Analysis of indentation creep
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Analysis of indentation creep Don S. Stonea) Department of Materials Science and Engineering, and Materials Science Program, University of WisconsinMadison, Madison, Wisconsin 53706
Joseph E. Jakes Materials Science Program, University of WisconsinMadison, Madison, Wisconsin 53706; and Performance Enhanced Biopolymers, United States Forest Service, Forest Products Laboratory, Madison, Wisconsin 53726
Jonathan Puthoff Materials Science Program, University of WisconsinMadison, Madison, Wisconsin 53706
Abdelmageed A. Elmustafa Department of Mechanical Engineering and The Applied Research Center–Jefferson Laboratory, Old Dominion University, Norfolk, Virginia 23529 (Received 25 November 2009; accepted 22 January 2010)
Finite element analysis is used to simulate cone indentation creep in materials across a wide range of hardness, strain rate sensitivity, and work-hardening exponent. Modeling reveals that the commonly held assumption of the hardness strain rate sensitivity (mH) equaling the flow stress strain rate sensitivity (ms) is violated except in low hardness/ modulus materials. Another commonly held assumption is that for self-similar indenters the indent area increases in proportion to the (depth)2 during creep. This assumption is also violated. Both violations are readily explained by noting that the proportionality “constants” relating (i) hardness to flow stress and (ii) area to (depth)2 are, in reality, functions of hardness/modulus ratio, which changes during creep. Experiments on silicon, fused silica, bulk metallic glass, and poly methyl methacrylate verify the breakdown of the area-(depth)2 relation, consistent with the theory. A method is provided for estimating area from depth during creep. I. INTRODUCTION
Materials scientists have long relied on indentation creep to study rate-sensitive deformation in solids.1–3 Although not as straight-forward to analyze and interpret as the more conventional uniaxial creep experiment, the indentation test is nevertheless easier to perform, especially when the specimen is too small to grip for uniaxial testing. Over the years the great majority of work in indentation creep has been performed at high homologous temperatures where the yield stress is a small fraction of the Young’s modulus. These kinds of experiments have motivated theoretical treatments to address the relationship between indentation and uniaxial creep under conditions where the a)
Address all correspondence to this author. e-mail: [email protected] This paper was selected as an Outstanding Symposium Paper for the 2007 MRS Fall Meeting, Symposium AA Proceedings, Vol. 1049. DOI: 10.1557/JMR.2010.0092 J. Mater. Res., Vol. 25, No. 4, Apr 2010
elastic deformations are small and therefore relatively unimportant.2,4–6 This research is motivated by the desire to investigate low-temperature, rate-sensitive deformation in high hardness/modulus (H / E*) materials like refractory coatings and bulk metallic glasses (BMGs). Although one does not normally think of hard materials as creeping at low temperatu
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