Effect of reinforcement morphology on matrix microcracking

Abstract

We quantitatively examine the conditions under which a particle matrix misfit leads to matrix crack growth as a function of inclusion shape. Such misfit stresses and cracks can be generated by thermal expansion mismatch, generated by cooling a brittle matrix containing ductile inclusions. Using fracture mechanics and perturbation theory, we analyze the case of a penny-shaped crack interacting with a misfitting spheroidal inclusion. A simple and direct relationship is established between the strain energy release rate and the physical and geometrical properties of the system including: the thermal expansion mismatch, temperature change, the crack and inclusion sizes, the elastic properties of the medium and the shape of the inclusion. In particular, the effects of inclusion shape on the stress intensity factors and strain energy release rate are analytically determined for nearly spherical inclusions. We use this information to determine the minimum crack size for crack growth to occur and the maximum size to which cracks may grow. The maximum crack size corresponds to the case where the elastic strain energy released upon crack growth is no longer sufficient to compensate for energy expended in extending the crack as the crack is growing into the rapidly decreasing stress field. We employ a nominally exact numerical procedure to study the effects of whiskers and platelets (i.e. spheroids very different from spheres) on matrix cracking. It is found that upon cooling a composite containing ductile inclusions, the propensity for matrix cracking is maximized for reinforcement shapes close to that of a sphere.