General Kinematic-Isotropic Hardening Model
Publication: Journal of Engineering Mechanics
Volume 125, Issue 4
Abstract
This paper first points out that an evolution rule of the yield center without a motion component in the plastic strain rate direction leads to ratchetting, while an evolution rule with such a component motion leads to proportional material response. The paper then successfully tackles such a dilemma by proposing a general kinematic-isotropic hardening model that is able to control the yield center motion and to allow the radius of the yield surface to evolve arbitrarily as needed. Theoretical analysis shows that this model is capable of describing all the possible material responses. With a plastic modulus also proposed in the paper, an example is then given to show that the theoretical prediction compares very well with the ratchetting test.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Batdorf, S. B., and Budiansky, B. ( 1949). “A mathematical theory of plasticity based on the concept of slip.” NACA TN 1971.
2.
Benallal, A., and Marquis, D. ( 1987). “Constitutive equations describing non-proportional effects in cyclic plasticity.” Constitutive laws for engineering materials—theory and applications, Vol. I, C. S. Desai et al., eds., Elsevier, New York, 505–512.
3.
Chaboche, J. L., Dang-Van, K., and Cordier, G. ( 1979). “Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel.” Proc., 5th Int. Conf. on Struct. Mech. in Reactor Technol., Berlin.
4.
Chaboche, J. L., and Nouailhas, D. ( 1989a). “Constitutive modeling of ratchetting effects—part I: Experimental facts and properties of the classical models.” J. Engrg. Mat. and Technol., 111(3), 384–392.
5.
Chaboche, J. L., and Nouailhas, D. ( 1989b). “Constitutive modeling of ratchetting effects—part II: Possibilities of some additional kinematic rules.” J. Engrg. Mat. and Technol., 111(3), 409–416.
6.
Dafalias, Y. F., and Popov, E. P. ( 1975). “A model of nonlinearly hardening materials for complex loading.” Acta Mechanica, 21, 173–192.
7.
Dafalias, Y. F., and Popov, E. P. ( 1976). “Plastic internal variables formalism of cyclic plasticity.” J. Appl. Mech., 43(4), 645–651.
8.
Drucker, D. C., and Palgen, L. ( 1981). “On stress-strain relations suitable for cyclic and other loading.” J. Appl. Mech., 48(3), 479–485.
9.
Eisenberg, M. A. ( 1976). “A generalization of plastic flow theory with application to cyclic hardening and softening phenomena.” J. Engrg. Mat. and Technol., 98, 221–228.
10.
German, I., and Hodge, P. G. Jr. ( 1959). “A general theory of piecewise linear plasticity for initially anisotropic materials.” Nadbithka Zeitschrift Archivum Mechaniki Strasowanej, 11, 514–540.
11.
Hassan, T., and Kyriakides, S. ( 1994a). “Ratcheting of cyclically hardening and softening materials; I. Uniaxial behavior.” Int. J. Plasticity, 10(2), 149–184.
12.
Hassan, T., and Kyriakides, S. ( 1994b). “Ratcheting of cyclically hardening and softening materials; II. Multiaxial behavior.” Int. J. of Plasticity, 10(2), 185–212.
13.
Iwan, W. D. ( 1967). “On a class of models for the yielding behavior of continuous and composite systems.” J. Appl. Mech., 34, 612–617.
14.
Jiang, W. (1994a). “New kinematic hardening model.”J. Engrg. Mech., ASCE, 120(10), 2201–2222.
15.
Jiang, W. (1994b). “Study of two-surface plasticity theory.”J. Engrg. Mech., ASCE, 120(10), 2179–2200.
16.
Jiang, W. ( 1997). “A general solution to the two-surface plasticity theory.” J. Engrg. Mat. and Technol., 119(1), 20–25.
17.
Krieg, R. D. ( 1975). “A practical two surface plasticity theory.” J. Appl. Mech., 42(3), 641–646.
18.
McDowell, D. L. ( 1985a). “A two surface model for transient nonproportional cyclic plasticity. Part 1: Development of appropriate equations.” J. Appl. Mech., 52(2), 298–302.
19.
McDowell, D. L. ( 1985b). “A two surface model for transient nonproportional cyclic plasticity. Part 2: Comparison of theory with experiments.” J. Appl. Mech., 52(2), 303–308.
20.
Mroz, Z. ( 1967a). “An attempt to describe the behaviour of metals under cyclic loads using a more general workhardening model.” Acta Mechanica, 7, 199–212.
21.
Mroz, Z. ( 1967b). “On the description of antisotropic workhardening.” J. Mech. and Phys. of Solids, 15, 163–175.
22.
Mroz, Z. ( 1969). “An attempt to describe the behavior of metals under cyclic loads using a more general workhardening model.” Acta Mechanica, 7, 199–212.
23.
Phillips, A., and Lee, C. W. ( 1979). “Yield surfaces and loading surfaces. Experiments and recommendations.”Int. J. Solids and Struct., 15, 715–729.
24.
Phillips, A., and Wang, G. J. ( 1975). “An analytical study of an experimentally verified hardening law.” J. Appl. Mech., 42(2), 375–378.
25.
Prager, W. ( 1956). “A new method of analyzing stresses and strains in work-hardening plastic solids.” J. Appl. Mech., 23, 493–496.
26.
Shiratori, E., Ikegami, K., and Yoshida, F. ( 1979). “Analysis of stress-strain relations by use of anisotropic hardening potential.”J. Mech. and Phys. of Solids, 27, 213.
27.
Tseng, N. T., and Lee, G. C. (1983). “Simple plasticity model of two-surface type.”J. Engrg. Mech., ASCE, 109(3), 795–810.
Information & Authors
Information
Published In
History
Published online: Apr 1, 1999
Published in print: Apr 1999
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.