NUMERICAL SIMULATION OF CRACK GROWTH PROBLEMS USING EFGM/XFEM

Abstract

All engineering materials have flaws/defects inside it. When subjected to a mechanical load, these defects grow and eventually the structures/components fail. The situation becomes more critical when cyclic load and/or adverse environmental conditions prevail. The objective of fracture mechanics as a scientific discipline is to avoid or at least predict failure so that damaging consequences of catastrophic failure can be avoided. Ensuring the safety and reliability of engineering component/structure is of great concern to the engineering community. It is more so when we deal with the nuclear industry. The failure of structures/components under these conditions may be quite dangerous and fatal to the society. The fracture behavior of man-made structures becomes a serious issue due to the presence of defects (inclusions, voids and cracks). External loading of these structures may cause either the initiation of new cracks or propagation of an existing crack. Over the years, a range of analytical, experimental and computational approaches has been developed to investigate the behavior of the material in the presence of flaws. The investigation of crack growth in a structure by analytical methods is practically impossible. Experimental evaluation is time consuming and resource intensive. The drawbacks linked with the analytical methods and experimental studies have encouraged researchers to use numerical techniques for the analysis of structures in the presence of flaws. Research work continues to focus on handling such problems with the existing as well as improved numerical schemes. A new class of numerical methods known as EFGM and XFEM has been developed over the years. Both the methods are interesting complement to the traditional finite element method. The advantages of EFGM include the requirement of only the nodal data for geometry description, smooth shape functions for higher order approximations, various choices for enrichment such as weight function, basis function and approximation function, and simple integration schemes. On the other hand, XFEM is a partition of unity enriched finite element method. A standard FEM mesh is created Abstract iii without accounting for the geometric discontinuity. The presence of cracks, voids or inhomogeneities is represented independently in the mesh by enriching the standard displacement approximation with additional functions. These characteristics enhanced the potential of EFGM and XFEM in modeling crack growth problems. This thesis work is focused on the effective implementation of EFGM and XFEM for analyzing a variety of fracture mechanics problem under different types of loading. The versatility and the effectiveness of these methods have been demonstrated through the solution of various problems. A comparison of various crack modeling techniques has been carried out to establish the advantage of PU enriched EFGM and XFEM. Due to its precision, simplicity and convergence, these are exploited to accomplish the present research work. Numerical simulations of 2-D cracks in homogenous material under different loadings have been performed using EFGM and XFEM. The results are found to be in good agreement with the FEM and other reference solutions. The crack paths obtained by EFGM and XFEM are also compared with each other. The interaction effect of multiple discontinuities shows that the presence of holes have the most severe effect and may significantly alter the crack growth path. Two-dimensional interfacial crack in bi-materials shows that an increase in the mismatch ratio (moduli ratio) does not have a significant effect on the stress intensity factor. The effect of minor crack/hole/inclusion on interfacial crack shows that the effect of the minor crack is the least severe among all. Numerical simulation of part though crack in pipe/pipe bend have been analyzed using XFEM and EFGM, and the results are compared with FEM. A wide range of geometric parameters like bend radius ratio, cross sectional ratio, relative crack depth and crack angle have a major effect on the SIFs of pipe/pipe bend. A number of cases are studied for an axial and circumferential part-through crack in pipe/pipe-bend under internal pressure, axial pull and bending moment. The values of SIFs are evaluated on entire crack front to determine crack growth path. The results obtained by EFGM and XFEM are found to be in good agreement with FEM solutions.