Experimental determination and finite element analysis of coefficients of the multi-parameter Williams series expansion in the vicinity of the crack tip in linear elastic materials. Part II

Abstract

In this study coefficients of the multi-parameter Williams power series expansion for the stress field in the vicinity of the central crack in the rectangular plate and in the semi-circular notched disk under bending are obtained by the use of the finite element analysis. In SIMULIA Abaqus, the finite element analysis software, the numerical solutions for these two cracked geometries are found. The rectangular plate with the central crack has the geometry similar to the geometry used in the digital photoelasticity. Numerical simulations of the same cracked specimen as in the experimental photoelasticity method are performed. The numerical solutions obtained are utilized for the determination of the coefficients of the Williams series expansion. The higher-order coefficients are extracted from the finite element method calculations implemented in Simulia Abaqus software package and the outcomes are compared to experimental values. Determination of the coefficients of the terms of this series is performed using the least squares-based regression technique known as the over-deterministic method, for which stresses data obtained numerically in SIMULIA Abaqus software are taken as inputs. The plate with a small central crack has been considered either. This kind of the cracked specimen has been utilized for comparison of coefficients of the Williams series expansion obtained from the finite element analysis with the coefficients known from the theoretical solution based on the complex variable theory in plane elasticity. It is shown that the coefficients of the Williams series expansion match with good accuracy. The higher-order terms in the Williams series expansion for the semi-circular notch disk are found.