The Analysis of Depth-Sensing Indentation Data
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THE ANALYSIS OF DEPTH-SENSING INDENTATION DATA
Shefford P. Baker Max-Planck-Institut fur Metallforschung, Institut fUr Werkstoffwissenschaft, SeestraBe 92, 7000 Stuttgart 1, Germany This paper was presented as an introduction to a special discussionsession on the analysis of depth-sensing indentationdata. A review of the discussionsessionfollows. ABSTRACT Common methods for analyzing depth-sensing indentation data are briefly reviewed and an overview of the principal factors limiting the accuracy and precision of results obtained using these methods is presented. The largest deviations from the elastic contact models used to interpret depth-sensing indentation data arise from time-dependent displacements and uncertainties in the shape of the indenter tip, the elastic/plastic nature of the contact and the compliance of the testing machine. INTRODUCTION The indentation test is the most common technique for determining the mechanical properties of materials. In such experiments, an indenter is pressed into the test material with a load P, and the hardness, H, is defined as the ratio of that load to some measure of the size of the resulting residual indentation. The projected area, A, is often used, so that H = P/A. Although no specific physical property is measured in an indentation test, empirical correlations relate hardness to specific properties for particular materials. For example, Tabor has shown that, for many metals, the yield strength, ay, is related to hardness byH - 3ory [11. Within limits, hardness is generally considered to be a good indicator of relative strength. Due to interest in the unique mechanical properties of very small volumes, depth-sensing techniques have been developed in order to extend indentation methods into smaller dimensional regimes. In this type of experiment, load and displacement data are collected throughout the indentation process and are subsequently interpreted to determine mechanical properties. The need to image very small indentations is obviated and, as an additional benefit, quantities other than hardness (e.g. stiffness), can be investigated. In recent years, the number of devices capable of obtaining data from indentations on the nanometer scale has risen dramatically and the methods used to interpret that data have continued to be refined. However, the reproducibility of reported results, particularly between laboratories, has not been established and the efficacy of the technique has been questioned. This paper contains a basic review of some data analysis methods and a brief discussion of the principal factors which limit the accuracy and precision of depth-sensing indentation results. ANALYSIS METHODS Figure 1 shows typical depth-sensing indentation data taken from single crystals of aluminum and sapphire. As the load, P, is increased, displacements, h, occur due to both elastic and plastic deformation of the sample material. If the indenter is held under constant load, plastic displacements due to time-dependent plasticity in the sample material can be detected. F
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