NUMERICAL SIMULATION OF 2-D FRACTURE MECHANICS PROBLEMS USING XFEM

Abstract

In the present work, the fatigue crack growth • life of homogeneous materials containing multiple discontinuities (holes, minor cracks and inclusions) is evaluated by extended finite element method (XFEIkI) under cyclic loading condition. The multiple discontinuities (holes, inclusions and cracks) of arbitrary size are randomly located in the material. The values of stress intensity factors (SIFs) are extracted from the XFEM solution by domain based interaction integral approach. Standard Paris fatigue crack growth law is used for the life estimation of various model problems. The effect of the minor cracks voids and inclusions on the fatigue life of the material is discussed in detail. XFEM was found to be particularly appropriate to solve these kinds of fatigue crack propagation problems. The elasto-plastic crack simulations are performed using elasto plastic enrichment functions. Ramberg-Osgood material model has been used to model material nonlinearity. The nonlinear constitutive equations are solved by two schemes: piecewise linear and Newton-Raphson iterative schemes. J-integral has been calculated for different values of Ramberg-Osgood parameters (n, a) using elasto-plastic enrichment functions. The results obtained by XFEM are compared with meshfree simulations for different values of Ramberg-Osgood parameters (n, a) . Large deformation problems involving geometric nonlinearities are formulated and solved by XFEM. To illustrate the accuracy and versatility of the XFEM in modelling large deformations, two numerical problems e.g. free die pressing with a horizontal material interface and free-die pressing with multiple material interfaces are solved by Updated Lagrangian formulation. The results obtained by XFEM are compared with results available in literature.