In the previous paper, micromechanical analysis was performed for a particle-reinforced composite with crack-bridging particles of various radii, by both introducing the stereological concept to the micromechanical model and considering interfacial debonding between a particle and a matrix. The expressions of energy release rates for both a matrix crack and a debonding crack were obtained. In the present paper, the criteria of crack propagation for matrix and debonding cracks are derived by adopting Griffith's concept for crack propagation. The critical length of the matrix crack, a_c, whose propagation will be arrested, can be obtained, which implies that the fracture toughness of such a composite can be evaluated using this criterion. The effect of material parameters such as the volume fraction of particles, the length of debonding, and the distribution of the radii of the particles, etc., on the toughness can be explained by the interfacial phenomenon. The results obtained are consistent with typical experimental findings.