13th International Conference on Fracture June 16-21, 2013, Beijing, China J(i) k ≤Gc (20b) dφ≤dφmax (20c) Developing a separation procedure to determineJ(i) k based on Eqs. (19), this method has to satisfy the conditions according to Eqs. (20). A numerical validation is achieved by calculating the Jk-integral along small contours around the crack tip, see Fig. 6(b). The loading quantities calculated by small contours Γi must be equal to the values that are calculated by the separation procedure. Here it must be taken into account that numerical errors dominate, if Γi is chosen too small, whereas large contours must not intersect other crack faces or boundaries. In Fig. 7(b) results of a simulation with two cracks are presented. The plate specimen is exposed to a uniform load P0 =100MPa and exhibits two nonsymmetric incipient cracks of the lengtha1 =a2 =5mm. All geometric dimensions are shown in Fig. 7(a). A crack growth simulation with fatigue crack growth rates assumed to be constant and equal for both cracks, leads to the crack paths as shown in Fig. 7(b). a1 a2 H=100mm h1 =50mm h2 =60mm W=70mm P0 (a) P0 (b) Figure 7. (a) Geometric dimensions of plate specimen exhibiting two non-symmetric incipient cracks. (b) Crack paths resulting from a crack growth simulation exposing the specimen to a uniformloadP0 =100MPa. 5.Closure Introducing path-independent integrals Jk and Mk, the necessity of the calculation of crack face integrals is outlined. Considering interfaces, internal boundaries or crack surfaces, it is beneficial to apply large contours including crack face integrals for the calculation of Jk or Mk. To achieve pathindependence for the Mk-integral considering curved crack faces, an integration along the fictitious crack faces of the corresponding auxiliary fields is nessecary. When calculating the stress intensity factors or the energy release rate from path independent integrals, it is inevitable to calculate these integrals accurately. The challenging calculation of the crack face integrals is explained and two new -9-
RkJQdWJsaXNoZXIy MjM0NDE=