A 2m fracture in an infinite rock mass is under pure shear stress of 50MPa. The elastic properties of the rock mass are the same as in Example 1.
According to Rao (1999), a fracture in pure shear may propagate in mode I or mode II depending on the ratio of the fracture toughness of mode I and mode II (KIc/KIIc). Only when KIc/KIIc>1.15, a mode II fracture propagation can occur. The FRACOD2D code is used in this example to compare with the theoretical results.
30 elements are used along the fracture. The critical mode II strain energy release rate (GIIc) is taken as 1000 J/m2. The critical mode I strain energy release rate (GIc) is varied to obtain the critical ratio (GIc/GIIc) at which the fracture propagation starts to change mode. It was found that GIc = 1289 J/m2 is the critical value for the fracture propagation to change mode. When GIc < 1289 J/m2, the fracture propagates in mode I in the direction of about 70° from the original fracture plane; when GIc > 1289 J/m2, the fracture starts to propagate in mode II in its own plane, see Figures.
Use the relation between the critical stress energy release rate and the fracture toughness
.
The critical toughness ratio for mode II fracture propagation obtained numerically by using the FRACOD2D code is 1.135, very close to the analytical solution of 1.15 reported by Rao (1999).
Using different number of elements along the fracture, the comparison between the FRACOD2D results and the theoretical results is shown in the figure below.
