Effect analysis of loading rate on relationship between strength and flaw size of ceramics using probabilistic model on the basis of SCG concept

Abstract

This paper presents the effect of loading rate on relationship between strength and flaw size of ceramics. First, a probabilistic effective inert strength model was proposed on the basis of SCG concept and upper limit flaw size in conjunction with the Weibull distribution. It was derived that the effective inert strength converted using fracture strength which depended on loading rate and effect loading time of ceramics conformed to a three-parameter Weibull distribution. Second, the effect of loading rate on the relationship between fracture strength and flaw size was theoretically derived on the basis of fracture criterion by applying the virtual equivalent crack length and a grain fracture model in conjunction with the probabilistic model. Third, four-point bending test was performed using alumina ceramics (Al₂O₃) under a wide range of loading rate. The fracture surface was then observed by scanning electron microscope. Fourth, the material constants and the Weibull parameters related to the probabilistic model were determined using the experiment data. Weibull plots of the inert strength calculated from the grain fracture model using the equivalent crack length accorded well with the three-parameter Weibull distribution calculated from the Weibull parameters for the effect inert strength. This result supported the conclusion derived from the probabilistic model. Finally, the validity of the theoretically presented effect of loading rate was confirmed through the comparison of the predicted relationship between fracture strength and flaw size at various loading rates with the experiment data.