Development of Smoothed Numerical Methods for Fracture Analyses and Interfacial Toughness Characterization in Thin Film Systems

Abstract

This thesis is to develop new numerical methods for fracture analyses, and to propose a novel approach to characterize the interfacial toughness in thin film systems. Firstly, a stain smoothing technique is introduced to the collapsed quadratic singular elements and the extended finite element method to formulate two novel numerical methods for fracture analyses in thin film systems: (1) the singular smoothed finite element method (sS-FEM), and (2) the smoothed extended finite element method (S-XFEM). Within the strain smoothing, domain integration is transformed into boundary integration, and the stiffness matrix calculation requires only evaluating the shape functions values (and not the derivatives). Therefore, the singular terms of functions are no longer necessary to compute the stiffness matrix, in addition, the need to subdivide elements cut by cracks in the XFEM settings can be eliminated. More importantly, a quasi optimal convergence rate is achieved even without geometrical enrichment or blending correction. Secondly, a new characterization approach is proposed to extract the interfacial toughness in thin film systems using the numerical simulation of wedge indentation experiments. The new approach eliminates the small plastic zone assumption and plane strain condition assumption that are present in de Boer?s equations, and make them more practical for evaluation of the interfacial toughness in thin film systems. Extensive numerical verifications are performed to show the present approach provides an accurate evaluation for the interfacial toughness. The experimental validations are also studied. The research work in this thesis can shed some light on the further development of new numerical methods for fracture analyses, and can also contribute to a better understanding of fracture behaviors in thin film systems.