Numerical simulations of crack propagation in screws with phase-field modeling

Abstract In this work, we consider a phase-field framework for crack propagation problems in elasticity and elasto-plasticity. We propose a rate-dependent formulation for solving the elasto-plastic problem. An irreversibility constraint for crack evolution avoids non-physical healing of the crack. The resulting coupled two-field problem is solved in a decoupled fashion within an augmented Lagrangian approach, where the latter technique treats the crack irreversibility constraint. The setting is quasi-static and an incremental formulation is considered for temporal discretization. Spatial discretized is based on a Galerkin finite element method. Both subproblems of the two-field problem are nonlinear and are solved with a robust Newton method in which the Jacobian is built in terms of analytically derived derivatives. Our algorithmic developments are demonstrated with several numerical tests that are motivated by experiments that study failure of screws under loading. Therefore, these tests are useful in practice and of high relevance in mechanical engineering. The geometry and material parameters correspond to realistic measurements. Our goal is a comparison of the final crack pattern in simulation and experiment.