.2 Suggestions for future work ...... 176 APPENDIX...... 178 APPENDIX A. 70 points microstructure information...... 178 LIST OF REFERENCES...... 191

LIST OF FIGURES

Figure 1.1 Process of (a) open die forging and (b) impression-die forging...... 4 Figure 1.2 Example risk profile ...... 9 Figure 1.3 Thermal-mechanical fatigue cracking and oxidation in a turbine blade ...... 11 Figure 1.4 Creep crack in a turbine vane ...... 12 Figure 1.5 Low cycle fatigue results for U 720 LI at 600 °C ...... 12 Figure 1.6 Effect of grain size on creep strength of IN 100...... 13 Figure 1.7 Broken disk caused by fatigue crack emanating from hard alpha...... 13 Figure 1.8 General procedure to reduce risk by forging process design ...... 15 Figure 2.1 Concept of the backward tracing scheme...... 21 Figure 2.2 Flow chart of shape sensitivity method...... 26 Figure 2.3 Phase diagram used to predict results of forging or heat treatment practice... 33 Figure 2.4 Microstructure developed in Ti-6Al-4V by different forging temperature ..... 34 Figure 2.5 Comparison of mechanical properties achieved in α+β and β forged titanium alloys...... 35 Figure 2.6 Typical stress strain curves for titanium alloys ...... 39 Figure 2.7 Power dissipation efficiency map and instability map obtained on Ti-6Al-4V ...... 41 Figure 2.8 Stress-rupture strength of superalloys ...... 47 Figure 2.9 Solidification segregation evident as grain size and second phase particle banding in wrought Alloy 718 ...... 49 Figure 2.10 Large freckles on transverse and longitudinal alloy 718 billet slices from a 710 mm diameter ingot ...... 50 Figure 2.11 Large discrete white spot in an alloy 718 billet slice. Scale in inches...... 51 Figure 2.12 Surface cracking caused by poor forging practice...... 54 Figure 2.13 Fully recrystallized grains and microstructure with many unrecystallized xii

grains in IN-718 ...... 54 Figure 2.14 IN-718 microstructure showing grain-size bands caused by too high a forging temperature ...... 55 Figure 3.1 Different types of material stress-strain curves ...... 59 Figure 3.2 Advantages of using FE simulations in forging ...... 64 Figure 4.1 Typical hard alpha inclusion...... 73

Figure 4.2 α segregation: voids surrounded by stabilized α ...... 74 Figure 4.3 3D multi-body model of upsetting ...... 82 Figure 4.4 Compression stress-strain curves of hard alpha Ti...... 84 Figure 4.5 Ti-6Al-4V flow data for 950°C from Seshacharyulu et al...... 85 Figure 4.6 Global equivalent strain distribution of forged part in Case 1 ...... 86 Figure 4.7 Global equivalent strain distribution of forged part in Case 2 ...... 86

Figure 4.8 Global equivalent strain distribution of forged part in Case 3 ...... 87 Figure 4.9 Global equivalent strain distribution of forged part in Case 4 ...... 87 Figure 4.10 Local equivalent strain distribution on inclusion in Case 1 ...... 88 Figure 4.11 Local equivalent strain distribution on inclusion in Case 2...... 89 Figure 4.12 Local equivalent strain distribution on inclusion in Case 3 ...... 89 Figure 4.13 Local equivalent strain distribution on inclusion in Case 4 ...... 90 Figure 4.14 Points selected for comparison...... 91 Figure 4.15 Defects exceedance curve (1×10 6 kg) for titanium rotor disk materials ...... 93 Figure 4.16 Titanium disk forging and machined disk ...... 96 Figure 4.18 Strains to initiate cavities and fracture for Ti-6Al-4V...... 98 Figure 4.19 Different forging paths and point positions...... 99 Figure 4.20 Points in slot area to be back tracked to billet...... 101 Figure 4.21 Points tracked back to billet for different forging paths...... 102 Figure 4.22 Monte Carlo sample points distribution in billet...... 104 Figure 4.23 Strategy to relate failure risk with applied stress...... 106 xiii

Figure 4.24 Failure probability assumed for slot area ...... 107 Figure 4.25 Determination of feasible region...... 111 Figure 4.26 Failure rates for different forging path with standard deviation...... 112 Figure 5.1 Superalloy disk forging and machined disk ...... 121 Figure 5.2 Cross section of forging and machined part ...... 122 Figure 5.3 Three different forging paths...... 123 Figure 5.4 Low cycle fatigue results for U 720 LI at 600°C ...... 124 Figure 5.5 Effect of grain size on creep strength of IN 100...... 124 Figure 5.6 Machined disk and 14 zones to check microstructure...... 126 Figure 5.7 Distribution of checking points ...... 126 Figure 5.8 Grain size distribution for different preforms ...... 129 Figure 5.9 Fraction of recrystallization for different preforms...... 130 Figure 5.10 Fraction of recrystallization for different temperatures with V=5 mm/s..... 134 Figure 5.11 Fraction of recrystallization for different die speeds with T=920°C...... 135 Figure 5.12 Grain size for different temperatures with V=5 mm/s...... 136 Figure 5.13 Grain size for different die speeds with T=5 mm/s ...... 137 Figure 5.14 Rim grain size dependence on temperature and die speed...... 138 Figure 5.15 Overall grain size dependence on temperature and die speed...... 139 Figure 5.16 objective1 as function of die speed...... 142 Figure 5.17 objective2 as function of die speed...... 142 Figure 5.18 objective3 as function of die speed...... 143 Figure 5.19 objective4 as function of die speed...... 143 Figure 6.1 a) Commercial hip; b) Material distribution along the hip axis ...... 151 Figure 6.2 Instability map for Ti-6Al-4V with microstructural observations in the α-β regime at a strain of 0.5...... 154 Figure 6.3 2D cross sections to be studied...... 156 Figure 6.4 Location of critical area and cross-section ...... 156 xiv

Figure 6.5 Flow chart of followed approach...... 157 Figure 6.6 Integration modelling of the hot working process...... 159 Figure 6.7 Strain distribution of symmetrical preform and unsymmetrical preform...... 160 Figure 6.8 Thickness measurement to validate the reliability of the process ...... 161 Figure 6.9 Strain rate distribution in the critical zone ...... 163 Figure 6.10 The thickness of unstable material (temperature lower than 800°C) ...... 163 Figure 6.11 Temperature and strain rate distribution after preforming with performing die temperature of 200°C a) temperature before cooling, b) temperature after cooling, c) strain rate...... 164 Figure 6.12 Temperature distribution before and after load adjustment for B-B and C-C section ...... 166 Figure 6.13 Preforming stage a) before forging, b) after forging ...... 166 Figure 6.14: Temperature comparison for C-C section in preforming stage a) 2D simulation, b) 3D simulation ...... 167 Figure 6.15 Temperature comparison of C-C cross section in final forming stage between 2D simulation and 3D simulation ...... 168 Figure 6.16 Temperature distribution on the hip implant at the end of the forging process ...... 169 Figure 6.17 Die wear on preforming die and finishing die...... 170 Figure 6.18 Die stress on preforming die and finishing die...... 171 Figure A.1 Checking points and coordinate system of machined disk...... 178

LIST OF TABLES

Table 1.1 Main forging parameters and their effects ...... 8

Table 2.1 Properties comparison between α+β and β forging...... 36 Table 4.1 Final positions of tracked points in 3D simulations...... 91 Table 4.2 Stress and strain of tracked points in 3D simulations ...... 91 Table 4.3 Final position comparison for small inclusion...... 92 Table 4.4 Comparison of point locations, strains and stresses in 2D and 3D simulations 95 Table 4.5 Max load and strain for four different forging paths in finishing step...... 100 Table 4.6 Calculated failure rate for four different forging paths...... 108 Table 4.7 Max load and strain for various forging paths in finishing step ...... 109 Table 4.8 Calculated failure rate for five different forging paths ...... 111 Table 5.1 Modeling constants for IN 718 ...... 119 Table 5.2 Model validation results 1 (compare to Zhou and Baker [1995])...... 119 Table 5.3 Model validation results 2 grain size (compare to Medeiros et al. [2000]) .... 120 Table 5.4 Average grain size/standard deviation for 3 preforms...... 127 Table 5.5 Design matrix with different temperature and die speed ...... 131 Table 5.6 Average grain size/standard deviation for different forging conditions...... 132 Table 5.7 Results for different objectives ...... 141 Table 6.1 Maximum thickness of unstable material at the end of process with same temperature of preforming die and finishing die ...... 161 Table 6.2 Maximum thickness of unstable material at the end of process with different temperature of preforming die and finishing die ...... 162 Table 6.3 Forging loads in different cross sections...... 165 Table A.1 Coordinates of checking points ...... 179 Table A.2 Microstructure information T=950°C V=5 mm/s preform 1...... 180

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Table A.3 Microstructure information T=950°C V=5 mm/s preform 2...... 181 Table A.4 Microstructure information T=920°C V=5 mm/s preform 3...... 182 Table A.5 Microstructure information T=920°C V=20 mm/s preform 3...... 183 Table A.6 Microstructure information T=920°C V=50 mm/s preform 3...... 184 Table A.7 Microstructure information T=950°C V=5 mm/s preform 3...... 185 Table A.8 Microstructure information T=950°C V=20 mm/s preform 3...... 186 Table A.9 Microstructure information T=950°C V=50 mm/s preform 3...... 187 Table A.10 Microstructure information T=980°C V=5 mm/s preform 3...... 188 Table A.11 Microstructure information T=980°C V=20 mm/s preform 3...... 189 Table A.12 Microstructure information T=980°C V=50 mm/s preform 3...... 190

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CHAPTER 1

INTRODUCTION

1.1 Forging processes

As one of the earliest metal working processes, forging has had a long history of development. But not until the last century did forging make a remarkable progress due to advancement of science and technology, which provided demands as well as technologies to improve the forging technique. Today, forging still plays an important role in providing parts and products that influence our modern lifestyle. According to annual report of

Forging Industry Association [ www.forging.org ], the 2007 custom impression die forging industry sales was 6,149.8 million dollars, an increase of 25% compared to that in 2004.

Automotive industry made up 30.3% share of the total forging market, and aerospace applications contributed 26.6%. The industry sales of custom open die forgings increased to 1,786.9 million dollars, which doubled the figure in 2004.

Forging is known as a secondary manufacturing process, which converts the products from the primary operation into semi-finished or finished parts. During forging, metal is 1

squeezed or compressed under high pressure to form the products. The deformation it undergoes gives the forged parts superior mechanical properties by aligning material’s structure along the direction of deformation, eliminating the cast dendritic structure and sometimes developing a fine-grained structure as a result of recrystallization. Compared to casting, forging is stronger and has a better response to heat treating. Compared to machining, forging has a wider size range of desired material grades and a preferable grain orientation along surface; besides, forging makes a better use of materials with the material savings as great as 75% compared to machining [SCHULER GmbH, 1998]. In cold and warm forging, it is possible to use a lower-cost steel grade since the strain hardening, which occurs during forming, can improve both ultimate and fatigue strength. Thus, forging is preferred in applications where reliability, strength, fatigue resistance and economy are critical.

1.1.1 Applications of forged parts

The main applications of forged parts are in the automotive and the aerospace industries.

More than 250 forgings can be found in a typical car or truck; most of these parts experience large stress and shock, such as connecting rods, crankshafts, transmission shafts and differential gears. Some aircrafts even contain more than 450 structural forgings as well as hundreds of forged engine parts. The high standard of reliability and performance reliability and performance has made both the ferrous and the nonferrous forgings the right choice for aerospace area. Considering the required material properties, high specific 2

strength materials like titanium alloys can increase the payloads as well as range and performance. Nickel-based and cobalt-based superalloys are widely used in turbine engine components for the superior mechanical properties in high temperature. Other industrial applications of forged parts are also found in agricultural machinery, off-highway equipment, industrial equipment, ordnance and oil field equipment.

1.1.2 Classification of forging processes

Based on how metal flow is confined, forging can mainly be classified as open die forging and impression-die forging (Figure 1.1). Open die forging is performed between two flat or near flat dies, with no side wall in the tooling so that the metal can flow freely in lateral direction. Open die forging can produce disks, blocks, bars, step shafts, etc. The main advantage of open die forging is the large size of the parts it can produce: forgings up to more than 150 tons can only be produced by the open die forging process. In impression-die forging, two or more die blocks with negative shapes are brought together to form a cavity, in which the metal being deformed undergoes plastic deformation. As the metal flow is confined by die impression, impression-die forging can yield more complicated shapes and closer tolerances than open die forging. The flash formed during forging increases the pressure in cavity, thus helps the filling of even the most complex detail. These advantages make impression-die forging predominant in the forging industry.

(a)

(b) Figure 1.1 Process of (a) open die forging and (b) impression-die forging

Flashless forging can be considered as a form of impression-die forging. No excess metal escapes the die cavity at the end of the stroke, this improves material utilization. The workpiece volume and die must be precisely controlled to ensure filling of the die cavity without generation of excessive die load. Net-shape forging and near-net forging can further reduce the wastage of material by significantly reducing or eliminating subsequent machining.

Depending on the temperature at which metal is forged, forging can be classified as cold forging, warm forging and hot forging. Cold forging is always performed at room temperature with the use of an interface lubricant. The high precision of cold forged parts, sometimes even draftless, enables their use with little finishing. Hot forging is conducted above the recrystallization temperature so that no strain hardening occurs and metal flow

stress is much lower. Improved metal flow ensures a more complex shape and more deformation. Most starting billets have to be hot forged in order to achieve a large shape change. With the advantages similar to cold forging, warm forging is carried out at a higher temperature than cold forging but still lower than recrystallization temperature.

In hot-die forging, a form of hot forging, dies are heated to a higher temperature than room temperature to help the metal flow. Similarly, isothermal forging is usually performed using a die with the same temperature as metal being worked. They are usually employed to forge alloys, which are temperature sensitive and difficult to forge, like titanium alloys and superalloys. Vacuum or protection atmosphere is usually used in isothermal forging to avoid oxidation of the die materials.

1.2 Tooling and process design issues

From the perspective of technology, the increasing global competition in forging industry comes from processes and materials [Barnett, 2000]. The improvement in the processes and the development of the new processes make it possible to enhance the quality of forgings, reduce the cost and increase productivity. The advances in forging and supporting equipment provide the basis for the process improvements. Forging produces closer tolerance, smaller draft angle and less flash; net and near-net forging technology is being combined with the advanced materials to achieve complex shape with minimum cost; some parts are able to be used after little or no subsequent processing. Forging research 5

also focuses on new materials since they give superior performance in their application field. Titanium alloys, aluminum alloys, superalloys and other difficult-to-fabricate alloys have different properties with steels so that research must be conducted to produce sound products. For some superalloys, titanium alloys, and aluminum alloys, specifically designed and controlled thermomechanical processing (TMP) technology has been used to produce products with the best possible mechanical properties and optimum forging microstructural uniformity [Thomas et al., 1985].

The main problems that most forging industries face include:

Forging defects like underfills, folds, and cracks, which lead to the scrap when they

exceed certain limit;

The metallurgical qualities of forgings are not sufficiently good to yield the desired

mechanical properties. The metallurgical quality problems may encompass: excessive

grain growth, non-uniformity of microstructure, and out-of-controlled phase, etc.;

Die failure due to excessive die wear and die softening.

Die design and forging parameter design are two major parts in forging process design.

Final die design depends on forging design, which includes finish allowance, forging draft, parting-line location, flash, and fillet. Final die design is not a concern in this research.

Forging is usually considered as a multiple-sequence process because most forgings cannot be produced in one operation. Generally, a forging produced prior to the final forging 6

operations is called a preform. Preform design is usually an important part of forging die design. Two main reasons to use preform are: the metal cannot flow smoothly to fill the die cavity completely; and the metal flow and stress are so high that finisher die will wear quickly [Vemuri, 1986]. Design of forging parameters mainly includes temperature at which the metal is deformed, die temperature and die velocity.

A well designed preform can remove defects, reduce die load and obtain the required strain distribution in forgings. The preheating temperature will influence the forging load, temperature distribution and metal flow. Die temperature mainly influences the temperature distribution and forging load. If isothermal forging is used, the cost is significantly higher than conventional forging. Die velocity mainly influences strain rate; however, temperature distribution is also a result of die velocity because of the heat generation and dissipation during deformation and heat transfer between workpiece and tools. The main design parameters and their effects are listed in Table 1.1. As these parameters will change the strain, strain rate, temperature and metal flow, process design can lead to different microstructure in forgings; thus by proper design of forging process, desired mechanical properties can be obtained.

Design parameters Effects/responses Forging feasibility, strain Die design/preform design distribution Billet temperature Temperature, metal flow, load Load, temperature distribution, Die temperature cost Strain rate, temperature Die velocity distribution

Table 1.1 Main forging parameters and their effects

1.3 Risk and forging

Before the introduction to risk, the definitions of hazards and event consequences must be given. A hazard is a source of harm, and can be defined as a phenomenon or act posing potential harm to some person and its potential consequences. Failure event consequences are the degree of damage or loss from some failure. Risk can be defined as the potential losses resulting from an exposure to a hazard or as a result of a risk event [Ayyub, 2003].

Risk can be linked to uncertainties associated with events.

Most commonly, risk is measured as the likelihood of occurrence of the event and consequences associated with the event. It can be described by the following equation:

Risk ≡ [( p1 ,c1 ), ( p2 ,c2 ),..., ( pi ,ci ),...( pn ,cn )] (1.1) where pi is the probability of occurrence of event i, and ci is the consequence of this event.

Similarly, risk is also evaluated as product of likelihood of occurrence and impact severity

of the occurrence of the event [Ayyub, 2003]:

 Consequenc e   Event   Consequenc e  RISK   = LIKELIHOOD   × IMPACT   (1.2)  Time   Time   Event 

In equation (1.2), risk is presented as an expected value of loss. Likelihood can be expressed as a probability. A risk profile, also called Farmer curve, is a plot of occurrence probabilities and consequences, as exemplified in Figure 1.2. In this figure, abscissa represents the number of fatalities, and ordinate represents annual frequency of occurrence.

Risk profiles can also be constructed using probabilities instead of frequencies, and economical losses instead of fatalities.

Figure 1.2 Example risk profile [Ayyub, 2003]

Forging and risk can be related by the failure of component manufactured by forging. For example, a defect in a forged component of aircraft engine may increase the likelihood of engine failure, which in turn, increases the risk of aircraft crash. As a forging engineer, one cannot control the exposure to the activity involving accident risks, like aircraft flying time; one cannot control the consequence of loss, either. The risk of component failure can be mitigated by reducing the probability of forging failure through the proper design of forging process.

In equation (1.2), impact is dependent on usage of parts so it cannot be controlled by forging process design. The risk can be reduced by forging process design only by reducing the likelihood of an event in equation (1.2). The likelihood of failure of a forged part can be related to:

1) Microstructure and mechanical properties of a component;

2) Possible location of a discrete defect in the material.

The first factor can be exemplified in Figure 1.3 and Figure 1.4. Figure 1.3 shows the fatigue crack in a turbine blade and Figure 1.4 shows a creep crack in a turbine vane. The failures could be prevented if the mechanical properties, like fatigue strength and creep rupture strength, are improved. It is well known that these properties can be influenced by microstructure of the parts. The low cycle fatigue testing results of superalloy U 720 LI 10

(Figure 1.5) show that for fixed stress amplitude, materials with fine grains have longer fatigue life than those with coarse grains. The creep strength property of superalloy IN 100 can be seen in Figure 1.6. Under the same testing conditions (same stress level and same temperature), materials with larger grain size have a longer creep life than those with smaller grain size. The dependencies of fatigue life and creep strength on grain size shown here are valid for almost all metals. Therefore, forging process design, including preform shape, temperature and forging speed etc., is able to change mechanical properties of forged part by means of manipulating microstructure.

Figure 1.3 Thermal-mechanical fatigue cracking and oxidation in a turbine blade [Benac

and Swaminathan, 2002]

Figure 1.4 Creep crack in a turbine vane [Becker, 2002]

Figure 1.5 Low cycle fatigue results for U 720 LI at 600 °C [Torster et al., 1997]

Figure 1.6 Effect of grain size on creep strength of IN 100 [Lasalmonie and Strudel, 1986]

The impact of second factor is seen in Figure 1.7. Discrete defect hard alpha in this titanium disk led to fatigue failure. Proper forging process design may move the defect to area which is subjected to lower stress or which will be removed by subsequent machining; in turn, this reduces the probability of part failure.

Figure 1.7 Broken disk caused by fatigue crack emanating from hard alpha [Millwater and

Wirsching, 2002] 13

1.4 Objective and outline

The objective of this dissertation is to develop a method to reduce the failure risk in critical components via forging process design. First, numerical model is used to study the deformation and movement of discrete defect in metal forming; the final location of defect is then related to applied stress to find the severity of this defect. Second, the microstructure of a forged part is manipulated by preform design, forging temperature and forging speed to satisfy the requirements for mechanical properties. Finally, the forging process design is made to reduce the cost of production of titanium hip implant. The work in this research demonstrates the way that failure risk of forged parts can be reduced by appropriate forging process design.

The general procedure of reducing risk of forged part is shown in Figure 1.8. For a component, service conditions and mechanical requirements are analyzed; material properties are then connected to component requirements; forging process design can manipulate metal flow and microstructure evolution during forging to achieve the objective of risk reduction.

Figure 1.8 General procedure to reduce risk by forging process design

This dissertation is organized as follows:

Chapter 1 gives the introduction of forging processes, design issues, the relation

between forging and risk and the dissertation outline.

Chapter 2 presents the background and literature review on forging process design,

especially preform design. Background of titanium alloys and superalloys (two kinds

of metals used in this dissertation) is also included.

Chapter 3 introduces the approaches and methodology used in this dissertation as part

of the research, such as Finite Element Method, Design of Experiments, and Monte

Carlo Simulation.

