The flow stress in the high-speed machining of titanium alloys depends strongly on the microstructural state of the material which is defined by the composition of the material, its starting microstructure, and the thermomechanical loads imposed during the machining process. In the past, researchers have determined the flow stress empirically as a function of mechanical state parameters, such as strain, strain rate, and temperature while ignoring the changes in the microstructural state such as phase transformations. This paper presents a microstructure-sensitive flow stress model based on the self-consistent method (SCM) that includes the effects of chemical composition, α phase and β phase, as well mechanical state imposed. This flow stress is developed to model the flow behavior of titanium alloys in machining at speed of higher than 5 m/s, characterized by extremely high strains (2–10 or higher), high strain rates (104–106 s−1 or higher), and high temperatures (600–1300 °C). The flow stress sensitivity to mechanical and material parameters is analyzed. A new SCM-based Johnson–Cook (JC) flow stress model is proposed whose constants and ranges are determined using experimental data from literature and the physical basis for SCM approach. This new flow stress is successfully implemented in the finite-element (FE) framework to simulate machining. The predicted results confirm that the new model is much more effective and reliable than the original JC model in predicting chip segmentation in the high-speed machining of titanium Ti–6Al–4V alloy.
Issue Section:
Research Papers
References
1.
Johnson
, G. R.
, and Cook
, W. H.
, 1983
, “A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates and High Temperatures
,” Seventh International Symposium on Ballistics
, The Hague
, The Netherlands
, pp. 541
–547
.2.
Johnson
, G. R.
, 1981
, “Dynamic Analysis of a Torsion Test Specimen Including Heat Conduction and Plastic Flow
,” ASME J. Eng. Mater. Technol.
, 103
(3
), pp. 201
–206
.3.
Johnson
, G. R.
, Hoegfeldt
, J. M.
, Lindholm
, U. S.
, and Nagy
, A.
, 1983
, “Response of Various Metals to Large Torsional Strains Over a Large Range of Strain Rates—Part 1: Ductile Metals
,” ASME J. Eng. Mater. Technol.
, 105
(1
), pp. 42
–47
.4.
Johnson
, G. R.
, Hoegfeldt
, J. M.
, Lindholm
, U. S.
, and Nagy
, A.
, 1983
, “Response of Various Metals to Large Torsional Strains Over a Large Range of Strain Rates—Part 2: Less Ductile Metals
,” ASME J. Eng. Mater. Technol.
, 105
(1
), pp. 48
–53
.5.
Lee
, W. S.
, and Lin
, C. F.
, 1998
, “Plastic Deformation and Fracture Behavior of Ti-6Al-4V Alloy Loaded With High Strain Rate Under Various Temperatures
,” Mater. Sci. Eng. A
, 241
(1–2), pp. 48
–59
.6.
Khan
, A. S.
, Suh
, Y. S.
, and Kazmi
, R.
, 2004
, “Quasi-Static and Dynamic Loading Responses and Constitutive Modeling of Titanium Alloys
,” Int. J. Plast.
, 20
(12
), pp. 2233
–2248
.7.
Khan
, A. S.
, Kazmi
, R.
, and Farrokh
, B.
, 2007
, “Multiaxial and Non-Proportional Loading Responses, Anisotropy and Modeling of Ti-6Al-4V Titanium Alloy Over Wide Ranges of Strain Rates and Temperatures
,” Int. J. Plast.
, 23
(6
), pp. 931
–950
.8.
Liu
, R.
, Melkote
, S.
, Pucha
, R.
, Morehouse
, J.
, Man
, X. L.
, and Marusich
, T.
, 2013
, “An Enhanced Constitutive Material Model for Machining of Ti-6Al-4V Alloy
,” J. Mater. Process. Technol.
, 213
(12
), pp. 2238
–2246
.9.
Gente
, A.
, Hoffmeister
, H. W.
, and Evans
, C. J.
, 2001
, “Chip Formation in Machining Ti6Al4V at Extremely High Cutting Speeds
,” CIRP Ann. Manuf. Technol.
, 50
(1
), pp. 49
–52
.10.
Molinari
, A.
, Musquar
, C.
, and Sutter
, G.
, 2002
, “Adiabatic Shear Banding in High Speed Machining of Ti-6Al-4V: Experiments and Modeling
,” Int. J. Plast.
