numero25

V. Veselý et alii, Frattura ed Integrità Strutturale, 25 (2013) 69-78; DOI: 10.3221/IGF-ESIS.25.11 69 Special Issue: Characterization of Crack Tip Stress Field Multi-parameter crack tip stress state description for estimation of fracture process zone extent in silicate composite WST specimens Václav Veselý, Jakub Sobek, Lucie Šestáková, Petr Frantík Brno University of Technology, Faculty of Civil Engineering, Institute of Structural Mechanics, Brno, Czech Republic Stanislav Seitl Academy of Sciences of the Czech Republic, v. v. i., Institute of Physics of Materials, Brno, Czech Republic A BSTRACT . 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. K EYWORDS . Near-crack tip fields; Williams series; Higher-order terms; Stress field approximation; Wedge splitting test; Fracture process zone. I NTRODUCTION he research of the author’s collective is focused on estimation of the size, shape and other relevant properties of the zone with nonlinear material behaviour evolving at the tip of a propagating crack in composite materials with disordered internal structure, particularly those with quasi-brittle nature which exhibit strain softening. Characteristics of the zone, in the case of the materials in question referred to as the fracture process zone (FPZ), are intended to be utilized within methods for evaluation of fracture mechanical parameters in order to diminish the effects of the test specimen’s size, geometry and free boundaries on their values, mainly the fracture energy, determined from records of tests on laboratory-sized specimens. This topic is intensively researched in last decades [1–6]. A determination procedure taking into account the mentioned effects is currently under development by the authors [7,8] and outputs of individual parts of the procedure are being tested, verified and validated at present, both from the perspective of the FPZ extent estimation [9–11] and also the crack tip stress state description [12–14]. This paper is particularly focused on investigation of differences in crack tip stress state caused by changes in the test geometry (the specimen’s shape and boundary conditions) resulting in differences in the shape and size of the FPZ. Variants of what is referred to as the wedge splitting test (WST) geometry are taking into account for this study. A precise description of the stress state in the cracked body is necessary for the procedure of the FPZ extent estimation. For that purpose, multi-parameter fracture mechanics is employed as the size proportions of the FPZ in relation to the whole specimen is much larger in the case of the studied quasi-brittle composites than that of e.g. plastic zone in metals. Therefore, the FPZ extent analysis is preceded by a detailed finite element method (FEM) analysis of the stress and displacement fields in the test specimens serving as input to the over-deterministic method [15] for evaluation of higher- order terms of the Williams power series [16] via which the fields are approximated. Main attention is given to this issue in T