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.

References

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.2007.05.009
2.
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.2018.01.197
3.
Giuliano
,
G.
,
2008
, “
Constitutive Equation for Superplastic Ti–6Al–4 V Alloy
,”
Mater. Des.
,
29
(
7
), pp.
1330
1333
. 10.1016/j.matdes.2007.07.001
4.
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)00214-3
5.
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-R
6.
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.2018.06.094
7.
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)00008-8
8.
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)00543-2
9.
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.2005.09.005
10.
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/nature09685
11.
Goldsby
,
D. L.
, and
Kohlstedt
,
D. L.
,
2001
, “
Superplastic Deformation of Ice: Experimental Observations
,”
J. Geophys. Res.: Solid Earth
,
106
(
B6
), pp.
11017
11030
. 10.1029/2000JB900336
12.
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)00837-5
13.
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.2017.08.017
14.
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.2016.05.295
15.
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-z
16.
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-z
17.
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/s00170-015-7967-4
18.
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.2010.02.009
19.
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.2012.08.110
20.
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.2005.06.026
21.
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-X
22.
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.2011.05.008
23.
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.2015.04.056
24.
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)00289-5
25.
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)00378-0
26.
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.2008.07.024
27.
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.2018.01.135
28.
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)90112-7
29.
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)00236-1
31.
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)01508-8
32.
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)00135-6
33.
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)90132-7
34.
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
. 10.1243/03093247V313187
35.
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)00003-8
37.
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.2014.02.110
38.
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)00445-0
40.
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-X
42.
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)90078-8
44.
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/BF00540932
45.
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/BF00754492
46.
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/BF00561984
47.
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/BF00808052
You do not currently have access to this content.