A Phase Field Approach to Two-Dimensional Quasicrystals with Mixed Mode Cracks

Quasicrystals (QCs) are representatives of a novel kind of material exhibiting a large number of remarkable specific properties. However, QCs are usually brittle, and crack propagation inevitably occurs in such materials. Therefore, it is of great significance to study the crack growth behaviors in QCs. In this work, the crack propagation of two-dimensional (2D) decagonal QCs is investigated by a fracture phase field method. In this method, a phase field variable is introduced to evaluate the damage of QCs near the crack. Thus, the crack topology is described by the phase field variable and its gradient. In this manner, it is unnecessary to track the crack tip, and therefore remeshing is avoided during the crack propagation. In the numerical examples, the crack propagation paths of 2D QCs are simulated by the proposed method, and the effects of the phason field on the crack growth behaviors of QCs are studied in detail. Furthermore, the interaction of the double cracks in QCs is also discussed.

Automated summary

In this work, the crack propagation of 2D decagonal QCs is studied using a fracture phase field method. The damage of QCs near the crack is evaluated using a phase field variable, and the crack topology is described by this variable and its gradient. Numerical examples simulate the crack propagation paths of 2D QCs and investigate the effects of the phason field on the crack growth behaviors. The interaction of double cracks in QCs is also discussed.