Prediction of Fracture Strength of Ceramics with Small Defects Based on R-Curve Method

Since the critical size of defects in ceramics is usually very small, the conventional method of fracture mechanics prediction often becomes inapplicable. In the present study, the fracture strength of silicon nitride with small defects is evaluated on the basis of the R-curve method. The parameters of the R-curve of silicon nitride are determined from the experimental relationship between the fracture strength and the defect size. For penny-shaped cracks, the fracture strength is constant for small defects and the critical stress intensity factor is constant for large defects. The equivalent defect size is an excellent parameter to correlate the fracture strength to the size of elliptical cracks with an aspect ratio between 0.3 and 1. For small voids, the fracture strength is nearly the same as that for a penny-shaped crack. On the other hand, for large voids, the fracture strength approaches a constant value which is equal to that of materials without voids divided by the elastic stress concentration factor. When the tip radius of deep long notches is small, the critical stress intensity factor for fracture is independent of the tip radius. A Monte Carlo simulation of bending fracture of silicon nitride was performed by randomly distributing penny-shaped cracks having random sizes in a specimen by a computer. On the basis of twenty-five runs of fracture simulation, the relationship between the bending strength and the equivalent defect length, and cumulative distribution function of the fracture strength were successfully derived.