Chapter 4 studies the effect of discrete defect on forging failure risk. A titanium 15

compressor disk is used as an example to show that the forging path can be designed to

minimize the risk of failure due to hard alpha inclusion in a titanium billet.

Chapter 5 demonstrates that both preform design and process parameters have

influence on final microstructure of a turbine disk made of superalloy. For different

optimization objectives, microstructure in final forging can be optimized by proper

selection of forging parameters.

Chapter 6 shows the design procedure of hot die forging of titanium hip implant.

Lower die temperature is used to reduce the cost without introducing material defect

due to flow instability.

Chapter 7 summarizes this dissertation and provides comments of future work.

CHAPTER 2

BACKGROUND AND LITERATURE REVIEW

As one of the most common and modern metal-working processes, forging has experienced greater development in recent years through continuous progress in many areas, including [Forging Industry Association, 1997]:

Alloys are being developed and refined to improve processing characteristics;

Industry’s understanding of the mechanics of the forging process is being increased by

growing manufacturing development in forging processes;

State-of-the-art equipment is being utilized to control critical processes;

As the usage of CAD/CAM throughout the design and production processes is

increasing, dimensional accuracy of forgings is improved and lead time is reduced;

Modeling and forging simulations are being used to minimize development time.

Based on the development achieved, research in forging continues seeking to make improvements in process parameters, die design, equipment, materials, etc. Specifically,

research in this dissertation can be divided into two aspects:

1) Design of preform die shape aiming to improve the property of forging;

2) Determination of processing parameters to produce a defect free part as well as obtain

desired microstructure through thermomechanical processing.

A lot of related research work has been done in these two areas; some are reviewed in this section.

2.1 Preform design in forging process

Preforms are traditionally designed by experience with no common rules that can be summarized easily. Briefly, three basic guidelines for designing performs are [Altan et al.,

1973]:

1) Each cross section along length of preform must be equal to final cross section

expanded by flash area;

2) Preforms should have larger radii than that of finished parts;

3) In die closing direction, preform should be larger than finished forging if possible.

In the last two decades, various new methods have been employed to help preform design to shorten the development period.

2.1.1 Backward finite element simulation

The FEM simulation has been widely used in metal forming processes to predict the metal flow and formation of defects. The forging dies designed using empirical guidelines and 18

designer’s intuition can be verified by forward simulation, but they cannot be directly used in forging die design. Intuitively, however, by inversely carrying out simulation from the final forging to the initial preform, backward simulation can help us improve the preform dies.

The idea of using backward simulation based on finite element method to design preforms was first put forward by Park et al. [Part et al., 1983]. Unlike the normal finite element method, which calculates stress and displacement step by step from the initial billet, backward FE method traces the loading path in forging process inversely from a final configuration. The calculation algorithm is illustrated in Figure 2.1. The left part of the figure shows coordinate changes of a specific point, while the right part shows the iteration process. The geometrical configuration at time t = t0-1 and t = t0 are x0-1 and x0, respectively, and they are represented by point P and Q, respectively. The displacement needed in time

∆t is denoted by u0-1, so for forward path P to Q

x0 = x0-1 + u0-1 (2.1)

The backward problem is: given a known geometrical configuration Q (x0), the geometrical configuration P is to be determined, so the problem is to calculate the displacement at time t0-1, which is u0-1.

The backward tracing method is conducted in this way: Take forward solution at Q, which is u0, a difference is calculated between x0 and u0 as the first estimate of point P, so 19

(1) P = x0 – u0 (2.2)

(1) (1) Then the first estimate of forward displacement u 0-1 can be calculated based on point P .

(1) The geometrical configuration in time t = t0 calculated from P , which is

(1) (1) (1) Q = P + u 0-1 (2.3) are then compared with the known configuration Q. If Q(1) and Q are close enough, P(1) is taken as the P; otherwise, the second estimate of P are calculated by

(2) (1) P = x0 –u 0-1 (2.5)

(2) (2) The displacement field solution u 0-1 based on P is then calculated and the second estimate of Q, which is

(2) (2) (2) Q = P + u 0-1 (2.6) is then compared to Q. The iteration continues until

(n) (n) (n) Q = P + u 0-1 (2.7) is sufficiently close to Q. Since metal forming is a non-linear problem, the unknown path is approximated by linear path within a sufficiently small step size. This deformation path can be seen as a result of trial and error search.

Figure 2.1 Concept of the backward tracing scheme

A more detailed description in rigid-plastic and rigid visco-plastic FEM is made by Zhao et al. [1995]. In backward simulation, there must be a criterion to detach the nodes from die surface. Zhao et al. [1995] put forward a shape complexity factor based criterion. In this method, shape complexity factor has been used to describe the complexity of axisymmetric forging. The shape complexity factor increases from initial billet to final forging. When metal enters the deep recesses and concaves with small radii, shape complexity factor and forging load increase sharply. In forging process, it is favorable to have these regions filled at the end of the stroke, so that the shape complexity factor increases sharply at the end.

Conversely, in backward simulation, it is better to have the shape complexity factor decreased as fast as possible at the beginning steps.

So, iterations are used for every node that can be detached from the die, and the resulted shape complexity factor is calculated. The node that causes the largest shape complexity factor reduction is detached from the die. This criterion is only dependent on the coordinates of boundary nodes and can be used to control both the top and bottom of the workpiece. But since the shape complexity factor only describes the complexity of axisymmetrical parts, this criterion is only suitable for axisymmetrical forging design.

An alternative node detachment criterion called inverse die contact tracking method was proposed by Zhao et al. [1996]. Tool is divided into several linear or arc segments. A trial preform, which probably does not meet the design objectives, is used in a forward simulation, and the momentary times that each die segment comes into contact with the preform are recorded. The boundary condition sequence obtained from trial forward simulation must be modified to remove the defects formulated because the trial preform is not the desired shape. A generic turbine disk die design using inverse die contact tracking method was reported [Zhao et al., 1998]. By reducing the flash at the beginning of backward simulation, this method can also be used to design a die cavity to achieve flashless forging [Zhao et al., 2002]. Biglari et al. [1998] incorporated fuzzy logic into backward deformation method to minimize defects and the strain range for an axisymmetric part. In each backward time increment, the boundary nodes are released according to strategy based on a fuzzy decision making method.

2.1.2 Sensitivity analysis approach

The gradient based method also draws lot of attention in preform design. In this method, the derivatives of the objective function with respect to the design variables are calculated.

This usually involves the perturbation of the finite element equations. The design iteration is then performed based on design sensitivity from those derivatives. This method is used not only in shape design, but also in design of processing parameters.

Fourment and coworkers [1995] treated final forging die as known while the preform die and the initial workpiece shape to be designed so that the objective, the difference between shape actually achieved and desired shape, can be satisfied. BFGS algorithm, in which gradient methods and sensitivity analysis have been employed, is used for optimizing both preform and preforming die.

An optimization algorithm developed by Zhao et al. [1997a] to design preforming die uses cubic B-spline curves to describe preforming die shape; the coordinates of the control points are taken as design variables to minimize the shape difference between actual shape and intended shape. In sensitivity analysis, the gradient of the objective function with respect to design variables can be transformed to nodal displacement derivatives, the nodal force derivatives and nodal velocity derivatives, so that it can be calculated eventually.

BFGS optimization algorithm is used to minimize objective. By die position compensation in each time increment, volume of material could maintain constant to avoid volume loss 23

due to remeshing and geometry updating [Zhao et al., 1997b]. In a later publication, Zhao et al. [2004a] modified the method to increase the computation efficiency.

Vieilledent and Fourment [2001] used direct differentiation of discrete equations to calculate the derivatives of tool geometry, velocity and state variables with respect to the shape parameters in axisymmetric problems. Better geometric conformity, homogenization of deformation and minimization of folds are taken as objectives and BFGS algorithm is used to solve the optimization problem. Later research [Do et al., 2004] even tested both deterministic and stochastic optimization algorithms in 3D problems.

Srikanth and Zabaras [2000] introduced a continuum sensitivity analysis to calculate the shape sensitivity of finite hyperelastic-viscoplastic deformation. Appropriate sensitivity kinematics and constitutive problems were defined. The sensitivity analysis was performed in an infinite-dimensional continuum framework. By utilizing finite element method, direct deformation and sensitivity deformation problems were carried out. A fully implicit algorithm was used for direct contact problem to improve accuracy of preform design for more complex contact and frictional conditions.

Another optimization method based on a modified sequential unconstrained minimization technique and a gradient method was developed by Castro et al. [2001]. Analytical derivatives of objective function were considered to avoid expensive cost in calculating the 24

numerical derivatives. Based on the differentiation of the equations of the discrete problem, the discrete derivatives of the objective function were calculated. The algorithm to solve an inverse two-step forging is:

1) Finite element analysis of the preforming step is performed with an initial guess of

preforming die;

2) In every incremental time step, the sensitivities of the nodal velocities with respect to

design variables are obtained using the direct differentiation method;

3) After preforming stage, the sensitivities of the nodal velocities in the final stage are

updated;

4) When the final forging is finished, the gradients of the objective function can be

calculated using the sensitivities of nodal coordinates with respect to the design

variables;

5) If the stopping criteria are not met, optimization program will provide a new design

parameter vector;

6) Using the updated design parameters, optimization iteration continues until the

convergence conditions are satisfied.

The same optimization technique has been applied in 3D forging considering both mechanical and thermal analysis by Sousa et al. [2002]. The goal of inverse problems is to determine input data of direct problem so that a prescribed result can be obtained. The authors intended to find an initial workpiece shape that can be forged to desired geometry 25

without excessive flash and underfill. A good agreement between simulation result and designed geometry is reported.

Figure 2.2 Flow chart of shape sensitivity method [Shim, 2003]

Shim [2003] applied a sensitivity method in the preform design for 3D free forging. The preform with a shape to be designed is to be forged by flat dies to produce a predetermined shape. When the finite element analysis shows that initial preform does not yield desired shape, an offset shape, which is produced by moving the nodes of the original shape, is introduced. A second finite element analysis is carried out for the offset shape to produce deformed offset shape. Shape sensitivities can be calculated by investigating how offsetting of undeformed nodes influences the offsetting of deformed nodes. Based on the shape error that represents how deformed geometry differs from target geometry, together with shape sensitivity, a new set of points can be given as the preform. This process is 26

performed iteratively until the shape error is less than a preset value. This method can be illustrated in flow chart shown in Figure 2.2. The method is used to eliminate barreling of free surface in upsetting of circular cylinder, elliptical cylinder, clover shaped cylinder, rectangular prism and stepped rectangular prism; the results demonstrate that the shape sensitivity method provides excellent prediction of preform shape.

2.1.3 Other approaches

Kim and Chitkara [2001] used upper bound elemental technique (UBET) to analyze the metal flow in forging of crown gear. Based on UBET analysis, several preforms were designed in order to make the inner corner and outer corner to be filled simultaneously.

Preform design using UBET to achieve a complete die fill for both 2D and 3D were reported [Bramley, 2001]. It provides rapid but approximate simulation and preform design, which can be used as precursor for more accurate finite element simulations.

Lapovok and Thomson applied a strategy described as “step backward, step forward” for rough draft design followed by “step-by-step forward” for finish design [Lapovok and

Thomson, 1995]. This method includes: choosing main parameters defining the shape, determining preform shape according to selected parameters, choosing criteria for optimization, solving the plasticity boundary problem and investigating the extreme value of objective function to determine optimal parameters. The same strategy was applied to minimize die damage accumulation by changing preform [Lapovok, 1998]. 27

Tomov and Radev [2004] created a criterion based on their shape complexity factor to decide if a preforming step is necessary. The application of this criterion reduces the tool cost by eliminating unnecessary preforming stages as well as reduces die wear by avoiding excessive deformation in one forging step.

Oh and Yoon [1994] applied low pass filtering method in preform design. The preform geometries can be obtained by expanding the finisher geometry in terms of Fourier series and eliminating the high frequency terms. Some modifications are needed according to conventional preform design. This method was used in 3D forging [Oh et al., 2004].

Similar method can be found in the work done by Lee et al. [2002]. It is observed that the equi-potential lines generated between two conductors of different voltages show similar trends for the minimum work path between the undeformed shape and deformed shape.

Thus, the equi-potential lines obtained by the arrangement of the initial and final shapes are utilized to design the preform.

When the derivative based approach may not be applicable, direct search approach such as genetic algorithm can be used. In the work done by Chung and Hwang [2002], genetic algorithm has been used to optimize the objective functions, which are minimum unfilled die cavity when material starts to form the flash and uniform temperature in the work, by changing preforming die shape. An integrated thermal-mechanical element model was 28

used to conduct forging calculations. Similar approach was used by Castro et al. [2004] to optimize the shape and energy consumption during forging by varying the shape and temperature of workpiece before forging.

Researchers also proposed and applied an iterative preform design technique to reduce forging volume [Hong et al., 2006]. A boundary region at the outlet of the flash was selected in initial FEM simulation. This region was traced back along the deformation path to initial billet; the initial shape was updated by removing this excessive section and the new shape was used in the next simulation. This approach can remove the excessive flash and thus reduce the tool load and tool wear. To achieve the same goal, a new approach has been proposed recently by coupling finite volume method (FVM) and parametric design method [Sedighi and Tokmechi, 2008]. Reduction on cost and time in the stages of designing and improving preform is claimed by authors.

2.2 Property control in titanium forging

Titanium and titanium alloys have been used widely in aerospace industry, chemical industry and energy industry for their high strength-to-weight ratio, outstanding corrosion resistance and excellent mechanical properties. The current level of performance, airframe strength, speed, range and other critical factors of aircrafts can only be achieved with the application of titanium alloys in aircraft engines, airframes and other components. These strong, light, corrosion resistant metals are also extremely suitable for implant purposes as 29

they possess exceptional biocompatible property. Titanium bone and joint replacements, dental implants, cardiovascular devices and other parts are produced and used for medical purposes worldwide every year. The properties of titanium alloys are primarily determined by the metallurgical features, which is a result of composition and processing history.

2.2.1 Metallurgy of conventional titanium alloys

There are two crystalline forms that exist in pure titanium: hexagonal close packed (hcp) α phase at low temperature and body centered cubic (bcc) β phase at an elevated temperature.

The temperature at which transition from α to β occurs (about 882 °C for pure titanium) is called β transus.

All technologically important forms of titanium contain deliberate alloying additions

[Williams, 1995]. These additions affect the phase equilibria and microstructure by way of altering the relative thermodynamic stability of α phase and β phase. According to how the alloying elements influence the β transus, these elements can be classified as α and β stabilizers, and neutral elements. The α and β stabilizers have a tendency of concentrating in either α or β phase, respectively, which is called solute partitioning. The volume fraction of the more stable phase is stabilized by adding these alloying elements.

Conventional titanium alloys are commonly categorized as α alloys, β alloys and α+β alloys according to which phase are predominantly present at room temperature under 30

normal conditions. The latter two alloys have higher strength and are easier to shape and work. Nowadays, the most commonly used titanium alloys are α+β alloys; among them,

Ti-6Al-4V constitutes the largest portion of all Ti alloy usage.

An interesting observation is that the strength of the two phase mixture in α+β alloys is considerably higher than either α or β alloys even in annealed condition. This synergism has significantly increased technical interest in using titanium alloys for light weight structures. Recently, the usage of β alloys in many fields such as aircraft and petrochemical equipment are growing rapidly. However, the total volume is still small compared to α+β alloys because of the reasons ranging from producibility to changes in design philosophy considering fracture toughness, strength, and other properties.

When α or β alloys are mentioned, that does not mean the other phase is totally absent in the material. In fact, β alloys are usually used in aged condition, in which some of α phase is present as strengthening precipitate. On the contrary, a small amount of β phase in α alloys can be considered beneficial because it increases hydrogen tolerance and acts as grain refining constituent.

Thermomechanical processing (TMP) is able to produce a variety types of microstructure in a single alloy that may not be available by using heat treatment alone. By using TMP, microstructures of titanium alloys can be controlled to balance strength and ductility. TMP 31

of α+β alloys can be divided into two categories: α+β processing and β processing. This depends on the temperature range at which the working operation is completed. Working in

α+β range below β transus produces α phase characterized by equiaxed microstructure, which is known as primary α. The volume fraction of primary α varies according to different finishing temperatures and subsequent heat treatment. In β forging, colonies of α plates develop and grain boundary α phase exists on prior β grain boundaries. The boundary α is deleterious to mechanical properties and is desired to be removed.

2.2.2 Hot working of titanium alloys

Nowadays, titanium alloy components can be manufactured by all kinds of forging methods. Titanium forgings may be superior to bar or other forms in all tensile strength, fatigue strength, creep resistance, and toughness [Donachie, 2000]. The mechanical properties and microstructure of the forgings are greatly influenced by the working history and forging parameters. For α+β alloys, the forging temperature relative to β transus, the plastic strain rate and the amount of deformation influence the microstructure of forgings; this is true for both as-forged parts and microstructural changes occur during post-forging heat treatments [Williams, 1995]. Over-exposure of titanium alloys to high temperature should be avoided since it can cause the formation of excessive scale and increase the formation of α phase due to interaction with the interstitial elements oxygen and nitrogen.

The forging pressure depends on composition, temperature, strain rate, and process and varies over a large range. However, a higher stress is required than that in the processing of 32

steels.

Figure 2.3 Phase diagram used to predict results of forging or heat treatment practice

[Donachie, 2000]

Most of secondary hot working of titanium alloys are performed in α+β phase range

[Semiatin et al., 1997]. Both α and β phases exist in the microstructure at all times. The amount of each phase during the forging process depends upon the temperature distance from β transus. Figure 2.3 illustrates how the percentage of each phase changes during the forging or heat treatment for Ti-6Al-4V. The microstructure after α+β forging is characterized by deformed or equiaxed α in a transformed β matrix as shown in Figure 2.4

(a). The microstructure detail is determined by the amount of deformation at various temperatures and the plastic strain rate. Thus, the uniform distribution of strain and strain 33

rate determines the uniformity of the microstructure.

(a) α+β processed (b) β processed

Figure 2.4 Microstructure developed in Ti-6Al-4V by different forging temperature

[Williams, 1995]

Compared to α+β forging, β forging is a relatively less common method in secondary processing. The acicular or Widmanstatten α (Figure 2.4 (b)) is developed and this structure has better toughness, fatigue crack propagation resistance and creep resistance.

During the cooling followed by β forging, α forms on the prior β grain boundary. To remove undesirable grain boundary α, it is a good practice to work continuously through β transus temperature. This results in continuous recrystallization of β phase and little or no grain boundary α formation [Williams, 1995]. Because of the high temperature and the formation of new grains by recrystallization every time the β transus is exceeded, the

influences of deformation in β forging are not necessarily cumulative. A significantly lower pressure is required for β forging and the cracking tendency is reduced; while non-uniform working and excessive grain growth may cause variant properties inside the parts.

The comparison of two forging approaches of different α+β alloys in strength can be seen in Figure 2.5. A qualitatively comparison of α+β forging and β forging is made in Table

2.1.

Figure 2.5 Comparison of mechanical properties achieved in α+β and β forged titanium

alloys [Donachie, 2000]

Properties ααα+βββ forging βββ forging Yield strength X Creep strength X Fatigue initiation X Fatigue crack growth resistance X Fracture toughness X Ductility and formability X hot salt stress corrosion cracking resistance X Aqueous stress corrosion cracking resistance X Hydrogen tolerance X

Table 2.1 Properties comparison between α+β and β forging [Davis, 1998; Donachie,

2000]

Hot die isothermal forging is an advanced technology in working titanium alloys. Since the die temperature is the same as the workpiece, absence of heat transfer between tool and titanium makes flow stress constant. The microstructure can be controlled better and the property variation is minimized. To protect the tools, which are commonly made of TZM, a

Mo based alloy, closed chamber with inert gas environment is utilized. This imposes a limitation in forging size and production cost.

For α+β titanium alloys, ensuring the sufficient workability is as important as controlling the microstructure and texture. Workability becomes a major issue during subtransus hot working. Fracture-related defects, shear-localization defects and gross metal flow defects are included in workability issue [Semiatin et al., 1997].

Defects related to fracture are created by large stress concentrations at grain boundaries caused by microscopically inhomogeneous deformation. When high strain rate is imposed, diffusion or plastic flow cannot relieve the stress, thus gaps are formed in the metal.

Various researchers revealed that workability can be significantly improved if high temperature and low strain rate are applied simultaneously during hot working.

In conventional hot forging, the metal close to tools is more susceptible to heat loss and undergoes less deformation than metal inside. Shear-localization defects such as shear cracks and shear bands tend to develop between low deformation zones and high deformation zones. Forging speed is the most prominent process variable, which influences the shear band severity in conventional hot forging by affecting the processing time and heat transfer. Excessive slow working rate may lead to the workpiece temperature drop into lower workability region and cause cracking along the shear bands. Even when isothermal forging is used, shear localization may occur due to flow stress property

[Semiatin et al., 1997].

Metal flow defects such as laps or flow-through defects are more likely to occur in conventional, closed-die hot forging of difficult-to-work materials. Usually, they can be avoided by proper die design, well-designed preform, appropriate lubrication and carefully chosen process variables. 37

In this dissertation, the microstructure characters of titanium alloys, such as volume fraction of each phase and grain size, are not qualitatively calculated because the microstructure evolution of titanium alloy in hot deformation is very complex so that it is not easy to be mathematically described. To author’s knowledge, there are no clear-cut equations used to predict the microstructure of titanium alloys. In this research, distribution of strain, strain rate, temperature and instability map, which will be introduced in the following section, will be used to evaluate the forging of titanium alloy.

2.2.3 Related work on forging of titanium alloys

Plenty of research has been done on forging of titanium alloys; some are fundamental research on material behavior, while others focus on specific parts from industrial application.

