Approximate theoretical solutions to the problem of an elastic square with rigid indenters

Abstract

A theoretical analysis is attempted of the `indenter' method of measuring the tensile strength of brittle materials. In this method a slab of the material, square in shape and of uniform thickness, is squeezed on opposite edges by a pair of symmetrically placed, rigid indenters, until a tensile crack develops along the axis of the indenters. Four approximate solutions for elastic stresses in the square are obtained and compared with a photoelastic analysis which gave tensile stress at the centre as a function of the ratio of indenter width to side of square. One solution is in good agreement with experiment. The inadequacy of the other three shows how careful it is necessary to be when approximating to boundary conditions, a consideration that applies equally to experiments with models.