A procedure for determining parameters for anisotropic forms of nonlinear kinematic hardening rules for cyclic plasticity or viscoplasticity models is described. An earlier reported methodology for determining parameters for isotropic forms of uncoupled, superposed Armstrong-Frederick type kinematic hardening rules is extended. For this exercise, the anisotropy of the kinematic hardening rules is restricted to transverse isotropy or orthotropy. A limited number of parameters for such kinematic hardening rules can be determined using reversed proportional tension-torsion cycling of thin-walled tubular specimens. This is demonstrated using tests on type 304 stainless-steel specimens and results are compared to results based on the assumption of isotropic forms of the kinematic hardening rules. [S0094-4289(00)00301-7]

1.
Chaboche, J. L., Dang-Van, K., and Cordier, G., 1979, “Modelization of the Strain Memory Effect on the Cyclic Hardening of 316 Stainless Steel,” Proceedings of 5th International Conference on Structural Mechanics in Reactor Technology, Berlin, L11/3.
2.
Chaboche
,
J. L.
,
1993
, “
Cyclic Viscoplastic Constitutive Equations, Part I: A Thermodynamically Consistent Formulation
,”
ASME J. Appl. Mech.
,
60
, pp.
813
820
.
3.
McDowell
,
D. L.
,
1992
, “
A Nonlinear Kinematic Hardening Theory for Cyclic Thermoplasticity and Thermoviscoplasticity
,”
Int. J. Plast.
,
8
, pp.
695
728
.
4.
McDowell
,
D. L.
,
1985
, “
An Experimental Study of the Structure of Constitutive Equations for Nonproportional Cyclic Plasticity
,”
ASME J. Eng. Mater. Technol.
,
107
, pp.
307
315
.
5.
Moosbrugger
,
J. C.
, and
McDowell
,
D. L.
,
1989
, “
On a Class of Kinematic Hardening Rules for Nonproportional Cyclic Plasticity
,”
ASME J. Eng. Mater. Technol.
,
111
, pp.
87
98
.
6.
Moosbrugger
,
J. C.
,
1991
, “
Some Developments in the Characterization of Material Hardening and Rate Sensitivity for Cyclic Viscoplasticity Models
,”
Int. J. Plast.
,
7
, pp.
405
431
.
7.
Moosbrugger
,
J. C.
,
1993
, “
Experimental Parameter Estimation for Nonproportional Cyclic Viscoplasticity: Nonlinear Kinematic Hardening Rules for Two Waspaloy Microstructures at 650°C
,”
Int. J. Plast.
,
9
, pp.
345
373
.
8.
Chaboche, J. L., 1989, “A New Constitutive Framework to Describe Limited Ratchetting Effects,” Proceedings of Plasticity’89, Pergamon, New York, p. 211.
9.
Chaboche
,
J. L.
, and
Nouailhas
,
D.
,
1989
, “
Constitutive Modeling of Ratchetting Effects—Part I: Experimental Facts and Properties of Classical Models
,”
ASME J. Eng. Mater. Technol.
,
111
, pp.
384
392
.
10.
Chaboche
,
J. L.
, and
Nouailhas
,
D.
,
1989
, “
Constitutive Modeling of Ratchetting Effects—Part II: Possibilities of Some Additional Kinematic Rules
,”
ASME J. Eng. Mater. Technol.
,
111
, pp.
409
416
.
11.
Bower
,
A. F.
,
1989
, “
Cyclic Hardening Properties of Hard-Drawn Copper and Rail Steel
,”
J. Mech. Phys. Solids
,
37
, pp.
455
470
.
12.
Chaboche
,
J. L.
,
1991
, “
On Some Modifications of Kinematic Hardening to Improve the Description of Ratchetting Effects
,”
Int. J. Plast.
,
7
, pp.
661
678
.
13.
Ohno, N., and Wang, J.-D., 1991, “Nonlinear Kinematic Hardening Rule: Proposition and Application to Ratchetting Problems,” Proceedings of the 11th International Conference on Structural Mechanics in Reactor Technology, Tokyo, L22/1., pp. 481–486.
14.
Ohno
,
N.
, and
Wang
,
J.-D.
,
1991
, “
Transformation of a Nonlinear Kinematic Hardening Rule to a Multisurface Form under Isothermal and Nonisothermal Conditions
,”
Int. J. Plast.
,
7
, pp.
879
891
.
15.
Ohno
,
N.
, and
Wang
,
J.-D.
,
1993
, “
Kinematic Hardening Rules with Critical State of Dynamic Recovery, Part I: Formulation and Basic Features for Ratchetting Behavior
,”
Int. J. Plast.
,
9
, pp.
375
390
.
16.
Ohno
,
N.
, and
Wang
,
J.-D.
,
1993
, “
Kinematic Hardening Rules with Critical State of Dynamic Recovery, Part II: Applications to Experiments of Ratchetting Behavior
,”
Int. J. Plast.
,
9
, pp.
391
403
.
17.
Jiang
,
Y.
, and
Sehitoglu
,
H.
,
1994
, “
Cyclic Ratchetting of 1070 under Multiaxial Stress State
,”
Int. J. Plast.
,
10
, pp.
579
608
.
18.
Jiang
,
Y.
, and
Sehitoglu
,
H.
