An approach to scaling size effect on strength of quasi-brittle biomedical materials

Abstract

Two-parameter Weibull statistics is commonly used for characterizing and modeling strength distribution of biomedical materials and its size dependence. The calibrated scale parameter and shape factor are usually sensitive to specimen size. Since Weibull statistics is subject to the weakest link postulate, this work proposed to directly resort to the weakest-link formulation for the cumulative failure probability to characterize size effect on strength distribution of quasi-brittle biomedical materials. As a preliminary examination, the approach was assessed by two sets of published strength data. It shows that the resultant expression for the cumulative probability follows either Weibull distribution or other type of distributions. The calibrated model parameters are independent of specimen size, so they can be used to transfer strength distribution from one set of specimens to another set of specimens with geometrical similarity under same loading mode. These initial results motivate a more comprehensive validation of the proposed approach to proceed via a larger set of case studies covering different quasi-brittle biomedical materials over a wider range of size variation.

Keywords: Size effect; Strength; Weakest-link postulate; Weibull distribution.