No abstract

This 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.

For wedge splitting test specimens, the stress and displacement fields both in the vicinity and also in larger distance from the crack tip are investigated by means of numerical methods. Several variants of boundary conditions were modeled. The stress intensity factor K, T-stress and even higher-order terms of William series were determined and subsequently utilized for analytical approximation of the stress field. A good fit between the analytical and numerical solution in dependence on the distance from the crack tip was shown, compared and discussed. Presented approach is considered as suitable for estimation of the fracture process zone extent in silicate composite materials.

No abstract

In this work, the crack tip stress field is investigated in two different configurations loaded in mode I as well as in mode I + II. The detailed two‐dimensional solution includes a conventional finite elements analysis that is compared to results obtained analytically from what is referred to as Williams expansion. The influence of consideration of various numbers of terms of the series expansion on the stress distribution is discussed, and the significance of the multi‐parameter fracture mechanics approach is emphasized for some engineering applications, for example, failure of quasi‐brittle materials and estimation of plastic zone extent.