INFLUENCE OF RESIDUAL SURFACE TENSION ON STRAIGHT CRACK UNDER MODE-I LOADING

Abstract

In this thesis, the influence of residual surface tension on the near-tip elastic field of a straight crack under mode-I loading condition is fully investigated. The surface effect via the Gurtin-Murdoch surface elasticity model without the in-plane modulus is integrated into the classical theory of linear elasticity to capture the nano-scale influence and the size-dependent behavior of the elastic field. The governing equation is formulated in terms of the crack-opening displacement and finally expressed in a form of an integro-differential equation involving a strongly singular kernel. A weighted residual technique together with the integration by parts is utilized to derive the symmetric weak-form equation involving only a weakly singular kernel. Standard Galerkin method is then adopted to construct numerical solutions of the weak-form equation. In the approximation, basis functions constructed locally on linear, quadratic, cubic, and Hermite finite element mesh have been employed. The rate of convergence of numerical solutions is fully explored and it is found that approximations using quadratic, cubic and Hermite shape functions yield the same rate of convergence that is higher than that of the linear case and the gradient of the crack-opening displacement becomes finite at the crack-tip for non-zero residual surface tension. Based on an extensive parametric study, it is indicated that the residual surface tension not only significantly reduces the overall crack-opening displacement and the near-tip stresses but also weakens the crack-tip stress singularity and renders the predicted solutions strongly size-dependent.