Time-dependent fracture of a two-phase brittle material

An approximate time-dependent statistical fracture model for two-phase materials, such as particulate-reinforced ceramics and cementitious materials, has been developed in this paper. It is assumed that the tougher second-phase particles, unlike pre-existing matrix microcracks, are not sensitive to environment-assisted slow crack growth. The effect of the particles is to stabilize otherwise unstable microfracture and to provide resistance to slow crack growth of pre-existing matrix cracks. As the second-phase particles and pre-existing matrix cracks are assumed to be randomly distributed, two cases are considered; in one case the particles bridge the matrix cracks if they intersect and in the other the particles are cut. Analytical results for the cutting case show that the slow crack growth parameters A and n in two-phase materials are not constant and that n is larger than that of the matrix material. However, provided that the final crack sizes at failure are similar, an effective n value can be used in conjunction with the stress-rate-dependent strength results to give good predictions of the lifetime data under constant stresses.