Analysis of Indentation Creep
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Analysis of Indentation Creep D. S. Stone1, and A. A. Elmustafa2,3 1 Materials Science and Engineering, University of Wisconsin-Madison, 1509 University Avenue, Madison, WI, 53706 2 Department of Mechanical Engineering, Old Dominion University, Norfolk, VA, 23529 3 The Applied Research Center, Old Dominion University, Newport News, VA, 23606 ABSTRACT Increasingly, indentation creep experiments are being used to characterize rate-sensitive deformation in specimens that, due to small size or high hardness, are difficult to characterize by more conventional methods like uniaxial loading. In the present work we use finite element analysis to simulate indentation creep in a collection of materials whose properties vary across a wide range of hardness, strain rate sensitivities, and work hardening exponents. Our studies reveal that the commonly held assumption that the strain rate sensitivity of the hardness equals that of the flow stress is violated except for materials with low hardness/modulus ratios like soft metals. Another commonly held assumption is that the area of the indent increases with the square of depth during constant load creep. This latter assumption is used in an analysis where the experimenter estimates the increase in indent area (decrease in hardness) during creep based on the change in depth. This assumption is also strongly violated. Fortunately, both violations are easily explained by noting that the “constants” of proportionality relating 1) hardness to flow stress and 2) area to (depth)2 are actually functions of the hardness/modulus ratio. Based upon knowledge of these functions it is possible to accurately calculate 1) the strain rate sensitivity of the flow stress from a measurement of the strain rate sensitivity of the hardness and 2) the power law exponent relating area to depth during constant load creep. INTRODUCTION Indentation tests have long been used to study rate sensitive deformation in solids. The great majority of work has been performed at high homologous temperatures where solids tend to be soft, that is, where the flow, or yield, stress is a small fraction of the Young’s modulus. Because of the work on materials under conditions where they are soft, there have been a number of theoretical treatments that address the issue of rate sensitive hardness measurements under conditions where the elastic deformations are small and therefore relatively unimportant [1-4]. The present research is motivated by the desire to investigate rate sensitive deformation in hard materials like refractory coatings and bulk metallic glasses where the yield stress and hardness constitute a significant proportion of the Young’s modulus. Our investigation differs from earlier studies because in the hard materials which we now consider the elastic deformations become large and therefore important. For low yield stress materials the indentation creep properties are not sensitive to modulus, so the modulus can therefore be neglected. For hard materials the modulus effects must be taken into ac
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