Application of phase field approach under 2D and 3D simulation for ductile fracture analysis

Abstract

Phase Field (PF) theory is based on the variational principle and emerges as an efficient mathematical tool for numerical simulation of fracture behavior. The crack initiation and propagation solution within a unified mathematical model presents an added benefit to PF theory. PF formulation introduces two additional parameters: (1) phase field variable (ø) that discriminates the cracked and uncracked surface and (2) length scale parameter (L) converting the sharp crack into a diffusive crack. This paper investigates a comparison study of 2D and 3D Finite Element (FE) anaysis results using PF concept w.r.t ductile fracture. The mathematical formulation for the phase field method considering plasticity is carried out using AT1 and AT2 model. Numerical FE modelling is performed using ABAQUS software by considering quadrilateral element for 2D and hexahedral element for 3D simulations. Three standard benchmark examples were discussed in detail, and numerically predicted load-displacement results were compared with the results available in the literature. Further, the effect of L on crack behavior and loading capacity of the specimen is studied. The primary observation from the study states that an increase in the value of L, decreases the load carrying capacity and plastic dissipation of the material.