Abstract
A physically based constitutive model with internal state variables (ISVs) is established, it is used to describe the flow stress and microstructure evolution of Ti–6Al–4V alloy in the superplastic forming (SPF). The ISVs in the constitutive model includes the dislocation density, grain size, and the volume fraction of dynamic recrystallization. The flow stress consists of σfd, σta, and σGB, which are related to forest dislocation, thermal activation, and grain boundary sliding (GBS), respectively. The material constants of the constitutive model are determined, and the genetic algorithm (GA) optimization. A modeling method path to optimize the flow stress model is established, which is on the basis of the errors between the predicted and experimental flow stresses. In the modified flow stress constitutive model, the grain rotation (GR) is applied as a hardening mechanism, and the void is treated as a softening mechanism. A new GR model is proposed to describe the flow stress which is related to the GR. The modified constitutive model can accurately predict the evolution of yield stress, grain size and flow stress in SPF. With the calculation results of the multi-scales constitutive model, the mechanism of Ti–6Al–4V in SPF is discussed, and a new deformation map with dominant mechanisms for Ti–6Al–4V is obtained.
Issue Section:
Research Papers
References
1.
Sen
, I.
, Tamirisakandala
, S.
, Miracle
, D. B.
, and Ramamurty
, U.
, 2007
, “Microstructural Effects on the Mechanical Behavior of B-Modified Ti–6Al–4 V Alloys
,” Acta Mater.
, 55
(15
), pp. 4983
–4993
. 10.1016/j.actamat.2007.05.0092.
Sun
, Y.
, Luo
, G.
, Zhang
, J.
, Wu
, C.
, Li
, J.
, Shen
, Q.
, and Zhang
, L.
, 2018
, “Phase Transition, Microstructure and Mechanical Properties of TC4 Titanium Alloy Prepared by Plasma Activated Sintering
,” J. Alloys Compd.
, 741
, pp. 918
–926
. 10.1016/j.jallcom.2018.01.1973.
Giuliano
, G.
, 2008
, “Constitutive Equation for Superplastic Ti–6Al–4 V Alloy
,” Mater. Des.
, 29
(7
), pp. 1330
–1333
. 10.1016/j.matdes.2007.07.0014.
Lin
, J.
, Ball
, A. A.
, and Zheng
, J. J.
, 2002
, “Surface Modelling and Mesh Generation for Simulating Superplastic Forming
,” CADDM
, 80–81
(2
), pp. 613
–619
. 10.1016/S0924-0136(98)00214-35.
Chokshi
, A. H.
, Mukherjee
, A. K.
, and Langdon
, T. G.
, 1993
, “Superplasticity in Advanced Materials
,” Mater. Sci. Eng., R
, 10
(6
), pp. 237
–274
. 10.1016/0927-796X(93)90009-R6.
Ilya
, R.
, Olga
, L.
, Ivan
, M.
, and Evgeny
, N.
, 2018
, “Superplastic Deformation Behavior of Ti-4Al-2V Alloy Governed by Its Structure and Precipitation Phase Evolution
,” Mater. Sci. Eng., A.
, 731
, pp. 577
–582
. 10.1016/j.msea.2018.06.0947.
Kim
, W. J.
, Chung
, S. W.
, Chung
, C. S.
, and Kum
, D.
, 2001
, “Superplasticity in Thin Magnesium Alloy Sheets and Deformation Mechanism Maps for Magnesium Alloys at Elevated Temperatures
,” Acta Mater.
, 49
(16
), pp. 3337
–3345
. 10.1016/S1359-6454(01)00008-88.
Troeger
, L. P.
, and Starke
, E. A.
, 2000
, “Microstructural and Mechanical Characterization of a Superplastic 6xxx Aluminum Alloy
,” Mater. Sci. Eng., A
, 277
(1
), pp. 102
–113
. 10.1016/S0921-5093(99)00543-29.
Xu
, X.
, Nishimura
, T.
, Hirosaki
, N.
, Xie
, R. J.
, Yamamoto
, Y.
