Investigating the Effective Fracture Toughness of Heterogeneous Materials

Heterogeneous materials are ubiquitous in nature, and are increasingly being engineered to obtain desirable mechanical properties. Naturally, the bulk properties of a heterogeneous material can be different from those of its constituents. Thus, one needs to determine its overall or effective properties. For some of these properties, like effective elastic modulus, the characterization is well-known, while for other such as effective fracture toughness, it is a matter of ongoing research. In this paper, we present a method to measure the effective fracture toughness. For the method, we apply a time-dependent displacement condition called the surfing boundary condition. This boundary condition leads the crack to propagate steadily macroscopically but in an unconstrained manner microscopically. We then use the grid method, a non-contact full-field displacement measurement technique, to obtain the displacement gradient. With this field, we compute the macroscopic energy release rate via the area J-integral. Finally, we interpret the effective toughness as the peak of the energy release rate. Using this method, we investigate the influence of heterogeneity on effective fracture toughness. We find that the effective toughness can be enhanced due to the heterogeneity. Consequently, engineered heterogeneity may provide a means to improve fracture toughness in solids