Article,
Glass hardness: Predicting composition and load effects via symbolic reasoning-informed machine learning
Affiliations
- [1] Indian Inst Technol Delhi, Dept Civil Engn, New Delhi 110016, India [NORA names: India; Asia, South];
- [2] Indian Inst Technol Delhi, Dept Civil Engn, New Delhi 110016, India [NORA names: India; Asia, South];
- [3] Brazilian Ctr Res Energy & Mat CNPEM, Ilum Sch Sci, BR-13083970 Campinas, SP, Brazil [NORA names: Brazil; America, South];
- [4] French Alternat Energies & Atom Energy Commiss, Lab study & Dev Nucl waste conditioning matr, Paris, France [NORA names: France; Europe, EU; OECD];
- [5] Aalborg Univ, Dept Chem & Biosci, DK-9220 Aalborg, Denmark [NORA names: AAU Aalborg University; University; Denmark; Europe, EU; Nordic; OECD];
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Abstract
Glass hardness varies in a non-linear fashion with the chemical composition and applied load, a phenomenon known as the indentation size effect (ISE), which is challenging to predict quantitatively. Here, using a curated dataset of over 3,000 inorganic glasses from the literature comprising the composition, indentation load, and hardness, we develop machine learning (ML) models to predict the composition and load dependence of Vickers hardness. Interestingly, when tested on new glass compositions unseen during the training, the standard datadriven ML model failed to capture the ISE. To address this gap, we combined an empirical expression (Bernhardt's equation) to describe the ISE with ML to develop a framework that incorporates the symbolic equation representing the domain reasoning in ML, namely Symbolic Reasoning-Informed ML Procedure (SRIMP). We show that the resulting SRIMP outperforms the data-driven ML model in predicting the ISE. Finally, we interpret the SRIMP model to understand the contribution of the glass network formers and modifiers toward composition and load-dependent (ISE) and load-independent hardness. The deconvolution of the hardness into load-dependent and load-independent terms paves the way toward a holistic understanding of the composition effect and ISE in glasses, enabling efficient and accelerated discovery of new glass compositions with targeted hardness.