Issue 35

E. Giner et alii, Frattura ed Integrità Strutturale, 35 (2016) 285-294; DOI: 10.3221/IGF-ESIS.35.33 292 predicted angle is 90º. In case 15 the same loads are considered, but the Young’s modulus of the indenter is changed to steel. The nonproportionality of the behaviour is more noticeable and the predicted angle is 78º. Fig. 9 shows cases 16 and 22 ( E indenter =20000 MPa and E indenter =1000000 MPa, respectively) with a non-negligible normal load on the indenter. It is verified that the larger the material stiffness of the indenter, the larger the deflection (84ºand 77º, respectively). -100 -80 -60 -40 -20 0 20 40 60 80 100 -250 -200 -150 -100 -50 0 50 100 150 200 250  (º) [MPa] 12345678  12 max  12 min  12 -100 -80 -60 -40 -20 0 20 40 60 80 100 -250 -200 -150 -100 -50 0 50 100 150 200 250  (º) [MPa] 12345678  12 max  12 min  12 Figure 9 : Application of the min(  ) criterion for cases 16 (left) and 22 (right), leading to predicted angles of 84ºand 77º, respectively. The reason governing crack deflection due to the material stiffness can be explained as follows. The indenter acts as a contacting solid through which the force lines escape and deviate, just due to its stiffness and geometry, since a stiff solid tends to carry a higher load than a compliant solid (assuming a parallel configuration). This can be visualized by the directions followed by the maximum principal stresses shown in Fig. 10 for case 15. It can be seen that the principal directions (that can be assimilated to local force lines) tend to escape to the indenter just behind the crack. Therefore, it is expected a deflection angle approximately normal to the directions of the force lines in this region. This angle has been correctly estimated by minimum shear stress range criterion. Note also that the amount of deflection becomes saturated, despite a high increase of E indenter , due to the geometric configuration of the model that does not allow further deviation of the force lines. Figure 10 : Maximum principal stress directions for case 15. Crack propagation using X-FEM In this section, the extended finite element method [10] is used to model crack propagation. The great advantage of the X- FEM method is that the crack faces do not need to conform to the element sides of a mesh. Therefore, a single mesh can be used for virtually any arbitrary crack intersecting the mesh. This avoids remeshing and it becomes especially useful