To understand the formation of direct chill (DC)-casting defects, e.g., butt curl and crack formation, it is essential to take into account the effect of temperature variation, strain rate, and their role in the constitutive behavior of the DC-cast alloys. For the correct prediction of defects due to thermal stresses during DC casting, one needs to rely on the fundamentals of mechanisms that may be relevant to the temperatures at below solidus temperatures. This research work aims to find a suitable physically based model for the as-cast aluminum alloys, namely AA3104, AA5182, and AA6111, which can describe the constitutive behavior at below solidus temperatures during complex loading conditions of temperatures and strain rates. In the present work, an earlier measured and modeled (Alankar and Wells, 2010, “Constitutive Behavior of As-Cast Aluminum Alloys AA3104, AA5182 and AA6111 at Below Solidus Temperatures,” Mater. Sci. Eng. A, 527, pp. 7812–7820) stress–strain data are analyzed using the Voce equation and Kocks–Mecking (KM) model. KM model is capable of predicting the hardening and recovery behavior during complex conditions of strain, strain rate, and temperatures during DC casting. Recovery is dependent on temperature and strain rate, and thus, relevant parameters are determined based on the temperature-sensitive annihilation rate of dislocations. For the KM model, we have estimated k1 parameter as a function of temperature, and k2 has been further modeled based on the temperature and strain rate. KM model is able to fit the constant temperature uniaxial tests within 1.5% of the regenerated data.

References

References
1.
Sengupta
,
J.
,
Maijer
,
D.
,
Wells
,
M. A.
,
Cockcroft
,
S. L.
, and
Larouche
,
A.
,
2001
,
Light Metals
,
The Minerals, Metals and Materials Society
,
Warrendale, PA
, pp.
879
885
.
2.
Drezet
,
J.-M.
, and
Rappaz
,
M.
,
1996
, “
Modeling of Ingot Distortions During Direct Chill Casting of Aluminum Alloys
,”
Metall. Mater. Trans. A
,
27
, pp.
3214
3225
.
3.
Ivar Farup
,
A.
, and
Drezet
,
J.-M.
,
2000
, “
Gleeble Machine Determination of Creep Law Parameters for Thermally Induced Deformations in Aluminium DC Casting
,”
J. Therm. Stress.
,
23
, pp.
47
58
.
4.
Boettinger
,
W. J.
,
Warren
,
J. A.
,
Beckermann
,
C.
, and
Karma
,
A.
,
2002
, “
Phase-Field Simulation of Solidification
,”
Annu. Rev. Mater. Res.
,
32
, pp.
163
194
.
5.
Alankar
,
A.
, and
Wells
,
M. A.
,
2010
, “
Constitutive Behavior of As-Cast Aluminum Alloys AA3104, AA5182 and AA6111 at Below Solidus Temperatures
,”
Mater. Sci. Eng. A
,
527
, pp.
7812
7820
.
6.
Angella
,
G.
,
Donnini
,
R.
,
Maldini
,
M.
, and
Ripamonti
,
D.
,
2014
, “
Combination Between Voce Formalism and Improved Kocks-Mecking Approach to Model Small Strains of Flow Curves at High Temperatures
,”
Mater. Sci. Eng. A
,
594
, pp.
381
388
.
7.
Choudhary
,
B. K.
, and
Rao Palaparti
,
D. P.
,
2012
, “
Comparative Tensile Flow and Work Hardening Behaviour of Thin Section and Forged Thick Section 9Cr-1Mo Ferritic Steel in the Framework of Voce Equation and Kocks-Mecking Approach
,”
J. Nucl. Mater.
,
430
, pp.
72
81
.
8.
Kocks
,
U. F.
,
1976
, “
Laws for Work-Hardening and Low-Temperature Creep
,”
ASME J. Eng. Mater. Technol.
,
98
, pp.
76
85
.
9.
Kocks
,
U. F.
,
1966
, “
A Statistical Theory of Flow Stress and Work Hardening
,”
Philos. Mag.
,
13
, pp.
541
566
.
10.
Kocks
,
U. F.
,
1970
, “
The Relation Between Polycrystal Deformation and Single-Crystal Deformation, Metall
,”
Mater. Trans.
,
1
, pp.
1121
1143
.
11.
Estrin
,
Y.
, and
Mecking
,
H.
,
1984
, “
A Unified Phenomenological Description of Work Hardening and Creep Based on One Parameter Models
,”
Acta Met.
,
32
, pp.
57
70
.
12.
Estrin
,
Y.
,
1998
, “
Dislocation Theory Based Constitutive Modelling: Foundations and Applications
,”
J. Mater. Process. Technol.
,
80–81
, pp.
33
39
.
13.
Choudhary
,
B. K.
,
Christopher
,
J.
, and
Samuel
,
E. I.
,
2012
, “
Applicability of Kocks–Mecking Approach for Tensile Work Hardening in P9 Steel
,”
Mater. Sci. Technol.
,
28
, pp.
644
650
.
14.
Christopher
,
J.
,
Choudhary
,
B. K.
,
Mathew
,
M. D.
, and
Jayakumar
,
T.