In order to accurately predict the forging process of titanium alloys, it is of great interest to make deformation behavior well understood. The flow behavior of titanium alloys is characterized by an initial hardening followed by flow softening (Figure 2.6). Depending on materials, forming temperature and strain rate, the strain associated with peak stress may vary a lot.

Figure 2.6 Typical stress strain curves for titanium alloys

With the consideration of dynamic recrystallization, viscoplastic constitutive equations have been employed by Zhou [1998] to model the flow stress of titanium alloy IMI834.

The dynamic recrystallization, which causes the flow softening, was modeled as internal variables. Material constants were determined by procedure developed by the author.

Experiments carried out at different temperatures and strain rates indicated that the model can predict the flow stress successfully in isothermal forging conditions.

Besides the use of stress-strain curves, another approach to model constitutive behavior is processing maps. It is based on principles of dynamic materials model, in which, the metal being hot worked is assumed to be a nonlinear dissipater of power [Prasad and

Seshacharyulu, 1998]. The energy is dissipated through temperature rise and microstructural change. How the input power is partitioned between the two is decided by strain rate sensitivity of flow stress m. The efficiency of power dissipation through microstructual process η is defined as:

2m η = m +1 (2.8)

The efficiency of power dissipation represents the constitutive response of the metal under various microstructural mechanisms. The power dissipation map, which is constituted by variation of η with temperature and strain rate, can be directly correlated with specific microstructural mechanisms such as dynamic recrystallization, dynamic recovery, and wedge cracking.

A continuum instability criterion is used to identify the regimes of flow instabilities. The instability parameter is defined as:

∂ln(m / m + 1) ξ( ε & ) = + m ∂ ln ε& (2.9)

Flow instability is predicted when ξ(ε&) becomes negative. Thus, the instability map can be superimposed on the power dissipation map to give a flow instability zone. This map is called processing map because it can guide process design to optimize workability.

Using power dissipation map and processing map, influences of oxygen content and starting microstructure on hot deformation of commercial pure titanium, ELI Ti-6Al-4V and IMI 685 were studied [Prasad and Seshacharyulu, 1998]. The authors concluded that wide instability regimes existed due to adiabatic shear bands formation at higher strain rates; the processing of titanium materials is very sensitive to oxygen content and starting microstructure. 40

The same method was taken by Sechacharyulu et al. [2000] to investigate high oxygen grade Ti-6Al-4V with equiaxed α-β microstructure. Material was tested by compression tests at strain rates of 0.0003, 0.001, 0.01, 0.1, 1, 10 and 100 s -1 and temperature range of

750-1100°C at an interval of 50°C. The flow stress values were given in great detail and power dissipation efficiency map and instability map were developed based on these values (Figure 2.7). The microstructures of compressed samples were examined and the correlations between the microstructure and maps were explained. The same material with lamellar starting structure had a different behavior [Seshacharyulu et al., 2002].

Figure 2.7 Power dissipation efficiency map and instability map obtained on Ti-6Al-4V

[Seshacharyulu et al., 2000]

Similarly, deformation behavior of a β alloy Ti-10V-4.5Fe-1.5Al in hot forging was studied by Balasubrahmanyam et al.[Balasubrahmanyam and Prasad, 2002]. Stress strain curves 41

were recorded at temperature range from 650°C to 900°C and strain rate of 0.001, 0.01, 0.1,

1, 10 and 100 s -1. Power dissipation efficiency maps and instability maps were plotted for strain of 0.2 and 0.4, respectively. It is noted that the power dissipation efficiency map did not change significantly with increase of strain; and the instability map at strain of 0.4 was almost the same as that at strain of 0.2.

The work done by Park et al. [2002] used compression tests to obtain flow stress curves by which processing maps can be plotted. The criterion authors used to distinguish instability is different from that mentioned before. One instability zone, which was predicted at temperature of 1000°C and strain rate of 0.001 s -1, indicated a coarse transformed β structure; a long time exposure at high temperature can cause dynamic grain growth. The processing maps were implemented into subroutine of DEFORM. A pancake forging was carried out using numerical simulation to show the successful prediction of instability in the experiments.

The mechanical behavior of Ti-6Al-4V at high and moderate temperatures was studied by

Majorell and co-workers [Majorell et al., 2002]. In addition to the test conducted in hot processing temperature range, more tests have been done at temperature between

380-680°C to investigate the influence of strain rate on the sharp drop in flow stress usually observed in low strain rate experiments. The test results were correlated with the evolution of the microstructure. The authors also proposed a physical-based model and the various 42

deformation mechanisms over the tested range were discussed [Picu and Majorell, 2002].

On the contrary, Bruchi et al. [2004] investigated workability of Ti-6Al-4V at high temperature and strain rate. Correlations between the microstructure of deformed specimen and deformation parameters were established. At the tested conditions, increasing temperature or decreasing strain rate can result in a more homogeneous microstructure.

The research also identified a stable flow zone at a temperature between 940 and 950°C and strain rate less than 15 s -1.

By conducting tests with Ti-6Al-4V of two different grain sizes, Semiatin et al. [1999a] evaluated the flow response and microstructure evolution in hot working with colony microstructure. A more quantitative understanding of mechanisms that control flow and globalization was obtained. With critically controlled heat treatment, samples with almost the same prior-beta grain size but different alpha platelet thickness enabled Semiatin and

Bieler [2001] to study the influence of α thickness on flow behavior.

Martin [1998] studied microstructure of Ti-4.4Al-5Mo-2Cr-1Ni by α+β forging and β forging with subsequent heat treatments. Both microstructure evolution and mechanical properties show the similar tendency as other α+β alloys. The research also covered hot working of non-conventional titanium aluminide. By studying phase transformation and microstructure, it was found that forging temperature, degree of deformation and annealing 43

temperature have pronounced effect on fatigue strength of α+β titanium alloys [Kubiak and Sieniawski, 1998].

Process design rules for non-isothermal forging of Ti-6Al-4V have been proposed in Lee and Lin’s work [1998]. In simulation of non-isothermal forging, since a dramatic temperature gradient exists, the flow stress was determined by localized linear fitting and interpolation method. The problem was modeled as a coupled thermal plasticity problem;

Young’s modulus, thermal conductivity and specific heat were modeled as temperature-dependent functions and interface heat conductivity coefficient was assumed to be pressure dependent. The final shape was considered as a result of deformation mechanism based on microstructure evolution and deformation index. By comparing the numerical results of temperature sensitivity factor and deformation index with forged billet, the authors could establish relations between these two parameters and deformation behavior.

In order to obtain reliable interfacial boundary data to increase the accuracy of computer simulation of hot forging of titanium alloys, experiments in conjunction with thermal-plastic coupled simulations were adopted by Hu and his colleagues [Hu et al.,

1998]. Ring upset tests were conducted at different temperatures with different lubricants and temperature changes were recorded. The reverse algorithm was applied to finite element simulation results to iteratively determine the heat transfer coefficient. The work 44

shows that the coefficient varies with die temperature, strain rate, lubricant and forging pressure.

A lot of research on manufacturing of titanium components, specifically turbine blades, has been done. Finite element modeling of titanium aluminide aerofoil forging conducted by

Brooks et al. [1998] incorporates flow stress model into finite element codes to simulate isothermal forging. The predictions of press load and microstructure were in good agreement with the experiments. The use of re-meshing in simulations also proved to improve the quality of the calculation. Hu et al. [1999] determined the evolution of microstructure in blade hot forging by internal state variables. This was extended to intermetallic alloys later [Hu and Dean, 2001].

Based on their extensive research on blade forging, Zhan et al. [2004] studied the precision forming of a complex blade with damper platform. In order to inspect and analyze the deformation process, 4 cross sections and one longitudinal vertical-section were selected.

By analyzing the metal flow and field variable distribution of these 2D cuttings, the complicated 3D deformation nature can be understood better.

Form errors of turbine blade due to cooling and die deflection caused by loading and unloading have been investigated by Lu and Balendra [2001]. Results indicated that forging temperature conditions have a significant influence on die and workpiece behavior. 45

A die shape compensation approach was introduced by Ou and Armstrong [2002] to reduce the thickness error and profile deviation of aerofoil sections due to die elasticity and thermal distortion. In their further research, effect of press elastic deflection was considered [Ou and Armstrong, 2006].

2.3 Property control in superalloys forging

Superalloys refer to those alloys designed to be used at high-temperature environment

(usually above 1000 °F or 540 °C). Superalloys have found their use from aircraft turbine engines, land-based gas turbines to rocket engines and petroleum equipment, where high performance alloys are required at elevated temperatures. Three major classes of superalloys are nickel-based, iron-nickel-based and cobalt-based alloys. Unlike at room temperature, material strength at high temperature has to be retained over a period of time.

Accordingly, creep strength or rupture strength is used to characterize mechanical behavior rather than yield strength or ultimate strength. A typical rupture strength plot of superalloys in Figure 2.8 indicates superior high-temperature strength of superalloys. Background of superalloys will be given in this section.

Figure 2.8 Stress-rupture strength of superalloys [Donachie and Donachie, 2002]

2.3.1 Metallurgy of superalloys

Superalloys are composed of austenitic fcc γ phase and other secondary phases including fcc ordered γ’ Ni 3(Al, Ti), bct ordered γ’’ Ni 3Nb, hexagonal ordered η Ni 3Ti, orthorhombic

δ Ni 3Nb intermetallic compounds in nickel- and iron-nickel-based superalloys and fcc carbides in all superalloy types [Donachie and Donachie, 2002].

The main strengthening mechanisms in superalloys are solid-solution hardening and precipitation hardening. The major precipitation strengthening phases in nickel-based and iron-nickel-based superalloys are γ’ and γ’’. Carbides, which exist in all three groups of superalloys, provide limited strengthening. Combined with γ’ phase, δ phase and η phase 47

can be used to control the structure of wrought nickel-based and iron-nickel-based superalloys.

Nickel-based superalloys are the most widely used group among the three. A majority of nickel-based superalloys are strengthened by intermetallic precipitation in austenitic fcc matrix. In alloys strengthened by titanium and aluminum such as wrought Astroloy,

Waspaloy, U-700, U-720 or cast Rene 80 and IN-713, the strengthening precipitate is γ’. In alloys strengthened by niobium, typified by IN-718, the strengthening phase is γ’’. Some nickel-based superalloy like IN-706 and IN-909 are strengthened by both γ’ and γ’’. Some nickel-based superalloys are strengthened by solid-solution such as IN-625; some include oxide-dispersion-strengthened alloys like IN-MA-754. Nickel-based superalloys are often used in both cast and wrought forms; while for some highly alloyed superalloys like Rene

95 and Astroloy, special processing techniques, for example, power metallurgy and isothermal forging, are frequently used to produce wrought forms. Iron-nickel-based superalloys can be classified as precipitation strengthened alloy (mainly by γ’) and solid-solution-hardened alloy. All cobalt-based superalloys are strengthened by both solid-solution and carbides.

2.3.2 Melt-related defects in superalloys

Some defects may develop during melting process. Vacuum arc remelting (VAR) is the most common secondary remelting process to produce the superalloy ingots. The 48

variations of VAR parameters during processing inevitably produce solidification defects in the ingot.

Banding often occurs during non-equilibrium solidification as a result of chemistry difference between dendrite core and interdendritic regions. They appear as banding of grain size and second phase particles [Kennedy et al., 1996] as shown in Figure 2.9. The homogenization heat treatment is able to enhance the diffusion of segregated elements, thus reduce the banding.

Figure 2.9 Solidification segregation evident as grain size and second phase particle

banding in wrought Alloy 718 [Kennedy et al, 1996]

Freckles (Figure 2.10) are a type of macrosegregation defects result from flow of solute rich interdentritic material in mushy zone [Wlodek and Field, 1994]. The formation of freckles can be related to mushy zone shape change and liquid density change during 49

solidification [Auburtin et al., 1997; Xu et al., 2002]. For large-size ingot, slight modifications of alloy chemistry may be an effective way to eliminate freckles. The improved control of VAR has progressed to the level that freckles are seldom found in normal production of the alloy [Mitchell, 1991; Zhang et al., 2002].

Figure 2.10 Large freckles on transverse and longitudinal alloy 718 billet slices from a 710

mm diameter ingot [Petit and Fesland, 1997]

The name of white spots comes from their localized light color appearance after etching, which makes them stand out from the matrix. Generally, white spots are depleted of solute elements, particularly Nb and Ti. The grain structure of white spots is usually coarser than surrounding matrix. The observed white spots are classified into three types according the mechanism of formation: discrete, dendritic and solidification white spot [Jackman et al.,

1993; Jackman et al., 1994].

A discrete white spot has a distinct boundary (Figure 2.11), and has a grain size larger than or at least equivalent to that of alloy. Usually, they can be found in the region from the mid-radius to the center of the cross section. Composition analysis shows the discrete white spots are lean in Nb, and contain slightly less Ti, Al and Mo than base alloy; they are enriched in Ni, Cr, and Fe.

Figure 2.11 Large discrete white spot in an alloy 718 billet slice. Scale in inches. [Jackman

et al., 1994]

The formation of the discrete white spots may probably be caused by the fall-in of shelf and crown materials during VAR process. The shelf or crown materials can be detached by combinational effects of thermal and mechanical conditions; the fall-in materials have a higher melting temperature and density so that the undissolved materials are entrapped in the ingot and form the discrete white spots. Under certain circumstances, discrete white spots are mixed with clusters of oxide, nitride or carbonitride particles; these white spots have dark boundaries surrounding them and are termed “dirty” discrete white spots. A

crack defect may be observed in dirty white spots if the cluster has a large enough size.

During the inspection of superalloys, a lot of ultrasonic indications are finally proved to be cracks at inclusions related to discrete white spots.

Dendritic white spots are usually located at the central region of the ingot cross section.

Unlike discrete white spots, they have a diffuse interface with the base material and appear as dendrite. Composition analysis indicates the solute depletion is not as much as that of discrete white spots. It has been widely accepted that dendritic white spots are remnants of fallen dendrites in electrode.

Solidification white spots are light areas between surface and mid-radius of a VAR ingot after etching. This kind of white spots generally have a thin linear appearance and associate with ring pattern. Sometimes, they look like hook or arc with concave side facing the center.

The interface between solidification white spots and base matrix is diffuse. They are formed as a result of localized decrease in solidification rate.

Effects of white spots on mechanical properties have been studied. Solidification white spots cause slightly drop in strength and discrete white spots result in a larger drop, but ductility is relatively higher. Metal contain dendritic white spots have a slightly lower ductility, while the strength is close to matrix. However, for pieces that have clusters of inclusions, no matter discrete white spots or dendritic white spots, the ductility is lowered 52

significantly [Jackman et al., 1993].

Low cycle fatigue life (LCF) is not significantly influenced by dendritic and solidification white spots. Studies show clean discrete white spots only cause minor drop on LCF life.

Because the clusters of inclusion may serve as sites for early initiation of cracks, the dirty discrete white spots considerably reduce the LCF life.

2.3.3 Forging of superalloys

Superalloys are more difficult to forge than most other metals because of their high hot strength, especially where precipitation hardened alloys dominate the market. Forging of superalloys is usually considered as part of total thermomechanical processing. Other than shaping, forging also has the objectives of uniform grain refinement, control of second-phase morphology and controlled grain flow. Recrystallization is desired in forging operation to obtain the controlled grain size and flow characteristics. It helps eliminate grain boundary and twin-boundary carbides that may develop during heating or cooling

[Donachie and Donachie, 2002].

Forging problems can come from various sources including poor grain size control, grain size banded areas, internal cracking and surface cracking. Figure 2.12 shows a forging with cracks due to poor forging practice. Figure 2.13 compares the microstructure resulted from temperature not properly controlled. The right figure shows that many coarse grains remain 53

in low-temperature region. When forging temperature in IN-718 is too high, grain size bands form in niobium lean region, as shown in Figure 2.14. Therefore, forging of superalloys requires accurate control in condition, especially forging temperature.

Figure 2.12 Surface cracking caused by poor forging practice [Donachie and Donachie,

2002]

Figure 2.13 Fully recrystallized grains (left) and microstructure with many unrecystallized

grains (right) in IN-718 [Donachie and Donachie, 2002]

Figure 2.14 IN-718 microstructure showing grain-size bands caused by too high a forging

temperature [Donachie and Donachie, 2002]

IN-718 is the most dominant alloy in superalloy production among various commercially available superalloys. It has been widely used in jet engine disks and other structural parts in aerospace industry for its high resistance to low cycle fatigue at high temperature and good castability, workability and weldability. The study on superalloy forging in this dissertation is based on IN-718, so remaining discussion in this section will focus on

IN-718.

In IN-718, δ phase is important in controlling grain size during hot working. It pins the grain boundary during processing and avoids the grain growth. Standard forged IN-718,

which is done above δ-solvus, produces fully recrystallized structure with grain size rating

ASTM 4-6. The forging is then strengthened by solution treatment above δ-solvus followed by age-hardening. Fine grain IN-718 has initial forging done above δ-solvus, and final forging done slightly below δ-solvus. Solution treatment below δ-solvus is used before age-hardening. Forgeability is dropped in this temperature range, but grain size around ASTM 8 can be obtained. In direct-age forged IN-718 parts, final forging or even all operations are done subsolvus and age hardened without solution treatment. This can lead to a grain size in the range of ASTM 10.

In IN-718, the amount of γ’’ and δ phase is greater than γ’ phase. At low temperature, metastable precipitate γ’’ predominates, while at the temperature higher than 1700 °F (927

°C), δ phase dominates and has a needlelike structure. Under even higher temperatures of

1800 °F to 1850 °F (982 °C to 1010 °C), δ phase is spherodized. A temperature higher than

δ-solvus causes the solution of δ phase. So, from the perspective of controlling grain size, the ideal forging temperature is 1800 °F to 1850 °F (982 °C to 1010 °C) [Donachie and

Donachie, 2002]. However, in practice, a wider range is used in forging of IN-718.

Depending on content of niobium, the δ-solvus can be in a range of 1005 – 1015 °C

[Azadian et al., 2004], 990 – 1020 °C [Mosser, et al., 1989], or 1040 °C [Prasad and

Srinivasan, 1994]. Different forging temperatures are also used in different researches, for example, 950 – 1200 °C [Prasad and Srinivasan, 1994], or 950 – 1120 °C [Mosse et al.,

1989]. Study also shows that lower temperature (940 °C) and more hits during forging may 56

generate significantly finer grain structure [Brooks, 2000].

Hot working of IN-718 is studied extensively from ingot breakdown to forging. In addition to conventional experiments, computer modeling of forging process are increasingly used in this area. Based on the physical data acquired from experiments, like material constitutive behavior [Zhao et al., 2004b], thermal properties, interface friction and heat transfer, forging process can be simulated by computer calculations [Srinivasan et al.,

1993]. With the help of computer simulations, researchers are able to understand the deformation behavior and design the forging process more easily.

CHAPTER 3

APPROACH AND METHODOLOGY

Many different approaches, including mathematical methods, engineering methods and design methods, will be used in this research. Some main approaches are briefly introduced in this section.

3.1 Finite element method

Finite element method (FEM) was first created to solve the complex elasticity, and structural analysis problems. From the viewpoint of mathematics, it is a method for finding approximate solutions of partial differential equations and integral equations. The essential characteristic of FEM is mesh discretizing a continuous domain into a set of subdomains.

In structural mechanics, the finite element methods are usually developed based on energy principle, such as virtual work and minimum total potential energy principle.

The application of FEM in metal forming can be traced back to 1960s. According to various constitutive formulations used for materials deformation, FEM in metal forming 58

can be classified as rigid-plastic, rigid-viscoplastic, elastic-plastic and elastic-viscoplastic.

Different stress-strain curves can be seen in Figure 3.1 for different material models

[Jackson and Ramesh, 1992].

σ σ

ε ε

σ ε& σ ε&

ε ε

Figure 3.1 Different types of material stress-strain curves

From the figure, it can be seen that neither rigid-plastic nor rigid-viscoplastic considers the elastic portion. The difference between plastic and viscoplastic is that flow stress is strain rate dependent in viscoplastic material models, while in plastic models, the strain rate has no influence on stress. For normal metal forming, where large deformation is imposed, elastic-plastic FEM (Prandtl-Reuss constitutive relation) and rigid-plastic FEM

(Levy-Mises constitutive relation) give almost the same results [Jackson and Ramesh,

1992]. For this reason, rigid-plastic and rigid-viscoplastic FEM are extensively used in metal forming calculations.

3.1.1 Rigid-plastic FEM

Rigid-plastic FEM is based on virtual work equations [Jackson and Ramesh, 1992]:

A Tiui dA = σ ij ε ij dV (3.1) ∫ & ∫V &

Here, Ti represents the surface traction components, u&i are velocity components and σij is the stress tensor. Strain rate is defined by

 ∂u  1  ∂u&i & j  ε&ij =  +  (3.2) 2  ∂x j ∂xi 

According to flow rule, stress tensor can be calculated by 1 σ = s + s δ (3.3) ij ij 3 kk ij 1 where sij denotes the stress deviator tensor, s is the mean stress and δ is the 3 kk ij

Kronecker delta. Stress deviator tensor sij can be calculated according to Levy-Mises equation: 2 σ sij = ε&ij (3.4) 3 ε& where σ and ε& are von Mises effective stress and effective strain rate, respectively.

Effective stress of a rigid-plastic work-hardening material can be represented by

σ = Y = Y0 1( + βε ) (3.5) where Y0 is initial yield stress and β is the work-hardening coefficient of the material.

Node velocity can be derived from contact boundary conditions; the velocity boundary condition is given by

u&ni = Vdie ⋅ nˆi (3.6)

This means normal component of nodal velocity at the boundary node is equal to the normal component of the die velocity. Surface traction component Ti mainly comes from friction boundary conditions. Traction due to friction is either calculated by Coulomb model or by Tresca model.

