THREE DIMENSIONAL CRACKS SIMULATION USING EFGM

Abstract

Flaws are inevitable in the structures or components in the form of inclusions, blow holes, cracks, etc. Among these, cracks play major role in the failure hence the analysis of the components/structures in the presence of cracks becomes crucial to predict the life and failure of the components/structures. The aim of this dissertation is to develop a simple and accurate methodology for the analysis of crack components. Therefore, in this work, a new meshfree element free Galerkin method (EFGM) algorithm is presented for the simulation of 3-D cracks under the assumption of linear elastic fracture mechanics. For the modeling of different cracks in EFGM, a partition of unity extrinsic enrichment has been used. This enrichment approach uses a Heavyside (jump) function accounting for the displacement discontinuity along the crack faces, and Westergaard's enrichment near the crack tip/front to capture crack tip singularity. Once the primary solution is obtained, different fracture parameters are evaluated as post processing. In the context of linear elastic fracture mechanics, usually the stress intensity factors (SIFs) are calculated while in case of elasto-plastic fracture mechanics; energy norms have been found out. In EFGM, the domain of interest is discretized with the nodes only, and there is no need of elemental connectivity over these nodes. Hence, EFGM eliminates the cumbersome efforts involved in meshing the complex domains, and remeshing needed in cracks growth problems. One of the major issues in the implementation of EFGM is its large computational time; hence EFGM is coupled with finite element method (FEM) which was another milestone of this dissertation work. In coupled FE-EFG method, meshfree method is used in the crack domain while remaining domain is discretized with the finite elements. EFGM results in a better convergence with good accuracy in the discontinuous domain where FEM has got limitations like conformal meshing and remeshing. This coupled FE-EFG method possesses good accuracy and convergence.