Bayesian analysis of fracture of polyamide 12 U-notched specimens

The analysis of U-notched specimens with different notch radii has emerged as a valuable approach for validating the applicability of failure criteria in a given material or determining the fracture toughness. The process involves selecting an appropriate failure criterion or fracture model that best describes the experimental results, fine-tuning the criterion parameters, and subsequently utilizing it to evaluate the case of a notch with a zero radius. To enhance this methodology, Bayesian statistical techniques are employed to ascertain the statistical distribution of fracture toughness. The present study has been carried out with polyamide 12 specimens manufactured by selective laser sintering tested in two different orientations. The a posteriori distribution of the fracture toughness has been numerically calculated using a Markov Chain Monte Carlo (MCMC) algorithm. This approach enables the estimation of uncertainty associated with the fracture toughness value, offering insights into the reliability of the proposed failure criteria.