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

By

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

ii

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

iii

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.

iv

Dedicated to my family

v

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.

vi

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.

vii

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

viii

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

ix

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

x

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

xi

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

xii

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 + and 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

xiii

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 segregation: voids surrounded by stabilized ............................................ 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 950C 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 (1106 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

xiv

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 600C .......................................... 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=920C........... 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 - 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

xv

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 800C) .......... 163 Figure 6.11 Temperature and strain rate distribution after preforming with performing die temperature of 200C 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

xvi

LIST OF TABLES

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

Table 2.1 Properties comparison between + and 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=950C V=5 mm/s preform 1.......................... 180

xvii

Table A.3 Microstructure information T=950C V=5 mm/s preform 2.......................... 181

Table A.4 Microstructure information T=920C V=5 mm/s preform 3.......................... 182

Table A.5 Microstructure information T=920C V=20 mm/s preform 3........................ 183

Table A.6 Microstructure information T=920C V=50 mm/s preform 3........................ 184

Table A.7 Microstructure information T=950C V=5 mm/s preform 3.......................... 185

Table A.8 Microstructure information T=950C V=20 mm/s preform 3........................ 186

Table A.9 Microstructure information T=950C V=50 mm/s preform 3........................ 187

Table A.10 Microstructure information T=980C V=5 mm/s preform 3........................ 188

Table A.11 Microstructure information T=980C V=20 mm/s preform 3...................... 189

Table A.12 Microstructure information T=980C V=50 mm/s preform 3...................... 190

1

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

2

squeezed or compressed under high pressure to form the products. The deformation it

undergoes gives the forged parts superior mechanical properties by aligning materials

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

3

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.

4

(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

5

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

6

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

7

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.

8

Design parameters Effects/responses

Die design/preform design Forging feasibility, strain distribution Billet temperature Temperature, metal flow, load

Die temperature Load, temperature distribution, cost

Die velocity Strain rate, temperature 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:

)],),...(,(),...,,(),,[( 2211 nnii cpcpcpcpRisk (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

9

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

=

EventeConsequencIMPACT

TimeEventLIKELIHOOD

TimeeConsequencRISK (1.2)

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]

10

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

11

(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]

12

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]

13

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]

14

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.

15

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

16

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.

17

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;

Industrys 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,

18

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

19

designers 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

20

P(1) = x0 u0 (2.2)

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

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

Q(1) = P(1) + u(1)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

P(2) = x0 u(1)0-1 (2.5)

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

estimate of Q, which is

Q(2) = P(2) + u(2)0-1 (2.6)

is then compared to Q. The iteration continues until

Q(n) = P(n) + u(n)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.

21

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.

22

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.

23

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

24

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

25

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

26

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

27

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].

28

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

29

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

30

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)

phase at low temperature and body centered cubic (bcc) phase at an elevated temperature.

The temperature at which transition from to occurs (about 882 C for pure titanium) is

called 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 phase and phase. According to how the

alloying elements influence the transus, these elements can be classified as and

stabilizers, and neutral elements. The and stabilizers have a tendency of concentrating

in either or 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 alloys, alloys and +

alloys according to which phase are predominantly present at room temperature under

31

normal conditions. The latter two alloys have higher strength and are easier to shape and

work. Nowadays, the most commonly used titanium alloys are + 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 + alloys is

considerably higher than either or alloys even in annealed condition. This synergism

has significantly increased technical interest in using titanium alloys for light weight

structures. Recently, the usage of alloys in many fields such as aircraft and petrochemical

equipment are growing rapidly. However, the total volume is still small compared to +

alloys because of the reasons ranging from producibility to changes in design philosophy

considering fracture toughness, strength, and other properties.

When or alloys are mentioned, that does not mean the other phase is totally absent in

the material. In fact, alloys are usually used in aged condition, in which some of phase

is present as strengthening precipitate. On the contrary, a small amount of phase in

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

32

of + alloys can be divided into two categories: + processing and processing. This

depends on the temperature range at which the working operation is completed. Working in

+ range below transus produces phase characterized by equiaxed microstructure,

which is known as primary . The volume fraction of primary varies according to

different finishing temperatures and subsequent heat treatment. In forging, colonies of

plates develop and grain boundary phase exists on prior grain boundaries. The

boundary 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 + alloys, the forging temperature relative to 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 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

33

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 + phase range

[Semiatin et al., 1997]. Both and phases exist in the microstructure at all times. The

amount of each phase during the forging process depends upon the temperature distance

from 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 + forging is

characterized by deformed or equiaxed in a transformed 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

34

rate determines the uniformity of the microstructure.

(a) + processed (b) processed

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

[Williams, 1995]

Compared to + forging, forging is a relatively less common method in secondary

processing. The acicular or Widmanstatten (Figure 2.4 (b)) is developed and this

structure has better toughness, fatigue crack propagation resistance and creep resistance.

During the cooling followed by forging, forms on the prior grain boundary. To

remove undesirable grain boundary , it is a good practice to work continuously through

transus temperature. This results in continuous recrystallization of phase and little or no

grain boundary formation [Williams, 1995]. Because of the high temperature and the

formation of new grains by recrystallization every time the transus is exceeded, the

35

influences of deformation in forging are not necessarily cumulative. A significantly

lower pressure is required for 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 + alloys in strength can be seen

in Figure 2.5. A qualitatively comparison of + forging and forging is made in Table

2.1.

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

alloys [Donachie, 2000]

36

Properties + forging 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 + and 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 + 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].

37

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.

38

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 authors 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.

39

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 is defined as:

40

21

m

m =

+ (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 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( / 1)( )ln

m mm

+= +

&

& (2.9)

Flow instability is predicted when )( & 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.

41

The same method was taken by Sechacharyulu et al. [2000] to investigate high oxygen

grade Ti-6Al-4V with equiaxed - 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

750-1100C at an interval of 50C. 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 alloy Ti-10V-4.5Fe-1.5Al in hot forging was studied

by Balasubrahmanyam et al.[Balasubrahmanyam and Prasad, 2002]. Stress strain curves

42

were recorded at temperature range from 650C to 900C 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 1000C and strain rate of 0.001 s-1, indicated a coarse transformed

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

380-680C 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

43

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 950C

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 thickness on flow behavior.

Martin [1998] studied microstructure of Ti-4.4Al-5Mo-2Cr-1Ni by + forging and

forging with subsequent heat treatments. Both microstructure evolution and mechanical

properties show the similar tendency as other + 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

44

temperature have pronounced effect on fatigue strength of + titanium alloys [Kubiak

and Sieniawski, 1998].

Process design rules for non-isothermal forging of Ti-6Al-4V have been proposed in Lee

and Lins 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;

Youngs 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

45

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.

46

A die shape compensation approach was introduced by Ou and Armstrong [2002] to reduce

the thickn