New Estimating Method of Weibull Parameters from Fracture Location Data

Abstract

Oh and Finnie developed the statistical theory of fracture location which can be used to estimate not only the fracture stress but also fracture location. However, this study is restricted only to one type of fracture origin. In fact, brittle materials like ceramics involve many types of fracture origins. Recently, we established a new theory by combining the statistical theory of fracture location with the competing risk theory. In the present study, we developed a new method of estimating Weibull's shape parameters on the basis of this theory, which has made it possible to estimate Weibull's shape parameters only from fracture location data. Using 3-point bending test data for silicon nitride, we estimated the shape parameters by the present method. The estimated results were compared with those obtained by the multi-maximum likelihood method. It was found that they coincide with each other satisfactorily. Further, the implications of Weibull's shape parameters for the fracture location in the 3-point bending test are discussed.