Given the information of boundary conditions, mesh settings, material yield criteria and flow rule, elemental contributions can be obtained by solving the governing equations in matrix form.

In metal forming, if the initial temperature is much higher than the environmental temperature or large amount of heat is generated due to mechanical work, heat transfer becomes an important consideration. Coupled thermal and mechanical FEM was developed for solving this problem. The coupling between deformation and heat analysis is given through the material constitutive relationship for the workpiece. The thermal analysis of the die and that of the metal being worked are connected through the boundary conditions imposed at the die-workpiece interface [Jackson and Ramesh, 1992].

3.1.2 Metal forming modeling using viscoplastic approach

During metal forming, materials can be seen as viscoplastic material; the constitutive laws may be expressed in terms of a viscoplastic potential [Chenot and Bellet, 1992].

Viscoplastic potential φ is a function of strain rate tensor ε& , the constitutive equation is ∂φ(ε) σ = & (3.7) ∂ε& Considering the material is incompressible, φ must be independent of the rate of compressibility:

θ& = tr( ε&) = div( v) (3.8) where v is the velocity field. φ must be a function of only invariants of the strain rate tensor.

The first invariant is θ& = 0 . The second invariant of stress is

3 σ = ∑ sij sij (3.9) 2 ij

The stress deviator s usually has the form of

∂φ(ε&) 2 1 ∂φ(ε&) s = = ε& (3.10) ∂ε& 3 ε& ∂ε&

If we denote

1 ∂φ(ε&) η(ε&) = (3.11) 3ε& ∂ε& as pseudo viscosity parameter, (3.10) can be transformed into

s = 2η(ε&)ε& (3.12)

Any constitutive law that takes the form of (3.10) corresponds to a viscoplastic potential

ε& φ(ε&) = 3η(λ)λdλ (3.13) ∫0

If the metal in forging is assumed to follow viscoplastic Norton-Hoff law

σ = Kε& m (3.14) stress deviator is generally written as:

m−1 s = 2K( 3ε&) ε& (3.15)

Here, m is strain rate sensitivity coefficient and K is the consistency of material. m =1 corresponds to the Newtonian fluid with a viscosity η = K; m =0 is the plastic flow rule for

a material obeying von Mises criterion with a yield stress σ 0 = 3K ; to approximate hot metals, 0 < m < 1, usually lies between 0.1 and 0.2 [Chenot and Bellet, 1992].

3.1.3 Applications in forging

In addition to rigid-plastic/viscoplastic methods mentioned above, elastic-plastic/viscoplastic methods have also been used in metal forming. The latter can be used to solve problems like residual stress after unloading or springback. Examples are

Abaqus and MARC.

When large deformations are involved, the neglect of elastic effects does not influence the metal flow and stress calculations significantly. Besides, the rigid-plastic/viscoplastic FEM are easier to code, more inclined to converge and require less computational cost. As a result, some well-developed and widely used FEM software specifically for metal forming are designed this way, for example, rigid-viscoplastic based FORGE and rigid-plastic based DEFORM. These software products serve as powerful tools in modeling various 63

forging processes and predict the metal flow, die filling, defect formation, stress and strain distribution, tool loads, thermal effect, etc.

The availability of reliable and robust software, together with high-performance computer at lower price, makes FE simulation not only an R&D level tool, but also a practical tool in production. The large amount of information obtained from simulations can be used to evaluate forging process and die design in both designing stage and trouble shooting stage

[Kim et al., 2000]. The advantages of using FE simulations in forging include: reduced lead time, reduced cost, and technological improvement (Figure 3.2).

Figure 3.2 Advantages of using FE simulations in forging [Kim et al., 2000]

Presently, the application and research of forging simulations focus on several aspects;

Hartley and Pillinger [2006] provides the summary of these aspects:

1) Process modeling. This is the most comprehensive aspect that covers numerous topics.

It includes geometric accuracy of forgings, forming of complex 3D components,

specific product related problems (for example, gear or aluminum alloy wheels),

multi-stage operations, microforging for electronic and medical devices, and so forth.

2) Tool and die design. FE simulations are being used by researchers to design

intermediate die shapes and final die shapes. It also includes specific die features like

flash design; for cold forging die, elastic deflection and failure analysis have been

investigated.

3) Interface phenomena. The phenomena take place between workpiece and die involve

friction between tool and forging, die wear, heat transfer (especially for hot forging).

The coupling of these phenomena is difficult because of the data acquisition.

4) Material phenomena. This aspect includes the development of constitutive models,

modeling of microstructure evolution, and modeling of damage.

5) Computational aspects. Other than FEM application, the algorithm itself is also being

studied by researchers. As forging always involves large deformation, the elements

continue degrade and remesh is needed. Different remesh algorithm is still being

studied to deal with various problems. Other efforts are being made to avoid

convergence problems and reduce the calculation time.

3.2 Design of experiments and response surface methods

Experiments are indispensable in science and engineering fields. Design of experiments

(DOE) refers to an organized method used to establish the relationship between input 65

factors and output of the process. The effective use of statistical principles in DOE ensures that experiments are designed efficiently and economically, and both individual and joint factor effects can be evaluated [Mason, et al., 1989].

A full factorial experiment design, which includes all the combinations of factor-level, is the most straight forward design. In a complete factorial design, all the factor-level combinations are randomly assigned to the sequence of test runs. For example, if there are l1 levels for factor 1, l2 levels for factor 2, … and lk levels for factor k, the complete factorial design gives l1×l2×…× lk test runs. Since experimenters may not include every major influence, or due to some unplanned complications, randomization is very important to cancel the bias effects in the design.

From factorial design, main effects and interaction effects can be calculated. Main effect is defined as the difference between the average responses at two levels; it measures the average effect of one factor over all conditions of the other factors. Two-factor interaction effect refers to half the difference between the main effects of one variable at the two levels of another variable. Similarly, interaction between more factors can be defined. Effects allow experimenters to analyze how a particular variable influences the response and how their interactions influence the response. Effects can be calculated by table of contrast coefficients or Yates’s algorithm [Box et al., 1978]. By running replicated experiments, standard errors for effects can be calculated. 66

By plotting ordered effects against normal probability, the effects that have larger influence can be identified since they are off the straight line, which means they are not explained as chance occurrences. A further normal plotting of residuals can provide a diagnostic check for included effects. If all points lie close to the line, we can conclude that effects not being included in the model can be explained by random noise.

When the number of variables increases, the number of runs required by factorial design increases geometrically. In this circumstance, fractional factorial experiments are widely used to save budget and time. Besides, when many factors are involved in experiments, it is not necessary to run all possible factor-level combinations to find the important factor effects.

Fractional factorial design can be constructed by confounded effects. If the calculated effects can only be attributed to their combined influence on the response instead of their individual ones, two experimental effects are said to be confounded. In design resolution R, no p-factor effect is confounded with any other effect containing less than R-p factors.

Data collect from experiments are meaningful only in relation to a conceptual model.

Sometimes, the phenomenon being studied is well understood, so a reasonable function form can be formulated from theoretical considerations. The model developed this way is 67

called theoretical or mechanistic model. Sometimes, however, the mechanism underlying a process is not well understood, or is so complicated that it is difficult to construct theoretical model. Under these circumstances, empirical models are always utilized.

Response surface methodology (RSM) is a collection of statistical and mathematical techniques used in the empirical study of relationship between output responses and input variables. It is useful for developing, improving, optimizing processes, and can also be used to design new products and improve existing designs [Myers and Montgomery, 1995].

A response surface is the geometrical representation of the response as s function of quantitative factors. The reasons that designing experiments to fit responses is important include [Mason et al., 1989]:

The response function is characterized in experimenters’ region of interest;

Statistical inferences can be made on the sensitivity of the response to interested input

variables;

Factor levels can be determined for which the response is optimal;

Factor levels can be made that several responses are simultaneously optimized; or

even if it is impossible, tradeoffs are readily apparent.

Though sometimes cubic terms are required for adequate fit, or even transformation of the design variables and responses, e.g. log transformation, may be needed, second-order model is the most widely used model to describe experimental data in which system 68

curvature is readily abundant [Myers and Montgomery, 1995]. It has a form of

2 2 y = β0 + β1 x1 + β2 x2 +…+ βk xk + β11 x1 +...+ βkk xk +β12 x1x2+…+βk-1, k xk-1xk + ε

(3.16)

It includes all terms through second order and a random error. The experimental design using this model must have at least 1 + 2 k + k(k-1)/2 distinct design points because the model has 1 + 2 k + k(k-1)/2 parameters, and at least three levels of each factor must be involved to estimate the pure quadratic terms.

There are two frequently used designs for fitting second order response surfaces with 3 levels, center composite design (CCD) and the Box-Behnken design (BBD). CCD involves

k a complete or fractional 2 factorial points, 2k star points along the coordinate axes and nc center points. Each component plays a different role:

1) The factorial points mainly contribute to estimation of linear terms and two-factor

interaction terms;

2) The star points mainly contribute to the quadratic terms;

3) The center runs give an internal estimate of error and contribute toward the

estimation of quadratic terms.

Box-Behnken design is another efficient three-level design for fitting second-order response surfaces. It constructs balanced incomplete block designs. For example, in a three factor design, block 1 can keep factor 1 at center level, while factor 2 and 3 are paired 69

together in a 2 2 factorial; by similar way, block 2 and 3 can be designed. Same as in CCD, a set of center points is also included. In the cases of k =3 and 4, BBD almost gives the same number of designs as CCD does. BBD is a spherical design since each point has an identical distance from center point. BBD should be limited to the situations that response at the extremes is to be predicted.

Other designs include equiradical design, like pentagon, hexagon and heptagon, and designs require less run number such as small composite design, Koshal design, and

Hybrid designs. However, CCD and BBD remain as two most important designs for fitting response surfaces.

3.3 Monte Carlo simulation

Monte Carlo (MC) simulation is a method of studying the distribution of a random variable by means of simulating real situation with random numbers. Consider a model that can be modeled as:

Y = f ( X) = f ( X1, X2, …, Xk) (3.17) where Xi is the random variable, and Y is model response, the distribution of Y is to be studied given the distributions of input parameters. Sometimes, response Y can be derived analytically based on statistical theory. However, in many real problems, the function f is often complicated and random vector X involves several kinds of probability distributions so that it is very difficult of even impossible to derive the exact distribution of Y. In these 70

cases, Monte Carlo simulation provides an alternative way to approximate distribution of Y.

Often, MC simulation is used in risk assessment, specifically in sensitivity analysis and uncertainty analysis [Millard and Neerchal, 2000]. The applications of MC simulation are widely seen in physics, chemistry, engineering, finance, business, and so on.

In calculation, a large number of random numbers were generated from some specified theoretical probability distribution for X; Y is then evaluated for each generated random vector based on the model. The resulting distribution of Y is assumed to be close to the real distribution. The factors influence how close the predicted distribution is to the real distribution include how well the model describes the true relationship between Y and X, how accurate the distribution of X reflects the true distribution, and how many samples are used for Monte Carlo simulation.

CHAPTER 4

EFFECT OF FORGING PATH ON MICROFEATURE LOCATION IN

COMPRESSOR DISK FORGING

4.1 Introduction to hard alpha inclusion

On July 16, 1989, United Airlines Flight 232 suffered a catastrophic failure in its number 2 engine. This engine failure destroyed the plane’s hydraulic systems and the plane lost control. The experienced pilots still kept it airborne long enough time for an emergency landing at Sioux City, Iowa. It broke up on the runway, killing 111 people

[http://en.wikipedia.org/wiki/United_Airlines_Flight_232]. This crash was a result of fatigue failure initiated by the presence of hard alpha inclusion in titanium alloy fan disk

[Ammari et al, 2002].

Hard alpha inclusion is a type of high interstitial defects, which is characterized by substantially higher hardness and low ductility than the material from the surrounding region. Figure 4.1 shows a typical example of hard alpha with the size of 200 µm. High interstitial defects result from high nitrogen or oxygen concentrations in sponge, master 72

alloy, or revert [Boyer, 1998; Donachie, 2000].

Figure 4.1 Typical hard alpha inclusion [Bellot et al., 1997]

Usually, hard alpha inclusions include voids or cracks (see Figure 4.2), which make them easily detected by non-destructive testing (NDT). It is difficult for NDT to detect uncracked hard alpha inclusions. Inclusion removal by non-destructive examination has also been proved to be difficult due to the background noise generated by α/β structure in thick sections [Bellot et al., 1997]. Other NDT techniques like thermoelectric detection has been studied to deal with uncracked inclusions [Carreon, 2007].

In titanium alloy producing sequences, melting step is most likely subjected to nitrogen contamination, such as air leakage into the melting equipment. Even the strictest control in double or triple melting cannot guarantee total elimination of hard alpha inclusions [Benz et al., 1999]. Currently, the detected incidence rate in aeroengine alloys is less than 1 inclusion/500,000 kg of alloy; however, this type of defect still leads to great concern due to high risk associated with it [Bellot et al., 1997].

(a) Large voids (b) Small voids

Figure 4.2 α segregation: voids surrounded by stabilized α [Donachie, 2000]

Hard alpha inclusions generally have a TiN core surrounded by a layer of α-titanium, which is surrounded by a layer of β-titanium. For some cases, nitrogen stabilized α phase may be there instead of TiN. The brittle inclusions are generally the initiation site of a crack.

Study in component application has shown the early fatigue initiation caused by an

inclusion with a diameter of only 1 mm. The hard alpha inclusions can also lead to voids during forging, thus increasing the size of potential initiation site [Benz et al., 1999]. This has also been confirmed by Chan et al. [2000] by observing that deformed specimens had more voids than the undeformed parts. They found that the flow behavior of the hard alpha inclusion is pressure sensitive due to opening and closure of the cracks during forming.

4.2 Multi-body simulation modeling

To study the complicated contact behavior between hard alpha inclusions and matrix material, different deformable objects have to be modeled. In complex mechanics systems with several components like metal forming, multiple body contacts occur frequently; commercial software FORGE provides the capability in modeling and solving 3D multi-body problems. It uses the concept of contact elements to handle the set of different bodies as different parts of a single mesh, and a global resolution for all the bodies in contact is solved. The equations in this section are identical or similar to the literature mentioned in the text.

4.2.1 Constitutive equations and friction

The plastic deformation induced in forging is considerably larger than elastic deformation; therefore, the elastic deformation of the material can be neglected in calculation. Although constitutive equation of a material can be viscoplastic, elastoplastic, elastic viscoplastic or

Newtonian, in this part, viscoplastic behavior is used to simply explain the algorithm. 75

In FORGE, isotropic Norton-Hoff law is used for viscolastic behavior:

m−1 s = 2K( 3ε&(v)) ε&(v) (4.1) where s is deviatoric stress tensor, ε& is strain rate tensor, ε& is effective strain rate and is defined as

2 ε 2 2/1 ε& = ( ∑ & ij ) (4.2) 3 i, j

ε & ij is the strain rate tensor. K is material constant and can be a function of strain hardening, m is strain rate sensitivity coefficient, v is velocity vector field. The following equation defines the material incompressibility:

div (v) = 0 (4.3)

Let Ω1 and Ω2 denote volumes of two bodies, and ∂ Ω1 and ∂ Ω2 be their boundaries.

Without considering the mass and inertia force, the equilibrium equation is simply

div (σ) = 0 on Ω = Ω1 ∪ Ω 2 (4.4) where σ is stress tensor. If viscoplastic friction behavior is used, the following equation is added to complete equation (4.4)

q−1 τ = −α f K ∆v t ∆v t (4.5) where τ is the shear stress, αf is viscoplastic friction coefficient; q, the sensitivity parameter to the sliding velocity, is always taken equal to m. ∆vt is the tangential relative velocity defined as

1 2 ∆v t = (v − v ) − ∆v n (4.6)

1 1 2 2 l ∆vn is normal relative velocity given calculated from ∆v n = v ⋅n + v ⋅ n . Here, v is velocity vector defined on Ωl, and nl is the outward normal to volume Ωl. For this friction law, either a unilateral or bilateral contact condition can be associated. The local form of equations (4.3), (4.4) and (4.5) can be translated to the global form through virtual work principle [Barboza and Fourment, 2002]. For any given admissible velocity field and admissible pressure field, a quasi-static equilibrium in two bodies can be given and the solved. The details of this algorithm are given in Barboza and Fourment [2002] and

Fourment et al. [1999].

4.2.2 Spatial and time discretization

To compute the velocity and pressure vl and pl, they must be discretized. In FORGE, this discretization is based on a continuous interpolation of the pressure. The linear tetrahedral elements are used to satisfy the velocity-pressure compatibility. The pressure and linear coordinates are interpolated linearly with piecewise linear functions N; and piecewise linear functions, which include internal degrees of freedom in each element, called bubble

~ shape functions N , are used to discretize velocity field [Arnold et al, 1984]. The definition of bubble shape function can be seen in Yamada [1998]. The discretizing equations are

l l l x h = ∑ X k N k (4.7) k

l l l ph = ∑ Pk N k (4.8) k

l l ~ l v h = ∑ Vk N k (4.9) k x, p, and v are discrete coordinates, pressure and velocity, respectively, and X, P, and V are nodal coordinates, pressure and velocity. Subscript h means discretized scalar or vector.

Strain rate tensor can be calculated by

3 ε l l ik l i & h (v h ) = ∑∑ B Vk (4.10) k i=1

B is the operator usually used to calculate strain tensor from velocity field. Explicit scheme

l l is used for time integration. Domain Ω t at time t is updated to domain Ω t+∆t at time t+∆t using the following equation:

l t+∆t l t l t ∀k, X k = X k + Vk ∆t (4.11)

4.2.3 Discrete contact treatment

The conditions that the two bodies do not penetrate each other must be satisfied in contact treatment. In FORGE, a master-slave algorithm is used where slave nodes cannot penetrate master surfaces, while master nodes can penetrate slave surfaces. The penetration can be minimized if the slave has a finer mesh than master.

The contact algorithm treats a slave node and a master face as the contact element. Assume

Ω1 is the slave body and Ω2 is the master body, the algorithm takes two steps for each time increment and each slave node S ∈ ∂ Ω1: (1) by normal projection, determine the closest node on master body M; and (2) choose the closest face (triangle) among all master faces

containing projection M of slave node S. The distance between two bodies at time t

(denoted by d t ) is defined as the dot product of vector and inward normal to the SM SM master face n.

d t SM n (4.12) SM = ⋅

To avoid violating the penetration constraints, the distance at time t+∆t must be greater than zero. The distance at time t+∆t can be calculated by equation (4.11)

d t +∆t = d t + (v − v ) ⋅n∆t + O(∆t 2 ) ≥ 0 (4.13) SM SM M S where d t+∆t is distance between two bodies at time t+∆t and v and v are velocity SM M S of master body and slave body, respectively.

4.2.4 Finite element formulation

Penalty method is used to impose the contact condition in formulation. The formulation equations are:

2 l l ik l l ik l l ∀k,∀i = 3,1 l s(v h ): B dV − l phtr ( B )dV − l T N k dS ∑∫ΩΩ ∫ ∫∂Ω l=1 T

t q−1 d ~ l k kk ' k + α K ∆v ∆v N dS + ρ l (k) (v − v ' )⋅n − n = 0 (4.14) ∫ f ht ht k con ∂Ωc k k i ∂Ωc ∆t

2 l l l N k div (v h )dV = 0 (4.15) ∑∫Ω i=1

In equation (4.14), T is the surface force, dV is differential volume, dS is differential

' surface area, ρcon is penalty factor, x is the positive part of x, k is the projection of node k on the master surface if k is a slave node, l (k ) is the characteristic function of ∂Ωc

∂Ωc , all other variables are consistent with the previous definition in this chapter. Equation

(4.15) guarantees the incompressibility of the material after discretization. The nonlinear system composed by equation (4.14) and (4.15) is solved by Newton-Raphson algorithm in

FORGE code.

In this master/slave approach, the usage of non-coincide meshes can result in non-symmetric formulation. If master mesh is significantly finer than slave mesh, severe convergence problem will arise. A quasi-symmetric contact formulation for 3D deformation has been studied [Fourment et al., 2004; Fourment and Popa, 2005; Popa,

2005] to deal with the problem with finer mesh in master body. However, the most recent version of FORGE, FORGE 2008, does not include the quasi-symmetric approach. In this research, there is no need to use quasi-symmetric formulation since the master does not have significantly finer mesh than the slave body. The master/slave formulation is enough to solve the problem.

4.3 Titanium forging modeling with hard alpha inclusion

The existence of the hard alpha defect in titanium alloys may significantly reduce the service performance of the final part. It is essential to study the flow behavior of hard alpha during the forging of the base material. Finite element analysis has been used to predict the movement of hard alpha inclusion during forging by some researchers. Although limited experiments have been done due to very high cost and huge amount of work needed, 80

comparison between FE analysis and experimental results shows numerical analysis provides good prediction of inclusion movement [Batzinger et al., 2005; FAA/DOT, 2000].

In the work in FAA report Turbine Rotor Material Design [FAA/DOT, 2000], commercial code DEFORM 2D was modified to simulation the hard alpha movement during forging. A normal 2D simulation, called macrosimulation, with base material was run at the beginning; then the geometry and location of hard alpha inclusion was defined in their “microcode”.

The boundary conditions of inclusion obtained from macrosimulation by point tracking were used to calculate the deformation of hard alpha, which is called microsimulation.

With the ability of to model 3D multi deformable bodies, the hard alpha inclusion can be better represented in FORGE without modification to the code. The objective of following work is to study the movement of hard alpha inclusion in forging with 3D code.

