Elastic recovery and reloading of hardness impressions with a conical indenter
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Elastic recovery and reloading of hardness impressions with a conical indenter A.C. Fischer-Cripps CSIRO Division of Telecommunications and Industrial Physics Bradfield Rd, West Lindfield, NSW 2070 Australia ABSTRACT The present work is concerned with the analysis of elastic unloading data in conventional methods of analysis of nanoindentation test data. Experimental and finite element results are used to show that the reloading of a residual impression with and without the presence of residual stress is an elastic event, and further shows that the estimation of modulus and hardness computed using established techniques is in error due to the assumption the sides of the residual impression are straight. This work calls into question the validity of commonly used methods of test and analysis of instrumented indentation test data that use the elastic unloading data as the basis for the calculation of modulus and hardness of the specimen material.
INTRODUCTION Presently available theoretical and numerical analyses [1,2] of elastic-plastic contact between an indenter and a specimen, such as that used in depth-sensing, or nanoindentation testing, generally concentrate on the loading part of the indentation cycle. However, in depth-sensing indentation, it is the unloading that is usually of most interest since in conventional methods of analysis [3,4] the unloading (and any subsequent reloading) is generally treated as a completely elastic event and assumes that the shape of the residual impression is that of a straight-sided cone. In the present work, experimental and finite element results are used to investigate these matters and their effect on the computed values of modulus and hardness.
EXPERIMENTAL WORK Two commonly used materials in nanoindentation testing are fused silica and hardened steel, they being representative of materials at a conveniently wide range of values of the ratio E/H. In the present work, a sample of optical grade fused silica and a specially prepared standard steel hardness block were selected for indentation testing with a Berkovich pyramidal diamond indenter with a UMIS nanoindentation testing instrument [5]. A load sequence was defined in a user-specified script file that matched the load steps in the subsequent finite element analysis. A maximum load of 100 mN was applied to both specimens and the resulting depths of penetration were 920 nm for fused silica and 752 nm for steel. The experimental load-displacement curves are shown as triangles in figures 1 and 2. The results shown in figures 1 and 2 have been corrected for initial penetration and instrument compliance, measured in this case to be 1 × 107 N/m. The temperature in the testing laboratory was kept stable to within 0.1 °C and no thermal drift correction was found to be required. The indenter tip shape function was measured and the ratio of the actual contact area and the ideal contact area to be 1.005 at these depths of penetration. As a consequence, no tip area correction was made to the load-displacement data or
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