Numerical simulations of crack deflection at a twist-misoriented grain boundary between two ideally brittle crystals

Finite-element simulations are used to model crack propagation across twist-misoriented grain boundaries, which are an important source of toughness in lamellar microstructures such as TiAl. We consider a twist grain boundary (GB) between two adjacent grains, and assume that each grain has a single cleavage orientation. The cleavage planes and GB are modeled as a set of cohesive surfaces, and the crack path and effective toughness of the system are simulated using a dynamic finite-element method (FEM). As the crack approaches the GB under remote mode I loading, it is allowed to either deflect along the GB and/or induce the nucleation of a periodic array of cracks in the adjacent grain. The simulations predict (i) a critical toughness ratio between the GB and the cleavage planes for the crack to propagate into the adjacent grain; (ii) an array of cracks in the GB and the twisted grain; (iii) the macroscopic mode I toughness of the solid as a function of a generalized measure of crack length; and (iv) the influence of GB toughness and twist misorientation on the effective toughness of the solid.