Simple Experimentally Motivated Cyclic Plasticity Model
Publication: Journal of Engineering Mechanics
Volume 113, Issue 3
Abstract
A two‐surface cyclic plasticity theory is presented with refinements based on analysis of nonproportional cyclic plasticity data. It is shown that the model accurately correlates nonproportional cyclic stress‐strain response, yet the model structure is simplified compared to previous models. New contributions include a more general isotropic hardening rule that reflects additional nonproportional hardening, and a more accurate plastic modulus representation for nonproportional loading. A kinematic hardening rule is used, which reflects experimental observations of backstress translation direction being related to deviatoric stress rate. Transient stress‐strain behavior from four axial torsional nonproportional loading blocks is predicted.
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References
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.” Trans. 5th SMiRT, L 11/3, Berlin, Germany.
2.
Dafalias, Y. F. (1981). “The concept and application of the bounding surface in plasticity theory.” Physical non‐linearities in structural analysis, J. Hult and J. Lemaitre, Eds., IUTAM Symposium, Senlis, France, Springer Verlag, 56–63.
3.
Dafalias, Y. F. (1984). “Modeling cyclic plasticity: Simplicity versus sophistication.” Mechanics of engineering materials, Desai and Gallagher, Eds., Wiley, New York, N.Y., 153–178.
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., ASME, 48, 479–485.
6.
Eisenberg, M. A. (1976). “A generalization of plastic flow theory with application to cyclic hardening and softening phenomena.” J. Engrg. Mats. Tech., ASME, 98, 221–228.
7.
Eraslan, H. V. (1969). “Supplementary notes on the solution of ordinary differential equations by Runge‐Kutta methods.” Prepared for the One‐week short course in numerical analysis and computer methods, Univ. Tennessee Space Inst., Tullahoma, Tenn.
8.
Hecker, S. S. (1976). “Experimental studies of yield phenomena in biaxially loaded metals.” Constitutive equations in viscoplasticity: Computational and engineering aspects, AMD, ASME, New York, N.Y., 20, 1–32.
9.
Kanazawa, K., Brown, M. W., and Miller, K. J. (1979). “Cyclic deformation of 1% Cr‐Mo‐V steel under out‐of‐phase loads.” Fatigue of engineering materials and structures, 2, 217–228.
10.
Krempl, E., and Lu, H. (1984). “The hardening and rate‐dependent behavior of fully annealed AISI type 304 stainless steel under biaxial in‐phase and out‐of‐phase strain cycling at room temperature.” J. Engrg. Mat. Tech., ASME, 106, 376–382.
11.
Krempl, E., McMahon, J. J., and Yao, D. (1984). “Viscoplasticity based on over‐stress with a differential growth law for the equilibrium stress.” Proc., 2nd Symposium on Nonlinear Constitutive Relations for High Temperature Applications, NASA Lewis Research Center, Cleveland, Ohio.
12.
Krieg, R. D. (1975). “A practical two surface plasticity theory.” J. Appl. Mech., 42, 641–646.
13.
Lamba, H. S., and Sidebottom, O. M. (1978a). “Cyclic plasticity for nonproportioal paths: Part 1—Cyclic hardening, erasure of memory, and subsequent strain hardening experiments.” J. Engrg. Mats. Tech., ASME, 100, 96–103.
14.
Lamba, H. S., and Sidebottom, O. M. (1978b). “Cyclic plasticity for nonproportional paths: Part 2—Comparison with predictions of three incremental plasticity models.” J. Engrg. Mats. Tech., ASME, 100, 104–111.
15.
Lindholm, U. S., Chan, K. S., Bodner, S. R., Weber, R. M., Walker, K. P., and Cassenti, B. N. (1985). “Constitutive modeling for isotropic materials.” NASA CR‐174980, SwRI‐7476/30, NASA.
16.
Liu, K. C., and Greenstreet, W. L. (1976). “Experimental studies to examine elastic‐plastic behaviors of metal alloys used in nuclear structures.” Constitutive equations in viscoplasticity: Computational and engineering aspects, AMD, ASME, New York, N.Y., 20, 35–56.
