Computer-Simulated Fracture Experiments and Strength Distribution for Brittle Materials

Abstract

As a part of the study to establish a suitable method for representing the variations of tensile and bending strengths of brittle materials, computer-simulated fracture experiments were carried out on a number of specimens having a fixed number of penny-shaped cracks of different sizes at randomly distributed positions, by using the fracture mechanics approach, and the values of tensile and bending strengths were plotted on the Weibull distribution diagrams.
The main results obtained were as follows:
(1) When the fracture origin is a deep-inner crack, the tensile strength varies depending upon maximum size of cracks and thus the variation of tensile strength is representable by one Weibull parameter. When the number of existing cracks is large, a surface or near-surface crack becomes the fracture origin and the strength drops considerably depending upon the crack size distribution as well as the position of the critical crack. Thus, more than one Weibull parameter are required to represent the variation of tensile strength.
(2) As for bending tests, the strength varies with the crack size as well as the position of the critical crack, and thus, it is difficult to represent the variation of bending strength with one Weibull parameter. By choosing both the numbers of surface and inner cracks and the positions of critical cracks, it seems possible to reproduce a Weibull distribution similar to the experimental one.