CRACK GROWTH SIMULATIONS IN DUCTILE MATERIALS USING XFEM/COUPLED FE-EFGM

Abstract

The quest for perfection has led us to many scientific developments and technological advancements. However, in spite of all scientific developments, the materials possess flaws/defects. External loading may result in either the propagation of pre existing cracks or may initiate new cracks in the structures. This may finally lead to catastrophic failure of components resulting in loss of property and lives. The objective of fracture mechanics as a scientific discipline is to avoid or at least predict failure so that the damaging consequences of catastrophic failure can be avoided. The fracture behavior of natural and man-made structures becomes a serious issue due to the presence of defects. Over the years, a range of analytical, experimental and numerical approaches has been proposed to investigate the behavior of materials in the presence of flaws. Due to the scarcity of analytical solutions and also due to the versatility of the numerical methods in handling complex practical problems, research efforts continue to focus on the existing as well as improved numerical schemes. A new class of numerical methods known as coupled FE-EFGM and XFEM has been developed over the years. Both the methods are attractive complement to the finite element method. In coupled FE-EFGM approach, EFGM is used in the discontinuous region, whereas FEM is utilized in the rest of the domain to exploit the advantages of both the methods. A ramp function is used in the transition region (region between the FE and EFG) to obtain the resultant shape functions. On the other hand, XFEM is a partition of unity enriched finite element method. In both the methods, the presence of cracks, voids/holes and inclusions is represented by introducing additional enrichment functions into the standard displacement approximation. These characteristics enhance the potential of coupled FE-EFGM and XFEM in modeling crack growth problems. This thesis work is focused on the effective implementation of coupled FE-EFGM and XFEM for the elasto-plastic analysis of crack growth problems. The material nonlinearity has been modeled using von-Mises yield criterion along with isotropic strain hardening. An elastic predictor-plastic corrector algorithm is used to solve the elasto- Abstract ii i plastic nonlinear equations. The geometric nonlinearity is modeled by updated Lagrangian approach. The versatility and effectiveness of these methods have been demonstrated by solving various crack growth problems. A comparative study of stable crack growth is performed for homogeneous and bi-material compact tension and triple point bend specimens using XFEM and coupled FE-EFGM. The numerical results obtained by XFEM and coupled FE-EFGM are compared with the experimental results available in the literature. The elasto-plastic fatigue analysis of homogeneous and bi-material CT specimen shows that the plasticity ahead of the crack tip significantly increases the predicted fatigue life due to crack closure phenomenon. The computational time required in case of coupled FE-EFGM is found much higher as compared to XFEM, thus XFEM is used further for the remaining thesis work. Numerical simulation of homogenous and bi-material CT specimen is performed in the presence of multiple defects. These simulations show that the presence of defects significantly diminishes the life of the structure, and the effect of holes is more severe as compared to inclusions. It is observed that the modeling of small size defects leads to tremendous increase in computational time, due to the requirement of very fine mesh. A strain energy based homogenization approach is proposed to evaluate the equivalent properties of the materials in the presence of multiple defects. In this approach, a region of radius equal to half the initial crack length (a/2) around the crack tip (having major influence on the crack) is modeled with defects, and the remaining portion is modeled with equivalent properties obtained through homogenization. This approach improves the computational efficiency without compromising on the accuracy. Finally, a semi homogenized multigrid XFEM (SHM-XFEM) is proposed to further improve the computational efficiency. The region with defects is modeled by a very fine mesh, while the remaining portion is modeled by a coarse mesh with equivalent properties. For the transition region, special elements are used to obtain the consistency in the displacement field at the junction nodes. This proposed approach tremendously reduces the computational time without compromising on the solution accuracy.