Analysis of Effects of Elastic Inhomogeneity and Residual Thermal Stress on Fracture Toughness by the Equivalent Inclusion Method

Abstract

Effects of microstructure on fracture toughness were investigated. Using the equivalent inclusion method, the change in Gibbs' free energy was calculated for a relatively large body containing a main crack and many spherical (or disk-shaped) inclusions with a Young's modulus (or thermal expansion coefficient) different from that of the matrix. Applying the Griffith's fracture criteria to the model, the effects of inclusions on fracture toughness were formulated. The fracture toughness increased with the increase in volume fraction of inclusions with a larger Young's modulus (or thermal expansion coefficient) than that of the matrix. The fracture toughness decreased with the increase in volume fraction of inclusions with a smaller Young's modulus (or thermal expansion coefficient) than that of the matrix. The difference in thermal expansion coefficient influenced the fracture toughness more strongly than that in Young's modulus. The present analysis explains the tendencies of the experimental results reported previously.