, 18
(4
), pp. 443
–459
.11.
Rahman
, M.
, Wang
, Z. G.
, and Wong
, Y. S.
, 2006
, “A Review on High-Speed Machining of Titanium Alloys
,” JSME Int. J. Ser. C
, 49
(1
), pp. 11
–20
.12.
Sun
, J.
, and Guo
, Y. B.
, 2009
, “Material Flow Stress and Failure in Multiscale Machining Titanium Alloy Ti-6Al-4V
,” Int. J. Adv. Manuf. Technol.
, 41
(7–8
), pp. 651
–659
.13.
Ye
, G. G.
, Xue
, S. F.
, Jiang
, M. Q.
, Tong
, X. H.
, and Dai
, L. H.
, 2013
, “Modeling Periodic Adiabatic Shear Band Evolution During High Speed Machining Ti-6Al-4V Alloy
,” Int. J. Plast.
, 40
(1
), pp. 39
–55
.14.
Jaspers
, S. P. F. C.
, and Dautzenberg
, J. H.
, 2002
, “Material Behavior in Metal Cutting: Strains, Strain Rates and Temperatures in Chip Formation
,” J. Mater. Process. Technol.
, 121
(1
), pp. 123
–135
.15.
Andrade
, U.
, Meyers
, M. A.
, Vecchio
, K. S.
, and Chokshi
, A. H.
, 1994
, “Dynamic Recrystallization in High-Strain, High-Strain-Rate Plastic Deformation of Copper
,” Acta Metall. Mater.
, 42
(9
), pp. 3183
–3195
.16.
Sartkulvanich
, P.
, Koppka
, F.
, and Altan
, T.
, 2004
, “Determination of Flow Stress for Metal Cutting Simulation—A Progress Report
,” J. Mater. Process. Technol.
, 146
(1
), pp. 61
–71
.17.
Hammer
, J. T.
, 2012
, “Plastic Deformation and Ductile Fracture of Ti-6Al-4V Under Various Loading Conditions
,” M.S. thesis
, The Ohio State University, Columbus, OH.18.
Recht
, R. F.
, 1964
, “Catastrophic Thermoplastic Shear
,” ASME J. Appl. Mech.
, 31
(2
), pp. 189
–193
.19.
Komanduri
, R.
, and Brown
, R. H.
, 1981
, “On the Mechanics of Chip Segmentation in Machining
,” ASME J. Eng. Ind.
, 103
(1
), pp. 33
–51
.20.
Komanduri
, R.
, 1982
, “Some Clarifications on the Mechanics of Chip Formation When Machining Titanium Alloys
,” Wear
, 76
(1
), pp. 15
–34
.21.
Semiatin
, S. L.
, and Rao
, S. B.
, 1983
, “Shear Localization During Metal Cutting
,” J. Mater. Sci. Eng.
, 61
(2
), pp. 185
–192
.22.
Ma
, W.
, Li
, X. W.
, Dai
, L. H.
, and Ling
, Z.
, 2012
, “Instability Criterion of Materials in Combined Stress States and Its Application to Orthogonal Cutting Process
,” Int. J. Plast.
, 30–31
(3
), pp. 18
–40
.23.
Umbrello
, D.
, 2008
, “Finite Element Simulation of Conventional and High Speed Machining of Ti6Al4V Alloy
,” J. Mater. Process. Technol.
, 196
(1–3
), pp. 79
–87
.24.
Arrazola
, P. J.
, Barbero
, O.
, and Urresti
, I.
, 2010
, “Influence of Material Parameters on Serrated Chip Prediction in Finite Element Modeling of Chip Formation Process
,” Int. J. Mater. Forming
, 3
(1
), pp. 519
–522
.25.
Arrazola
, P. J.
, Özel
, T.
, Umbrello
, D.
, Davies
, M.
, and Jawahir
, I. S.
, 2013
, “Recent Advances in Modeling of Metal Machining Processes
,” CIRP Ann. Manuf. Technol.
, 62
(2
), pp. 695
–718
.26.
Molinari
, A.
, Soldani
, X.
, and Miguélez
, M. H.
, 2013
, “Adiabatic Shear Banding and Scaling Law in Chip Formation With Application to Cutting of Ti-6Al-4V
,” J. Mech. Phys. Solids
, 61
(11
), pp. 2331
–2359
.27.
