An Evaluation of Recent Developments in Hardening and Flow Rules for Rate-Independent, Nonproportional Cyclic Plasticity

Abstract

The Mroz kinematic hardening rule has previously demonstrated superior capability to correlate cyclically stable nonproportional stress-strain response. In this paper, recently proposed kinematic hardening rules for single and multiple surface cyclic plasticity models are evaluated. Significant improvement over the Mroz rule, without loss of generality, is achieved with a deviatoric stress rate-dominated rule proposed by Tseng and Lee for two surface theory. Recent approaches for correlation of the modulus function and isotropic hardening are discussed. The norm of the Mroz distance vector is found to uniquely correlate the variation of plastic hardening modulus through a cycle; it is necessary to include a measure of instantaneous nonproportionality, however, to properly normalize the modulus function. A new evolution equation is offered to correlate the additional isotropic hardening observed during nonproportional loading, and several contemporary approaches are also considered.

Load path sensitivity and fatigue life estimation of 30CrNiMo8HH

“…Von Mises equivalent stress in deviatoric stress space is defined as (6) where are the components of deviatoric stresses.…”

“…The prediction of this model for austenitic stainless steel type 316 under nonproportional loading agreed with the experimental results. McDowell et al [6] developed a nonproportionality factor introduced in the plastic strain space. This model consisted of two coefficients: hardening coefficient and path dependent coefficient.…”

Model for plasticity effects in metals under nonproportional cyclic loading

“…Maximum cyclic hardening in both cases was reached for circular strain paths. McDowell [6] refers to experiments in which the value of cr~ for a circular path was 75-80% higher than that for a proportional path. Itoh et al [3] studied the tendency toward additional cyclic hardening for a number of metals subjected to proportional and nonproportional (in a cross-shaped path) cyclic deformation in the total strain subspaee (e+ = 0.004-0.008).…”

“…The local plastic properties of some widely used metals under nonproportional cyclic loading are characterized by a number of effects not found in nonproportional monotonic and proportional cyclic types of loadings [1][2][3][4]. The difficulties in deriving constitutive elastoplastic relations for complex cyclic loading, which are noted by all specialists (see, for example, [5][6][7]), motivate the necessity of choosing a physically justified structure of these relations and the study of the causes and physical mechanism of the phenomenon. The paper presents a mathematical model that describes the effect of additional hardening and a number of other plasticity effects in nonproportional cyclic loading of macrohomogeneous specimens.…”

Constitutive Model for the Subsequent Time-Dependent Deformations of Type 304 Stainless Steel at Room Temperature

“…Most of the constitutive models incorporated into FEM codes are too simple to describe the complex deformations. Therefore, many constitutive models have been proposed [1][2][3][4][5][6][7][8][9][10]. To construct more accurate constitutive model, it is important to know the deformation mechanisms of polycrystalline metallic materials.…”