Abstract: We have studied numerically a simple crack growth model in a two-dimensional triangular lattice of bonds and nodes which incorporates the sudece of a growing crack bond-breaking probability Pi~ exp{(-Vi+Ei)φ(T)}, where Ei is elastic eneny stored in the i-th bond. Different energy temperature factors φ(T) are employed during crack formation and propagation process with a uniform dilation strain case and a shear case and with periodic boundary condition in the horizontal direction. Our results show that the patterns of the cracks generated are fractal structure and the effective fractal dimensionalities decrease with the increase of the temperature factor φ(T)(the absolute temperature T decreasing). In the paper we also discuss the relation between the effective fractal dimension Deff (the radius Rg Of gyration) and the fractal dimensions D (the radius R of circular), and also give their modification values Ω about two kinds of methods in the lattice model