A 3D Phase-Field Approach to Simulating the Brittle Fracture of Single Crystal Silicon

Abstract

Single crystal silicon (SCS) is widely used in the design of semiconductors. In order to better understand and predict its fracture behavior, a 3D phase-field approach is proposed to simulate its brittle fracture. A modified phase-field model is proposed by incorporating the anisotropic fracture toughness of SCS into its formulation. The critical energy release rate is determined by finding the most probable cleavage direction (i.e., the direction of the maximum tensile principal strain component of the local strain tensor). An iso-parametric monolithic finite element algorithm is then developed using four-node tetrahedral elements and eight-node hexahedral elements to predict crack initiation and crack growth direction in an SCS brick specimen under uniaxial extension. The result agrees well with the analytical solution. In addition, brittle fracture of an SCS tapered double cantilever beam is simulated. Analysis result agrees well with the experiment, such as compliance versus crack length and the crack growth direction.