Thermal Misfit and Thermal Fatigue Induced Damage in Brittle Composites

We examine the conditions under which differences in thermal expansion between a particle and the matrix leads to crack growth within the matrix. Using linear elastic fracture mechanics, we obtain closed-form, analytical results for the case of a penny shaped crack present in the matrix interacting with a spherical inclusion which is misfitting with respect to the matrix. A simple and direct relationship is established between the strain energy release rate, the crack size, the crack orientation with respect to the inclusion, the crack/inclusion separation, the degree of thermal expansion mismatch and the elastic properties of the medium. We also analyze the size to which these cracks can grow and find that for a given misfit strain and material properties, crack growth is inhibited beyond a certain critical crack size. Finally, the preferred orientation of these cracks as a function of misfit strain is predicted. The implication of these results for thermal cycling are analyzed.