Nanoindentation-based multidimensional deconvolution framework for gel-phase creep characterization and loading protocol optimization in fly ash–based geopolymers

This study develops a three-dimensional Gaussian mixture model (3D-GMM) framework and corresponding nanoindentation loading protocols for gel-phase creep characterization in fly ash–based geopolymers. The optimal cluster number of 3D-GMM was found to be 4, enabling the identification of the gel phase, which is characterized by an by an elastic modulus ( E ) of 14–19 GPa, hardness ( H ) of 0.6–0.7 GPa, and creep modulus ( C ) of 140–230 GPa in this study. A clear correlation among E , H , and C is revealed by the correlation analysis, indicating coupled elastic, plastic, and viscoelastic responses that likely originate from a common microstructural mechanism. Backscattered electron imaging analysis confirms the accuracy of the 3D-GMM phase identification, with gel-phase fractions showing good agreement with image-based estimates . Further analysis reveals that a holding duration of 180 s provides a balance between stable results and minimized environmental noise. A holding load of 10 mN offers a suitable compromise between bulk representativeness and substrate effects, whereas 2 mN is more appropriate for probing isolated gel phases. Based on these findings, a standardized nanoindentation workflow is proposed, integrating parameter selection, data quality control, 3D-GMM deconvolution, statistical analysis, and microstructural validation. This framework improves the robustness of nanoindentation data and provides a systematic methodology for characterizing heterogeneous geopolymer systems.