Stress intensity factors for a centrally cracked Brazilian disk under non-uniformly distributed pressure

Abstract

To simulate the real distribution of pressure on the specimen in the Brazilian test, non-uniform distribution is assumed to be the form of pressure distribution on the disk. The analytic solutions of the stress field for an uncracked Brazilian disk under several typical non-uniformly distributed pressures are obtained by the power series expansion method and mathematical method. Then the analytic solutions of the mode I and mode II stress intensity factors for a centrally cracked Brazilian disk under the same pressures are obtained by the weight function method. The results show that the influence of distribution form on stress intensity factors cannot be ignored for the case of large relative crack length and load distribution angle. The applicable ranges of the formulae to calculate stress intensity factors under concentrated force, uniformly and non-uniformly distributed pressure are given according to the analysis results. In addition, the loading conditions for pure mode I and II fracture are discussed when a disk with a central crack is subjected to non-uniformly distributed pressure.