,
2013
, “
Applicability of the One-Internal-Variable Kocks-Mecking Approach for Tensile Flow and Work Hardening Behaviour of Modified 9Cr-1Mo Steel
,”
Mater. Sci. Eng. A
,
575
, pp.
119
126
.
15.
Choudhary
,
B. K.
, and
Christopher
,
J.
,
2013
, “
Tensile Work Hardening Behavior of Thin-Section Plate and Thick-Section Tubeplate Forging of 9Cr-1Mo Steel in the Framework of One-Internal-Variable Kocks-Mecking Approach
,”
Metall. Mater. Trans. A Phys. Metall. Mater. Sci.
,
44
, pp.
4968
4978
.
16.
Khani Moghanaki
,
S.
, and
Kazeminezhad
,
M.
,
2016
, “
Modeling of the Mutual Effect of Dynamic Precipitation and Dislocation Density in Age Hardenable Aluminum Alloys
,”
J. Alloys Compd.
,
683
, pp.
527
532
.
17.
Dunlop
,
J. W.
,
Bréchet
,
Y. J. M.
,
Legras
,
L.
, and
Estrin
,
Y.
,
2007
, “
Dislocation Density-Based Modelling of Plastic Deformation of Zircaloy-4
,”
Mater. Sci. Eng. A
,
443
, pp.
77
86
.
18.
Dini
,
H.
,
Svoboda
,
A.
,
Andersson
,
N. E.
,
Ghassemali
,
E.
,
Lindgren
,
L. E.
, and
Jarfors
,
A. E. W.
,
2018
, “
Optimization and Validation of a Dislocation Density Based Constitutive Model for As-Cast Mg-9%Al-1%Zn
,”
Mater. Sci. Eng. A
,
710
, pp.
17
26
.
19.
He
,
S. H.
,
He
,
B. B.
,
Zhu
,
K. Y.
, and
Huang
,
M. X.
,
2018
, “
Evolution of Dislocation Density in Bainitic Steel: Modeling and Experiments
,”
Acta Mater.
,
149
, pp.
46
56
.
20.
Prabhakar
,
A.
,
Verma
,
G. C.
,
Krishnasamy
,
H.
,
Pandey
,
P. M.
,
Lee
,
M. G.
, and
Suwas
,
S.
,
2017
, “
Dislocation Density Based Constitutive Model for Ultrasonic Assisted Deformation
,”
Mech. Res. Commun.
,
85
, pp.
76
80
.
21.
Krishnaswamy
,
H.
,
Kim
,
M. J.
,
Hong
,
S. T.
,
Kim
,
D.
,
Song
,
J. H.
,
Lee
,
M. G.
, and
Han
,
H. N.
,
2017
, “
Electroplastic Behaviour in an Aluminium Alloy and Dislocation Density Based Modelling
,”
Mater. Des.
,
124
, pp.
131
142
.
22.
Lin
,
Y. C.
,
Dong
,
W. Y.
,
Zhou
,
M.
,
Wen
,
D. X.
, and
Chen
,
D. D.
,
2018
, “
A Unified Constitutive Model Based on Dislocation Density for an Al-Zn-Mg-Cu Alloy at Time-Variant Hot Deformation Conditions
,”
Mater. Sci. Eng. A
,
718
, pp.
165
172
.
23.
Seetharamu
,
K. N.
,
Paragasam
,
R.
,
Quadir
,
G. A.
,
Zainal
,
Z. A.
,
Prasad
,
B. S.
, and
Sundararajan
,
T.
,
2001
, “
Finite Element Modelling of Solidification Phenomena
,”
Sadhana
,
26
, pp.
103
120
.
24.
Weckman
,
D. C.
, and
Niessen
,
P.
,
1984
, “
Mathematical Models of the D.C. Continuous Casting Process
,”
Can. Metall. Q
,
23
, pp.
209
216
.
25.
Weckman
,
D. C.
, and
Niessen
,
P.
,
1982
, “
A Numerical Simulation of the D.C. Continuous Casting Process Including Nucleate Boiling Heat Transfer
,”
Metall. Trans. B
,
13
, pp.
593
602
.
26.
Boender
,
W.
,
Burghardt
,
A.
,
van Klaveren
,
E. P.
, and
Rabenberg
,
J.
,
2016
, “Numerical Simulation of DC Casting; Interpreting the Results of a Thermo-Mechanical Model,”
Essential Readings in Light Metals
,
Springer International Publishing
,
Cham, Switzerland
, pp.
933
938
.
27.
Sistaninia
,
M.
,
Drezet
,
J.-M.
,
Phillion
,
A. B.
, and
Rappaz
,
M.
,
2013
, “
Prediction of Hot Tear Formation in Vertical DC Casting of Aluminum Billets Using a Granular Approach
,”
JOM
,
65
, pp.
1131
1137
.
28.
Sistaninia
,
M.
,
Terzi
,
S.
,
Phillion
,
A. B.
,
Drezet
,
J.-M.
, and
Rappaz
,
M.