Guo
, Y. B.
, Wen
, Q.
, and Woodbury
, K. A.
, 2006
, “Dynamic Material Behavior Modeling Using Internal State Variable Plasticity and Its Application in Hard Machining Simulations
,” ASME J. Manuf. Sci. Eng.
, 128
(3
), pp. 749
–759
.28.
Calamaz
, M.
, Coupard
, D.
, and Girot
, F.
, 2008
, “A New Material Model for 2D Numerical Simulation of Serrated Chip Formation When Machining Titanium Alloy Ti-6Al-4V
,” Int. J. Mach. Tools Manuf.
, 48
(3–4
), pp. 275
–288
.29.
Calamaz
, M.
, Coupard
, D.
, and Girot
, F.
, 2010
, “Numerical Simulation of Titanium Alloy Dry Machining With a Strain Softening Constitutive Law
,” Mach. Sci. Technol.
, 14
(2
), pp. 244
–257
.30.
Anurag
, S.
, and Guo
, Y. B.
, 2007
, “A Modified Micromechanical Approach to Determine Flow Stress of Work Materials Experiencing Complex Deformation Histories in Manufacturing Processes
,” Int. J. Mech. Sci.
, 49
(7
), pp. 909
–918
.31.
Karpat
, Y.
, 2010
, “A Modified Material Model for the Finite Element Simulation of Machining Titanium Alloy Ti-6Al-4V
,” Mach. Sci. Technol.
, 14
(3
), pp. 390
–410
.32.
Obikawa
, T.
, and Usui
, E.
, 1996
, “Computational Machining of Titanium Alloy-Finite Element Modeling and a Few Results
,” ASME J. Manuf. Sci. Eng.
, 118
(2
), pp. 208
–215
.33.
Bammann
, D. J.
, 1990
, “Modeling Temperature and Strain Rate Dependent Large Deformation of Metals
,” ASME Appl. Mech. Rev.
, 43
(5S
), pp. S312
–S319
.34.
Khan
, A. S.
, and Huang
, S. J.
, 1992
, “Experimental and Theoretical Study of Mechanical Behavior of 1100 Aluminum in the Strain Rate Range 10−5-104 s−1
,” Int. J. Plast.
, 8
(4
), pp. 397
–424
.35.
Khan
, A. S.
, and Liang
, R. Q.
, 1999
, “Behaviors of Three BCC Metal Over a Wide Range of Strain Rates and Temperatures: Experiments and Modeling
,” Int. J. Plast.
, 15
(10
), pp. 1089
–1109
.36.
Bäker
, M.
, 2003
, “The Influence of Plastic Properties on Chip Formation
,” Comput. Mater. Sci.
, 28
(3–4
), pp. 556
–562
.37.
Rhim
, S. H.
, and Oh
, S. I.
, 2006
, “Prediction of Serrated Chip Formation in Metal Cutting Process With New Flow Stress Model for AISI 1045 Steel
,” J. Mater. Process. Technol.
, 171
(3
), pp. 141
–146
.38.
Shi
, J.
, and Liu
, C. R.
, 2006
, “On Predicting Chip Morphology and Phase Transformation in Hard Machining
,” Int. J. Adv. Manuf. Technol.
, 27
(7–8
), pp. 645
–654
.39.
Zerilli
, F. J.
, and Armstrong
, R. W.
, 1987
, “Dislocation-Mechanics-Based Constitutive Relations for Material Dynamics Calculations
,” J. Appl. Phys.
, 61
(5
), pp. 1816
–1825
.40.
Nemat-Nasser
, S.
, Guo
, W. G.
, and Cheng
, J. Y.
, 1999
, “Mechanical Properties and Deformation Mechanisms of a Commercially Pure Titanium
,” Acta Mater.
, 47
(13
), pp. 3705
–3720
.41.
Nemat-Nasser
, S.
, Li
, Y. F.
, and Isaacs
, J. B.
, 1994
, “Experimental Computational Evaluation of Flow Stress at High Strain Rates With Application to Adiabatic Shear Banding
,” Mech. Mater.
, 17
(2–3
), pp. 111
–134
.42.
Nemat-Nasser
, S.
, and Isaacs
, J. B.
, 1997
, “Direct Measurement of Isothermal Flow Stress of Metals at Elevated Temperatures and High Strain Rates With Application to Ta-W Alloys
,” Acta Mater.
