Issue 49

E. Breitbarth et alii, Frattura ed Integrità Strutturale, 49 (2019) 12-25; DOI: 10.3221/IGF-ESIS.49.02 17 subdomains. But this contour leads to discontinuity in the corners of C L and C R in the derivative functions shown in Fig. 4 (c) and (d). Due to the rectangular shape of the domain these discontinuities are unavoidable. This shape was preferred instead of a circular shape as it is more flexible and much more space of the image section could be used. Furthermore, the q-function should not significantly influence the results of the J or interaction integral. R 2 out  2 i out,R i C out in out,R  in,R 2 2 2 h y b x q h h b b                         L 2 out  2 i out,L i C out in out,L  in,L 2 2 2 h y b x q h h b b                         out i B out in 2 2 2 h y q h h    R out,R i A out,R in,R b x q b b    L out,L i A out,L in,L b x q b b    (7) Finally, all values required for solving the J and interaction integral are available (Fig. 1 ⑬ ). As mentioned before, for the computation of the interaction integral an auxiliary field is needed (Fig. 1 ⑥ , ⑫ ), as given in the next part (Eq. 8). Auxiliary field As mentioned above, the computation of the interaction integral requires an auxiliary field. All values with the superscript (2) correspond to this field; please see Eqns. (3) and (6). For the determination of K I and K II the first term of the Williams series expansion is utilized. Generally, the Williams field describes the stress field in the vicinity of the crack tip under linear elastic conditions. Here, K I and K II represent the coefficients of the first term. The corresponding stresses and displacements are summarized in Eqn. 8 [26] [26]. The elastic strains can be calculated from the stresses using Hooke’s law (see Eqn. 1).                       2 I II 11 11 11 2 2 2 I II I II 22 22 22 I II 2 12 12 12 2  2  f f K K f f r r f f                                                                  2 I II 2 2 1 1 1 I II I II 2 2 2 2 2 2 2 2 g g u K K r r g g u                                   (8)