Fracture Mechanics of Functionally Graded Materials (FGMs): Stress Intensity Factor Solutions and the Nature of Crack Arrest

摘要

A generalized method to determine the stress intensity factor (SIF, K) solutions for cracks in finite-width specimens of functionally graded materials (FGMs), based on force balance is presented. The method uses the modified form of Westergaard's stress distribution ahead of the crack in an infinite plate and is based on the requirement of isostrain deformation of layers of varying moduli ahead of the crack tip. Closed-form analytical equation for the stress intensity factors of cracks in a linearly-graded, finite-width center cracked specimens was derived. Comparisons of the K values from the analytical equation with that obtained from FEM simulations indicate that the derived SIF equations for FGMs are reasonably accurate. For the finite-width center-cracked-tension (CCT) specimen, the errors are less than 10% for most of the crack lengths for materials with the outer layer modulus ratios varying from 0.2 to 5. These SIF solutions are convenient for engineering estimates of stress intensity factors as well as useful in the experimental determinations of fracture toughness of FGMs. The study also performed an analysis of the position-dependent fracture toughness of FGMs. The predictions from this analysis are compared with the applied K levels to demonstrate the nature of crack-arrest capabilities of FGMs. The results demonstrate that the fracture mechanical characteristics of FGMs are quite different from that of conventional homogeneous materials.