The indentation size effect is one of several size effects on strength for which “smaller is stronger.” Through use of geometrically self-similar indenters such as cones and pyramids, the size effect is manifested as an increase in hardness with decreasing depth of penetration and becomes important at depths of less than approximately 1 μm. For spherical indenters, the diameter of the sphere is the most important length scale; spheres with diameters of less than approximately 100 μm produce measurably higher hardnesses. We critically review experimental observations of the size effect, focusing on the behavior of crystalline metals, and examine prevailing ideas on the mechanisms responsible for the effect in light of recent experimental observations and computer simulations.

The Indentation Size Effect: A Critical Examination of Experimental Observations and Mechanistic Interpretations

The Brinell, Vickers, Meyer, Rockwell, Shore, IHRD, Knoop, Buchholz, and nanoindentation methods used to measure the indentation hardness of materials at different scales are compared, and main issues and misconceptions in the understanding of these methods are comprehensively reviewed and discussed. Basic equations and parameters employed to calculate hardness are clearly explained, and the different international standards for each method are summarized. The limits for each scale are explored, and the different forms to calculate hardness in each method are compared and established. The influence of elasticity and plasticity of the material in each measurement method is reviewed, and the impact of the surface deformation around the indenter on hardness values is examined. The difficulties for practical conversions of hardness values measured by different methods are explained. Finally, main issues in the hardness interpretation at different scales are carefully discussed, like the influence of grain size in polycrystalline materials, indentation size effects at micro- and nanoscale, and the effect of the substrate when calculating thin films hardness. The paper improves the understanding of what hardness means and what hardness measurements imply at different scales.

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Indentation Hardness Measurements at Macro-, Micro-, and Nanoscale: A Critical Overview

An analysis of Knoop microhardness

The indentation size effect (ISE) in Vickers hardness for several ceramic materials was observed in a relatively wider range of applied test load. It was shown that the proportional specimen resistance (PSR) model proposed by Li and Bradt is insufficient for describing the experimental data. By considering the effect of the machining-induced plastically deformed surface on the hardness measurements, the PSR model was modified and the empirical equation proposed originally by Buckle was proven to be more suitable for correlating the measured indentation dimension to the applied test load. ©

Examination of the indentation size effect in low-load vickers hardness testing of ceramics

The mechanics of hardness indentation are considered. On the basis of a cycle in which the loading is elastic-plastic and the unloading (and subsequent reloading) elastic, an expression is derived for the relative depth recovery of the impression as a function of hardness/modulus,H/E. Experimental observations on indented surfaces of selected materials, mostly ceramics, using a tilting procedure in the scanning electron microscope to measure the residual depths, confirm the predicted trends. The analysis offers a simple means of characterizing the deformation properties of materials and should provide a basis for evaluating a range of contact-related properties, particularly surface damage phenomena in sharp-particle impact.

Elastic recovery at hardness indentations

As the concept of micro-indentation hardness testing has not yet become commonly accepted, nor has any definition of it been universally agreed upon, it is desirable to begin by reviewing the development and the present state of hardness testing under low load, and to say something about the terminology.

Progress in micro-indentation hardness testing

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Progress in micro-indentation hardness testing