4.3.1 3D modeling of hard alpha in forging

The first step of compressor disk forging is modeled to study the effect of hard alpha on metal flow. In this isothermal upsetting, 3D modeling is used to fully capture the deformation in all three principal directions: axial direction, radial direction and hoop direction. The billet is modeled in a section of 30° to reduce the computation cost. The hard alpha in the billet is a cylinder with a diameter and height of 5.08 mm. The dimensions of billet and hard alpha are taken from the disk forging and synthetic seeds in FAA/DOT 81

reports [2000; 2008]. The 3D multi-body model before and after forming is shown in

Figure 4.3.

(a) Initial shape of billet and hard alpha (b) Final shape of billet and hard alpha

Figure 4.3 3D multi-body model of upsetting

The constitutive properties of hard alpha titanium have been studied by Chan et al. [2000].

Compression tests, indirect tension tests, indentation tests and plane strain compression tests were conducted. The engineering stress strain curves of hard alpha titanium under different test conditions for compression tests are shown in Figure 4.4. Materials with different nitrogen content show that under normal forging condition material with less than

4% nitrogen can be plastically deformed. Compare the flow data of hard alpha with

Ti-6Al-4V data from Seshacharyulu et al. [2000] (see Figure 4.5), it is found that the flow 82

stress of hard alpha is about 2 to 4 times higher than the flow stress of Ti alloys, if cracked material has been neglected. It should be noted the following equations must be used to convert engineering stress and strain to true stress and strain

1 ε = ln ; σ = σ e exp( −ε ) (4.16) 1− ε e where ε is true strain, εe is engineering strain, σ is true stress and σe is engineering stress.

Figure 4.4 Compression stress-strain curves of hard alpha Ti [Chan et al., 2000]

120

100

40 Stress (MPa) Stress 20

0 0 0.1 0.2 0.3 0.4 0.5 Strain

Strain rate = 0.01 Strain rate = 1

Figure 4.5 Ti-6Al-4V flow data for 950°C from Seshacharyulu et al. [2000]

The material properties of hard alpha are approximated by scaling the flow stress of base material, which is Ti-6Al-4V. A flow stress same as base material is denoted by Case 1; in

Case 2 and Case 3, the flow stresses is magnified 2 times and 4 times, respectively. In FAA report [2000], 10% of the flow stress of uncracked hard alpha is taken after cracking. In

Case 4, 20% of the flow stress of Ti-6Al-4V was taken to represent cracked hard alpha inclusion. The forging is done isothermally with a billet and die temperature of 950 °C, the die velocity is 5 mm/s. The global equivalent strain distributions in each forged part are shown in Figure 4.6 to Figure 4.9. Differences in center of the billet due to presence of the hard alpha anomaly can be observed, but the strains near the inclusion, shown in red box, are similar. The hard alpha inclusion does not change the global metal flow noticeably.

Figure 4.6 Global equivalent strain distribution of forged part in Case 1 σHA =σTi64

T=950°C, V D=5 mm/s, reduction =65.6% (inclusion shown in red box)

Figure 4.7 Global equivalent strain distribution of forged part in Case 2 σHA =2× σTi64

T=950°C, V D=5 mm/s, reduction =65.6% (inclusion shown in red box) 86

Figure 4.8 Global equivalent strain distribution of forged part in Case 3 σHA =4× σTi64

T=950°C, V D=5 mm/s, reduction =65.6% (inclusion shown in red box)

Figure 4.9 Global equivalent strain distribution of forged part in Case 4 σHA =0.2× σTi64

T=950°C, V D=5 mm/s, reduction =65.6% (inclusion shown in red box) 87

To examine the deformation takes place at the hard alpha cylinder, Figure 4.10 to 4.13 illustrate the close-up pictures of the inclusion for each case. Although the constitutive equations for the four cases are different, at the final stage, the cylindrical inclusions all have the same shape; the contour lines in each inclusion are similar under the same scale.

These figures indicate that a flow stress change up to 20 times has minor influence on the deformation of the hard alpha during the forging process.

Figure 4.10 Local equivalent strain distribution on inclusion in Case 1

Figure 4.11 Local equivalent strain distribution on inclusion in Case 2

Figure 4.12 Local equivalent strain distribution on inclusion in Case 3

Figure 4.13 Local equivalent strain distribution on inclusion in Case 4

Again, material flows of each case are compared by the location of the points on inclusion.

The final locations of five points from the deformed hard alpha anomaly, defined in Figure

4.14, are compared. Point A, B, C, and D are four corner points on the symmetry plane, and point E is the deepest point from the symmetry plane, located on the upper periphery of the cylinder. The point coordinates are compared in Table 4.1, and equivalent strain values and von Mises equivalent stress values are compared in Table 4.2. X value represents the radial coordinate, Y value represents the hoop coordinate, and Z value represents the axial coordinate. The origin is located on symmetry axis and on bottom.

Figure 4.14 Points selected for comparison

Case 1 (X,Y,Z) Case 2 (X,Y,Z) Case 3 (X,Y,Z) Case 4 (X,Y,Z) Points (mm) (mm) (mm) (mm) A (76.9,0,18,4) (76.5,0,18,6) (75.2,0,19.3) (77.5, 0,18.2) B (85.0,0,17.7) (84.6,0,17.7) (83.2,0,18.1) (85.6, 0,17.5) C (74.3,0,16.5) (73.8,0,16.8) (72.1,0,17.4) (74.9, 0,16.3) D (82.0,0,15.9) (81.8,0,16.1) (80.1,0,16.7) (83.0, 0,15.8) E (81.2,3.9,18.1) (80.8,3.8,18.2) (79.5,3.8,18.8) (81.8, 3.9,17.9)

Table 4.1 Final positions of tracked points in 3D simulations

Case 1 Case 2 Case 3 Case 4 Points ε σ ( MPa ) ε σ (MPa) ε σ (MPa) ε σ (MPa) A 1.08 34 1.12 74 1.1 126 1.11 9.8 B 1.13 32 0.99 86 1.19 181 1.03 7.8 C 0.87 34 0.92 61 0.81 118 0.88 7.4 D 1.11 22 1.11 66 1.14 150 1.14 9.4 E 1.06 43 1.05 70 1.08 135 1.05 9.3

Table 4.2 Stress and strain of tracked points in 3D simulations

In Table 4.1, it can be seen that harder material moves less distance than softer material.

However, their final position difference is small compared to measurement scatter of ultrasonic inspection. The ultrasonic inspection results in FAA report [2000] show that the difference between repeated measurements can be as high as 4 mm. In Table 4.2, the equivalent strain for the same point between difference cases have little differences. The stress differences are mainly caused by material model.

A smaller hard alpha size with dimension of 2mm by 2mm has been tried to see the effect of inclusion size on point movement. Since final location is the main concern, so only the final locations of the five points are compared for 3 cases. The results are listed in Table

4.3.

Case 1 (X,Y,Z) Case 3 (X,Y,Z) Case 4 (X,Y,Z) Points (mm) (mm) (mm) A (78.0, 0, 17.3) (78.2, 0, 17.2) (77.7, 0, 17.5) B (81.2, 0, 16.9) (81.3, 0, 16.9) (80.8, 0, 17.0) C (76.9, 0, 16.6) (77.1, 0, 16.5) (76.8, 0, 16.8) D (80.0, 0, 16.3) (80.2, 0, 16.1) (79.7, 0, 16.4) E (79.5, 1.5, 17.2) (79.8, 1.5, 17.0) (79.3, 1.5, 17.3)

Table 4.3 Final position comparison for small inclusion

Comparison between Table 4.1 and Table 4.3 reveals that as inclusion size decreases, the difference of final locations for different materials decreases. A research on hard alpha size distributions show that the majority of hard alpha anomalies are pretty small compare to the inclusions in previous 3D simulations (5.08 mm×5.08mm and 2 mm×2 mm). Figure

4.15 shows an exceedance curve to characterize the defect occurrence rate and defect size in 1×10 6 kg titanium rotor materials. The illustration indicates that large defects are very rare.

Figure 4.15 Defects exceedance curve (1×10 6 kg) for titanium rotor disk materials (1 mm 2

= 1550 mil 2) [Wu et al., 2002]

Therefore, the change of flow properties for hard alpha inclusion does not have noticeable influence on the strain, stress distribution as well as global metal flow given the dimension of inclusion is small compared with compressor disk. The constitutive behavior of 93

Ti-6Al-4V will be used for inclusion in this research. As a result, intensive computation effort of 3D multi-body numerical simulation can be replaced by single deformable body model. It should be noted that even for upsetting, 3D multi-body simulation takes 15-18 hours for 5.08 mm×5.08mm inclusion and 80-100 hours for 2 mm×2 mm inclusion.

4.3.2 Simplification of 3D modeling to 2D modeling

The 2D finite element model is usually more cost efficient than 3D counterpart. 3D modeling can be used to model any complicated 3D feature, while 2D modeling can only be used to model plane strain and axisymmetric deformation. In this section, further study has been conducted to compare the metal flow of 3D and 2D axisymmetric modeling.

In 2D modeling, the cylindrical microfeature in 3D case is modeled as a ring. Same material for billet and inclusion makes it possible to us 2D axisymmetrical single-body simulation. Because 2D cannot capture the deformation in hoop direction, point E in Figure

4.14 is not investigated. Final positions of point A, B, C, and D tracked in FORGE are compared with 3D simulation Case 1. The comparisons of point coordinates, equivalent strains and von Mises stresses are listed in Table 4.4.

Location (X,Z) mm ε σ (MPa) Points 3D 2D 3D 2D 3D 2D A (76.9, 18.4) (76.7, 18.4) 1.08 1.02 34 41 B (85.0, 17.7) (85.0, 17.6) 1.13 1.07 32 42 C (74.2, 16.5) (73.8, 16.4) 0.87 0.89 34 41 D (82.0, 15.9) (82.0, 15.8) 1.11 1.05 22 42

Table 4.4 Comparisons of point locations, strains and stresses in 2D and 3D simulations

The strains of 3D and 2D are close because all four points are located on the symmetry plane; strains in hoop direction are all zero. The difference between stresses is caused by the difference between 2D and 3D code. Although the 2D case models the cylindrical feature as a ring, the comparison between 2D and 3D simulations on point locations shows that the metal flow in revolving plane is not changed much by changing from 3D modeling to 2D modeling. Therefore, calculation efficiency can be greatly improved by replacing 3D simulation with 2D axisymmetric simulation.

4.4 Risk mitigation by changing forging paths

Complicated forgings are generally done by multiple steps. Metal flow can be greatly different with different forging paths. Based on previous discussions, 2D axisymmetric modeling is used to track the point movement in forging process for various forging

sequences. The initial billet, made of Ti-6Al-4V, has a height of 254 mm, and diameter of

141.5 mm; in the first step, it is upset to a pancake; the second step deforms the pancake to disk. Both steps are done isothermally with a temperature of 950 °C, the die velocity is 5 mm/s, and friction factor is m = 0.3. The 3D shapes of disk forging and machined disk are shown in 4.16. Figure 4.17 shows the cross section of the disk forging and machined part.

Figure 4.16 Titanium disk forging (left) and machined disk (right)

Figure 4.17 Cross section of disk forging (solid line) and machined disk (dotted line)

4.4.1 Forging path selection and constraints

In present research, billet and final disk dimensions are fixed; the only possible change is the preform dimension. The pancake is upset between two flat dies; pancakes with different heights in the second forging operation will produce different metal flow. The constraints in forging equipment, material behavior and forging feasibility can all impose restrictions on forging process design.

For a complex forging, one reason of using multi-step operation is that the deformation from billet directly to final forging is too large to produce defect free part. Preform is designed accordingly to move metal step by step, so that the strain in each step is less than a certain critical value. For a piece of metal, the ability to complete the shape change

without producing fracture or undesirable microstructure is called workability [Semiatin,

2003a]. For Ti-6Al-4V, tension tests were conducted to study the workability by Semiatin

et al.[1999b]. Figure 4.18 shows the strain to initiate cavities ( εi) and fracture ( εf) under different strain rates. Care must be taken during designing process to limit the strain below

the strain to initiate cavities ( εi). Strain rate and temperature during the forging must fall in the stable region in instability map describe in Figure 2.7. Other constraints need to be considered are load capacity of the press. The load capacity is set to be 5,000 tons in this case study.

Figure 4.18 Strains to initiate cavities and fracture for Ti-6Al-4V [Semiatin et al., 1999b]

With the aforementioned constraints, 4 preform heights are selected from a relatively large range. The preforms with heights of 80 mm, 95 mm, 110 mm, and 125 mm are denoted by 98

Design 1, Design 2, Design 3 and Design 4, respectively. For each design, strain limit, load, and flow instability are checked to make sure the forgings are feasible. Figure 4.19 illustrates the preform design and constraints check process. In these cases, temperatures in region of machined disk range from 940 – 970 °C and strain rate are less than 0.9. The processing falls into the stability region in instability map. Also, from the temperature and strain rates, the maximum strain allowed in forging is chosen to be 2.80. The loadings and maximum strains for the 4 designs in finishing step are listed in Table 4.5.

Figure 4.19 Different forging paths and point positions

Design 1 Design 2 Design 3 Design 4 Height (mm) 80 95 110 125 Max Load (ton) 4920 4480 4400 4280 Max Strain 2.13 2.21 2.44 2.72

Table 4.5 Max load and strain for four different forging paths in finishing step

Among the four preforms, as height decreases, more metal needs to be extruded to form the mid-radius part, so load is higher; as height increases, less deformation takes place in preforming step, so max strain in the second step is larger. In all four cases, no constraints are violated.

4.4.2 Numerical simulations to build regression models

Tracking the movements of reasonable amount of points can be done by FEM, but for a huge amount of points, FEM will take a long time. So in this section, RSM models are built based on design of experiments to calculate the point positions.

From the stress analysis on rotor disk [Witek, 2006], it is known that the maximum stress occurs at the mounting slots on the rim due to centrifugal force of the blade, contact stress and stress concentration. Thus, in this study, the slot area will be tracked back to billet and studied. In Figure 4.20, 27 points were chosen to represent this area.

100

Figure 4.20 Points in slot area to be back tracked to billet

Obviously, different forging paths have different metal flow. Figure 4.21 shows the initial locations of these points in billet for different forging paths.

101

Figure 4.21 Points tracked back to billet for different forging paths

The box in Figure 4.21 covers all the metals to be moved to slot area in all forging paths.

The design of experiments (DOE) will be done only in boxed area. Full quadratic models are used to represent the metal flow: the initial coordinates ( x, y) in billet is the design parameters, and final coordinates ( X, Y) in disk is the response, the models have the form of:

2 2 X = f (x, y) = a1 x + a2 y + a3 xy + a4 x + a5 y + a6

2 2 Y = g(x, y) = b1 x + b2 y + b3 xy + b4 x + b5 y + b6 (4.17)

The RSM model will be more accurate if it is fit over a smaller region; for this reason, the 102

boxed area is further divided into several subregions and an individual RSM model is created for each subregion. By this way, according to which subregion a point is located and which forging path is used, a corresponding regression model will be used to find the point locations in forging.

4.4.3 Stochastic simulations for risk evaluation

Ultrasonic inspection is used during the forging process to detect if there is any crack due to hard alpha inclusion. If a crack in billet was detected in billet, or a crack is formed after deformation, the part has to be discarded. But there is still a chance that hard alpha with low nitrogen content occurs in the billet, and they can deform with the base material without developing crack. In order to understand the effects of stochastic point locations on final disk, stochastic simulations using the Monte Carlo method are performed to study the influence of forging path on component failure risk.

For titanium alloys, no research has been reported in literature on the probability of hard alpha’s occurrence in the billet. So in this research, the probability of hard alpha being present is assumed to be equal anywhere. 10,000 points are generated in the boxed area; they are uniformly distributed in axial direction and linearly distributed in radial direction because of the change in radius. The typical distributions are shown in the histograms in

Figure 4.22.

103

0.18 0.17 0.16 0.15 0.14 0.13 0.12 Probability 0.11 0.1 0.09 0.08 51 53 55 57 59 61 63 X coordinate (mm)

0.18 0.17 0.16 0.15 0.14 0.13 0.12 Probability 0.11 0.1 0.09 0.08 67.5 87.5 107.5 127.5 147.5 167.5 187.5 Y Coordinate (mm)

Figure 4.22 Monte Carlo sample points distribution in billet

Tracking the movements of 10,000 points using FEM can be computationally prohibitive, while using regression models (4.17) can significantly reduce the calculation cost. The final location of each point is calculated by RSM model for each forging path.

104

To relate defect location with risk of failure, stress analysis during service must be done.

Witek [2006] concludes that the maximum stress occurs at the root of slot. The strategy to relate the applied stress, possible defect locations and severity of the locations is shown in

Figure 4.23. From applied stress distribution, material strength and fatigue information, the failure rate that a defect occurs in a specific location can be determined. For a possible defect tracked from billet to disk, the risk can be determined.

In the slot area, a relation between probability of failure at certain service condition up to a certain service cycles and the location of defect is assumed in Figure 4.24 to demonstrate this approach. The failure probability is the highest at the root of slot, as the defect goes away from the root, the probability decreases.

105

Figure 4.23 Strategy to relate failure risk with applied stress

106

Figure 4.24 Failure probability assumed for slot area

If we denote event F as disk failure, event B as hard alpha’s occurrence in boxed area, then the probability of disk failure can be calculated by the following equation:

Pr( F) = Pr( B) × Pr( F | B) (4.18)

The first term on right hand side of equation (4.18) can be calculated by:

Pr( B) = p ⋅ c ⋅ w ⋅ d (4.19) where p is probability of hard alpha presence in boxed area if there is a hard alpha in billet, in this case, the ratio of boxed volume and billet volume is used; c is the hard alpha occurrence rate in alloy, here 1/500,000 kg is used; w is the weight of the billet; and d is the percentage of hard alpha cannot be detected during forging, in this case, 1% is assumed.

107

The second term on right hand side of equation (4.18) is calculated on final possible defect locations by the following equation:

N 1 Pr( F | B) = ∑ ⋅ k ⋅ Pi (4.20) i=1 N where N is the number of sample points, k is location parameter, k = 1 if this point is in slot area and k = 0 if not. Pi is the probability of failure for a given defect location in slot area, which is obtained in Figure 4.24.

Since the variation can be introduced by Monte Carlo sample points, 4 different Monte

Carlo simulations are performed for each design to calculate standard deviation. The calculated failure probabilities Pr( F) for four different forging paths are listed in Table 4.6.

Probability of failure (×10 -9) Design 1 Design 2 Design 3 Design 4 MC run 1 6.387 6.633 8.468 6.978 MC run 2 6.406 6.846 8.492 6.901 MC run 3 6.293 6.665 8.456 6.890 MC run 4 6.418 6.712 8.373 6.718 Average 6.376 6.714 8.447 6.872 Standard deviation 0.057 0.094 0.052 0.110

Table 4.6 Calculated failure rate for four different forging paths

Although different Monte Carlo runs have different failure rates, the standard deviations are small compare to the difference between various forging paths. This proves that the 108

difference in failure rates is not a result of variation of Monte Carlo simulation. In addition, in all four runs, the same trend can be observed for failure rate: 3>4>2>1.

4.4.4 Further investigation on other possible paths

The failure rate calculation indicates Design 3 (preform height = 110 mm) has the highest failure rate. As height goes away from 110 mm in both directions, the failure rate decreases.

In this section, further work is done to investigate if the failure rate could be reduced by changing preform height while still make the forging process remain in the feasible region.

Two different preform heights have been tried beyond 80 mm and two tried beyond 125 mm; each trial is made with 5 mm change in height. From Table 4.5, it is expected that the maximum load constraint could be violated when preform height is decreased, and maximum strain constraint could be violated when preform height is increased. Also, flow instability has to be checked for each forging path. The results are shown in Figure 4.7.

Height (mm) 70 75 80 95 110 125 130 135 Max Load (ton) 2530 3310 4920 4480 4400 4280 4230 4280 Max Strain 2.69 2.62 2.13 2.21 2.44 2.72 2.78 2.90

Table 4.7 Max load and strain for various forging paths in finishing step

109

Some observations from different forging simulations are listed below:

1) When preform height is reduced below 80 mm, the forging load is not increased as

expected. On the contrary, the maximum load decreases sharply. It is confirmed that

when preform height is below 80 mm, underfill occurs. A short preform tends to

squeeze more metal outward in the first step so that the second step cannot extrude the

metal to fully fill the cavity.

2) The maximum strain also increases as preform height is reduced. This is also caused

by underfill; as the preform becomes thinner, more deformation is needed to fill

center-radius region. Even so, this region still cannot be filled.

3) As preform height increases, load decreases because forming tends to be an upsetting

step instead of extrusion step. However, more deformation is needed in second step for

thicker pancake, so the max strain is higher.

4) Flow instability check shows that no metal falls into unstable region in Figure 2.7

because both strain rate and temperature are carefully controlled.

5) Because of underfill, 80 mm is already the lower bound of feasible region; the upper

bound is determined to be 130 mm to have maximum strain below 2.80; in all cases,

load capacity constraints are satisfied.

From previous observations, the upper bound and lower bound can be determined (Figure

4.25) to be 80 mm and 130 mm, respectively. For preform height of 130 mm, the failure rate must be computed according to the same procedure used for other forging paths. This 110

case is denoted by Design 5. Table 4.8 shows the comparison results of the five designs.

Figure 4.25 Determination of feasible region

Probability of failure (×10 -9) Design 1 Design 2 Design 3 Design 4 Design 5 MC run 1 6.387 6.633 8.468 6.978 6.943 MC run 2 6.406 6.846 8.492 6.901 6.881 MC run 3 6.293 6.665 8.456 6.890 6.869 MC run 4 6.418 6.712 8.373 6.718 6.964 Average 6.376 6.714 8.447 6.872 6.914 Standard deviation 0.057 0.094 0.052 0.110 0.046

Table 4.8 Calculated failure rate for five different forging paths

Table 4.8 is an expansion of Table 4.6. It should be noted that Monte Carlo samples for

Design 5 are different from that those 4 designs because samples are not generated in the same box. But the final result is not influenced because whole billet is considered in the 111

calculation of failure rate. The result is more clearly illustrated in Figure 4.26, in which both average probability of failure and standard deviation are plotted. Design 5 has no improvement over Design 4. Obviously, in the feasible region, Design 1 with a preform height of 80 mm is the best design. About 25% reduction in failure rate can be obtained compared to the worst design path.

