A mixed-mode crack analysis of rectilinear anisotropic solids using conservation laws of elasticity

Abstract

A very simple and convenient method of analysis for studying two-dimensional mixed-mode crack problems in rectilinear anisotropic solids is presented. The analysis is formulated on the basis of conservation laws of anisotropic elasticity and of fundamental relationships in anisotropic fracture mechanics. The problem is reduced to a system of linear algebraic equations in mixed-mode stress intensity factors. One of the salient features of the present approach is that it can determine directly the mixed-mode stress intensity solutions from the conservation integrals evaluated along a path removed from the crack-tip region without the need of solving the corresponding complex near-field boundary value problem. Several examples with solutions available in the literature are solved to ensure the accuracy of the current analysis. This method is further demonstrated to be superior to other approaches in its numerical simplicity and computational efficiency. Solutions of more complicated and practical engineering problems dealing with the crack emanating from a circular hole in composites are presented also to illustrate the capacity of this method.

An experimental/numerical investigation into the main driving force for crack propagation in uni-directional fibre-reinforced composite laminae

“…Hence, two SIFs are required, one for each mode (mode 1 and mode 2). In order to evaluate these, the interaction integral of [41] is utilised. The interaction integral is an extension to the widely accepted J-Integral of Rice [42].…”

“…Therefore, in accordance with Wang [41], if Equation 9 is used in conjunction with the conservation law for two independent equilibrium states of the linearly elastic solid, both SIFs can be computed. By defining two equilibrium states, and in accordance with the Principle of Superposition, the J-integral for the superimposed (combined) state is shown to be,…”

An accurate scheme for mixed‐mode fracture analysis of functionally graded materials using the interaction integral and micromechanics models

“…aux ij; j = 0 (no body forces). In this case, the auxiliary displacement ÿeld is given by Equation (2), and the auxiliary strain ÿeld is the symmetric part of the gradient of the auxiliary displacement ÿeld, i.e. aux ij = (u aux i; j + u aux j; i )=2.…”

A micromechanical approach of crack-induced damage in orthotropic media: Application to a brittle matrix composite

“…Despite the progresses concerning the mathematical formulation of constitutive laws and the evaluation of overall properties of engineering materials ( [29,9,10,48,19,51,34,41,21,45] and many others, especially in the 2D context), the 3D modelling of interaction between initial and damage-induced anisotropies remains a difficult task, even in the context of phenomenological models (see, for example, [26,44,16,5]). In this paper, this coupling is addressed by means of Eshelby-type homogenization techniques.…”