Relationship between Fracture Toughness and Crack Morphology of Brittle Materials

Abstract

A theoretical analysis of crack morphology based on the fractal geometry was made to derive an equation correlating the fractal dimension of crack, D" (the fractal dimension of crack profile in the two dimensional plane, 1<D"<2) with the fracture toughness, K_IC. The fracture toughness, K_IC, can be expressed as a following function of D": lnK_IC=1/2{ln[2ΓE/(1-v²)]-(D"-1)lnr_L}, where Γ is the work done in creating a unit crack surface, E is Young's modulus, v is Poisson's ratio, and r_L is r_min/r_max, the ratio of the lower limit, r_min, to the upper limit, r_max, of the scale length, r, between which the crack exhibits a fractal nature (r_min≤r≤r_max). The relationship between the indentation fracture toughness, and the fractal dimension of crack was then examined on various specimens of oxide, carbide and nitride ceramics and a hard metal.