, 45
(3
), pp. 907
–919
.43.
Nemat-Nasser
, S.
, and Hori
, M.
, 1999
, Micromechanics: Overall Properties of Heterogeneous Materials
, Elsevier Science B.V.
, Amsterdam, The Netherlands
.44.
Nemat-Nasser
, S.
, Guo
, W. G.
, Nesterenko
, V. F.
, Indrakanti
, S. S.
, and Gu
, Y. B.
, 2001
, “Dynamic Response of Conventional and Hot Isostatically Pressed Ti-6Al-4V Alloys: Experiments and Modeling
,” Mech. Mater.
, 33
(8
), pp. 425
–439
.45.
Luo
, J.
, Li
, M. Q.
, Li
, X. L.
, and Shi
, Y. P.
, 2010
, “Constitutive Model for High Temperature Deformation of Titanium Alloys Using Internal State Variables
,” Mech. Mater.
, 42
(2
), pp. 157
–165
.46.
Brown
, A. A.
, and Bammann
, D. J.
, 2012
, “Validation of a Model for Static and Dynamic Recrystallization in Metals
,” Int. J. Plast.
, 32–33
(3
), pp. 17
–35
.47.
Wedberg
, D.
, Svoboda
, A.
, and Lindgren
, L. E.
, 2012
, “Modelling High Strain Rate Phenomena in Metal Cutting Simulation
,” Modell. Simul. Mater. Sci. Eng.
, 20
(20
), pp. 85006
–85024
.48.
Kanel
, G. I.
, Razorenov
, S. V.
, Zaretsky
, E. B.
, Herrman
, B.
, and Meyer
, L.
, 2003
, “Thermal “Softening” and “Hardening” of Titanium and Its Alloy at High Strain Rates of Shock-Wave Deforming
,” Phys. Solid State
, 45
(4
), pp. 656
–661
.49.
Picu
, R. C.
, and Majorell
, A.
, 2002
, “Mechanical Behavior of Ti-6Al-4V at High and Moderate Temperature—Part II: Constitutive Modeling
,” Mater. Sci. Eng. A
, 326
(2
), pp. 306
–316
.50.
Bayoumi
, A. E.
, and Xie
, J. Q.
, 1995
, “Some Metallurgical Aspects of Chip Formation in Cutting Ti-6wt.%Al-4wt.%V Alloy
,” Mater. Sci. Eng. A
, 190
(1–2
), pp. 173
–180
.51.
Semiatin
, S. L.
, Seetharaman
, V.
, and Weiss
, I.
, 1997
, “The Thermomechanical Processing of Alpha/Beta Titanium Alloys
,” J. Mater.
, 49
(6
), pp. 33
–39
.52.
Semiatin
, S. L.
, Seetharaman
, V.
, and Weiss
, I.
, 1999
, “Flow Behavior and Globularization Kinetics During Hot Working of Ti-6Al-4V With a Colony Alpha Microstructure
,” Mater. Sci. Eng. A
, 263
(2
), pp. 257
–271
.53.
Semiatin
, S. L.
, Montheillet
, F.
, Shen
, G.
, and Jonas
, J. J.
, 2002
, “Self-Consistent Modeling of the Flow Behavior of Wrought Alpha/Beta Titanium Alloys Under Isothermal and Nonisothermal Hot-Working Conditions
,” Metall. Mater. Trans. A
, 33
(8
), pp. 2719
–2727
.54.
Weiss
, I.
, and Semiatin
, S. L.
, 1998
, “Thermomechanical Processing of Beta Titanium Alloys: An Overview
,” Mater. Sci. Eng. A
, 243
(1–2), pp. 46
–65
.55.
Weiss
, I.
, and Semiatin
, S. L.
, 1999
, “Thermomechanical Processing of Alpha Titanium Alloys—An Overview
,” Mater. Sci. Eng. A
, 263
(2
), pp. 243
–256
.56.
Lütjering
, G.
, 1998
, “Influence of Processing on Microstructure and Mechanical Properties of (α+β) Titanium Alloys
,” Mater. Sci. Eng. A
, 243
(1–2), pp. 32
–45
.57.
Shivpuri
, R.
, Hua
, J.
, Mittal
, P.
, and Srivastava
, A. K.
