Studies in the use of the element-free galerkin method for linear elastic fracture mechanics
thesisposted on 02.03.2017 by Muthu, Nelson Muthu, Nelson Madalai Muthu
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The main aim of the thesis is to expand the scope of the element-free Galerkin (EFG) method in its application to linear elastic fracture mechanics (LEFM). Specific objectives include an accurate assessment of the stress intensity factors (SIFs) for variety of loading and material combinations, and the study of crack propagation in isotropic and composite materials. The present study also deals with modelling interacting cracks that are frequently encountered in fracture of brittle materials. Two new techniques within the framework of the EFG method have been developed based on the crack closure integral (CCI) to compute the SIFs: CCI with a local smoothing (CCI-LS) technique and modified crack closure integral (MCCI) technique. The first scheme involves extraction of displacement and stress at few locations near a crack tip, and construction of a smooth variation of these parameters in conformity with the crack tip solutions using a suitable smoothing technique. The CCI-LS technique has also been applied to extract the SIFs in FGMs. The second technique is based on computing crack closure forces at some nodes ahead of a crack tip and multiplying with corresponding crack opening displacements (CODs) to determine the potential energy release rate and the SIFs. A novel approach to extract the crack closure forces accurately within the framework of EFG method is proposed. In addition to these techniques, classical SIF extraction methods like the displacement and stress methods have also been used to extract the SIFs. The extracted SIFs are compared with those obtained using the popular M-integral technique to highlight the differences. The dependence of the computed SIFs accuracy, using both the techniques, on nodal density, local refinement at the crack tip, domain of influence and order of Gauss integration have been examined. Varieties of problems including crack face loading and thermal loading have been solved to demonstrate the simplicity and the efficiency of these techniques. A new variant of the EFG method has been proposed to address the problem of crack propagation through non-homogenous materials. This method eliminates the difficulty associated with the selection of the enrichment functions that are dependent on material properties and location of the crack tip. The SIFs and CODs obtained using this method, for a range of material combinations and interfaces, are compared with published results. The criterion suitable for study of crack propagation has also been investigated. There are a number of criteria to study crack propagation through brittle materials. Noting the computational advantages offered by the maximum tangential principal stress (MTPS) criterion, it has been selected for the study of the crack propagation in bi-material and composite materials. To facilitate its application, a scheme has been given first to obtain the T-stress and then apply it to bi-materials. Further, the criterion has been amended by bringing in the differences in crack growth resistances. This criterion has been applied to particle-reinforced composites to carry out study at the microscale. Effects of inter particle distance, crack growth resistances of matrix and particle, and location of the initial crack with respect to the particle on the crack path has been presented. To model multiple interacting cracks, an EFG scheme based on multiple crack weight (MCW) function coupled with level set method has been proposed. Case studies involving crack-crack, crack-microcrack, interface crack-microcrack interaction, and crack propagation have been presented to demonstrate the efficiency of the scheme. This too has been applied to show its usefulness for problems involving knee and crack tip singularities during step-by-strep propagation of a starter crack. Thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy of the Indian Institute of Technology Bombay, India and Monash University, Australia.