17.
Mair, W. M., and Pugh, H. (1964). “Effect of pre‐strain on yield surfaces in copper.” J. Mech. Engrg. Sci., 6(2), 150–163.
18.
McDowell, D. L. (1983a). “On the path dependence of transient hardening and softening to stable states under complex biaxial cyclic loading.” Proc. Int. Conf. Constitutive Laws for Engrg. Mats., Desai and Gallagher, Eds., Tucson, Ariz., 125–132.
19.
McDowell, D. L. (1983b). “Transient nonproportional cyclic plasticity.” Report No. 107. Design and Materials Div., Dept. of Mech. and Indust. Engrg., Univ. of Illinois at Urbana‐Champaign, Ill.
20.
McDowell, D. L. (1985a). “An experimental study of the structure of constitutive equations for nonproportional cyclic plasticity.” J. Engrg. Mats. Tech., ASME, 107, 307–315.
21.
McDowell, D. L. (1985b). “The significance of nonproportional loading tests for characterization of cyclic response of metals.” Proc. 1985 Spr. Conf. on Exper. Mech., Soc. for Expermntl. Stress Anal., Las Vegas, Nev., 229–236.
22.
McDowell, D. L. (1985c). “A two surface model for transient nonproportional cyclic plasticity: Part I—Development of appropriate equations.” J. Appl. Mech., ASME, 52, 298–302.
23.
McDowell, D. L. (1985d). “A two surface model for transient nonproportional cyclic plasticity: Part II—Comparison of theory with experiments.” J. Appl. Mech., ASME, 52, 303–308.
24.
McDowell, D. L. (1986). “An evaluation of recent developments in hardening and flow rules for rate‐independent, nonproportional cyclic plasticity.” J. Appl. Mech., ASME.
25.
McDowell, D. L., Payne, R. K., Stahl, D., and Antolovich, S. D. (1984). “Effects of nonproportional cyclic loading histories on type 304 stainless steel.” Crack initiation under complex loadings, French Metallur. Soc., Paris, France, 53–86.
26.
Mroz, Z. (1967). “An attempt to describe the behaviour of metals under cyclic loads using a more general workhardening model.” Acta mechanica, 7, 199–212.
27.
Nouailhas, D., Policella, H., and Kaczmarek, H. (1983). “On the description of cyclic hardening under complex loading histories.” Proc. Int. Conf. Constitutive Laws for Engrg. Matls., Desai and Gallagher, Eds., Tucson, Ariz., 45–49.
28.
Ohno, N. (1982). “A constitutive equation of cyclic plasticity with a non‐hardening strain region.” J. Appl. Mech., ASME, 49, 721–727.
29.
Phillips, A., Tang, J. L., and Ricciuti, M. (1974). “Some new observations on yield surfaces.” Acta mechanica, 20, 23–39.
30.
Prager, W. (1956). “A new method of analyzing stresses and strains on work‐hardening plastic solids.” J. Appl. Mech., ASME, 23, 493–496.
31.
Sotolongo, W. (1985). “On the numerical implementation of cyclic elasto‐plastic materials models.” thesis presented to the School of Mechanical Engineering, Georgia Institute of Technology, at Atlanta, Georgia, in partial fulfillment of the requirements for the degree of Master of Science.
32.
Tanaka, E., Murakami, S., and Ooka, M. (1985). “A constitutive model of cyclic plasticity in multiaxial non‐proportional loading.” L 2/4, SMirt 8, Berlin, Germany.
33.
Tseng, N. T., and Lee, G. C. (1983). “Simple plasticity model of the two‐surface type.” J. Engrg. Mech., ASCE, 109(3), 795–810.
34.
Ziegler, H. (1959). “A modification of Prager's hardening rule.” Quart. Appl. Math., 17, 55–60.
Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 113 • Issue 3 • March 1987
Pages: 378 - 397
Copyright
Copyright © 1987 ASCE.
History
Published online: Mar 1, 1987
Published in print: Mar 1987
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