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V. Veselý et alii, Frattura ed Integrità Strutturale, 25 (2013) 69-78; DOI: 10.3221/IGF-ESIS.25.11 70 the paper; the accuracy of the approximation is investigated. Some examples of results of the verification analyses are presented in conclusion. M ULTI - PARAMETER DESCRIPTION OF THE STRESS AND DISPLACEMENT FIELDS IN A CRACKED BODY Multi-parameter fracture mechanics [17–19] is based on the analytical description of the stress and deformation fields in the body with crack by means of Williams expansion [16]. This infinite power series for a homogeneous elastic isotropic body can be expressed for the stress tensor {  } and deformation vector { u } as 1 2 1 2 ( 1) cos 1 1 cos 3 2 2 2 2 2 ( 1) cos 1 1 cos 3 2 2 2 2 2 ( 1) sin 1 1 sin 3 2 2 2 2 n x n n y n n xy n n n n n n n n n n r A n n n n                                                                                                                                         (1)     /2 1 1 cos cos 2 2 2 2 2 2 1 sin sin 2 2 2 2 2 n n n n n n n n n u r A v n n n n                                                                  (2) respectively, where r and  are polar coordinates centered at the crack tip (considering the direction of the crack propagation in positive x -axis),  is a shear modulus, E and  are Young’s modulus and Poisson’s ratio; n represents index of term of the power expansion and  is Kolosov’s constant (depends on plane stress or plane strain state). Coefficients A n are functions of relative crack length  . They can be with convenience expressed as dimensionless functions (with regard to the loading) in various ways. We alternatively employ the two most frequently used ones in this paper which are adopted from [20,21] and [22,23], and they are expressed here only for the parameters presented later in the paper. With respect to the mentioned references they can be written as     1 I 1 0 0 2 ( ) A K B K K       and         2 2 I I 4 ( ) A a T a B K K          (3) and   2 2 ( ) n n n A g W      for 1, 3, 4 , n N   and   2 2 4 ( ) A g t      (4) respectively. In these formulas,  is nominal stress in the central plane of the specimen caused by (usually only the splitting component P sp of) the applied load (i.e.  = P sp / BW ), K 0 is the normalized stress intensity factor (i.e. 0 sp K P B W  ) , K I is the stress intensity factor, T is T -stress, a is the crack length, W and B is the specimen’s width and breadth, respectively. The crack length a is defined as a distance from the point of the splitting force application to the crack tip, i.e. a = c + d n – h in the case of the WST, see Fig. 3. Consequently, the relative crack length  is defined as the ratio of the crack length a and the effective specimen width n ef ( )       c d h a W W h (5)