Failure Analysis of Advanced Ceramics using Bivariate Weibull Distribution and Bayesian Estimation

Abstract This research paper presents a comprehensive study on modeling the failure behavior of advanced ceramics by integrating phenomenological and physics-based approaches. The proposed methodology utilizes the bivariate Weibull distribution to capture the complex failure mechanisms in advanced ceramics, considering the impact of Subcritical Crack Growth (SCG). Approximate Bayesian Computation (ABC) is employed for parameter estimation, leveraging Metropolis-Hastings (MH) and Hamiltonian Monte Carlo (HMC) algorithms to enhance computational efficiency. The study validates the proposed models against a physics-based Batdorf theory approach using NASA’s CARES/Life. Results demonstrate the robustness of the ABC MH and ABC HMC models, highlighting the capability of statistical approach to predict failure dynamics in advanced ceramics under varying conditions. This research contributes to a deeper understanding of advanced ceramic failure mechanisms, paving the way for further advancements in material science and engineering applications of ceramics.