Optimum Material Distributions for Minimizing the Stress Intensity Factor of Edge Crack in Thick-Walled FGM Circular Pipes under Thermomechanical Loading

Abstract

This study treats the optimization problem of material distributions for minimizing the stress intensity factor of radial edge crack in thick-walled functionally graded material (FGM) circular pipes under thermomechanical loading. Homogenizing the FGM circular pipes by simulating the nonhomogeneity of thermal conductivity by a distribution of equivalent eigentemperature gradient and the nonhomogeneities of Young's modulus and Poisson's ratio by a distribution of equivalent eigenstrain, we present an approximation method to obtain the stress intensity factor for a radial edge crack in the FGM circular pipes. The optimum material distributions for minimizing the stress intensity factor of edge crack are determined using a nonlinear mathematical programming method. Numerical results obtained for a thick-walled TiC/Al₂O₃ FGM circular pipe reveal that it is possible to minimize the stress intensity factor of edge crack by choosing an optimum material distribution profile.