The elastic stress fields of elliptic and tapered cracks with predefined shapes

The shape of a tapered crack is more alike cracks in brittle materials than an elliptical crack. The deformation and stress fields for a tapered crack are therefore estimated for hydrostatic pressure and tensional stress by applying the method of complex potentials. The stress fields for the tapered and elliptical cracks are quite similar, which suggests that the elliptical crack can be used as a model for the stress fields for cracks in general. However, the tapered crack has a larger tensional stress at the crack tip, which show that fracture propagation occur at lower applied stresses than for the elliptical crack. A tapered shape of fluid filled fractures can account for their discontinuous propagation. The discontinuous fracture propagation is observed in a large scale by volcanic eruptions where the fracture propagation generates seismic activity.