Simple Model for Directional Distortional Hardening in Metal Plasticity within Thermodynamics
Publication: Journal of Engineering Mechanics
Volume 134, Issue 9
Abstract
Directional distortion, observed in many experiments on various types of metals, refers to the formation of a region of high curvature (sharpening) on the yield surface approximately in the direction of loading, and a region of low curvature (flattening) approximately in the opposite direction. Constitutive modeling of directional distortion was recently presented by the writers where an evolving fourth-order tensor-valued internal variable was introduced. In the current paper a much simpler mathematical formulation describing directional distortional hardening is presented without the use of a fourth-order tensor, in conjunction with kinematic and isotropic hardening. Two versions of the model in ascending level of complexity follow similar lines of development, which include derivation of all hardening rules on the basis of conditions sufficient to satisfy the thermodynamic dissipation inequality. As a tradeoff for its simplicity the present model does not fit experimental data as well as the model with the evolving fourth-order tensor, but it still captures the salient features of directional distortion in a rather satisfactory way.
Get full access to this article
View all available purchase options and get full access to this article.
References
Bardet, J. P., and Choucair, W. (1991). “A linearized integration technique for incremental constitutive equations.” Int. J. Numer. Analyt. Meth. Geomech., 15, 1–19.
Boucher, M., Cayla, P., and Cordebois, J. P. (1995). “Experimental studies of yield surfaces of aluminum alloy and low carbon steel under complex biaxial loadings.” Eur. J. Mech. A/Solids, 14(1), 1–17.
Dafalias, Y. F., Schick, D., and Tsakmakis, C. (2002). “A simple model for describing yield surface evolution.” Lecture note in applied and computational mechanics, K. Hutter and H. Baaser, eds., Springer, Berlin, 169–201.
Feigenbaum, H. P., and Dafalias, Y. F. (2007). “Directional distortional hardening in metal plasticity within thermodynamics.” Int. J. Solids Struct., 44, 7526–7542.
François, M. (2001). “A plasticity model with yield surface distortion for nonproportional loading.” Int. J. Plast., 17, 703–717.
Kurtyka, T., and Zyczkowski, M. (1996). “Evolution equations for distortional plastic hardening.” Int. J. Plast., 12(2), 191–203.
McComb, H. G. (1960). “Some experiments concerning subsequent yield surfaces in plasticity.” Rep. No. D-396, National Aeronautics and Space Adminstration, Washington, D.C.
Naghdi, P. M., Essenburg, F., and Koff, W. (1958). “An experimental study of initial and subsequent yield surfaces in plasticity.” J. Appl. Mech., 25(2), 201–209.
Ortiz, M., and Popov, P. E. (1983). “Distortional hardening rules for metal plasticity.” J. Eng. Mech., 109(4), 1042–1057.
Phillips, A., Tang, J.-L., and Ricciuti, M. (1975). “Some new observations on yield surfaces.” Acta Mech., 20, 23–39.
Voyiadjis, G. Z., and Foroozesh, M. (1990). “Anisotropic distortional yield model.” J. Appl. Mech., 57, 537–547.
Wei-Ching Yeh, C.-D. H., and Pan, W.-F. (1996). “An endochronic theory accounting for deformation induced anisotropy of metals under biaxial load.” Int. J. Plast., 12(8), 987–1004.
Wu, H. C., and Yeh, W. C. (1991). “On the experimental determination of yield surfaces and some results of annealed 304 stainless steel.” Int. J. Plast., 7, 803–826.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 134 • Issue 9 • September 2008
Pages: 730 - 738
Copyright
© 2008 ASCE.
History
Received: Nov 15, 2007
Accepted: Feb 14, 2008
Published online: Sep 1, 2008
Published in print: Sep 2008
Notes
Note. Associate Editor: George Z. Voyiadjis
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.