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.

A description of stress and displacement fields by means of the Williams power series using also higher-order terms is the focus of this paper. Coefficients of this series are determined via the over-deterministic method from the results of conventional finite element (FE) analysis. A study is conducted into the selection of the FE node set whose results are processed in this regression technique. Coefficients up to the twelfth term were determined with high precision. The effect of the position of the FE node set on the accuracy of the values of the higher-order term coefficients is reported.

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The paper deals with an analysis of the stress and displacement fields in a cracked body. The intention of the authors is to determine the sufficient number of terms of the Williams power series for an accurate approximation of the near-crack-tip fields which can be subsequently used e.g. for estimation of the extent of the fracture process zone in quasi-brittle materials. Values of coefficients of these terms are determined via regression from results of numerical simulations; the coefficients are expressed as functions of the relative crack length. The analysis is conducted on a 2D numerical model of the wedge-splitting test on a modified standard cube-shaped specimen used commonly for testing of cementitious composites; ANSYS FE computational system is employed.

Creation of an automatic utility to determine the values of coefficients of higher order terms of Williams power series by usage of over-deterministic method applied to results of finite element analysis is a main goal of this research. The developed procedure based on the support of Java programming language considerably simplifies analyses on optimization of selection of FE nodal results for improvement of accuracy of the near-crack-tip fields’ approximation using Williams series.

A quality of multi-parameter approximation of the stress and displacement fields around a crack tip in a non-brittle material test specimen is studied in the paper. The stress field approximation using Williams power series is intended to be utilized for estimation of the nonlinear zone extent which potentially plays a role within methods for determination of true values of fracture parameters of materials exhibiting nonlinear failure. Considering the fact that in the case of elastic-plastic and especially quasi-brittle materials the size of this zone is substantial in comparison to the specimen dimensions, it is necessary to take a large region around the crack tip into account for this task. An automatic utility created to determine the values of coefficients of the higher order terms of Williams power series by usage of over-deterministic method applied on results of finite element analysis of arbitrary mode I test geometry is one of the tested procedures. The second one provides a backward reconstruction of the crack-tip stress field analytically by means of truncated Williams expansion. The developed procedures are based on the support of Java programming language and considerably simplify analyses of the mechanical fields' description in a farther distance from the crack-tip. The presented research is focused on optimization of selection of FE nodal results for improvement of accuracy of the approximation.

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