,
2013
, “
3-D Granular Modeling and In Situ X-ray Tomographic Imaging: A Comparative Study of Hot Tearing Formation and Semi-Solid Deformation in Al–Cu Alloys
,”
Acta Mater.
,
61
, pp.
3831
3841
.
29.
Sistaninia
,
M.
,
Phillion
,
A. B.
,
Drezet
,
J.-M.
, and
Rappaz
,
M.
,
2012
, “
Three-Dimensional Granular Model of Semi-Solid Metallic Alloys Undergoing Solidification: Fluid Flow and Localization of Feeding
,”
Acta Mater.
,
60
, pp.
3902
3911
.
30.
Chobaut
,
N.
,
Carron
,
D.
,
Arsène
,
S.
,
Schloth
,
P.
, and
Drezet
,
J.-M.
,
2015
, “
Quench Induced Residual Stress Prediction in Heat Treatable 7xxx Aluminium Alloy Thick Plates Using Gleeble Interrupted Quench Tests
,”
J. Mater. Process. Technol.
,
222
, pp.
373
380
.
31.
Chobaut
,
N.
,
Carron
,
D.
,
Saelzle
,
P.
, and
Drezet
,
J.-M.
,
2016
, “
Measurements and Modeling of Stress in Precipitation-Hardened Aluminum Alloy AA2618 During Gleeble Interrupted Quenching and Constrained Cooling
,”
Metall. Mater. Trans. A
,
47
, pp.
5641
5649
.
32.
Jamaly
,
N.
,
Phillion
,
A. B.
, and
Drezet
,
J.-M.
,
2013
, “
Stress–Strain Predictions of Semisolid Al-Mg-Mn Alloys During Direct Chill Casting: Effects of Microstructure and Process Variables
,”
Metall. Mater. Trans. B
,
44
, pp.
1287
1295
.
33.
Drezet
,
J.-M.
,
Evans
,
A.
, and
Pirling
,
T.
,
2011
, “
Residual Stresses in DC cast Aluminum Billet: Neutron Diffraction Measurements and Thermomechanical Modeling
,”
AIP Conf. Proc.
,
1353
, pp.
1131
1136
.
34.
Drezet
,
J.-M.
,
Evans
,
A.
,
Pirling
,
T.
, and
Pitié
,
B.
,
2012
, “
Stored Elastic Energy in Aluminium Alloy AA 6063 Billets: Residual Stress Measurements and Thermomechanical Modelling
,”
Int. J. Cast Met. Res.
,
25
, pp.
110
116
.
35.
Wang
,
Q. G.
,
2003
, “
Microstructural Effects on the Tensile and Fracture Behavior of Aluminum Casting Alloys A356/357
,”
Metall. Mater. Trans. A
,
34
, pp.
2887
2899
.
36.
Ceschini
,
L.
,
Jarfors
,
A. E. W.
,
Morri
,
A.
,
Morri
,
A.
,
Rotundo
,
F.
,
Seifeddine
,
S.
, and
Toschi
,
S.
,
2014
, “
High Temperature Tensile Behaviour of the A354 Aluminum Alloy
,”
Mater. Sci. Forum
,
794–796
, pp.
443
448
.
37.
Katgerman
,
L.
,
Van Haaften
,
W. M.
, and
Kool
,
W. H.
,
2004
, “
Constitutive Behaviour and Hot Tearing During Aluminium DC Casting
,”
Mater. Forum
,
28
, pp.
312
318
.
38.
Mo
,
A.
, and
Farup
,
I.
,
2000
, “
The Effect of Work Hardening on Thermally Induced Deformations in Aluminium DC Casting
,”
J. Therm. Stress.
,
23
, pp.
71
89
.
39.
Eskin
,
D. G.
,
Suyitno
, and
Katgerman
,
L.
,
2004
, “
Mechanical Properties in the Semi-Solid State and Hot Tearing of Aluminium Alloys
,”
Prog. Mater. Sci.
,
49
, pp.
629
711
.
40.
Lalpoor
,
M.
,
Eskin
,
D. G.
, and
Katgerman
,
L.
,
2009
, “
Cold-Cracking Assessment in AA7050 Billets During Direct-Chill Casting by Thermomechanical Simulation of Residual Thermal Stresses and Application of Fracture Mechanics
,”
Metall. Mater. Trans. A
,
40
, pp.
3304
3313
.
41.
Van Haaften
,
W. M.
,
Kool
,
W. H.
, and
Katgerman
,
L.
,
2002
, “
Hot Tearing Studies in AA5182
,”
J. Mater. Eng. Perform.
,
11
, pp.
537
543
.
42.
Farup
,
I.
,
2000
, “
Thermally Induced Deformations and Hot Tearing During Direct Chill Casting of Aluminium
,” Ph.D. thesis,
University of Oslo
,
Norway
.
43.
Chaudhary
,
A.
,
2006
, “
Constitutive Behaviour of Aluminum Alloys AA3104, AA5182, and AA6111 at Below Solidus Temperatures
,” M.S. thesis,
The University of British Columbia
,
Vancouver, Canada
. .
44.
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.
,
741
, pp.
432
441
.
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