, 2002
, “Microstructure-Mechanics Interactions in Modeling Chip Segmentation During Titanium Machining
,” CIRP Ann. Manuf. Technol.
, 51
(1
), pp. 71
–74
.58.
Hua
, J.
, and Shivpuri
, R.
, 2004
, “Prediction of Chip Morphology and Segmentation During the Machining of Titanium Alloys
,” J. Mater. Process. Technol.
, 150
(1–2
), pp. 124
–133
.59.
Hershey
, A. V.
, 1954
, “The Plasticity of an Isotropic Aggregate of Anisotropic Face-Centered Cubic Crystals
,” ASME J. Appl. Mech.
, 21
(3
), pp. 241
–249
.60.
Hershey
, A. V.
, 1954
, “The Elasticity of an Isotropic Aggregate of Anisotropic Cubic Crystals
,” ASME J. Appl. Mech.
, 21
(3
), pp. 236
–240
.61.
Hill
, R.
, 1965
, “A Self-Consistent Mechanics of Composite Materials
,” J. Mech. Phys. Solids
, 13
(4
), pp. 213
–222
.62.
Kröner
, E.
, 1978
, “Self-Consistent Scheme and Graded Disorder in Polycrystal Elasticity
,” J. Phys. F Met. Phys.
, 8
(11
), pp. 2261
–2267
.63.
Kim
, J. H.
, Semiatin
, S. L.
, Lee
, Y. H.
, and Lee
, C. S.
, 2011
, “A Self-Consistent Approach for Modeling the Flow Behavior of the Alpha and Beta Phases in Ti-6Al-4V
,” Metall. Mater. Trans. A
, 42
(7
), pp. 1805
–1814
.64.
Segurado
, J.
, Lebensohn
, R. A.
, LLorca
, J.
, and Tomé
, C. N.
, 2012
, “Multiscale Modeling of Plasticity Based on Embedding the Viscoplastic Self-Consistent Formulation in Implicit Finite Elements
,” Int. J. Plast.
, 28
(1
), pp. 124
–140
.65.
Vo
, P.
, Jahazi
, M.
, Yue
, S.
, and Bocher
, P.
, 2007
, “Flow Stress Prediction During Hot Working of Near-α Titanium Alloys
,” Mater. Sci. Eng. A
, 447
(1–2), pp. 99
–110
.66.
Suquet
, P. M.
, 1993
, “Overall Potentials and Extremal Surfaces of Power Law or Ideally Plastic Composites
,” J. Mech. Phys. Solids
, 41
(6
), pp. 981
–1002
.67.
Seshacharyulu
, T.
, Medeiros
, S. C.
, Frazier
, W. G.
, and Prasad
, Y. V. R. K.
, 2000
, “Hot Working of Commercial Ti-6Al-4V With an Equiaxed α-β Microstructure: Materials Modeling Considerations
,” Mater. Sci. Eng. A
, 284
(1–2
), pp. 84
–194
.68.
Seshacharyulu
, T.
, Medeiros
, S. C.
, Frazier
, W. G.
, and Prasad
, Y. V. R. K.
, 2002
, “Microstructural Mechanisms During Hot Working of Commercial Grade Ti-6Al-4V With Lamellar Starting Structure
,” Mater. Sci. Eng. A
, 325
(1–2), pp. 112
–125
.69.
Oikawa
, H.
, and Oomori
, T.
, 1988
, “Steady State Deformation Characteristics of α-Ti-Al Solid Solutions
,” Mater. Sci. Eng. A
, 104
(10
), pp. 125
–130
.70.
Oikawa
, H.
, Nishimura
, K.
, and Cui
, M. X.
, 1985
, “High-Temperature Deformation of Polycrystalline Beta Titanium
,” Scr. Metall.
, 19
(7
), pp. 825
–828
.71.
Oomori
, T.
, Yoneyama
, T.
, and Oikawa
, H.
, 1988
, “High-Temperature Deformation Behavior of Alpha Ti-5.6 mol%Al Alloy
,” Trans. Jpn. Inst. Met.
, 29
(5
), pp. 399
–405
.72.
Castro
, R.
, and Seraphin
, L.
, 1966
, “Contribution à l'étude métallographique et structurale de l'alliage de titane T A 6 V
,” Mem. Etud. Sci. Rev. Metall.
, 63
(4
), pp. 1025
–1058
.73.