, and Tanaka
, H.
, 2006
, “Superplastic Deformation of Nano-Sized Silicon Nitride Ceramics
,” Acta Mater.
, 54
(1
), pp. 255
–262
. 10.1016/j.actamat.2005.09.00510.
Hiraga
, T.
, Miyazaki
, T.
, Tasaka
, M.
, and Yoshida
, H.
, 2010
, “Mantle Superplasticity and Its Self-Made Demise
,” Nature
, 468
(7327
), pp. 1091
–1094
. 10.1038/nature0968511.
Goldsby
, D. L.
, and Kohlstedt
, D. L.
, 2001
, “Superplastic Deformation of Ice: Experimental Observations
,” J. Geophys. Res.: Solid Earth
, 106
(B6
), pp. 11017
–11030
. 10.1029/2000JB90033612.
Saotome
, Y.
, Itoh
, K.
, Zhang
, T.
, and Inoue
, A.
, 2001
, “Superplastic Nanoforming of Pd-Based Amorphous Alloy
,” Scr. Mater.
, 44
(8
), pp. 1541
–1545
. 10.1016/S1359-6462(01)00837-513.
Hu
, Z. Y.
, Cheng
, X. W.
, Li
, S. L.
, Zhang
, H. M.
, Wang
, H.
, Zhang
, Z. H.
, and Wang
, F. C.
, 2017
, “Investigation on the Microstructure, Room and High Temperature Mechanical Behaviors and Strengthening Mechanisms of the (TiB + TiC)/TC4 Composites
,” J. Alloys Compd.
, 726
, pp. 240
–253
. 10.1016/j.jallcom.2017.08.01714.
Liu
, Y. G.
, Li
, M. Q.
, and Liu
, H. J.
, 2016
, “Surface Nanocrystallization and Gradient Structure Developed in the Bulk TC4 Alloy Processed by Shot Peening
,” J. Alloys Compd.
, 685
, pp. 186
–193
. 10.1016/j.jallcom.2016.05.29515.
Wahed
, M. A.
, Gupta
, A. K.
, Sharma
, V.
, Mahesh
, K.
, Singh
, S. K.
, and Kotkunde
, N.
, 2019
, “Material Chaacterization, Constitutive Modelling, and Processing Map for Superplastic Deformation Region in Ti-6Al-4V Alloy
,” Int. J. Adv. Manuf. Technol.
, 104
(9–12
), pp. 3419
–3438
. 10.1007/s00170-019-03956-z16.
Quan
, G. Z.
, Wen
, H. R.
, Pan
, J.
, and Zou
, Z.
, 2016
, “Construction of Processing Maps Based on Expanded Data by BP-ANN and Identification of Optimal Deforming Parameters for Ti-6Al-4V Alloy
,” Int. J. Precis. Eng. Manuf.
, 17
(2
), pp. 171
–180
. 10.1007/s12541-016-0022-z17.
Escamilla-Salazar
, I. G.
, Torres-Trevi No
, L.
, and Gonzalez-Ortiz
, B.
, 2016
, “Intelligent Parameter Identification of Machining Ti64 Alloy
,” Int. J. Adv. Manuf. Technol.
, 86
(5–8
), pp. 1997
–2009
. 10.1007/s00170-015-7967-418.
Sun
, Z. C.
, Yang
, H.
, Han
, G. J.
, and Fan
, X. G.
, 2010
, “A Numerical Model Based on Internal-State-Variable Method for the Microstructure Evolution During Hot-Working Process of TA15 Titanium Alloy
,” Mater. Sci. Eng., A
, 527
(15
), pp. 3464
–3471
. 10.1016/j.msea.2010.02.00919.
Bai
, Q.
, Lin
, J.
, Dean
, T. A.
, Balint
, D. S.
, Gao
, T.
, and Zhang
, Z.
, 2013
, “Modelling of Dominant Softening Mechanisms for Ti-6Al-4V in Steady State Hot Forming Conditions
,”Mater. Sci. Eng., A
, 559
, pp. 352
–358
. 10.1016/j.msea.2012.08.11020.
