Crack Path Prediction in Anisotropic Brittle Materials

A force balance condition to predict quasistatic crack paths in anisotropic brittle materials is derived from an analysis of diffuse interface continuum models that describe both short-scale failure and macroscopic linear elasticity. The path is uniquely determined by the directional anisotropy of the fracture energy, independent of details of the failure process. The derivation exploits the gradient dynamics and translation symmetry properties of this class of models to define a generalized energy-momentum tensor whose integral around an arbitrary closed path enclosing the crack tip yields all forces acting on this tip, including Eshelby’s configurational forces, cohesive forces, and dissipative forces. Numerical simulations are in very good agreement with analytic predictions.

Figure 1

Spatially diffuse crack tip region with $\varphi =1/2$ contour separating broken and unbroken material (thick solid line).

Figure 2

Kink angle $\theta$ versus surface energy anisotropy $ϵ$ predicted as $\theta =ϵ/2$ and extracted from phase-field simulations (solid circles) for $G/G_c\approx 1.1$. Inset: phase-field simulation for $ϵ=1.2$ ($\varphi =1/2$ contours are equally spaced in time).