A Bayesian inverse approach to measure the anisotropic plasticity properties of materials using spherical indentation experiment. (February 2021) - Wang, Mingzhi; Gao, Libo; Cao, Ke; Wu, Jianjun; Wang, Weidong
Highlights: A Bayesian inverse approach for measuring anisotropic properties is proposed. POD algorithm effectively captures non-linear indentation imprint deformation. Potential uncertainties and statistical information of parameters are considered. Weighting applied on log-likelihood functions gives stable posterior PDF results. Parameters measured by indentation and uniaxial tests show good agreement. Abstract: This paper presents an inverse computation method for measuring the anisotropic plasticity properties of materials using indentation. The advantage of this method is that, material plastic parameters are treated as stochastic variables with statistical distributions, of which potential uncertainties in numerical optimization process are considered. In new method, Bayesian inference model is established based on the average and difference imprint snapshots, S ¯ and Δ S of anisotropic materials in spherical indentation. Proper orthogonal decomposition (POD) is used to correlate the material parameters with indentation imprint snapshots in a dimension-reduced sub-space, and the weighting is applied on the log-likelihood functions to balance the sources of errors from imprint snapshots, S ¯ and Δ S . Effectiveness of the numerical method is verified by its application on SiCw/A6061. Posterior probabilistic distribution results indicate the unique solution of anisotropic parameters are achieved. Besides, the influence of weighting factor on posterior probabilistic distribution of anisotropic parameters, and well-posedness of the inverse problem are analyzed. The anisotropic material parameters estimated by indentation and uniaxial tests show good agreement, with the maximum error less than 10%. Results indicate the proposed measuring method in present work is very effective.