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V. Veselý et alii, Frattura ed Integrità Strutturale, 25 (2013) 69-78; DOI: 10.3221/IGF-ESIS.25.11 71 Coefficients of the terms of the Williams power expansion used/presented in this paper were determined using direct methods which evaluate results gained via FEM computations. Values of first two terms ( K and T -stress) were computed both using the direct method (e.g. [24]) or determined with help of quarter-point crack-tip elements (e.g. [25]). For the latter case, following formulas are used to calculate K and T   (C) (B) (A) (B) (C) I 2 2 2 4 , 4 2 3(1 )(1 ) 2 1 i i i i i v E E K v T u u u l l                        (6) where l is the element length, u and v are displacement components in the x and y directions, respectively. The (A), (B), and (C) superscripts indicate the FE node positions as follows: A – node at the crack tip, B – node at a distance of 1/4 l from the crack tip, and C – node at a distance of l . For the direct method [24] the estimation of the fracture parameters is derived directly from the stress description via eq. (1) (for max. n = 2). Let us note that several alternatives to the methods used in this paper are available in literature, especially for the determination of K (e.g. [26]). Coefficients of even the higher-order terms of the power expansion were calculated (alternatively to the previously- mentioned techniques for the first two ones, however, as the only used technique for the other ones) by using the over- deterministic method (ODM) [15]. ODM, based on the linear least-squares formulation, provides solution of the system of 2 k equations (resulting from eq. (2)), where k represents the number of selected nodes around the crack tip, leading to values of N selected terms of the series. They can be calculated from the knowledge of the values of components u , v of the displacement vector and coordinates r ,  of the selected nodes. Similarly to the above-mentioned techniques, inputs to the ODM were also obtained by FEM computations. Motivation of the determination of the higher-order of terms of the power series dwells in the requirements on the estimation of the crack-tip nonlinear zone extent. They must be taken into account in order to describe the fields in more distant surroundings of the crack tip, especially in the case of the quasi-brittle materials. W EDGE SPLITTING TEST GEOMETRY – DEFINITION OF NUMERICAL STUDY edge splitting test is a convenient and popular configuration for estimation of fracture parameters of silicate- based composites, mainly building materials. It has been introduced in 80ies of the last century [27,28]. For its advantages it is often used as an alternative of standard three-point bending test of notched beams. The test can be performed on specimens of various shapes, however also the test setup, i.e. the boundary conditions, can significantly differ. And that is true both for the boundary conditions related to the load application (see Fig. 1) and the specimen supports (see Figs. 2 and 3). The differences in the load application and supporting are usually neglected, even fracture analyses utilizing functions of geometry corresponding to the compact tension test configuration are commonly published [29,30]. And if the K - calibration curves are computed for the WST geometry and presented in the literature (e.g. [31]), details of supports and load application are not properly taken into account. Particularly, the compressive component of the loading force ( P v in Figs. 2 and 3) is ignored and only one central support is considered (except to [32], with regard to both aspects). Karihaloo and co-workers published the stress and displacement field description using as many as five terms of the Williams series [22,23]. Two variants of supports were modeled, but the compressive component of the applied loading was not considered too. It is worth noticing that if a certain fracture analysis has to be conducted for which the stress/displacement fields in only the very vicinity of the crack tip is required (i.e. the case of brittle fracture with description of the fields via K only), the simplifications mentioned in previous paragraph are possible (to some extent, i.e. when T -stress value is not too low or high). In our work, three variants of supports (one central support, and two supports positioned 1/4 W and 1/8 W from the central plane, see Figs. 2 and 3) and two alternatives of load imposition (via loading platens with bearings placed inside the specimen’s groove – platens I – and platens with bearings axes outside the groove – platens II, see Figs. 1, 3 left and right, respectively) are considered. The influence of the boundary conditions of the WST test was analyzed in several relevant aspects in detail in previous works by the authors [32–34, 12–14] and results were compared with the crack-tip fields descriptions published in literature. Selected parts of the rather thorough study are presented in this paper. The study was first conducted in the W