Brittle fracture strength prediction via XML with reliability considerations

This study presents a Machine Learning (ML)-based framework for predicting the brittle fracture strength of glass and ceramic materials in tension and flexure. Traditional empirical methods rely on subjective interpretations and oversimplified formulas that overlook critical factors such as specimen geometry, residual stresses, elastic properties, and microstructural heterogeneity, leading to inconsistent and unreliable strength estimates. To overcome these limitations, this research utilizes a dataset of over 4,600 fractured specimens spanning 44 brittle material types and employs both single and ensemble ML algorithms, including Multi-Layer Perceptron (MLP), XGBoost, and LightGBM. Two approaches are proposed: (i) Practical Solution (PS) derived from a simplified MLP architecture, offering explicit mathematical equations for ease of use, and (ii) high-accuracy Model-Based Solution (MBS) integrated into a user-friendly GUI. The results demonstrate that LightGBM outperforms empirical methods, PS, and other MBS, achieving superior predictive accuracy with lower RMSE and MAE, along with higher correlation coefficient across different material types and loading conditions. Specifically, for glass or glass-like (glass) in flexure, the LightGBM model achieved RMSE, MAE, and correlation coefficient values of 0.07, 0.044, and 0.98, respectively, compared to 0.116, 0.078, and 0.93 for the PS and 0.210, 0.170, and 0.93 for empirical solutions. Similar trends were observed for other cases, with non-glass (ceramic) materials exhibiting slightly lower accuracy due to their complex microstructure and the inherent challenges in fracture surface interpretation. A reliability analysis using Monte Carlo Simulation (MCS) confirmed that ensemble ML solutions provide robust and generalizable predictions across varying input conditions, while PS, though more conservative, exhibits lower predictive accuracy. Feature importance analysis via SHAP revealed that the non-dimensional parameter $\sqrt{t/R}$ (where $t$ is the thickness of the plate or the diameter of the rod, and $R$ is the mirror radius) is the most influential factor in fracture strength prediction, consistent with classical fracture mechanics. For further validation of the developed ML-based solutions, additional experimental studies were conducted, confirming both their accuracy and practical applicability in engineering applications.