Cyclic Plasticity for Nonproportional Paths: Part 2—Comparison With Predictions of Three Incremental Plasticity Models

Abstract

Experiments that demonstrate the basic quantitative and qualitative aspects of the cyclic plasticity of metals are presented in Part 1. Three incremental plasticity kinematic hardening models of prominence are based on the Prager, Ziegler, and Mroz hardening rules, of which the former two have been more frequently used than the latter. For a specimen previously fully stabilized by out of phase cyclic loading the results of a subsequent cyclic nonproportional strain path experiment are compared to the predictions of the above models. A formulation employing a Tresca yield surface translating inside a Tresca limit surface according to the Mroz hardening rule gives excellent predictions and also demonstrates the erasure of memory material property.

On the consistency of nested surfaces models and their kinematic hardening rules

“…However, when the load is nonproportional the results are not always as good as expected (Montáns, 2001;Lamba and Sidebottom, 1978;Jiang and Sehitoglu, 1996).…”

“…It is traditional that the rule employed in this type of models is the original one proposed by Mró z, although other rules have been proposed in the literature (Montáns, 2001;Lamba and Sidebottom, 1978;Garud, 1981;Itoh et al, 2000;Jiang and Sehitoglu, 1994). Aside, only one translating surface is usually considered at a time when integrating the stresses and, hence, when computing the effective hardening modulus.…”

Two-Dimensional Strain Cycling in Plasticity

“…Only the portion of the stress trajectory which corresponds to the (post saturation) strain path 0-8 is shown. of Lamba and Sidebottom (1978b) for OFHC copper according to the prescribed strain path in the inset of Fig. 3(a).…”

“…Now, with reference to the third experiment of Lamba and Sidebottom (1978b), consider the predicted response for a "complex" nonproportional strain path (using the terminology of Lamba and Sidebottom) applied after the material has reached a state of saturation. The state of saturation is attained in the same way as discussed earlier in the preceding paragraph, namely by cycling first in shear followed by cycling along an elliptical path in the e lie 12 plane.…”

“…3(c) Comparison of the theorttical (-) shear stress response, measured in MPa, with the corresponding experimental data (---) of Lamba and Sidebottom (1978b) for OFHC copper according to the prescribed strain path in the inset of Fig. 3(a).…”