Model for predicting temperature-dependent indentation yield strength and hardness considering size effects

The development of theoretical models to facilitate access to the mechanical properties of materials has been a long-standing pursuit of scholars. In this study, temperature-dependent yield strength models and temperature-dependent hardness models considering indentation size effects were developed under different loading modes (loading to the same displacement or the same load at different temperatures), respectively. Based on the Force-Heat Equivalence Energy Density Principle, the proposed models are free of any adjustable fitting parameters, and the quantitative relationships among temperature, yield strength/hardness, Young's modulus, and indentation load/displacement were successfully captured. All the available 36 groups of experimental data validate the accuracy of the proposed models over a wide temperature range. The yield strength and hardness of metallic materials over a wide temperature range can be easily predicted by using the developed models. Based on the parametric analysis of the models, it has been theoretically clarified for the first time that the two loading modes have opposite indentation size effects for the same material. Although the indentation size effect all decreases gradually with increasing temperature for different loading modes. The influence of loading modes should be noted in future studies where temperature-dependent indentation size effects need to be considered. This work systematically considers the effects of temperature, loading mode, indentation load/displacement, and Young's modulus on the indentation yield strength and hardness, which is important to facilitate the study of the deformation behavior of materials at different temperatures by indentation methods.