9.0

8.5 )

-9 8.0

7.5

7.0 Failure rate (×10 rate Failure

6.5

6.0 70 80 90 100 110 120 130 140 Preform height (mm)

Figure 4.26 Failure rates for different forging path with standard deviation

4.5 Summary and conclusions

Hard alpha anomalies in titanium and titanium alloy can cause disastrous failure if found in stress critical components like aircraft parts. They cannot be avoided completely in primary manufacturing process. As a main manufacturing process of compressor disk, 112

forging process is studied to examine the influence on hard alpha movement. The research in numerical simulation of forging, regression model, and stochastic study of possible locations of microfeature leads to the following conclusions:

1) The presence of hard alpha anomaly in large titanium components like compressor

disk does not change the metal flow around it significantly. Thus, the material model

same as base material can be used to in finite element model without creating

noticeable difference.

2) Although in 2D axisymmetric simulation, hard alpha inclusion is always modeled as a

ring, the metal flow other than hoop direction has minimum difference from that of 3D

simulation. 2D model can be used instead of 3D model to save calculation time.

3) To study the effect of a random located defect, large amount of points need to be

studied. Using RSM to track point moving instead of FEM is an efficient way.

4) With Monte Carlo simulation, the probability of disk failure caused by a random hard

alpha anomaly can be obtained provided that their statistical distribution in billet is

known.

5) By changing forging path, the final position of the hard alpha in forged component can

be different; this in turn changes the probability of failure. Consequently, the design of

forging sequence contributes to the reduction of failure risk of components.

113

CHAPTER 5

MICROSTRUCTURE CONTROL IN TURBINE DISK FORGING

5.1 Modeling microstructure in hot working

The thermal, mechanical and metallurgical phenomena take place during and after hot working change the microstructure of metals. As the microstructure plays an important role in material properties, the modeling of microstructure evolution during hot working has been studied since 1970s [Sellars, 1985].

5.1.1 Microstructure evolution during forging

In general, the mechanisms control microstructure evolution during forging and subsequent heat treatments include dynamic recovery, dynamic recrystallization, metadynamic recrystallization, static recovery, static recrystallization and grain growth

[Semiatin, 2003b].

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Dynamic recovery and dynamic recrystallization occur during forging. In high stacking-fault-energy (SFE) metals, dislocations are annihilated by each other, so dynamic recovery predominates. In low SFE metals, deformation leads to nucleation and growth of strain free grains via dynamic recrystallization. They both reduce the dislocation density.

After forging, depending on material type, stored work and annealing temperature, static recovery, static recrystallization or both will occur. In static recovery, climb of dislocations and absorption of dislocation into subboundaries occur. In low SFE metals, depending on the level of strain, static recrystallization or metadynamic recrystallization may occur.

Grain growth also occurs following the static recovery and recrystallization, or during heating.

Since superalloys will be used in this research, the evolution and modeling of microstructure of superalloys are covered in detail in this chapter.

5.1.2 Microstructure modeling of superalloys

In low SFE materials such as superalloys, recrystallization is the most important mechanism in the processing [Stockinger and Tockner, 2005]. Typically, three kinds of recrystallization may occur in superalloy forging:

1) Dynamic recrystallization (DRX). DRX is the process in which nucleation and growth

of nuclei occur during the deformation. The dislocation density increases after

deformation begins, and recrystallization nuclei start to form when a critical 115

dislocation density is reached; thus, DRX can only take place when strain exceeds a

critical value.

2) Metadynamic recrystallization (MDRX). When the strain in deformation process

exceeds the critical strain to initiate DRX, but recrystallization is not finished, then the

main part of the recrystallization will take place after forging. Since there is no strain

applied in MDRX, the recrystallization process is a function of time.

3) Static recrystallization (SRX). This occurs when the strain applied in forging step is

less than the critical strain to start nucleation for DRX, but the energy stored is enough

to start nucleation and growth during the subsequent reheating and annealing process.

SRX process is also a function of time, but it is much slower than MDRX.

Various researches done in this area were summarized by Devadas et al. [1991]. All researches employed the similar models based on physical metallurgy principles to characterize DRX, MDRX and SRX. Because those models well represent the microstructural changes, they are ideal to be combined with FEM code during thermomechanical processing. The typical works on complex parts made by superalloys include the work of Shen et al. [1995] on Waspaloy and Stockinger et al. [2005] on IN 718.

Other works cover from cogging of IN 718 [Dandre et al., 2000] to forging of alloy 706

[Huez and Uginet, 2000] and alloy 720 LI [Matsui et al., 2000].

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In present work, microstructure evolution model for IN 718 will be selected to predict the microstructure in final forging. It is known that the final microstructure of forging is mainly influenced by DRX and MDRX [Zhou and Baker, 1995] because the critical strain for DRX is usually exceeded in forging step. Consequently, SRX rarely occurs in forging and is not modeled in this work.

Experimental observation of IN 718 forging shows most grains are dynamically recrystallized under strain rate of 0.005 s -1 at forging temperature; at a higher strain rate, dynamically recrystallized microstructure is very difficult to preserve and finally leads to microstructure with high proportion of metadynamically recrystallized grains [Zhou and

Baker, 1995]. Medeiros et al. [2000] point out DRX takes place at a low strain rate typified by 0.001 s -1; for industrial operations, the strain rate is usually larger than 0.01 s -1, MDRX is the main recrystallization mechanism. This is also confirmed by processing map of IN

718 [Medeiros et al., 2000]. Mosser et al. [1989] also indicate that at higher strain rate,

DRX is negligible, only MDRX is to be considered.

In FORGE®, the FEM code used to simulation the forging process in the present work, metadynamic recrystallization is modeled by the following equations [FORGE 2008 documentaion, 2008]:

n   t  0  X =1− exp − ln 2   (5.1)  t    5.0  

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α  β  t = A d 1 ε n1ε& m1 exp  1  (5.2) 5.0 1 0  T 

α  β  D = A d 2 ε n2 ε& m2 exp  2  (5.3) 2 0  T 

In these equations, X is the fraction of recrystallization, D is the recrystallized grain size for full recrystallization, t0.5 is time for 50% recrystallization, d0 is initial grain size, T is temperature in Kelvin, n0, n1, n2, m1, m2, α1, α2, β1, β2 are material constants to be determined. It can be seen that both X and D are dependent on forging conditions before

MDRX begins, and X is also a function of time t.

The material parameters for microstructure models used in this research are collected from the work done by Huang et al. [2001], Zhou and Baker [1995], Medeiros et al. [2000],

Mosser et al. [1989], and Zhang et al. [1999]. MDRX is a recrystallization process takes place after deformation; when MDRX occurs, the energy needed has already been put into the system. The initial grain size before deformation has little effect on MDRX. This is confirmed by Stockinger and Tockner [2005]. In their work, the models used to predict

MDRX do not include initial grain size. Since this is the case, in equation (5.2) and (5.3),

α1 α2 A1d 0 and A2 d 0 are considered one parameter respectively. The values are listed in

Table 5.1.

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α1 α2 n0 n1 n2 m1 m2 β1 β2 A1d 0 A2 d 0 1 -1.42 -0.41 -0.408 -0.028 23574.7 -28866.97 5.043×10 -9 4.85×10 10

Table 5.1 Modeling constants for IN 718

5.1.3 Microstructure model validation for IN 718

Experimental data from literature are used to validate the model. Compression test were conducted by Zhou and Baker [1995], and Medeiros et al. [2000] under conditions that

MDRX predominates; the modeling results are compared with experiments in Table 5.2 and 5.3.

Recrystallized fraction/grain size Temperature (°C) Strain rate(s-1) Experiments Model prediction 0.1 76/-- 77/6.9 950 0.05 63/-- 62/4.8 0.1 94/9.0±0.4 94/13.7 1000 0.05 88/10.2±0.5 80/10.0 0.1 100/17.2±0.4 99/25.6 1050 0.05 100/17.8±0.4 96/20.4

Table 5.2 Model validation results 1 (compare to Zhou and Baker [1995])

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Temperature(°C) Experiments Model prediction 950 5 4 1000 7 9 1050 25 21

Table 5.3 Model validation results 2 grain size (compare to Medeiros et al. [2000])

Table 5.2 shows the fraction of recrystallization can be predicted reasonably well; although there is some discrepancies in grain size between experiments and prediction, the magnitudes of the predicted grain size are correct. The effects of temperature on grain size are also predicted. The difference in effects of strain rate on grain size mainly comes from the way the parameters are derived. The parameter calculates strain rate effect on grain size m2 is mainly from Medeiros et al. [2000]. In their test, temperature rise during deformation was taken out. The temperature increase caused by increasing strain rate has more influence on grain size than strain rate itself. This trend agrees with the conclusion that increasing strain rate increases the extent of MDRX and the grain size [Zhou and Baker,

1995]. This has also been observed by Huang et al. [2001]. The MDRX model will be used in this section to calculate the microstructure in IN 718 forging.

5.2 Effects of forging path design on microstructure of disk forging

From microstructure evolution models, it can be seen that strain, strain rate and temperature all may have influence on the microstructure. Changing forging paths will

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change the strain distribution in forging; while changing the processing parameters will change the temperature and strain rate in the forging. A turbine disk is chosen to study the effect of those factors on microstructure of a forged component in the case study.

5.2.1 Various forging path designs

The disk to be forged and the machined disk are shown in Figure 5.1. The cross section of the forging and machined disk are shown in Figure 5.2 with solid line and dotted line, respectively. Because material outside the machined part outline will be removed after forging, only the microstructure of machined part will be examined.

Figure 5.1 Superalloy disk forging (left) and machined disk (right)

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Figure 5.2 Cross section of forging and machined part

Starting billet has a diameter of 228.6 mm and height of 258 mm. Three steps are used to form the final forging. The billet is first upset to a height of 120 mm, then three preforms are designed. Preform 1 moves the material outward while creating thinner section at the rim. Preform 2 and preform 3 are created by simple upsetting but with different heights. In preform 2, because the height is lower than thickest part of final forging, some metal experiences back flow from rim to center; the two cavities are almost filled at the same time. For preform 3, metal always flows outward in the final step, the inner cavity is filled earlier than the outer cavity. The forging routes are shown in Figure 5.3.

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Figure 5.3 Three different forging paths

5.2.2 Risk associated with microstructure

Risk of turbine disk failure can be changed by controlling the microstructure of turbine disk because mechanical properties are dependent on microstructure. For example, in a turbine disk application, rim area is subjected to high temperature so good creep strength is preferred at rim. However, in bore area, a good low cycle fatigue property is preferred.

Both properties are correlated with grain size. As we can see from Figure 5.4, fine grain 123

size is beneficial to low cycle fatigue property. Figure 5.5 indicates superalloy with coarse grain size has higher creep strength. Thus, a turbine disk failure risk can be controlled by forging process design via microstructure control.

Figure 5.4 Low cycle fatigue results for U 720 LI at 600°C [Torster et al., 1997]

Figure 5.5 Effect of grain size on creep strength of IN 100 [Lasalmonie and Strudel, 1986]

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5.2.3 Microstructure comparison for different forging paths

As we are studying the effect of preform design, the processing parameters are fixed. Initial billet temperature is 1150 °C and die temperature 650 °C; first two steps are performed at a temperature above δ-solvus; after cooling, the preform is reheated to 950 °C and final step is performed below δ-solvus; die speed is 5 mm/s. After die closure, the forging is held in the die for 10 seconds to facilitate the metadynamic recrystallization. Microstructure is examined after 1 min cooling in the air.

To check the final microstructure of the forging, the machined part is divided into 14 zones, which are shown in Figure 5.6. In each zone, several checking points are selected to check microstructure; the number of points in each zone is chosen considering the radius of each zone so that the density of points are approximately even over all disk. In Figure 5.6, the number before a slash is zone number, and number after a slash is the number of points in this zone. Zone 1 to zone 6 are from hub area, zone 7 to zone 10 are from web area, and zone 11 to zone 14 belong to rim area. Figure 5.7 shows the locations of these 70 checking points. The coordinates of checking points are listed in Appendix.

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Figure 5.6 Machined disk and 14 zones to check microstructure

Figure 5.7 Distribution of checking points

The average grain size and standard deviation for different areas are shown in Table 5.4.

The grain size distribution and the fraction of recrystallization are shown in Figure 5.8 and

Figure 5.9. The detailed microstructure information for all checking points is listed in

Appendix. Since the majority part of the disk has been fully recrystallized under these conditions, the grain size is the main criterion to evaluate the quality of disk; the fraction of recrystallization can be used as a secondary criterion. 126

Overall, preform 2 produces the finest grain size, which is preferred for better fatigue strength. Preform 3 produces larger grain size than that produced by preform 2 in all three areas, but the grain size of the rim area is larger than other areas. In the rim area, a larger grain size is preferred for better creep properties. For this reason, preform 3 is better than preform 1 and preform 2 as it has already produced desired difference between areas.

Figure 5.8 clearly shows that the rim area has coarse grains than other areas in forging produced by preform 3.

Average grain size/standard deviation ( µm) Hub Web Rim Overall Preform 1 6.9/1.7 4.9/2.4 6.9/2.3 6.5/2.2 Preform 2 6.8/0.9 2.2/1.8 5.9/2.2 5.6/2.4 Prefrom 3 7.1/1.3 5.2/2.1 9.3/3.3 7.4/2.6

Table 5.4 Average grain size/standard deviation for 3 preforms

The fraction of recrystallization in Figure 5.9 shows in forging produced by preform 1, zone 1 and zone 4 have small amount of material with 70-90% fraction of recrystallization.

In forging produced by preform 2, some material in web area has fraction of recrystallization less than 90%. In forging produced by preform 3, although a small amount of metal in zone 1 and zone 4 is not fully recrystallized, the recrystallization ratio exceeds

90%. The details of microstructure information can be seen in tables in Appendix. For this

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secondary criterion, preform 3 is also the best design among the three. Therefore, preform

3 will be used in the next section to study effect of forging temperature and die speed.

It should be noted that the grain size calculated in this step is not the grain size in final disk.

Additional heat treatments, like aging, have to be applied to produce the desired microstructure. However, having such a forging microstructure is still a good preparation as starting microstructure for subsequent heat treatments.

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(a) Preform 1

(b) Preform 2

Figure 5.8 Grain size distribution for different preforms

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(a) Preform 1

(b) Preform 2

Figure 5.9 Fraction of recrystallization for different preforms

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5.3 Effects of forging parameters on microstructure of disk forging

For a fixed preform, temperature and forging speed are varied to investigate the influence of processing parameters on microstructure of forging.

5.3.1 Different combinations of temperature and die speed

The microstructure model equations (5.1) to (5.3) are derived from simple deformation test like upsetting. If strain rate and temperature are considered independently, it is obvious that as temperature increases, both the fraction of metadynamic recrystallization and grain size increase; as strain rate increases, metadynamic recrystallization ratio increases but grain size decreases. In reality, temperature is also strain rate dependent as increasing strain rate will increase the temperature by both generating more heat and reduce the contact time with die. For complex part, since strain, strain rate and temperature are not homogeneous during forging, simulations are done following the design matrix with different combinations of temperature and die speed. The design matrix is shown in Table 5.5. A full factorial design produces 9 runs. Preform 3 from previous section will be used for final forging.

Low Medium High Temperature (°C) 920 950 980 Die speed (mm/s) 5 20 50

Table 5.5 Design matrix with different temperature and die speed

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5.3.2 Analysis of simulation results

Table 5.6 gives the average grain size and standard deviation of each zone under different forging conditions. In all cases, the average grain size in rim area is always larger than hub area and web area as expected.

Average grain size/standard deviation ( µm) Temperature Die velocity hub web rim overall (°C) (mm/s) 920 5 4.5/0.9 3.6/1.3 7.1/2.7 5.1/0.4 920 20 5.6/0.5 10.7/2.6 24/6.8 12.2/8.9 920 50 6.2/0.6 15.9/6 34.7/13 16.7/14.4 950 5 7.1/1.3 5.2/2.1 9.3/3.3 7.4/2.6 950 20 8.5/0.7 13.9/2 28/8.2 15.4/9.7 950 50 9.2/0.8 19.1/3.9 42.7/14.2 21.2/16.6 980 5 10.9/1.9 8.2/3.3 11.4/3.9 10.5/3.1 980 20 13/1 20.4/2.7 36.6/11.2 21.6/12 980 50 14.1/1.2 26.6/5.2 52.9/15.5 28.2/19.1

Table 5.6 Average grain size/standard deviation for different forging conditions

Figure 5.10 shows the fraction of recrystallization for die velocity of 5 mm/s for different temperatures. In terms of recrystallization ratio, temperature T=920°C and die velocity

V=5 mm/s produces least recrystallized grains. In zone 1, a small amount of metal has less than 90% recrystallization ratio; some non-fully-recrystallized areas have been observed in zone 4 and zone 6, but fraction of recrystallization exceeds 90%. For the same die velocity

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V=5 mm/s, increasing temperature T from 920°C to 980°C improves the fraction of recrystallization only a little bit for the whole forging. However, for the same temperature

T=920°C, increasing die velocity from V=5 mm/s to V=50 mm/s increases the fraction of recrystallization in less recrystallized area significantly. This can be seen from Figure 5.11.

Even for the worst case, only a small fraction of material in machined disk is not fully recrystallized, the grain size of fully recrystallized material is examined in following research.

Figure 5.12 compares the grain size distributions for different temperature with the same die velocity V=5 mm/s. For the same die velocity, the temperature rise can increase the grain size as expected from microstructure evolution models, but overall, the difference in grain size is not as remarkable as that caused by varying die velocity. The grain size distributions for different die speeds with the same temperature can be seen in Figure 5.13.

In rim and web areas, die velocity has more contribution to grain size than temperature. In hub area, temperature has more contribution than die speed, but the margin is small. The reason behind this is the strain rate in hub area is much less than those in web and rim areas.

As die speed increases, strain rate in web and rim increases significantly while the strain rate in hub area only increase a small amount. As a result, the increase of forging speed leads to more temperature rise in web and rim areas so that grain sizes in those areas are dominated by temperature. This tendency can also be observed in Table 5.6.

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(a) T=920°C, V=5 mm/s

(b) T=950°C, V=5 mm/s

Figure 5.10 Fraction of recrystallization for different temperatures with V=5 mm/s 134

(a) T=920°C, V=5 mm/s

(b) T=920°C, V=20 mm/s

Figure 5.11 Fraction of recrystallization for different die speeds with T=920°C 135

(a) T=920°C, V=5 mm/s

(b) T=950°C, V=5 mm/s

Figure 5.12 Grain size for different temperatures with V=5 mm/s 136

(a) T=980°C, V=5 mm/s

(b) T=980°C, V=20 mm/s

Figure 5.13 Grain size for different die speeds with T=5 mm/s

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Figure 5.14 plots the rim area grain size dependence on temperature and die speed. It is observed that in this temperature and die speed range, for a fixed forging speed, temperature rise can increase the grain size about 1.5 times; but for a fixed temperature, die speed increase can increase the grain size about 4 to 5 times. So the figure on the left shows flatter curve than those on the right.

Figure 5.14 Rim grain size dependence on temperature (left) and die speed (right)

The overall grain size dependence on temperature and die speed is shown in Figure 5.15.

Because in hub area, temperature has a little bit more effect than forging speed on grain size, this will counteract the effect of strain rate in web and rim area. However, the overall average grain size is still influenced more by die speed more than by temperature in this temperature and die speed range. 138

Figure 5.15 Overall grain size dependence on temperature (left) and die speed (right)

5.3.3 Optimization of forging parameters for various objectives

Given the fact that the microstructure dependence on forging parameters has been thoroughly studied, some work can be done to optimize the microstructure for specific objectives. Often, more than one objective is to be optimized simultaneously, this is called multi-objective optimization. In this section, a simple yet effective method is used to solve the problem by creating a new variable which combines other objectives.

For any forging, risk of failure is closely correlated with mechanical properties. Many properties can be improved by creating desired microstructure. In the turbine disk, fine grain size is good for fatigue and strength, while coarse grain size boosts the creep properties, and sometimes, a homogeneous microstructure is preferred. 139

In this section, different objectives are formulated and optimal solution is selected.

Generally, the optimization problem can be simply formulated as follows:

optimize objective i

subject to 920°C ≤ T ≤ 980°C

5 mm/s ≤ V ≤ 50 mm/s (5.4)

In above equations, objective i can be a function of several variables, optimization can be either maximization or minimization, although usually minimization is used for standard formulation.

The following objectives will be used in this section. Since fine grain is preferred in hub area and coarse grain is preferred in rim area, both the ratio and difference of grain size in these two areas can be used as objectives. They are defined as:

D objective 1= rim (5.5) Dhub

objective 2 = Drim − Dhub (5.6) where D is the diameter of the grain. To measure the grain size homogeneity, an area weighted relative standard deviation is defined:

  nrim σ rim nweb σ web nhub σ hub objective 3 =  + + ×100 % (5.7)  N Drim N Dweb N Dhub  where σ is the standard deviation, n is the number of checking points in individual area and

N is the total number of checking points. To maximize the difference between rim and hub 140

area, while at the same time, finer overall grain size is to be considered, the following objective function can be defined:

D − D objective 4 = rim hub (5.8) Doverall

In objectives shown above, objective1 , objective2 and objective4 are to be maximized while objective 3 is to be minimized. The results for all four objectives are listed in Table

5.7. These data can be better understood if they are plotted. Figure 5.16 to Figure 5.19 clearly show the trend of each objective function.

