Universality and specificity of fractal dimension of fractured surfaces inmaterials

After calculation on the fracture angles under various conditions of specif ic surface energies with different symmetry operations of rotation, the com plicated behavior of dependence of fractal dimension on the structure of cr ystal is shown. It is found that the crack propagates along the weakest cry stal plane no matter what the direction of the maximum stress is if the ani sotropy is sufficiently strong; and then, the fractal dimension of the frac tured surfaces might be determined by the approximate fractal structure alr eady existed in the material. Specificity of the fractal dimension of fract ured surfaces would be easy to appear in this case. Reversely, the crack pr opagates along the direction of the maximum stress no matter what direction of the weakest crystal plane is if the anisotropy is sufficiently weak. Un iversality of the fractal dimension of fractured surfaces would be possible to appear in this case. In many real materials, universality and specifici ty of the materials are associated. The fractal dimension measured may more or less be influenced by the structure of materials and it shows its unive rsality through the specificity of materials.