Study of crack propagation in multi-phase composites embedded with both stiff and compliant particles using phase field method

Crack propagation in two-phase particle-reinforced composites is extensively studied using the phase field method. Typically, the particle either has a higher stiffness(stiff) or a lower stiffness(compliant) than the matrix. However, the crack propagation in multi-phase composites with both the stiff and compliant particles is not yet understood well. In this work, we report on the crack propagation characteristics and the resulting enhanced effective fracture toughness in multi-phase composite materials with both stiff and compliant particles using the phase filed method. Three different geometric arrangements of particles are considered: a diagonal array, a cubic array, and a honeycomb array. The honeycomb configuration had the best combination of strength and effective fracture toughness. We show that apart from the local geometric arrangement of the individual particles, the ratio of the stiffness of the individual particles is an important factor in crack propagation. Furthermore, we show that the ratio of the critical energy release rate of the individual particles can be tuned to increase the effective fracture toughness.