Fracture toughness and crack morphology in indentation fracture of brittle materials

The relationship between the indentation fracture toughness, K-C, and the fractal dimension of the crack, D, has been examined on the indentation-fractured specimens of SIC and AIN ceramics, a soda-lime glass and a WC-8%Co hard metal. A theoretical analysis of the crack morphology based on a fractal geometry model was then made to correlate the fractal dimension of the crack, D, with the fracture toughness, K-IC, in brittle materials. The fractal dimension of the indentation crack, D, was found to be in the range 1.024-1.145 in brittle materials in this study. The indentation fracture toughness, K-C, increased with increasing fractal dimension, D, of the crack in these materials. According to the present analysis, the fracture toughness, K-IC, can be expressed as the following function of the fractal dimension of the crack, D, such that InKIC = 1/2{In[2 Gamma E/(1 - v(2))] - (D-1)Inr(L)} where Gamma 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) less than or equal to r less than or equal to r(max)). The experimental data (except for WC-8%Co hard metal) obtained in this study and by other investigators have been fitted to the above equation. The factors which affect the prediction of the value of K-IC from the above equation have been discussed.