THERMOELASTIC ANALYSIS OF MATRIX CRACK-GROWTH IN PARTICULATE COMPOSITES

We examine the conditions under which differences in thermal expansion between a particle and the matrix lead to crack growth within the mat rix. Using linear elasticity fracture machanics, we obtain closed-form , analytical results for the case of a penny shaped crack present in t he matrix interacting with a spherical inclusion which is misfitting w ith respect to the matrix. A simple and direct relationship is establi shed between the strain energy release rate, the crack size, the crack orientation with respect to the inclusion, the crack/inclusion separa tion, the degree of thermal expansion mismatch and the elastic propert ies 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. We fin d that beyond this critical size, the elastic strain energy released u pon crack growth is no longer sufficient to compensate for the energy expended in extending the crack, since the crack is growing into the r apidly decreasing stress field. The modification of the above conditio ns for crack growth due to the superposition of an external stress fie ld has also been analyzed. The preferred orientation of these cracks a s a function of misfit strain is predicted. The implication of these r esults for thermal cycling are analyzed.