Direction-dependent fracture in solids: Atomistically calibrated phase-field and cohesive zone model

We propose a new phase-field damage formulation which takes into account anisotropic damage evolution in solids. Such anisotropy projects itself in fracture energy values which depend on the direction of the crack surface. Therefore, instead of one constant scalar parameter for the fracture energy value, we use a direction-dependent fracture energy function. By incorporating a direction-dependent fracture energy function, only a single damage variable as well as a first order damage gradient need to be used within the standard phase-field damage model. This is in contrast to other available anisotropic phase-field models which typically use multiple variables or higher order gradient terms. To obtain values for the fracture energy function, atomistic calculations are performed. Here, molecular static simulations are utilized to calculate the energy of free surfaces within an Aluminum crystal. As a result, we report the fracture energy value as a function of the surface orientation. The obtained fracture energy function is passed directly to the phase-field damage formulation to investigate transgranular fracture within a single crystalline. Moreover, the grain boundary is represented via a cohesive zone model to take into account intergranular fracture in a bi-crystalline structure. The predicted crack path is in good agreement with obtained results from molecular dynamics simulations. Finally, by calibrating the length scale parameter in the phase-field damage model, it is possible to compare the reaction forces from finite element calculations with atomistic ones.