FRACTURE-ANALYSIS OF NONHOMOGENEOUS MATERIALS VIA A MODULI-PERTURBATION APPROACH

This paper presents a first-order moduli-perturbation algorithm for fracture analysis of nonhomogeneous materials. The formulation is based on the Bueckner-Rice weight function theory. In the perturbation procedure a homogeneous body is chosen as the reference so that nonhomogeneous quantities are treated as being perturbed from the reference solutions. It is shown that the perturbation formulae can be derived from the potential energy bounds for nonhomogeneous materials, but they generally do not give bounds for estimating stress intensity factors. The perturbation algorithm is applied to calculate the stress intensity factors for several crack problems involving spatially varying material moduli. Comparisons with a few exact solutions indicate that the perturbation results give reasonable predictions over a substantial range of moduli variation. The solution for a cracked body with sinusoidally-varying shear modulus is obtained from perturbation analysis and then used to construct general solutions for arbitrarily-varying modulus via Fourier analysis.