Fracture toughness improvement due to crack deflection and crack trapping by elliptical voids or particles

The paper investigates how voids and particles can be used to deflect and arrest cracks in order to enhance the failure stress and the fracture toughness of intrinsically brittle materials. This is done by investigating crack propagation near single elliptical voids and particles that are located in an elastic matrix material. The shapes of the inhomogeneities are varied, but their cross section is held constant. Uniaxial and biaxial loading conditions are considered and also the Young’s modulus ratio between particle and matrix material is varied. The crack trajectories near the material inhomogeneities are evaluated by applying a computationally very efficient approach, the crack trajectory interpolation (CTI) method, which has been introduced in an earlier work of the authors. With this method, critical distances are determined where an approaching crack runs into an elliptical void and gets trapped. Similarily, zones for crack arrest and crack deflection near stiff particles are found. Combinations of particles and voids are studied, too. A damage-based approach is used to investigate the improvements in failure stress and fracture toughness when a crack runs into a void. The results show that voids and particles that are elongated perpendicular to the crack plane are most useful for crack arrest. The trapping distances increase with increasing ellipticity of the inhomogeneities. However, the improvement in failure stress is highest for voids with moderate ellipticity. The results of this paper will be used to find optimum arrangements of voids or particle-void combinations for the design of structural components with increased fracture toughness.