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V. Veselý et alii, Frattura ed Integrità Strutturale, 25 (2013) 69-78 ; DOI: 10.3221/IGF-ESIS.25.11 76 displays distributions of selected stress components (in this case e.g.  x ,  1 ) over the specimen (symmetrical half) taking into account various ranges of terms of the Williams series (whose coefficients were determined via methods mentioned above). The fields correspond to load P sp = 1 kN. Different relative crack lengths were chosen for each case. It is clearly visible that if the knowledge of the stress field is requested even in larger distance of the crack tip, the approximation of the field by higher number of terms of the series is essential. The isolines in the second row of Fig. 7 may represent a nonlinear (plastic) zone extent provided that Rankine failure criterion was applied. If the strength limit of the material were 2 (1 and 0.5) MPa, 4 (around 7 and more than 12, respectively) terms would be necessary for the accurate enough description of the nonlinear zone. N = 1 N = 2 N = 4 N = 7 N = 12 FEM solution  = 0.5, σ x [Pa]  = 0.85, σ 1 [Pa] Figure 7 : Comparison of stress fields (  x ,  1 ) in WST specimen reconstructed by means of Williams power expansion using various ranges of terms of the series (from left 1, 2, 4, 7, and 12, respectively) with the numerical solution (right). The crack tip region is magnified in the second row (the axes scale is kept the same as in the first row). C ONCLUSIONS nalysis of the stress and displacement fields near a crack tip in a WST specimen is presented. For this purpose, multi-parameter fracture mechanics was applied. Influence of the boundary conditions on the stress intensity factor and the T -stress (representing the first two terms of Williams expansion) was investigated and several resulting conclusions discussed. Moreover, even the higher-order terms of the series (up to order of 12) were calculated by means of the over-deterministic method. Subsequently, various ranges of them were used for reconstruction of the stress field around the crack tip and compared with stress distribution obtained by means of FEM. The results clearly show that especially for long cracks and/or in larger distances from the crack tip the accurate approximation of the stress field requires using more terms of the Williams expansion than it is usual within classical fracture mechanical approaches. A CKNOWLEDGEMENTS he work has been supported by the Czech Science Foundation, the project No. 104/11/0833, and Brno University of Technology, Specific Research program, project No. FAST-S-12-21/1653. A T