Hartung
, P. D.
, Kramer
, B. M.
, and Von Turkovich
, B. F.
, 1982
, “Tool Wear in Titanium Machining
,” CIRP Ann. Manuf. Technol.
, 31
(1
), pp. 75
–80
.74.
Narutaki
, N.
, and Murakoshi
, A.
, 1983
, “Study on Machining of Titanium Alloys
,” CIRP Ann. Manuf. Technol.
, 32
(1
), pp. 65
–69
.75.
Kitagawa
, T.
, Kubo
, A.
, and Maekawa
, K.
, 1997
, “Temperature and Wear of Cutting Tools in High-Speed Machining of Inconel 718 and Ti-6Al-6V-2Sn
,” Wear
, 202
(2
), pp. 142
–148
.76.
Zhang
, X. Q.
, Zhang
, X. P.
, and Srivastava
, A. K.
, 2011
, “Predicting the High Speed Cutting Process of Titanium Alloy by Finite Element Method
,” ASME
Paper No. MSEC2011-50208.77.
Bai
, Y. L.
, Xue
, Q.
, Xu
, Y. B.
, and Shen
, L. T.
, 1994
, “Characteristics and Microstructure in the Evolution of Shear Localization in Ti-6Al-4V Alloy
,” Mech. Mater.
, 17
(2–3
), pp. 155
–164
.78.
Daymi
, A.
, Boujelbene
, M.
, Ben Salem
, S.
, Hadj Sassi
, B.
, and Torbaty
, S.
, 2009
, “Effect of the Cutting Speed on the Chip Morphology and the Cutting Forces
,” Arch. Comput. Mater. Sci. Surf. Eng.
, 1
(2
), pp. 77
–83
.79.
Majorell
, A.
, Srivatsa
, S.
, and Picu
, R. C.
, 2002
, “Mechanical Behavior of Ti-6Al-4V at High and Moderate Temperature—Part I: Experimental Results
,” Mater. Sci. Eng. A
, 326
(2
), pp. 297
–305
.80.
Sastry
, S. M. L.
, Lederich
, R. J.
, Mackay
, T. L.
, and Kerr
, W. R.
, 2013
, “Superplastic Forming Characterization of Titanium Alloy
,” J. Met.
, 135
(1
), pp. 48
–53
.81.
Qu
, Y. D.
, Wang
, M. M.
, Lei
, L. M.
, Huang
, X.
, Wang
, L. Q.
, Qin
, J. N.
, Lu
, W. J.
, and Zhang
, D.
, 2012
, “Behavior and Modeling of High Temperature Deformation of an α+β Titanium Alloy
,” Mater. Sci. Eng. A
, 555
(14
), pp. 99
–105
.82.
Lesuer
, D. R.
, 2000
, “Experimental Investigations of Material Models for Ti-6Al-4V Titanium and 2024-T3 Aluminum
,” U.S. Department of Transportation/Federal Aviation Administration, Report No. UCRL-ID-134691
, pp. 1
–36
.83.
HKS
, 2008
, “Abaqus/Explicit Analysis User Manual, Version 6.8.1
,” Simulia
, Providence, RI
.84.
Zhang
, X. P.
, Shivpuri
, R.
, and Srivastava
, A. K.
, 2014
, “Role of Phase Transformation in Chip Segmentation During High Speed Machining of Dual Phase Titanium Alloys
,” J. Mater. Process. Technol.
, 214
(12
), pp. 3048
–3066
.85.
Sutter
, G.
, and List
, G.
, 2013
, “Very High Speed Cutting of Ti-6Al-4V Titanium Alloy-Change in Morphology and Mechanism of Chip Formation
,” Int. J. Mach. Tool Manuf.
, 66
(3
), pp. 37
–43
.86.
Miguélez
, M. H.
, Soldani
, X.
, and Molinari
, A.
, 2013
, “Analysis of Adiabatic Shear Banding in Orthogonal of Ti Alloy
,” Int. J. Mech. Sci.
, 75
(10
), pp. 212
–222
.87.
Macdougall
, D. A. S.
, and Harding
, J.
, 1999
, “A Constitutive Relation and Failure Criterion for Ti6Al4V Alloy at Impact Rates of Strain
,” J. Mech. Phys. Solids
, 47
(5
), pp. 1157
–1185
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