Abstract
The present paper proposes a simple numerical analytical method for crack extension simulation in the particle reinforced composite, and reveals the effect of crack extension on the macroscopic material properties of the particle reinforced composite. This numerical method is based on the homogenization method and Dugdale-type cohesive elements. In the present paper, we first present the formulation of the numerical model. We then verify the validity of the numerical model by comparing the simulated crack extension with the linear fracture mechanics. Finally we perform the crack extension simulation for the composite reinforced by spherical particle. We consider the inclusion crack and interfacial crack between inclusion and matrix. The analytical results reveal that the inclusion crack extends always unstably regardless of the size of initial crack, and the evolution of inclusion crack sharply decreases the apparent Young's modulus in the perpendicular direction to the crack surface and shear modulus in the out-of-plane direction of crack surface. The results also demonstrated that the interfacial crack always extends stably regardless of the size of initial crack, and the evolution of interfacial crack gradually degrades the stiffness in all direction.