Lin
, J.
, and Dean
, T. A.
, 2005
, “Modelling of Microstructure Evolution in Hot Forming Using Unified Constitutive Equations
,” J. Mater. Process. Technol.
, 167
(2
), pp. 354
–362
. 10.1016/j.jmatprotec.2005.06.02621.
Roucoules
, C.
, Pietrzyk
, M.
, and Hodgson
, P. D.
, 2003
, “Analysis of Work Hardening and Recrystallization During the Hot Working of Steel Using a Statistically Based Internal Variable Model
,” Mater. Sci. Eng., A
, 339
(1
), pp. 1
–9
. 10.1016/S0921-5093(02)00120-X22.
Fan
, X. G.
, and Yang
, H.
, 2011
, “Internal-State-Variable Based Self-Consistent Constitutive Modeling for Hot Working of Two-Phase Titanium Alloys Coupling Microstructure Evolution
,” Int. J. Plast.
, 27
(11
), pp. 1833
–1852
. 10.1016/j.ijplas.2011.05.00823.
Alabort
, E.
, Putman
, D.
, and Reed
, R. C.
, 2015
, “Superplasticity in Ti–6Al–4V: Characterisation, Modelling and Applications
,” Acta Mater.
, 95
, pp. 428
–442
. 10.1016/j.actamat.2015.04.05624.
Roters
, F.
, Raabe
, D.
, and Gottstein
, G.
, 2000
, “Work Hardening in Heterogeneous Alloys—A Microstructural Approach Based on Three Internal State Variables
,” Acta Mater.
, 48
(17
), pp. 4181
–4189
. 10.1016/S1359-6454(00)00289-525.
Stoller
, R.
, and Zinkle
, S.
, 2000
, “On the Relationship Between Uniaxial Yield Strength and Resolved Shear Stress in Polycrystalline Materials
,” J. Nucl. Mater.
, 283
, pp. 349
–352
. 10.1016/S0022-3115(00)00378-026.
Hosseini
, E.
, and Kazeminezhad
, M.
, 2009
, “A Hybrid Model on Severe Plastic Deformation of Copper
,” Comput. Mater. Sci.
, 44
(4
), pp. 1107
–1115
. 10.1016/j.commatsci.2008.07.02427.
Guo
, R.
, and Wu
, J.
, 2018
, “Dislocation Density Based Model for Al-Cu-Mg Alloy During Quenching With Considering the Quench-Induced Precipitates
,” J. Alloys Compd.
, p. 741
. 10.1016/j.jallcom.2018.01.13528.
Mecking
, H.
, and Kocks
, U. F.
, 1981
, “Kinetics of Flow and Strain-Hardening
,” Acta Metall.
, 29
(11
), pp. 1865
–1875
. 10.1016/0001-6160(81)90112-729.
Courtney
, T.
, 2004
, Mechanical Behavior of Materials
, McGraw-Hill
, New York
.30.
Semiatin
, S. L.
, and Bieler
, T. R.
, 2001
, “The Effect of Alpha Platelet Thickness on Plastic Flow During Hot Working of TI–6Al–4 V With a Transformed Microstructure
,” Acta Mater.
, 49
(17
), pp. 3565
–3573
. 10.1016/S1359-6454(01)00236-131.
Picu
, R. C.
, and Majorell
, A.
, 2002
, “Mechanical Behavior of Ti-6Al-4V at High and Moderate Temperatures-Part II: Constitutive Modeling
,” Mater. Sci. Eng., A
, 326
(2
), pp. 306
–316
. 10.1016/S0921-5093(01)01508-832.
Dunne
, F. P. E.
, and Kim
, T. W.
, 1998
, “Modelling Heterogeneous Microstructures, Inhomogeneous Deformation and Failure in Superplasticity
,” J. Mater. Process. Technol.
, s80–81
(8
), pp. 96
–100
. 10.1016/S0924-0136(98)00135-633.
Sandstrom
, R.
, and Lagneborg
, R.
