Perturbation approach to elastic constitutive relations of polycrystals
type: Item
instance of: scholarly article
title: Perturbation approach to elastic constitutive relations of polycrystals
zbMATH Open document ID: 1104.74055
author: Mojia Huang
published in: Journal of the Mechanics and Physics of Solids
publication date: 2005-02-22T00:00:00Z
review text: This paper focuses on a statistical continuum theory of polycrystals and on the determination of their effective stiffness tensors. It is known that the orientation distribution function (ODF) is used to describe the probability density of a crystallite with some orientation in SO(3). Since single crystals are anisotropic and the elastictity stiffness tensor of any crystallite in a polycrystal is orientation-dependent, the effective elastic stiffness tensor of the polycrystal depends on the orientational distribution of crystallites in the polycrystal. In this paper, the ergodic hypothesis is employed (i. e. the volume averages of stress, strain, elastic stiffness tensor of a polycrystal are equivalent to their corresponding ensemble). The author derives simple expression for effective stiffness tensor with quadratic texture dependence by the perturbation method. Decomposing the stress, strain and displacement fields, and also stiffness tensor into their ensemble average parts and perturbation parts, the author gives a formula for the perturbation displacement field, in which Green's function of an orthorhombic aggregate of cubic crystallites is included, and then derives a formula for effective stiffness tensors with quadratic texture dependence. For Voigt and Reuss' models, and Man theory, the information on the relevant microstructure is restricted to the ODF of a polycrystal. The author finds that this restriction is valid if the orientations of all crystallites in a polycrystal are uncorrelated and any crystallite orientation is unrelated to its shape and size, otherwise the effect of the \(n\)-point orientation correlation function to effective stiffness tensor is included. Also, the author considers the effect of grain shapes on effective elastic stiffness tensors of polycrystals. Numerical examples relate to copper, steel and aluminum crystals.
reviewed by: Ivan A. Parinov
Mathematics Subject Classification ID: 74Q15
Mathematics Subject Classification ID: 74E15
Mathematics Subject Classification ID: 74G10
zbMATH DE Number: 2136851
zbMATH Keywords: effective stiffness tensor
zbMATH Keywords: quadratic texture dependence
zbMATH Keywords: Green's function
MaRDI profile type: Publication
full work available at URL: j.jmps.2004.02.006
OpenAlex ID: W2020332385
cites work: Q5546684
cites work: Mean field variations in a statistical sample of heterogeneous linearly elastic solids
cites work: Q3929699
cites work: Effective elastic constants of polycrystalline aggregates
cites work: The determination of the elastic field of an ellipsoidal inclusion, and related problems
cites work: Green's function for orthorhombic aggregates of weakly anisotropic cubic crystals
cites work: Constitutive relation of elastic polycrystal with quadratic texture dependence
cites work: Q3996839
cites work: Elastic moduli of perfectly disordered composite materials
cites work: On the constitutive equations of some weakly-textured materials
cites work: Identification of material parameters in yield functions and flow rules for weakly textured sheets of cubic metals
cites work: Q3798341
cites work: Homogenization of polycrystalline aggregates
cites work: Constitutive equations of elastic polycrystalline materials
cites work: Q3243480
cites work: Variational and Related Methods for the Overall Properties of Composites
DOI: 10.1016/J.JMPS.2004.02.006
description: scientific article; zbMATH DE number 2136851