Numerical Estimation of a Mode III Fracture Mechanics Parameter for a Three-Dimensional V-Notch on a Steel Bold

Abstract

In this work a couple of three-dimensional problems in the domain of linear elastic Fracture Mechanics are examined. These are problems of solid bodies (they could be steel bolds or rivets) with a surface crack singularity (V-notch). They are reduced to Laplace equation problems by considering a Lamé potential. The boundary singularity is numerically treated as per the singular function boundary integral method (SFBIM), which in the literature is known as one of the so-called Trefftz methods. Thus, the general solution of the governing equation, in the vicinity of the surface crack, is expressed as an asymptotic expansion, the coefficients of which are approximated by polynomials. The remaining numerical steps are followed according to this method with which very fast convergence and very high accuracy are observed. In fact, the CPU time and the numerical error recorded with this numerical technique are significantly smaller than those achieved with the finite element method (FEM) which was also used to solve the same problems. The calculated value of Mode III Fracture Mechanics parameter (FMP) indicates that there is no danger of crack propagation. Thus, the extension of the method to this category of problems is considered as a novel application of this algorithm in Fracture Mechanics. Keywords: Mode III Fracture Mechanics parameter, crack singularity, governing equation, singular