Abstract

In this paper the author has analysed a simple crack propagation lattice model which incorporates the bond-breaking probability Pi alpha ( delta i- delta c)eta , where delta i is the ith bond elongation and delta c is the bond-breaking threshold below which the bond is unbroken. A two-dimensional triangular lattice has been employed with nearest-neighbour central forces. The cases of a uniform small dilation strain and of a small shear in the horizontal direction with different exponents eta have been considered. He has found that the crack patterns during the breaking process are fractal structures with the fractal dimensions depending on the bond-breaking probability exponent eta in a limited large lattice.

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