Fracture under compression: the direction of initiation
Tóm tắt
The preferential orientation for the initiation of a crack is the one which gives the maximum strain energy reduction for a given crack length. This proposed criterion is a logical extension of the maximum energy release rate criterion. It makes no assumptions on the configuration, the homogeneity, the stress condition on the crack faces, or the material response, consequently it is applicable to the usual engineering cases as well as to cases under compression and/or high confining pressures such as obtain inside the Earth. Numerical results for brittle materials (rocks) agree with laboratory and field data, and show that the criterion is an improvement over the empirical and approximate Coulomb-Mohr criterion which has been used for compressive fracture problems for more than 200 years. They also show that our method can be used in cases where it is not a priori evident whether the fracture will remain closed or will open. The mathematical formulation of the criterion is approached by way of constrained optimization, and the solution is proven to exist uniquely. The numerical implementation is based on a finite element scheme. An iterative method is employed to handle the material and geometric non-linearities.
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