T (°C) V (mm/s) objective1 objective2 objective3 objective4 920 5 1.58 2.6 28.6 0.51 920 20 4.29 18.4 17.8 1.51 920 50 5.60 28.5 23.6 1.71 950 5 1.31 2.2 27.9 0.30 950 20 3.29 19.5 15.8 1.27 950 50 4.64 33.5 18.4 1.58 980 5 1.05 0.5 27.0 0.05 980 20 2.82 23.6 15.7 1.09 980 50 3.75 38.8 17.0 1.38

Table 5.7 Results for different objectives

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objective1 values

objective1 2

0 0 10 20 30 40 50 60 Die speed (mm/s)

T=920 C T=950 C T=980 C

Figure 5.16 objective1 as function of die speed

objective2 values

45 40 35 30 25 20 objective2 15 10 5 0 0 10 20 30 40 50 60 Die speed (mm/s)

T=920 C T=950 C T=980 C

Figure 5.17 objective2 as function of die speed

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objective3 values

15 objective3 10

0 0 10 20 30 40 50 60 Die speed (mm/s)

T=920 C T=950 C T=980 C

Figure 5.18 objective3 as function of die speed

objective4 values

1.8 1.6 1.4 1.2 1 0.8 objective4 0.6 0.4 0.2 0 0 10 20 30 40 50 60 Die speed (mm/s)

T=920 C T=950 C T=980 C

Figure 5.19 objective4 as function of die speed

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Since there are only 3 data points in each curve, fitting the curve with second order polynomial will cause overfitting. Fitting with linear curve will not capture the curvature.

Fortunately, in this rectangular design space, the objective function values change in a simple manner, and in most cases, the curve values change monotonically with design parameters.

objective1 increases with die speed and decreases with temperature. So if ratio of rim grain size and hub grain size is to be maximized, T=920°C and V=50 mm/s is the optimal setting. objective2 monotonically increases with die speed, when die speed is low, it decreases with temperature increase, but as die speed is higher, objective2 increase with temperature.

From Figure 5.17, the conclusion can be drawn that forging under T=980°C and V=50 mm/s produces largest grain size difference between rim and hub. For objective3 , higher temperature always produces a better value, but it looks like V=20 mm/s is better than other settings. At T=950°C and T=980°C, the curves between V=20 mm/s and 50 mm/s are rather flat; from current data, this means area weighted relative standard deviation may take minimum value in a rather large area. objective4 shows the same trend as objective1 , and a lower temperature and higher die speed are helpful in maximizing objective function.

5.4 Summary and conclusions

The failure risk of forged part depends very much on the microstructure, which is a result of forging process and heat treatment. Microstructure produced by forging can serve as a 144

good starting microstructure for heat treatment. The microstructure evolution model for superalloy IN 718 based on experimental data from literature has been applied to FEM code FORGE to predict the microstructure from forging. Preform, forging temperature and die speed are varied to study how they change the fraction of recrystallization and recrystallized grain size. The conclusions are listed as follows:

1) The preform shape is able to change material recrystallization behavior through its

effect on strain and temperature. Although the difference is not considerable, it does

create different grain size distribution over the forging.

2) Forging temperature and forging speed have major influence on microstructure. By

changing the material temperature and strain rate, the fraction of recrystallization and

grain size vary accordingly.

3) In the studied forging range, temperature has more effect on microstructure than strain

rate. The way strain rate produces effect on microstructure is mainly by means of

changing temperature.

4) Given the forging range used in this research, change in strain rate has more effect on

forging microstructure than change in workpiece temperature.

5) As the relation of forging parameters and microstructure is fully understood,

optimization problem can be solved in the forging range. There may be multiple

optimal solutions for various optimization objectives.

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CHAPTER 6

APPLICATION TO TITANIUM HIP IMPLANT FORGING

6.1 Introduction

The joints of human body have tendency to catch degenerative diseases such as rheumatoid arthritis, osteoarthritis and chondromalacia. To relieve the pain and increase mobility of the affected joints, arthroscopic surgeries, or even replacements of joint with artificial materials, are performed. The research on total hip and total knee replacement has become the main focus of total joint replacement arthroplasty. Merely in US, 275,000 artificial hip and knee joint replacements were performed in 1995 [Long and Rack, 1998]. In 2001, the number of replaced orthopedic joints increased to 491,000 [Crompton, 2004]. In 2003, the numbers of primary total hip arthroplasties and primary total knee arthroplasties performed in US have increased to 202,500 and 402,100, respectively [Kurtz et al., 2007].

To imitate the natural motion of hip joint, the femoral head and cup must be securely positioned. The hip stem is plugged in the intramedullary canal of femur and the cup used to articulate with femoral head is fixed in the acetabulum. The articulating pair must be 146

designed to be highly wear resistant to avoid loosening and detrimental reaction induced by rubbed-off particles. Different combinations of materials have been studied to reduce the wear, including metal-polyethylene, alumina-polyethylene, alumina-alumina and metal-metal [Windler and Klabunde, 2001].

The fixations of hip joints are made by either cemented or cementless method. In cemented way, the cup and femur with cement mantle are placed inside the implant bed, which bone cement is applied. The cement penetrates the porous bone structure so that implant is well fixed into the bone. In cementless method, the bone fits the prosthesis needs to be prepared to ensure a stable anchoring of the implant. The subsequent oessointegration provides additional fixation. In clinical application, elderly patients are usually treated with cemented anchoring, while cementless implants are more used for young patients [Windler and Klabunde, 2001].

The general requirements for all biomaterials contain biocompatibility, corrosion resistance, bioadhesion and biofunctionality etc. The materials for implant must be bio-inert so that no adverse tissue reactions and allergic reactions are produced by ions released from implant [Long and Rack, 1998]. After the prosthesis is implanted into the body, the materials should have the ability to be integrated into the bone or soft tissue. The cells are prone to attach and proliferate on surface of the osseointegratable material [Freese et al., 2001]. Moreover, a hip implant may bear a dynamic load of 1-2 million cycles a year 147

and articulating forces may reach 3-5 times of the body weight. The materials used for hip prosthesis must have superior fatigue properties [Windler and Klabunde, 2001]. Another desired property of hip prosthesis is a relatively lower Young’s modulus, which contributes to a lower stiffness. This is helpful in avoiding insufficient load transfer from implant to proximal bone. The underloading of bone may lead to stress shielding to the bone [Long and Rack, 1998; Windler and Klabunde, 2001].

Though a variety of metals, ceramics and polymers are used on joint and bone replacements, metals are the most widely used for load-bearing implants [Davis, 2003]. In recent years, titanium and its alloys have been increasingly used as biomaterials for their outstanding biocompatibility, lower modulus, enhanced corrosion resistance and excellent osseointegration properties compared to more conventional implant-grade stainless steels and cobalt-based alloys [Long and Rack, 1998; Windler and Klabunde, 2001; Davis, 2003;

Liu et al., 2004].

Presently, however, nearly all cemented hip prostheses are not made of titanium alloys

[Windler and Klabunde, 2001]. The reason is the combination of mechanical micro-motion and debonding between cement and titanium results in crevice corrosion [Schenk, 2001].

The application of titanium alloys is mainly in cementless hip prosthesis. In addition to the mechanical anchorage during the surgery, the ingrowth or ongrowth of the bone on implant surface provides secondary fixation. A porous structure is often made on surface of implant 148

to facilitate bone ingrowth so that bone can grow into the structure. Usually, the ingrowth surfaces are processed by blasting, etching or machining. In bone ongrowth, the bone grows onto the prosthesis under the help of micro- or macro-structure on the surface. The structures include cast structures, sintered structures, cancellous-structured titanium, sintered beads, mesh structures and coatings by plasma spraying [Windler and Klabunde,

2001]. Even in titanium hip implants, the femoral heads are commonly made of alumina, zirconia, CoCr or stainless steel to obtain a low wear rate.

The main manufacturing processes of titanium alloys include casting, forging, machining and chemical milling; among them, forging is the primary method that shape and structure control are reached in titanium alloy components [Donachie, 2000]. Other than shape forming, forging also produces a combination of mechanical properties which usually do not exist in bar or billet. In forgings, a better tensile strength, creep resistance, fatigue strength, and toughness may be obtained compared to those in bar or other forms.

The main difficulty of the titanium forging is the manufacturability of the material: the low heat transfer coefficient, low specific heat, along with its high sensitivity to strain rate and temperature make the process must be carefully designed to avoid flow instability.

The use of isothermal forging has been recently used in titanium parts with complex shape to produce a homogeneous microstructure resulted from less temperature variation within 149

the forging. It is suitable for net or near net shape forming of titanium alloys. A high die temperature (900-1000°C) required for isothermal forging increases the cost of the process: tooling materials with high hot hardness, protective atmosphere to prevent die oxidizing.

Effort has to be made to use hot die with reduced temperature in the processes. Lowering the cost of forging is the incentive to use hot die with reduced temperature.

In this chapter, a strategy to determine the optimal forging process for a titanium hip implant is presented. The complexity of 3D model restrains the designer from using enough finite element method (FEM) simulations to obtain the proper process parameters and preform shape. To simplify the design procedure, the complex 3D model is broken into several 2D plane strain problems. Finally, 3D forging process has been simulated for verification after the 2D problems have been solved separately.

6.2 Problem definition and constraints

Hip implant is designed to mate the upper femur (thigh bone) with the pelvis (hip bone).

Good fit and bonding are important. Despite commercial pure titanium and other titanium alloys are used, Ti-6Al-4V is clinically successful and is the most widely employed alloy for total joint replacement arthroplasty [Davis, 2003; Bronzino, 2000].

The hip implant is characterized by highly varied volume distribution along its spindle, as can be seen in Figure 6.1. 150

Figure 6.1 a) Commercial hip; b) Material distribution along the hip axis

The main objective of this study is to develop a more economical process by reducing the die temperature necessary to produce a sound product. The main constraint is the flow instability caused by low thermal conductivity and high susceptibility to thermal and strain rate gradients of the material. The processing window, which is a combination of strain rate and temperature, must be chosen carefully to avoid defects like [Semiatin et al., 1997]:

1) Wedge cracking and cavitation produced by stress concentrations at grain interface.

Voids are formulated because stresses cannot be relieved by diffusion or plastic

processes at a high strain rate.

2) Shear-localization (shear bands and shear cracks) due to nonuniformity of the

deformation owing to temperature variations inside the workpiece combined with 151

friction effect.

A higher strain rate is preferred to reduce cycle time and chilling, yet it is restricted by processing window. The non-symmetry of the part also causes unbalanced load resulting in die deflection and non-balanced die wear. Therefore, even load distribution is desired.

For forging of titanium alloys, the final properties of the part are strongly dependent on the thermomechanical history of forging. In order to accurately simulate this thermomechanical process, the model should also be able to adequately represent metal constitutive behavior and boundary conditions.

6.3 Methodology and Procedure

In this study, heuristic strategy has been used to find the optimized process parameters.

Given the problem definition, the optimization is mainly guided by available knowledge, experience and process constraints.

6.3.1 Material modeling

The accuracy of numerical simulation strongly depends on material behaviors at different temperature and strain rate. The stress-strain curve used in the present work is based on the testing data obtained by Seshacharyulu et al. [2000] on Ti-6Al-4V with an equiaxed α-β microstructure. The flow stress data were corrected for adiabatic temperature rise and 152

covered a wide range of temperature and strain rates in hot forging.

4.3.2 Thermal data

The significant heat transfer between titanium alloy and tools makes the accuracy of interfacial heat transfer coefficient very important; the thermal data published by Hu and his colleagues [Hu et al., 1998] have been used in this study. The heat transfer coefficient was calculated using a reverse technique from a thermal-plastic coupled FEM simulation combined with experimental data. Different heat transfer coefficients have been used when the temperature of die is changed during the simulation; thermal conductivity is modeled as a function of material temperature, too.

4.3.3 Material instability

The processing maps are usually used to forecast Ti-6Al-4V titanium alloy behaviour. As introduced in Chapter 2, processing maps are created by superimposing power dissipation map and instability map developed in a frame of temperature and strain rate; it can guide process design to optimize workability [Seshacharyulu et al., 2000]. The unstable regime in which flow instabilities like adiabatic shear bands and flow localization can be identified in instability map.

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Figure 6.2 Instability map for Ti-6Al-4V with microstructural observations in the α-β

regime at a strain of 0.5 [Seshacharyulu et al., 2000]

The instability map to analyze the feasibility of the forging process is reported

[Seshacharyulu et al., 2000] (Figure 6.2). The contour numbers represent the value of instability parameter (negative values indicate unstable flow, see Chapter 2 for definition).

This map is for a strain of 0.5; however, the process can be seen as steady-state since it has very short transients and the map remains almost the same as strain changes. This map gives a large regime of flow instability at a strain rate higher than 1 s -1 in the entire test temperature range; for this reason, 1 s -1 has been chosen as upper bound of strain rate. The material instability is the main constraint on the parameter optimization.

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6.3.4 Geometry simplification

The hip implant in Figure 6.1 does not show the ball (articulating portion of the femoral component) because it is common that the stem and ball are made of different materials.

The usage of this modular design is due to insufficient wear resistance of titanium alloys.

Only the stem is to be considered here. Due to the difficulty of modeling 3D problems, a geometry simplification is made to shorten the time for modeling and calculations.

7 cross sections are made for 2D study, as shown in Figure 6.3. More cross sections are made in complex portion, while less 2D cross sections are studied in simple portion.

According to the research on fatigue failure of hip bone implant conducted by Raimondi and Pietrabissa [1999], the area subject to largest von Mises stresses is located right below the bending portion. Figure 6.4 shows the location of the so called “critical area” and its cross-section D-D. In the present study, the optimization of the forging process has been mainly made on this area; then the obtained process parameters have been used in other cross-sections of the hip implant. Loads at different cross-sections are balanced by flash design to minimize the die deflection. This approach is illustrated in Figure 6.5.

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Figure 6.3 2D cross sections to be studied

D D D-D

Figure 6.4 Location of critical area and cross-section

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Figure 6.5 Flow chart of followed approach

6.3.5 Process variables

An estimated theoretical value of strain rate can be obtained utilizing the die velocity and stroke. The upper bound of this variable is set to 1s -1; besides, if the process is carried out with a lower die velocity, a longer process time can reduce the billet temperature excessively and so has to be avoided. Based on the experimental data, a lower strain rate of

0.125s -1 has been tried and the results obtained indicate that the process falls into unstable region. So, the whole study has been developed utilizing die velocity in order to have an 157

estimated theoretical strain rate value equals to 1 s -1.

The temperature at which the forging is completed determines microstructure, and consequently the mechanical properties. Working below β transus produces equiaxed primary α in transformed β matrix. By forging at above β transus, β forging is characterized by colony microstructure. This structure is inclined to form slip bands, which result in early crack initiation. Qualitative comparisons show that α+β forgings of

Ti-6Al-4V are better than β forgings in strength, fatigue crack initiation and fatigue crack growth rate [Williams, 1995].

The initial temperature of billet has been chosen equals to 980°C in order to maintain a specific quantity of equiaxed primary alpha phase inside the final shape (the β transus of this material is about 1010°C). Moreover a time cooling of 1s, which can also be seen as time to transfer workpiece between dies, is scheduled between the preforming and the final forming dies; this break permits a temperature homogenization inside the billet that otherwise, due to the internal heat generation (results from plastic deformation), poor conductivity of material and excessive cooling near the die, would be very different.

The part is forged in two step process; the shapes of preform dies are important because they influence the strain distribution inside the material; this can have a great effect on heat generation due to plastic deformation and consequently, on the microstructure of the 158

forging. They are also considered in this study.

Figure 6.6 Integration modelling of the hot working process

All in all, the strategies used in this research, presented in Figure 6.6, involve the integration of material, mechanical properties, tool design, equipment and production.

6.4 Results and Discussion

6.4.1 Simulation results

Several preforms have been designed in order to optimize the process; the comparison of two very different preforms for a particular cross-section starting from round billet can be seen in Figure 6.7. According to the utilized preforming, deformation changes a lot; the symmetrical one shows a more homogeneous strain distribution that can yield a more 159

uniform grain size [Vieilledent and Fourment, 2001]. By this criterion, the symmetrical preform is chosen for this study.

According to instability map, 850°C is set to lower boundary at the strain rate of about 1s -1.

From the previous research, it is appropriate to use a depth of cut of 1mm in the machining process; thus, the thickness of the material with a temperature lower than this limit is to be controlled below 1mm [Che-Haron and Jawaid, 2005; Ribeiro et al., 2005] (Figure 6.8); the limited wasted material can be removed by a final process.

Figure 6.7 Strain distribution of symmetrical preform (left) and unsymmetrical preform

(right)

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Figure 6.8 Thickness measurement to validate the reliability of the process

A series of die temperature and corresponding maximum unstable material thickness are listed in Table 6.1; same temperatures have been used for preforming die and finishing die.

Temperature Preforming die Finishing die Unstable of billet (°C) temperature (°C) temperature (°C) thickness (mm) 980 200 200 2.05 980 300 300 1.98 980 400 400 1.60 980 500 500 1.15 980 600 600 0.55

Table 6.1 Maximum thickness of unstable material at the end of process with same

temperature of preforming die and finishing die

From this result, it can be seen that the minimum possible temperature is about 500°C.

Table 6.2 gives the result for different die temperatures. Obviously, the unstable material thickness is more influenced by temperature of the final forming die. As a result, the

161

preforming die can have a lower temperature than the finishing die.

Temperature Preforming die Finishing die Unstable of billet (°C) temperature (°C) temperature (°C) thickness (mm) 980 20 400 1.78 980 100 400 1.75 980 200 400 1.70 980 400 400 1.60 980 20 500 1.40 980 100 500 1.35 980 200 500 1.30 980 400 500 1.15

Table 6.2 Maximum thickness of unstable material at the end of process with different

temperature of preforming die and finishing die

Further investigation can be done on the obtained data. The imposed strain rate, fixed to 1 s-1, is just an estimate. In fact, the strain rate varies over all the section, and near the maximum thickness of unstable material, its value is very small (Figure 6.9). In the zone near surface with more cooling, a value of lower than 0.1s -1 is observed. It is safe to set the bottom temperature limit to 800 °C.

The new boundary enables the reduction of the die temperatures without influencing the material instability; as a consequence, the effective limits of 200°C and 300°C have been found for the preforming die and finishing die, respectively (Figure 6.10).

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Figure 6.9 Strain rate distribution in the critical zone

Figure 6.10 The thickness of unstable material (temperature lower than 800°C)

In addition, it has been analyzed that the temperature at the end of the preforming, before and after the cooling, to check if same problems could be in the blocker; the results in

Figure 6.11 show that the preforming is feasible at this fixed die temperature.

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Figure 6.11 Temperature and strain rate distribution after preforming with performing die temperature of 200°C a) temperature before cooling, b) temperature after cooling, c) strain

rate

To study the forging process beyond the critical cross section (D-D), other areas of the hip implant have been cut and analyzed to have a full investigation of the hip shape. 2D simulations of these crosscuts have been performed using the same parameter as obtained from D-D section. The resultant strain rates and temperature distributions show that no obvious instability zone is observed in all of cross sections.

Another consideration in the die design for other cross sections is the load balance. Since the areas of various cross sections have large differences, the forging loads also differ a lot along the axis, which may cause the die deflection. To eliminate the potential problem, a wider flashland together with a larger billet size are designed for smaller cross sections.

The change leads to increased amount of flash and more flow resistance, thus a larger load is needed in this cross-section. The final flashland widths and forging loads for different

164

cross sections are listed in Table 6.3. It is not necessary for them to have exactly the same values; a relative smaller difference will help balancing the dies during forging. The temperature distribution after load optimization still makes the material in stable region.

Selected sections are shown in Figure 6.12.

Having obtained the billet size and die shape for different 2D cross sections, 3D models can be created for billet and dies. The starting billet is straight geometry with a taper. It needs to be bended to a specific angle and reheated before forging operation. The bended billet and the shape after preforming operation are shown in Figure 6.13. The larger flash generated in thinner section is a result of the design for balancing load.

Flashland width Forging loads (tons/mm) Cross section (mm) Preforming Final forging A-A 8 0.3 2.01 B-B 7 0.47 1.76 C-C 6 0.66 1.86 D-D 3 0.35 2.4 E-E 3 0.35 3 F-F 3 0.12 1.8 G-G 6 0.43 1.97

Table 6.3 Forging loads in different cross sections

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Figure 6.12 Temperature distribution before and after load adjustment for B-B and C-C

section

Figure 6.13 Preforming stage a) before forging, b) after forging

Figure 6.14 compares the temperature distribution of 2D and 3D simulation for C-C cross section. The comparison shows that the difference is small; this may be due to the

166

difference between 2D plane strain deformation and 3D deformation, and geometrical difference. Other cross sections also show the similar results.

Figure 6.14: Temperature comparison for C-C section in preforming stage a) 2D simulation,

b) 3D simulation

However, for the final forging process, more problems exist due to preforming deformation; the complex shape of preform makes it impossible to place every cross section in a way exactly the same as in 2D deformation; the preform cannot fit in the finishing die as perfectly as in 2D case. For this reason, the total stroke in final step, defined as the distance from the upper die just touches the preform to die closure, is larger than the stroke in 2D; this will result in a lower temperature. The comparison between 2D and 3D temperature distribution for C-C cross section is shown in Figure 6.15. It can be seen that the shape of the temperature field differs a lot; the temperature in 3D is lower due to longer die contact time; the temperature field is not symmetric because of non-symmetric preform placement

167

in the tool. However, the amount of material with temperature lower than 800 °C is still small, which means the instability is unlikely to take place in this cross section. The similar temperature fields in all other cross sections indicate that the 3D forging gives an acceptable result.

Figure 6.15 Temperature comparison of C-C cross section in final forming stage between

2D simulation (left) and 3D simulation (right)

Figure 6.16 shows the temperature distribution at the final stage in forged hip implant. The observation that the temperature is not evenly distributed over the part is a reflection of the complex shape of both tools and part being forged.

