Modeling method for periodic cracks in functionally graded strips with arbitrary properties

Abstract

A piecewise exponential model is developed to investigate the problems of periodic cracks in functionally graded strips with arbitrary material properties. The problem of a row of embedded cracks vertical to strip surfaces under a mode I load in a functionally graded strip with arbitrary nonhomogeneous properties is considered in a plane elasticity state. The true properties of functionally graded materials (FGMs) are approached by a series of sub-layers with material properties varying exponentially and without losing continuity. The thicknesses of different sub-layers can be set to improve calculation accuracy and efficiency. The formulation for doing so is derived using Fourier integral transformation and Fourier series, and the problem is finally reduced to an integral equation with Cauchy-type singularity. Crack-surface displacement derivative is selected as an auxiliary function and is numerically solved to calculate the stress intensity factors (SIFs) at crack tips. The results of previous research are compared with those of the current study to verify the present model. Four representative functions of material properties are considered and the SIFs are presented. The effects of crack spacing, nonhomogeneous properties and crack length on SIFs are discussed. The conclusions are beneficial to the knowledge of fracture behaviors of FGMs.