Model for plasticity effects in metals under nonproportional cyclic loading

Abstract

A possible physical mechanism for additional hardening is proposed on the basis of an analysis of experiments on nonproportional cyclic loading of metals. A model for an elastoplastic polycrystal with a hardening law taking into account the interaction of slip systems is develIntroduction. In real processes of plastic deformation of metallic polycrystals, any small material particle is subjected to complex loading even when components of the boundary forces and displacements change proportionally. This is due to the complex geometry of the surface on which the boundary conditions are specified and (from a physical point of view) to the presence of internal boundaries separating crystallites in the body. 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.1. Effect of Additional Hardening in Nonproportional Cyclic Loading. Results of systematic experimental studies of the local plastic properties of metals with variation in the shape of cyclic strain paths are given in [1][2][3][4]. The object of research was a thin-walled tubular specimen subjected to compressiontension and alternating torsion (P-M experiments [7]). Symmetric periodic actions, shown by phase paths in the two-dimensional strain subspace el = e and e2 = ~/V~ (~ is the axial strain and 7 is the torsional strain), were delivered to the longitudinal and torsional operating mechanisms. Tanaka et al.[1] studied elliptic paths in the subspace of total strains, and Ishikawa and Sasaki [2] studied various closed paths in the subspace of plastic strains. In studies of the relationship between the plastic properties and the strain path shape, the maximum intensities of cyclic strains e+ were fixed in corresponding series of experiments. The tests were performed at room temperature, and the strain rate was varied in the range from 10 -4 to 10 -3 sec -1. In the initial state, the specimen material was isotropic.The experiments showed some new properties of the tested materials in a cyclically stabilized state. In particular, for a number of metals, additional hardening was found to depend strongly on the strain path shape. For chromium-nickel austenite stainless steel AISI 304 subjected to deformation in the elliptic paths [1] el = e+v/'2(1 + ~2)1/2 COS (0 -t-eft), e2 = e+v~(1 + 62)U2cos (0 -~), 5 = tan ~ = e_/e+, and 0 = wt with