Issue 33

V. Veselý et alii, Frattura ed Integrità Strutturale, 33 (2015) 120-133; DOI: 10.3221/IGF-ESIS.33.16 120 Focussed on characterization of crack tip fields Multi-parameter approximation of stress field in a cracked specimen using purpose-built Java applications V. Veselý, J. Sobek, D. Tesař, P. Frantík, T. Pail Brno University of Technology, Faculty of Civil Engineering, Institute of Structural Mechanics, Brno, Czech Republic vesely.v1@fce.vutbr.cz, sobek.j@fce.vutbr.cz, tesar.d1@study.fce.vutbr.cz, kitnarf@centrum.cz , pail.t@fce.vutbr.cz S. Seitl Academy of Sciences of the Czech Republic, v. v. i., Institute of Physics of Materials, Brno, Czech Republic seitl@ipm.cz A BSTRACT . 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. K EYWORDS . Cracked specimen; Near-crack-tip fields; Williams expansion; Higher order terms; Stress field reconstruction; Finite element analysis, Java application. I NTRODUCTION he concept of fracture process zone (FPZ) has been introduced into analysing fracture behaviour of nonlinearly failing (especially softening) materials already several decades ago [1-3]. Estimation of the size, shape and other relevant properties of the FPZ evolving at the tip of propagating crack in these materials is not commonly utilized within fracture analyses of these materials; however, the situation has changed recently. The FPZ issue is also among the main goals of the presented research. This is motivated by the fact that fracture properties of softening materials exhibit strong size-dependence, know under the term size-effect, linked mainly to the mutual proportions of the internal length of their coarse material structure, the extent of their large FPZ which varies during the crack propagation, and the structural dimensions. Thus, properties of the FPZ are prospected to be utilized, T