Employing Williams' series for the identification of fracture mechanics parameters from phase-field simulations

Fracture mechanics and damage mechanics are two theories that describe the degradation of the bearing capacity of structures. Fracture mechanics is based on a discontinuous description of cracking, while damage mechanics proposes a continuous description of material degradation. These two approaches are often opposed in the literature, from both theoretical and numerical points of view. This work suggests correlating the two approaches by applying Williams' series, usually dedicated to experimental results, to phase-field computations. Williams' series are employed to extract equivalent fracture mechanics parameters as a post-processing step. The proposed analysis based on a fracture mechanics description excludes the fracture process zone. Typical fracture mechanics parameters such as energy release rate, stress intensity factors, fracture process zone size, and crack tip position are determined from the phase-field computations. The approach is illustrated on a two-dimensional structure representing a beam whose notch opening displacement is controlled. The dependence on the choice of the internal length of the phase-field model is studied. Similarities and differences between both modeling routes are discussed.