Abstract
Anisotropy is inherent to crystalline materials (among others) due to the symmetry of the atomic lattice. However, failure anisotropy is questioning the foundations of brittle failure as the equivalence between the principle of local symmetry and the maximum energy release rate criterion is no longer valid. Many experimental observations have been reported in the literature but anisotropic failure is thus still an open path for fundamental research. The aim of the paper is to propose a phase field model that could reproduce (energetically) non-free anisotropic crack bifurcation within a framework allowing for robust and fast numerical simulations. After the model and its finite element implementation have been detailed, its ability to capture the thought phenomenon is illustrated through several examples.
Highlights
Anisotropy is inherent to crystalline materials due to the symmetry of the atomic lattice
Failure anisotropy is questioning the foundations of brittle failure as the equivalence between the principle of local symmetry and the maximum energy release rate criterion is no longer valid
The proposed model is based on the consideration of several cleavage planes, each of these planes having its own damage variable
Summary
Anisotropy is inherent to crystalline materials (among others) due to the symmetry of the atomic lattice. Even more recently, Li et al (2014) developed a numerical implementation of a phase field model with strong anisotropy including the explicit dependency of fracture energy to the local crack orientation. In their paper, they have been able to reproduce zigzag crack paths which are in qualitative agreement with experimental observations. There is no direct link between the model parameters and the energy cost for crack bending This is an important point as experimental evidences were reported in Takei et al (2013)
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