A Phase Field Model for Ductile to Brittle Failure Mode Transition

The computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in dynamic problems with complex crack topologies. This can be overcome by a diffusive crack modeling based on the introduction of a crack phase field. We outline a conceptual framework for phase field models of crack propagation in brittle elastic and ductile elastic-plastic solids under dynamic loading and investigate the ductile to brittle failure mode transition observed in the experiment performed by Kalthoff and Winkeler 3]. We develop incremental variational principles and consider their numerical implementations by multi-field finite element methods. To this end, we define energy storage and dissipation functions for the plastic flow including the fracture phase field. The introduction of local history fields that drive the evolution of the crack phase field inspires the construction of robust operator split schemes. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)