Comparison of three different deconvolution methods for analyzing nanoindentation test data of hydrated cement paste

Abstract

The micromechanical properties of hydrated cement paste were investigated by nanoindentation with a large data set (4000 indentation points) to reveal the influences of multiple factors on analysis results. Three different deconvolution analysis methods, i.e. the Gaussian mixture model (GMM) with the maximum likelihood evaluation (MLE) algorithm, the probability distribution function (PDF) and the cumulative distribution function (CDF) with least square estimate (LSE) algorithm, were employed to analyze the nanoindentation test data. It was found that the GMM with a diagonal-unshared matrix is the most appropriate for the deconvolution of nanoindentation data of hydrated cement paste for the MLE algorithm. The PDF and CDF methods are equally effective for the LSE algorithm, but the former is subjected to the influences of bin sizes and the optimal bin size is 1.5–2 GPa for elastic modulus and 0.075–0.1 GPa for hardness. The threshold number of indentation points necessary to obtain reliable micromechanical parameters and phase contents by all three deconvolution methods is approximately 800-1000, significantly higher than the values used in the literature. The phase content seems to show more variations than elastic modulus and hardness when the number of indentation point is insufficient. With sufficient number of indentation points, the three different deconvolution methods give consistent results regarding the properties and contents of six phases identified. The various phase contents calculated by deconvolution of nanoindentation test data are in reasonable agreement with that estimated by QXRD and SEM except for the pore phase.