Bayesian Uncertainty Update to a Model of Flexural Strength of α-SiC

Abstract

This article demonstrates a statistical method to update the uncertainty in the flexural strength of silicon carbide, α-SiC. The previously reported uncertainty for the flexural strength of α-SiC was a constant ±15%.  However, this uncertainty should be adjusted as more data becomes available.  A Bayesian approach is proposed to rapidly and precisely update the uncertainty.  To validate the method, five scenarios are demonstrated.  The first scenario assumes the experimental data is distributed as the model predicts.  The second and third scenarios have the model underestimating and overestimating flexural strength, respectively.  The fourth and fifth scenarios use data from a thermo-mechanical fracture model.  The thermo-mechanical fracture model introduces a change in the temperature transition of flexural strength.  The uncertainty decreased from 15% to a range between 8.3% and 13.4%.  Two parameters are inferred in the fourth scenario while five are inferred in the fifth scenario.  Inferring five parameters leads to more consistent uncertainty across temperature.