Constitutive relations of nanoscale hydration products present in engineered cementitious composites from machine learning assisted experimental nanoindentation

Abstract

In this work, a method to evaluate the stress-strain properties (at nano-scale) of constitutive phases present in the hydration cement matrix is presented. Using an experimental grid nanoindentation using Berkovich indenter, the constituent phases i.e., Low Density Calcium Silicate Hydrate (LD CSH), High Density Calcium Silicate Hydrate (HD CSH) and clinkers are indented upon during different points of Ordinary Portland Cement (OPC) paste hydration. Further, this study is conducted on four other cement pastes: OPC +20% fly ash, OPC +40% fly ash, OPC +0.5% nanosilica and OPC +1% nanosilica. Using experimental grid nanoindentation technique results in a large dataset depending upon the size of the gird. Three different machine learning algorithms including K-means, Gaussian mixture model (GMM) clustering and, support vector machine (SVM) have been implemented. The developed stress-strain evaluation method has allowed to ascertain the constitutive relations as yield stresses of 354 MPa for LD CSH, 393 MPa for HD CSH and 4340 MPa for clinkers, yield strains of 1.8 × 10−2 for LD CSH, 1.1 × 10−2 for HD CSH and 3.7 × 10−2 for clinkers; ultimate stresses of 371 MPa for LD CSH, 424 MPa for HD CSH and 6085 MPa for clinkers, ultimate strains of 2 × 10−2 for LD CSH, 1.4 × 10−2 for HD CSH and 4.4 × 10−2 for clinkers; and strain hardening exponents of 0.85 for LD CSH, 0.72 for HD CSH and 2.1 for clinkers. Elastic modulus, hardness and the stress-strain values obtained from the load vs. displacement curves are used for the clustering analysis and compared with deconvolution results. These properties have been used to test the feasibility of application of machine learning algorithms to classify the grid nanoindentation data. It was found that the machine learning algorithms were indeed capable of clustering the data obtained from experimental grid nanoindentation. This study presents a novel method to evaluate stress-strain properties of the constituent phases present in the cement microstructure and application of machine learning in the field of material characterisation using nanoindentation technique.