Inhomogeneity effects on the crack driving force in elastic and elastic-plastic materials

This article evaluates the effect of material inhomogeneities on the crack-tip driving force in general inhomogeneous bodies and reports results for bimaterial composites. The theoretical model, based on Eshelby material forces, makes no assumptions about the distribution of the inhomogeneities or the constitutive properties of the materials. Inhomogeneities are modeled by making the stored energy have an explicit dependence on the reference coordinates. Then the material inhomogeneity effect on the crack-tip driving force is quantified by the term C_inh, which is the integral of the gradient of the stored energy in the direction of crack growth. The model is demonstrated by two model problems: (i) bimaterial elastic composite using asymptotic solutions and (ii) graded elastic and elastic-plastic compact tension specimen using numerical methods for stress analysis.