Influence of nano-inclusionsa grain boundaries on crack propagation modes in materials

The effect of nano-inclusions on materialsa strength and toughness has attracted great interest in recent years. It has been shown that tuning the morphological and microstructural features of materials can tailor their fracture modes. The existence of a characteristic size of inclusions that favours the fracture mode (i.e. transgranular or intergranular) has been experimentally observed but also predicted by a 2D model based on energetic arguments which relates the crack propagation mode to the ratio of the interface area between the crystalline inclusion and the matrix with the area of the crystallite inclusion in a previous work. In the present work, a 3D model is proposed in order to extend the 2D model and take into account the influence of the size of grain boundary zone on the toughening/hardening behavior of the material as it was observed experimentally in the literature. The model relates crack propagation mode to the ratio of the volume of the grain boundary zone between the crystalline inclusion and the matrix with the volume of the nano-inclusion. For a ratio below a critical value, transgranular propagation is favoured while for larger values, intergranular propagation is favoured. We also demonstrate that the extent of the grain boundary region also can significantly affect this critical value. The results of the model are in agreement with the literature experimental observations related to the toughening/hardening behavior as a function of the size of crystalline inclusions as well as the width of the grain boundary regions.