Point-loaded discs and blocks applicable to tensile testing of brittle materials

Abstract

A method of numerically approximating the solutions of plane-stress or plane-strain elasticity problems with boundary conditions consisting of concentrated forces or distributed loads is presented herein. The effect of each concentrated force (commonly termed a point load) that acts on the boundary is represented by a Flamant solution. Usually, the combined effect of these Flamant solutions indicates the presence of distributed loadings or ‘residual stresses’ on some portions of the boundary that are not consistent with the actual boundary conditions. The negatives of these ‘residual stresses’ are used as stress boundary conditions in a singular integral method of numerical analysis that is applicable to plane elasticity problems involving distributed loadings on the boundaries. Since the method presented herein involves only stress boundary conditions, the solutions are valid for both plane stress and plane strain. The accuracy of this superposition method is demonstrated by consideration of a circular disc or cylinder subjected to diametrically opposed concentrated forces for which accuracy to within 0.2 per cent of the exact solution is obtained. Parametric analyses of rectangular and elliptical compression members subjected to point loads are presented. Results determined herein are found to compare relatively well with those determined in previous numerical and experimental investigations of specific cases. These results make possible the design and analysis of compression members used to evaluate the tensile fracture strength of brittle materials.