Anisotropic yield criterion for polycrystalline metals using texture and crystal symmetries
type: Item
instance of: scholarly article
title: Anisotropic yield criterion for polycrystalline metals using texture and crystal symmetries
zbMATH Open document ID: 0961.74014
DOI: 10.1016/S0020-7683(98)00248-0
author: V. Pereyra
published in: International Journal of Solids and Structures
publication date: 2001-05-17T00:00:00Z
review text: The authors make an attempt to bridge continuum and crystallographic approaches by exploiting the symmetries found in each grain of a polycrystalline metal, and by making use of isotropic plasticity equivalent (IPE) method of \textit{A. P. Karafillis} and \textit{M. C. Boyce} [J. Mech. Phys. Solids 41, No. 12, 1859-1886 (1993; Zbl 0792.73029)]. Using some linear transformation, this method allows to operate with a stress state of isotropic plasticity equivalent material instead of the actual stress state existing in an anisotropic material. Usually, in the continuum approach a phenomenological yield criterion, which is a function of the stress, is used to define the yield surface in stress space. At the same time, in crystallographic approaches the yield surface of a polycrystalline aggregate is determined from the yielding behavior of each grain in the aggregate. In this paper, using the IPE method, the authors obtain a continuum yield function for fcc polycrystalline metals. In order to bring microstructural information into the continuum model, they use two Taylor's assumptions, namely: (i) each grain has the same yield surface, and differs from the others only in its orientation, and (ii) each grain undergoes the same homogeneous deformation as the macroscopic deformation. To avoid theoretical difficulties, the present work is limited by modeling weakly-textured materials (the crystallographic yield theory of Bishop and Hill is used to determine the parameters for the IPE linear transformation tensor for a single fcc crystal). By assuming that the rates of work in anisotropic and IPE materials are equal, the authors find the IPE transformation tensor for a polycrystal by using only polycrystalline texture data. Thus, the developed IPE criterion can be viewed as a generalizaton of the Hill's anisotropic criterion, adding to him the abilities to describe non-quadratic yielding behavior, to account for microstructural texture, and to choose the number of data point…
Mathematics Subject Classification ID: 74E15
Mathematics Subject Classification ID: 74E25
Mathematics Subject Classification ID: 74C05
Mathematics Subject Classification ID: 82D35
Mathematics Subject Classification ID: 74E10
zbMATH DE Number: 1340825
zbMATH Keywords: anisotropic yield criterion
zbMATH Keywords: Bishop-Hill crystallographic yield theory
zbMATH Keywords: isotropic plasticity equivalent method
zbMATH Keywords: crystal symmetry
zbMATH Keywords: linear transformations
zbMATH Keywords: yield surface
zbMATH Keywords: fcc polycrystalline metals
zbMATH Keywords: Taylor's assumptions
zbMATH Keywords: weakly-textured materials
zbMATH Keywords: polycrystalline texture data
reviewed by: Ivan A. Parinov
MaRDI profile type: Publication
Wikidata QID: Q126778518
full work available at URL: s0020-7683(98)00248-0
OpenAlex ID: W1973727633
description: scientific article; zbMATH DE number 1340825