A Well-Posed Definition for Plastic Strain Rate in Indentation

To compare hardness versus strain rate data from different kinds of indentation creep test can be challenging. It is often difficult to determine whether measured differences in material response along different loading paths, such as constant load creep or load relaxation, are real or merely arise as artifacts from the analysis. We argue that the difficulty lies in how indentation strain rate is defined. For traditional definitions of strain rate, such as epsilon(center dot)h\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{\varepsilon }_{h}$$\end{document}, which measures the rate of penetration, or epsilon(center dot)A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{\varepsilon }_{{\text{A}}}$$\end{document}, which measures the growth of indent area, material response might seem path-dependent even when it is not. We introduce a new definition of plastic strain rate, epsilon(center dot)irr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{\varepsilon }_{{{\text{irr}}}}$$\end{document}, which is based on irreversible work and is well-posed in the sense that it gives the same results from different loading paths when deformation is path-independent. This property frees experimenters to isolate and explore deformation mechanisms that respond differently along different loading paths, which is useful for revealing the influences of time and strain rate on evolution of structure. epsilon(center dot)irr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{\varepsilon }_{{{\text{irr}}}}$$\end{document} is important for exploring path-dependence in high-hardness/modulus (greater than or similar to 0.02)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ 0.02)$$\end{document} materials like ceramics and polymers. For low-hardness-modulus materials other measures of strain rate suffice.