, 1975
, “A Model for Hot Working Occurring by Recrystallization
,” Acta Metall.
, 23
(3
), pp. 387
–398
. 10.1016/0001-6160(75)90132-734.
Zhou
, M.
, and Dunne
, F. P. E.
, 1996
, “Mechanisms-Based Constitutive Equations for the Superplastic Behavior of a Titanium Alloy
,” J. Strain Anal. Eng. Des.
, 31
(3
), pp. 187
–196
. 10.1243/03093247V31318735.
X.G.
Fan
, 2012
, “Study on Microstructure Evolution during Isothermal Local Loading Forming of Large-scale Integral Complex Component of Titanium Alloys
,” PhD thesis, Northwestern Polytechnical University
, Xian
, pp. 78
–80
.36.
Kocks
, U. F.
, and Mecking
, H.
, 2003
, “Physics and Phenomenology of Strain Hardening: The FCC Case
,” Prog. Mater. Sci.
, 48
(3
), pp. 171
–273
. 10.1016/S0079-6425(02)00003-837.
Gao
, P.
, Yang
, H.
, Fan
, X.
, and Zhu
, S.
, 2014
, “Unified Modeling of Flow Softening and Globularization for Hot Working of Two-Phase Titanium Alloy With a Lamellar Colony Microstructure
,” J. Alloys Compd.
, 600
(1
), pp. 78
–83
. 10.1016/j.jallcom.2014.02.11038.
Roberts
, W.
, 1984
, “Deformation, Processing and Structure,” American Society for Metals
, Metal Park
, pp. 109
–184
.39.
Bae
, D. H.
, and Ghosh
, A. K.
, 2000
, “Grain Size and Temperature Dependence of Superplastic Deformation in an Al–Mg Alloy Under Isostructural Condition
,” Acta Mater.
, 48
(6
), pp. 1207
–1224
. 10.1016/S1359-6454(99)00445-040.
Orowan
, E.
, 1948
, “Symposium on Internal Stresses in Metals and Alloys
,” Inst. Met.
, p. 451
.41.
Khaleel
, M. A.
, Zbib
, H. M.
, and Nyberg
, E. A.
, 2001
, “Constitutive Modeling of Deformation and Damage in Superplastic Materials
,” Int. J. Plast.
, 17
(3
), pp. 277
–296
. 10.1016/S0749-6419(00)00036-X42.
Holt
, D. L.
, 1968
, “The Relation Between Superplasticity and Grain Boundary Shear in the Aluminum-Zinc Eutectoid Alloy
,” Trans Met. Soc. AIME
, 242
(1
), pp. 25
–31
.43.
Alden
, T. H.
, 1967
, “The Origin of Superplasticity in the sn-5%bi Alloy
,” Acta Metall.
, 15
(3
), pp. 469
–480
. 10.1016/0001-6160(67)90078-844.
Geckinli
, A. E.
, and Barrett
, C. R.
, 1976
, “Superplastic Deformation of the Pb-Sn Eutectic
,” J. Mater. Sci.
, 11
(3
), pp. 510
–521
. 10.1007/BF0054093245.
Hotz
, W.
, Ruedl
, E.
, and Schiller
, P.
, 1975
, “Observation of Processes of Superplasticity With the Scanning Electron Microscope
,” J. Mater. Sci.
, 10
(11
), pp. 2003
–2006
. 10.1007/BF0075449246.
Beere
, W.
, 1977
, “Grain-Boundary Sliding Controlled Creep: Its Relevance to Grain Rolling and Superplasticity
,” J. Mater. Sci.
, 12
(10
), pp. 2093
–2098
. 10.1007/BF0056198447.
Chandra
, T.
, Jonas
, J. J.
, and Taplin
, D. M. R.
, 1978
, “Grain-Boundary Sliding and Intergranular Cavitation During Superplastic Deformation of α/β Brass
,” J. Mater. Sci.
, 13
(11
), pp. 2380
–2384
. 10.1007/BF00808052Copyright © 2019 by ASME
You do not currently have access to this content.