,
1994
, “
Multiaxial Ratchetting under Multiple Step Loading
,”
Int. J. Plast.
,
10
, pp.
849
870
.
19.
Jiang
,
Y.
, and
Sehitoglu
,
H.
,
1996
, “
Modeling of Cyclic Ratchetting Plasticity, Part I: Development of Constitutive Relations
,”
ASME J. Appl. Mech.
,
63
, pp.
720
725
.
20.
Jiang
,
Y.
, and
Sehitoglu
,
H.
,
1996
, “
Modeling of Cyclic Ratchetting Plasticity, Part II: Comparison of Model Simulations with Experiments
,”
ASME J. Appl. Mech.
,
63
, pp.
726
733
.
21.
McDowell
,
D. L.
,
1995
, “
Stress State Dependence of Cyclic Ratchetting Behavior of Two Rail Steels
,”
Int. J. Plast.
,
11
, pp.
397
421
.
22.
Chaboche
,
J. L.
, and
Jung
,
O.
,
1997
, “
Application of a Kinematic Hardening Viscoplasticity Model with Thresholds to the Residual Stress Relaxation
,”
Int. J. Plast.
,
13
, pp.
785
807
.
23.
Sutco
,
M.
, and
Krempl
,
E.
,
1990
, “
A Simplified Orthotropic Viscoplasticity Theory Based on Overstress
,”
Int. J. Plast.
,
6
, pp.
247
261
.
24.
Lee
,
K.-D.
, and
Krempl
,
E.
,
1991
, “
An Orthotropic Theory of Viscoplasticity Based on Overstress for Thermomechanical Deformations
,”
Int. J. Solids Struct.
,
27
, pp.
1445
1459
.
25.
Nouailhas, D., and Chaboche, J. L., 1991, “Anisotropic Constitutive Modeling for Single Crystal Superalloys using a Continuum Phenomenological Approach,” TIRE A PART N° 1991-6, Office Nationale d’Etudes et de Recherches Aerospatiales, France.
26.
Nouailhas, D., and Culie, J.-P., 1991, “Development and Application of a Model for Single Crystal Superalloys,” TIRE A PART N° 1991-214, Office Nationale d’Etudes et de Recherches Aerospatiales, France.
27.
Nouailhas
,
D.
, and
Freed
,
A. D.
,
1992
, “
A Viscoplastic Theory for Anisotropic Materials
,”
ASME J. Eng. Mater. Technol.
,
114
, pp.
97
104
.
28.
Moosbrugger
,
J. C.
, and
Morrison
,
D. J.
,
1997
, “
Nonlinear Kinematic Hardening Rule Parameters—Direct Determination From Completely Reversed Proportional Cycling
,”
Int. J. Plast.
,
13
, pp.
633
668
.
29.
Lubliner, J., 1990, Plasticity Theory, Macmillan, New York.
30.
Khan, A. S., and Huang, S., 1995, Continuum Theory of Plasticity, Wiley, New York.
31.
Moosbrugger, J. C., 1988, “A Rate-Dependent Bounding Surface Model for Non-proportional Cyclic Viscoplasticity,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA.
32.
Kuhlmann-Wilsdorf
,
D.
, and
Laird
,
C.
,
1979
, “
Dislocations Behavior in Fatigue II. Friction Stress and Back Stress as Inferred from an Analysis of Hysteresis Loops
,”
Mater. Sci. Eng.
,
37
, pp.
111
120
.
33.
Cottrell, A. H., 1953, Dislocations and Plastic Flow in Crystals, Oxford University Press, London, pp. 111–116.
34.
Barrett, C., and Massalski, T. B., 1980, Structure of Metals, 3rd revised edition: Crystallographic Methods, Principles and Data, International Series on Materials Science and Technology, Pergamon, New York, Vol. 35, pp. 543–544.
35.
Kocks, U. F., Tome´, C. N., and Wenk, H.-R., 1998, Texture and Anisotropy: Preferred Orientations in Polycrystals and their Effect on Materials Properties, Cambridge University Press, Cambridge, U.K.
36.
Mughrabi
,
H.
,
1978
, “
The Cyclic Hardening and Saturation Behavior of Copper Single Crystals
,”
Mater. Sci. Eng.
,
33
, pp.
207
223
.
37.
Morrison
,
D. J.
,
Jones
,
J. W.
, and
Was
,
G. S.
,
1990
, “
Cyclic Strain Localization in Ion Beam Microalloyed Nickel
,”
Scr. Metall.
,
24
, pp.
2309
2314
.
38.
McDowell
,
D. L.
,
Stahl
,
D. R.
,
Stock
,
S. R.
, and
Antolovich
,
S. D.
,
1988
, “
Biaxial Path Dependence of Deformation Substructure of Type 304 Stainless Steel
,”
Metall. Trans. A
,
19A
, pp.
1277
1293
.
39.
Doong
,
S. H.
,
Socie
,
D. F.
, and
Robertson
,
I. M.
,
1990
, “
Dislocation Substructures and Nonproportional Hardening
,”
ASME J. Eng. Mater. Technol.
,
112
, pp.
456
463
.
40.
Armstrong, P. J., and Frederick, C. O., 1966, “A Mathematical Representation of the Multiaxial Bauschinger Effect,” C.E.G.B. RD/B/N 731.
You do not currently have access to this content.