Fracture analysis of single edge notched specimen using phase field approach

Abstract

For the damage tolerant design of cracked structural components, two important parameters namely, residual strength and remaining life are very important. To evaluate these, a reliable fracture parameter such as stress intensity factor (SIF) is to be determined. Phase field (PF) based finite element formulation for a brittle fracture to determine crack propagation trajectory is presented in this paper. PF methodologies have been formulated by coupling partial differential equations (PDEs) after minimizing the total potential energy, which includes elastic strain energy and fracture energy, with respect to the displacement field and PF variable. Solutions of these PDEs for PF variable resulted in identifying crack path geometry, while PDEs displacement field obtained near the crack field is used to determine SIF. In the present study, extending PF formulation to fracture analysis of a structural component is first of its kind. To simulate PF phenomena, a four noded 2-D bilinear quadrilateral element with three degrees of freedom (DOF) at each node (two translations and one for phase field) has been developed to analyze single edge notched (SEN) specimen under tensile and shear loading. By combining the displacement results of PF method with displacement extrapolation technique, SIF has been determined for various crack lengths representing crack propagation in SEN specimens. It is then compared with the analytical SIF solution available in Handbook, and also with the contour integral method SIF results. It is found that the SIF obtained by PF method is in good agreement (±10%) with the other solutions.