Prediction of fracture initiation zones on the surface of three-dimensional structure using the surface curvature

Abstract

Using the well-known formula of Bažant for the prediction of structure nominal strength that depends on the structure characteristic size an expression for the local tensile strength is constructed and used in the maximal tensile stress criterion. This expression takes size effect into account not by using the characteristic size of a specimen but by using the minimal curvature radius of the specimen surface. The parameters of the expression for the local tensile strength depend on the material but do not depend on the geometry and the size of specimen. The distinctive feature of the R-criterion is its independence on the characteristic size of the specimen and therefore its convenience in practical application for 3D problems of complex geometry. It allows to take into account the difference of surface shape and strength among various points. The R-criterion is able to provide the accurate prediction of the static failure initiation of brittle three-dimensional complex components and to identify the location of initiated fractures. The tensile stress criterion enriched by the modified local tensile strength which depends on the minimal curvature radius in the analysed point is examined by the comparison of 2D and 3D numerical and experimental data.