Temperature-dependent hardness model of high-temperature materials can account for indentation size effect. (November 2022) - Liu, Yumeng; Wang, Ruzhuan; Wan, Yu; Zhou, Shan; Cai, Hongwei; Gu, Mingyu; Li, Dingyu; Li, Weiguo
Abstract: Indentation size effect has been found in the micro-nano hardness tests of both ceramic materials and metallic materials, even at high temperature. However, there are few temperature-dependent hardness theoretical models that can quantitatively characterize the indentation size effect of materials. This work introduces the indentation size effect into a novel temperature-dependent hardness model of materials by using energy method. The model takes into account the Young's modulus, indentation depth, melting point, and constant pressure heat capacity of materials without any fitting parameters. Further, for solving the problem of the difficulty to obtain the heat capacity of some materials, a simpler temperature-dependent model that just includes the Young's modulus, indentation depth and melting point is proposed. The remarkably excellent agreements between predicted and measured data of both ceramic materials and metallic materials verify the currency of the models. In addition, the effects of indentation depth and Young's modulus on the hardness of materials and their evolution with temperature are studied. Graphical abstract: Unlabelled Image Highlights: Temperature-size-dependent hardness of material is quantitatively characterized. The proposed theoretical models have no fitting parameters. The proposed theoretical models are verified by comparing with experimental data. Both of metallic materials and ceramic materials are discussed by the models. The main controlled mechanisms of the temperature-dependent hardness are studied.