Dynamic Caustic Analysis of a Propagating Mode-III Crack in Functionally Graded Material Based on a Higher-order Transient Crack Tip Expansion

Abstract

In this study, the influence of the material gradient on the dynamic mode-III crack tip singularity in a functional gradient material (FGM) is analyzed by means of the optical method of caustics. The elastic constants and, and the density of the FGM are assumed to vary in an exponential manner paralleling the crack, while the Poisson’s ratio is assumed to be constant. The correlation among the stress intensity factor, the material gradient, and the crack velocity is established using the equations of the dynamic caustics and the initial curves for the moving mode-III crack tip under a higher-order asymptotic expansion equation. The dynamic stress intensity factors (SIFs) of the mode-III propagating crack tip is evaluated by the characteristic distance of the caustics and the correction factors including the velocity effects and the material gradient effect. The theoretical caustics and the respective initial curves for different material gradients are simulated under the K-dominant condition. The influence of the material gradient on the shape and size of the caustics and the initial curves is analyzed. These works are helpful to understand the mechanical behaviors of the advanced polymer reinforced composites.