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Figure 6.16 Temperature distribution on the hip implant at the end of the forging process

The die wear on the lower preforming die and lower finishing die are compared in Figure

6.17. Die stresses are also compared in Figure 6.18. Here, die wear is defined as the product of normal stress and material sliding distance; while die stress is the norm of stress vector. The maximum die wear in preforming die occurs on stem portion, and maximum die wear in finishing die occurs near bending portion. The value of wear on finishing die is much larger than that of preforming die because the flash is squeezed out of the narrow opening at the end of final forging. The other place where severe die wear occur is the flashland, especially near the thin end. The wider flashland designed to balance the load creates larger flash, and the low temperature of the flash increases the load and die wear on the wider flashland. The die stresses for both dies are larger for the thin ends because of the same reason. Although the die wear and die stress cannot be homogeneous over the whole die cavity because of the complexity of the geometry, the relatively homogeneous die 169

stress distribution in finishing die is highly favorable.

Figure 6.17 Die wear on preforming die (above) and finishing die (below)

170

Figure 6.18 Die stress on preforming die (above) and finishing die (below)

The total simulation time for a 3D preforming and finishing forging is about 50-80 hours using a Xeon multiprocessor workstation depending on the deformation. A 2D preforming 171

and finishing forging usually takes the same computer 30-40 minutes. It can be seen that a great computational time saving can be achieved by taking 2D plane strain simulations.

6.4.2 Relation to risk

By reducing the production cost, the manufacturer can obviously reduce the possible fiscal risk. At the same time, a defect-free product also reduces the product failure risk. This further decreases the liability risk followed by failure of implant. The modification of forging process demonstrated in this chapter is able to mitigate the risk in respect of both product and economy.

6.5 Summary and conclusions

In this chapter, the traditional hot die forging with a lower tool temperature has been investigated utilizing numerical simulations. 3D numerical simulation starting from the processing parameters obtained from 2D crosscut investigation has been optimized. The results show that:

1) The choice of preform is important to obtain the desired deformation inside the hip.

2) A strain rate higher than 1 s -1 can probably bring the flow instability of material

according to the instability map; on the contrary, excessive low strain rates have to be

avoided due to the cooling of material with a lower die temperature.

3) It has been found that the temperature of final die has more influence on the

temperature of final forging than the preforming die; a lower temperature of 200°C 172

and 300°C can be used for preforming die and final die, respectively, for the analyzed

hip replacement.

4) Generally, a good agreement between 2D and 3D simulations has been observed,

although some difference can be found between 2D plane strain deformation and 3D

deformation.

5) The die wear and die stress are non homogeneous over the die cavity. Thinner portions

have more severe wear and larger stress because of the wider flashland for load

balancing.

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CHAPTER 7

CONCLUSIONS AND FUTURE WORK

7.1 Summary and conclusions

In this research, forging process design with consideration on risk reduction is investigated for different forged components, especially risk critical parts such as turbine engine components. Finite element analyses have been used extensively throughout this research to model the forging behavior of material.

Hard alpha inclusion in titanium alloys represents the typical discrete defect in billet. By tracking the hard alpha inclusion movement in 3D upsetting using multi-body model, it is found that the existence of small hard alpha inclusion have minor influence on the global metal flow. 2D axisymmetric model also gives a result consistent with 3D model. Thus, computation cost can be significantly reduced by replacing 3D multi-body model with 2D axisymmetric model. Regression models have been built based on FEM results to track a large amount of points in forging. Monte Carlo simulation is used to study the random located discrete defects; the different preform designs will influence the metal flow; thus 174

the failure probability of the components can be changed in forging stage by proper preform design.

Material properties of a forged part such as fatigue strength and rupture strength are greatly affected by microstructure, which is a result of forging and heat treatments. In the effort to yield a desired microstructure in final components, the contribution of forging on microstructure is studied. For fixed forging conditions, varying preforms will produce different microstructures. For a fixed preform, varying die speeds and forging temperatures also creates different grain size distributions over the forging. Although die speed itself can change the grain size, the temperature rise because of higher deformation rate and less heat transfer between workpiece and die has more contribution in grain size. Selection of optimal forging process depends on the optimization objective.

One difficulty of titanium alloy forging is the narrow processing window; flow instability is described in processing map. Temperature in the workpiece can be limited to a specified range with isothermal forging. However, high cost of isothermal forging impedes the widely usage of this process. In the forging of titanium hip implant, the breakdown of complex 3D shape into several 2D cross sections shows the advantage of reduced computation cost. With proper design, the die temperature can be reduced greatly without violating process window constrictions placed by processing map. A well balanced load distribution can be achieved by flashland design. 175

7.2 Suggestions for future work

Since forgings are mainly used as critical components where impact, high stress or cyclic loading are likely to occur, the effort to reduce the risk of failure in forging is never-ending.

Much work could be done to extend the scope of this research.

Firstly, the discrete defect has its specific distribution in billet made of different material.

For example, the discrete white spot defect tends to take place at the mid-radius to center, while dendritic white spots are usually located at the center region of the ingot. The distribution of the discrete defect will affect the failure risk of forging. Also, the failure risk of rotation components are assumed based on general stress distribution in the disk. A specific force analysis combined with material fatigue behavior could give more realistic failure information.

Secondly, the effects of preform and forging parameters like temperature and die speed for superalloy forging are studied separately. By putting those into one design matrix could find interaction between those two. Metadynamic recrystallization model is used in this research because it is the main recrystallization mechanism in the forging range used by present research. Under other forging conditions, for example, isothermal forging of IN

718, dynamic recrystallization will be the main recrystallization mechanism. Integrating dynamic recrystallization, metadynamic recrystallization, and grain growth model into the 176

FEM code can predict the microstructure of forging in a more realistic situation.

Last but not least, more constraints could be introduced into the optimization of processing parameters in superalloy forging. Like the instability map for titanium alloys, superalloys also have their processing window restricted by processing map. More constraints together with possibly more than one objective to be optimized could make optimization more difficult and trade-off has to be taken into account.

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APPENDIX

APPENDIX A. 70 points microstructure information

Microstructure information about the 70 points in Chapter 5 is given in this section. The point locations and coordinate system is shown in Figure A.1 and locations are listed in

Table A.1. Grain size and fraction of recrystallization are listed from Table A.2 to Table

A.12.

Figure A.1 Checking points and coordinate system of machined disk

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zone 1 (77,44) zone 6 (100,13) zone 11 (225,27) (63,48) (102,6) (228,23) (63,38) (111,15) (237,32) (92,48) (112,8) (237,24) (92,38) (120,13) (232,27) zone 2 (77,26) (124,7) zone 12 (225,19) (64,29) (132,11) (235,19) (64,23) zone 7 (145,25) zone 13 (252,28) (91,29) (175,25) (252,24) (91,23) (160,24) (252,32) zone 3 (67,-3) zone 8 (145,19) (260,30) (68,13) (175,19) (260,25) (75,6) (160,20) (244,30) (85,13) zone 9 (185,24) (244,25) (88,6) (216,25) zone 14 (255,15) zone 4 (100,38) (197,25) (260,18) (100,52) (209,24) (260,12) (103,45) zone 10 (185,20) (250,20) (115,46) (216,19) (250,12) (113,54) (197,19) (243,18) (116,38) (209,20) (248,16) zone 5 (102,30) (102,22) (111,32) (112,24) (120,30) (122,22) (135,21)

Table A.1 Coordinates of checking points

179

D( µm) X(%) D( µm) X(%) D( µm) X(%) zone 1 5.7 100 zone 6 7.4 100 zone 11 3.4 100 2.3 85 6.5 100 4.1 100 4.6 100 7.8 100 6.8 100 5.1 98 7.5 100 8.4 100 7 100 8.2 100 8.7 100 zone 2 7.4 100 8 100 zone 12 2.5 100 7.2 100 9.2 100 3.5 100 7.7 100 zone 7 8.3 100 zone 13 8.1 100 7.5 100 4.7 100 8.7 100 7.5 100 6.4 100 6.6 100 zone 3 4.7 100 zone 8 9.8 100 6.6 100 7.5 100 5.1 100 7.7 100 7.2 100 8.3 100 7 100 7.4 100 zone 9 3.4 100 10.8 100 6.9 100 2.9 100 zone 14 7.6 100 zone 4 7.3 100 3 100 7.4 100 3.9 95 3.2 100 4.7 100 6.4 100 zone 10 4.2 100 10.3 100 5.3 100 1.9 100 5.7 100 2.1 71 3.5 100 7.8 100 7.6 100 3.8 100 9.2 100 zone 5 7.7 100 7.7 100 8 100 8.1 100 8.8 100 8.7 100 9.6 100

Table A.2 Microstructure information T=950°C V=5 mm/s preform 1

180

D( µm) X(%) D( µm) X(%) D( µm) X(%) zone 1 6.8 100 zone 6 6.8 99 zone 11 3.1 100 4.1 99 5.7 96 3.4 100 6.3 100 6.9 100 7.1 100 7.4 100 5.9 99 6.6 100 7.7 100 6.8 100 6 100 zone 2 7.6 100 6.3 100 zone 12 1.1 100 7.1 100 7 100 3.2 100 7.4 100 zone 7 4.8 99 zone 13 6.8 100 7.6 100 1.3 99 8.4 100 7.4 100 2.4 100 4.9 100 zone 3 6.6 100 zone 8 7.2 100 3.3 100 7.4 100 1.7 100 7.6 100 7.1 100 3.4 100 8.1 100 7.1 100 zone 9 1.4 96 9.3 100 6.6 99 1.1 100 zone 14 6.4 100 zone 4 7.5 100 1.1 96 8.6 100 7.1 100 1.1 100 4.3 100 7.3 100 zone 10 1.7 100 8.4 100 5.2 99 0.7 100 4.1 100 4.4 98 2 100 6.4 100 6.6 100 1.2 100 6.8 100 zone 5 7.5 100 7.3 100 7.3 100 7.2 100 7 100 7.2 100 7.7 100

Table A.3 Microstructure information T=950°C V=5 mm/s preform 2

181

D( µm) X(%) D( µm) X(%) D( µm) X(%) zone 1 4.4 100 zone 6 4.5 99 zone 11 2.8 100 1.7 86 3.6 94 4.4 100 3.6 100 4.6 98 5.5 100 4.3 100 3.9 97 7.4 100 4.9 100 4.6 99 5.7 100 zone 2 5 100 4.3 100 zone 12 1.6 100 4.7 100 5.4 100 4.6 100 4.9 99 zone 7 5.5 100 zone 13 9.3 100 4.9 100 3.7 100 10.2 100 4.8 100 4.2 99 6.7 100 zone 3 3.3 98 zone 8 6.3 100 6 100 4.8 99 3 96 10.3 100 4.5 100 4.9 100 8.9 100 4.6 100 zone 9 3.9 100 10.2 100 4.1 100 1.6 100 zone 14 8.7 100 zone 4 5 100 3.3 100 8.9 100 3.7 98 2.4 100 4.1 100 4.6 100 zone 10 3 100 10.8 100 3.5 100 2.6 100 5.4 100 2.4 95 2.9 100 9 100 5.3 100 3.3 100 8.5 100 zone 5 5 100 4.9 100 5.3 100 5.1 100 5.6 100 5.5 100 6.2 100

Table A.4 Microstructure information T=920°C V=5 mm/s preform 3

182

D( µm) X(%) D( µm) X(%) D( µm) X(%) zone 1 5.5 100 zone 6 5.2 100 zone 11 12.5 100 4.5 100 4.7 99 17.8 100 5.9 100 5.4 100 24.4 100 5.4 100 5 100 27.4 100 5.6 100 5.6 100 22.8 100 zone 2 5.6 100 5.3 100 zone 12 14.6 100 5.8 100 6.8 100 19.2 100 5.8 100 zone 7 8.8 100 zone 13 26.7 100 5.5 100 10 100 27.7 100 5.4 100 8.3 100 22.9 100 zone 3 5.9 100 zone 8 8.5 100 19.1 100 5.7 100 9.5 100 19.5 100 5.6 100 9.1 100 30.8 100 5.4 100 zone 9 12 100 32.7 100 5.2 100 8.1 100 zone 14 22.7 100 zone 4 5.7 100 10.5 100 18.1 100 5.3 100 12.4 100 16.4 100 5.6 100 zone 10 11.1 100 36.2 100 5.9 100 16.1 100 27.3 100 5.1 100 9.8 100 31.3 100 6.2 100 15.8 100 35.2 100 zone 5 5.6 100 5.4 100 5.8 100 5.7 100 6.4 100 6.1 100 7.5 100

Table A.5 Microstructure information T=920°C V=20 mm/s preform 3

183

D( µm) X(%) D( µm) X(%) D( µm) X(%) zone 1 6.1 100 zone 6 5.6 100 zone 11 17.7 100 6.5 100 5.1 100 24.5 100 6.6 100 5.8 100 38.7 100 5.9 100 5.5 100 40.5 100 5.9 100 6 100 26.5 100 zone 2 6 100 5.8 100 zone 12 24.2 100 6.2 100 8 100 34.2 100 6.1 100 zone 7 10.8 100 zone 13 38.1 100 6 100 11.8 100 38.1 100 5.9 100 9.7 100 32.7 100 zone 3 6.8 100 zone 8 9.6 100 24.2 100 6.1 100 11.8 100 21.7 100 6.2 100 9.4 100 44.4 100 6 100 zone 9 17.9 100 53.6 100 5.6 100 12.7 100 zone 14 24.4 100 zone 4 6 100 21.3 100 19.9 100 5.9 100 18.5 100 20.5 100 6 100 zone 10 15.6 100 49.9 100 6.3 100 27.5 100 41.6 100 6.1 100 21.4 100 59.6 100 6.6 100 24.5 100 53.2 100 zone 5 5.8 100 5.8 100 6.2 100 6 100 6.7 100 6.6 100 8.6 100

Table A.6 Microstructure information T=920°C V=50 mm/s preform 3

184

D( µm) X(%) D( µm) X(%) D( µm) X(%) zone 1 6.6 100 zone 6 7.3 100 zone 11 4.7 100 2.8 93 6.5 100 6.5 100 6 100 7.8 100 8.7 100 6.5 100 7 100 10.6 100 7.5 100 7.9 100 8.6 100 zone 2 7.6 100 7.2 100 zone 12 2.4 100 7.3 100 8.8 100 4.5 100 7.6 100 zone 7 8.8 100 zone 13 9.7 100 7.5 100 4.5 100 13.9 100 7.4 100 5.7 100 7.5 100 zone 3 5.6 100 zone 8 9.4 100 8.6 100 7.5 100 4.9 100 12.5 100 7 100 8.1 100 11.3 100 7.3 100 zone 9 4.7 100 13.1 100 6.7 100 2.2 100 zone 14 10.3 100 zone 4 7.7 100 4 100 11.6 100 6.2 100 3.9 100 6.4 100 7.1 100 zone 10 3.8 100 14.5 100 6 100 3.7 100 7.1 100 3.6 97 4.9 100 10.6 100 8.2 100 3.9 100 12.4 100 zone 5 7.7 100 7.5 100 8.1 100 7.8 100 8.5 100 8.3 100 9.1 100

Table A.7 Microstructure information T=950°C V=5 mm/s preform 3

185

D( µm) X(%) D( µm) X(%) D( µm) X(%) zone 1 8.1 100 zone 6 8.1 100 zone 11 17.3 100 6.7 100 7.8 100 20.7 100 8.5 100 8.3 100 32.4 100 8.2 100 7.9 100 29.5 100 8.5 100 8.6 100 26.6 100 zone 2 8.3 100 8.8 100 zone 12 16.9 100 8.4 100 10.2 100 19.4 100 8.4 100 zone 7 12.7 100 zone 13 31.8 100 8.4 100 13.4 100 36.7 100 8.2 100 11.9 100 27.8 100 zone 3 8.7 100 zone 8 11.8 100 19.6 100 8.4 100 13 100 22.8 100 8.3 100 12.3 100 36.2 100 8.1 100 zone 9 16.4 100 41.7 100 8.1 100 14.2 100 zone 14 23.1 100 zone 4 8.6 100 11 100 22 100 8.1 100 14.5 100 19.4 100 8.5 100 zone 10 14.9 100 39.1 100 9 100 13.6 100 25.6 100 7.6 100 16.4 100 38.6 100 9.6 100 18 100 40.3 100 zone 5 8.5 100 8.3 100 9 100 8.7 100 9.6 100 9.4 100 10.8 100

Table A.8 Microstructure information T=950°C V=20 mm/s preform 3

186

D( µm) X(%) D( µm) X(%) D( µm) X(%) zone 1 8.8 100 zone 6 8.4 100 zone 11 25.3 100 8.8 100 7.9 100 33.5 100 9.3 100 8.7 100 49.4 100 8.7 100 8.4 100 49.1 100 9.1 100 9.1 100 44.8 100 zone 2 8.8 100 9.2 100 zone 12 28.8 100 9.2 100 10.9 100 41.2 100 8.9 100 zone 7 16.5 100 zone 13 43.8 100 8.9 100 15.5 100 45.2 100 8.9 100 15 100 38 100 zone 3 9.5 100 zone 8 13.6 100 28.5 100 8.9 100 17.2 100 28.3 100 9.1 100 14.4 100 51.5 100 8.8 100 zone 9 21.7 100 64.9 100 8.5 100 20 100 zone 14 32.5 100 zone 4 9.2 100 21 100 27.8 100 8.6 100 20.1 100 23.9 100 9.1 100 zone 10 18.1 100 58.3 100 9.8 100 24.4 100 43 100 8.9 100 23.8 100 71.9 100 10.1 100 25.4 100 66.2 100 zone 5 8.8 100 8.8 100 9.4 100 9.1 100 10.1 100 9.8 100 12.1 100

Table A.9 Microstructure information T=950°C V=50 mm/s preform 3

187

D( µm) X(%) D( µm) X(%) D( µm) X(%) zone 1 10.3 100 zone 6 11.3 100 zone 11 6 100 5.3 100 10.2 100 6.9 100 8 100 11.8 100 8.4 100 10.4 100 11.3 100 11.7 100 11.3 100 12.1 100 9.7 100 zone 2 11.5 100 12.3 100 zone 12 2.5 100 11.2 100 13.5 100 6.3 100 11.5 100 zone 7 13.3 100 zone 13 14.2 100 11.3 100 7.9 100 16.9 100 11.3 100 9.9 100 11.7 100 zone 3 8.2 100 zone 8 14.5 100 9.3 100 11.4 100 8.4 100 13.5 100 11 100 12.4 100 13.1 100 11.2 100 zone 9 8.5 100 15.5 100 10.7 100 4.6 100 zone 14 13.3 100 zone 4 11.6 100 5.8 100 15.2 100 8.7 100 4.4 100 8.9 100 11.1 100 zone 10 8.5 100 17 100 8.4 100 4 100 12.5 100 5.9 99 6.6 100 11.9 100 12.3 100 5.8 100 14.4 100 zone 5 11.7 100 11.4 100 12.2 100 11.9 100 13 100 12.7 100 13.9 100

Table A.10 Microstructure information T=980°C V=5 mm/s preform 3

188

D( µm) X(%) D( µm) X(%) D( µm) X(%) zone 1 12.1 100 zone 6 12.5 100 zone 11 17.5 100 11.7 100 12.4 100 28 100 12.8 100 12.9 100 42.5 100 12.1 100 12.5 100 42.7 100 12.8 100 13 100 43.9 100 zone 2 12.4 100 13.3 100 zone 12 20.1 100 12.5 100 15.3 100 23.1 100 12.4 100 zone 7 18.5 100 zone 13 41.5 100 12.8 100 19.2 100 44.6 100 12.7 100 18.4 100 30.9 100 zone 3 13.2 100 zone 8 17.8 100 27.3 100 12.5 100 18.8 100 29 100 12.7 100 18.7 100 50.1 100 12.5 100 zone 9 19.7 100 53.8 100 12.6 100 22.4 100 zone 14 30.5 100 zone 4 13.1 100 20.7 100 28.4 100 12.1 100 18.5 100 25 100 12.8 100 zone 10 21.7 100 48.3 100 13.2 100 20.6 100 44.1 100 11.3 100 23.3 100 45.2 100 14.4 100 27.7 100 52 100 zone 5 13.2 100 12.9 100 13.9 100 13.6 100 14.8 100 14.4 100 16.5 100

Table A.11 Microstructure information T=980°C V=20 mm/s preform 3

189

D( µm) X(%) D( µm) X(%) D( µm) X(%) zone 1 13.3 100 zone 6 13.1 100 zone 11 37.9 100 12.7 100 13 100 43.5 100 13.9 100 13.4 100 63.7 100 13.3 100 13 100 63.5 100 13.9 100 14.6 100 60.8 100 zone 2 13.1 100 14.6 100 zone 12 33.3 100 13.2 100 17.1 100 53.3 100 13.2 100 zone 7 25 100 zone 13 50.1 100 13.6 100 24.2 100 51.8 100 13.5 100 21.7 100 44.5 100 zone 3 14.6 100 zone 8 20.6 100 38.4 100 13.2 100 21.9 100 37.8 100 13.8 100 21.3 100 64.8 100 13.4 100 zone 9 29.8 100 74.7 100 13.3 100 24.1 100 zone 14 36.9 100 zone 4 14.1 100 25.3 100 37.6 100 13.5 100 28 100 33 100 14.1 100 zone 10 26.3 100 64.2 100 14.4 100 37.6 100 59.8 100 13.4 100 31 100 84.9 100 16 100 35.3 100 77 100 zone 5 14 100 13.8 100 14.7 100 14.5 100 16.2 100 15.3 100 18.2 100

Table A.12 Microstructure information T=980°C V=50 mm/s preform 3

190

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