Phase Field Approach for Damage in Quasi-Brittle Polycrystalline Microstructures

Damage is a process that occurs on several scales. From the separation of atomic bonds over the formation and localization of defects like microvoids and microcracks several mechanisms act conjointly in the damage process. The initiation and evolution of microdamage inside of a quasi-brittle polycrystalline microstructure representing the brittle phases in a brazed joint of nickel-based alloys is studied by means of numerical simulations. A phase field approach for brittle damage is employed on the microscale. The simulation approach is capable of depicting phenomena of microcracking like kinking and branching due to heterogeneous stress and strain fields on the microscale. No information regarding the initiation sites and pathways of microcracks is needed a priori. The reliability of calculating effective critical energy quantities as a microstructure-based criterion for macroscopic damage is assessed. The effective critical strain energy density as well as the effective critical energy release rate are evaluated. The local critical strain energy density turns out to be better suited as a model input parameter on the microscale as well as for a microstructure-based prediction of macroscopic damage compared to a model employing the energy release rate. The choice of the local part in the formulation of the crack surface density allows to model not only ideally brittle material behavior, but also quasi-brittle failure involving a continuous process of microdamage.