Identification of plastic properties of metal materials using spherical indentation experiment and Bayesian model updating approach

Abstract

In this paper, we proposed a novel approach to extract the plastic properties of materials using the loading curve (P-h) in spherical indentation experiment. The new method uses proper orthogonal decomposition to build the sub-space of indentation P-h snapshots, and then a statistical Bayesian inference model is derived based on the correlations between constitutive parameters and the sub-space coordinates of indentation P-h snapshots. Posterior sampling of material plastic parameters is performed using the Transitional Markov chain Monte Carlo (TMCMC) algorithm. The established new method has several advantages: 1). Bayesian model updating is performed in the sub-space of indentation P-h snapshots, of which the overall computation costs can be reduced greatly; 2). unlike most of the current analysis which can only give a single optimal estimation point of material properties, the present method can take account of the potential model and experiment uncertainties in indentation analysis. It's able to give the probabilistic information of the estimates, and provide a confidence interval (CI) of the inverse identified set of material properties under a certain confidence level, e.g. 95%. The effectiveness of the method is verified by its application on the 20MnB5 steel, of which two hardening laws, Hollomon and Ludwigson, are separately used. The unique solution of material plastic properties is obtained, and the parameters estimated by indentation and uniaxial experiment show good agreement. The influence of the selected hardening law and prescribed maximum indentation experiment depth on the numerical results are also investigated. Results indicate the new method is very reliable and effective. Besides, Ludwigson law gives more stable numerical results of 20MnB5.