Bayesian estimation of material properties from indentation test results using the replica exchange Monte Carlo method

Abstract

The Load-Depth (L-D) curves obtained from indentation tests have scatters due to the measurement and material microstructure. However, previous research has primarily focused on estimating the elastic-plastic properties based on representative curves. It is essential to consider statistical estimation methods that take the scatters into account and the optimal material constitutive equations used for the estimation. At a first step, this study proposes using Bayesian inference with replica exchange Monte Carlo to statistically estimate material parameters from the averaged L-D curve obtained from indentation tests with a spherical indenter and to investigate the estimation accuracy. Type 316L stainless steel was used as the test specimen. The material was assumed to follow the Swift law, and four parameters in the equation were estimated. As a result, the most appropriate set of material parameters, i.e., the set that minimizes the mean square error between the experimental results and the finite element analysis results, was determined. However, a posterior distribution showed that there were parameters with insufficient estimation accuracy, and it was found that it was necessary to clarify the factors behind them to estimate the material properties from indentation results with the scatters.