Local and non-local modeling aspects of three-dimensional cracks growth initiation

Three-dimensional crack growth initiation is examined under the assumption that the crack front remains smooth. Two important modeling issues, specific to three-dimensional rather than two-dimensional cracks, are addressed. First, it is established that, at each point along the crack front, the velocity and configurational force are two-dimensional vectors, lying in the local normal plane. This allows one to generalize any two-dimensional crack growth criterion to three dimensions. Second, a simple mesoscopic model to account for along-the-front non-locality is proposed. This model eliminates pathological growth patterns ubiquitous to basic models applied to three-dimensional cracks. Further, the model is straightforward to use as it relies on standard fracture properties only.