Multi‐parameter crack tip stress state description for evaluation of nonlinear zone width in silicate composite specimens in component splitting/bending test geometry

Abstract

AbstractThis paper is aimed at the approximation of the stress and displacement fields both in the vicinity and also at a larger distance from the crack tip in test specimens utilised for the determination of the fracture characteristics of quasi‐brittle materials. A novel geometry is considered, which, with changes in the specimen's shape proportions, offers a wide variety of crack tip constraint levels and consequently also a broad range of extents/shapes of the nonlinear zone evolving around the crack tip. The combination of (four‐point) bending and wedge splitting tests of notched prismatic specimens is proposed and numerically investigated. Several variants of boundary conditions are modelled. The stress intensity factor K, the T‐stress and the coefficients of even higher‐order terms of the Williams series are determined and subsequently utilised for analytical approximations of the stress field. The agreement between the analytical and numerical solution depending on the distance from the crack tip and the number of terms of the series, and taking into account the analytical expression, is discussed. The presented approach is expected to be a suitable technique employed as part of a procedure being developed for the estimation of the fracture process zone extent in silicate composite materials. Such materials are characterised by their quasi‐brittle fracture response, which is caused by the softening of the material in the nonlinear zone. It is shown that changes in specimen proportions and/or the positions of supports slightly influence the crack tip constraint level resulting in possible differences in the width of the nonlinear zone.