New Kinematic Hardening Model
Publication: Journal of Engineering Mechanics
Volume 120, Issue 10
Abstract
The present paper proposes two rules to develop a new kinematic hardening model. The first rule regulates the movement of the yield surface. It states that during loading, the yield center moves such that the kinematic hardening of the yield surface results in a plastic strain rate that an isotropic hardening model would also predict. The second rule introduces a new concept, the hardening center, and assumes that whenever the direction of the loading path undergoes abrupt change, the hardening center immediately shifts to the current center of the kinematic hardening yield surface. A tube problem is solved to demonstrate this new model. It is shown that this model is able to describe all the possible responses of the material, satisfy those aspects of material behavior that are generally deemed essential, and permit various forms of the plastic modulus to be used to correlate with experiments, while still being simple and mathematically tractable.
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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, N.Y., 505–512.
3.
Chaboche, J. L., Dang‐Van, K., and Cordier, G. (1979). “Moderation of the strain memory effect on the cyclic hardening of 316 stainless steel.” Proc., 5th Int. Conf. on Struct. Mech. in Reactor Technol., Berlin, Germany.
4.
Dafalias, Y. F., and Popov, E. P. (1975). “A model of nonlinearly hardening materials for complex loading.” Acta Mechanica, 21, 173–192.
5.
Drucker, D. C., and Palgen, L. (1981). “On stress‐strain relations suitable for cyclic and other loading.” J. Appl. Mech., 48(3), 479–485.
6.
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.
7.
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.
8.
Jiang, W. (1993a). “The elastic‐plastic response of thin‐walled tubes under combined axial and torsional loads: I—monotonic loading.” J. Pressure Vessel Technol., 115(3), 283–290.
9.
Jiang, W. (1993b). “The elastic‐plastic response of thin‐walled tubes under combined axial and torsional loads: II—variable loading.” J. Pressure Vessel Technol., 115(3), 291–296.
10.
Jiang, W. (1994). “A study of the two‐surface plasticity theory.” J. Engrg. Mech., ASCE, 120(10), 2179–2200.
11.
Jiang, W., and Wu, K. H. (1993). “Thin‐walled tubes subjected to combined internal pressure and axial load.” AIAA J., 31(2), 377–387.
12.
Krieg, R. D. (1975). “A practical two surface plasticity theory.” J. Appl. Mech., 42(3), 641–646.
13.
Lamba, H. S., and Sidebottom, O. M. (1978a). “Cyclic plasticity for nonproportional paths: part 1—cyclic hardening, erasure of memory and subsequent strain hardening experiments.” J. Engrg. Mat. and Technol., 100, 96–103.
14.
Lamba, H. H., and Sidebottom, O. M. (1978b). “Cyclic plasticity for nonproportional paths: part 2—comparison and predictions of three‐incremental plasticity models.” J. Engrg. Mat. and Technol., 100, 104–111.
15.
Masing, G. (1926). “Eigenspannungen und verfestignung beim messing.” Proc. Second Congr. for Appl. Mech., Zurich, Switzerland.
16.
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.
17.
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.
18.
Megahed, M. M. (1990). “Influence of hardening role on prediction of cyclic plasticity in pressurized thin tubes subjected to cyclic push‐pull.” Int. J. Mech. Sci., 32(8), 635–652.
19.
Mroz, Z. (1967a). “On the description of anisotropic workhardening.” J. Mech. and Physics of Solids, 15, 163–175.
20.
Mroz, Z. (1967b). “An attempt to describe the behaviour of metals under cyclic loads using a more general workhardening model.” Acta Mechanica, 7, 199–212.
21.
Phillips, A., and Wang, G. J. (1975). “An analytical study of an experimentally verified hardening law.” J. Appl. Mech., 42(2), 375–378.
22.
Prager, W. (1955). “The theory of plasticity—a survey of recent achievements.” Proc. Instn. of Mech. Engrgs., London, England, 169, 41–57.
23.
Tseng, N. T., and Lee, G. C. (1983). “Simple plasticity model of two‐surface type.” J. Engrg. Mech., ASCE, 109(3), 795–810.
24.
Ziegler, H. (1959). “A modification of Prager's hardening rule.” Quarterly of Appl. Mathematics, 17, 55–65.
Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 120 • Issue 10 • October 1994
Pages: 2201 - 2222
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: Aug 30, 1993
Published online: Oct 1, 1994
Published in print: Oct 1994
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