Crack Nucleation in Phase Field Fracture Models

Abstract Phase field fracture models are able to reproduce a wide range of phenomena, which are observed in fracture experiments. These phenomena include the nucleation of new cracks in initially undamaged material. However, none of the material parameters of a phase field fracture model is directly connected to the fracture strength of the material. Thus, the critical stress for the nucleation of new cracks is not a priori clear. Crack nucleation in a phase field fracture model is preceded by a localization of the initially homogeneous crack field in an area surrounding the nucleating crack. For homogeneous problems, it can be shown analytically that the onset of the localization is caused by the loss of stability of the crack-free homogeneous solution of the phase field equations at a certain load level. This critical stability load provides a definition of the fracture stress in the phase field model depending on the stiffness of the material, the cracking resistance and the internal length of the phase field model. The analytical findings are illustrated in finite element simulations of the phase field fracture model. Further numerical investigations analyze the crack nucleation behavior of the phase field model in more complicated scenarios, where analytical stability results are not available