Computational mechanical property determination of viscoelastic/plastic materials from nanoindentation creep test data
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Timothy C. Ovaerta) Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana 46556 (Received 7 August 2008; accepted 8 December 2008)
Nanoindentation is a widely accepted test method for materials characterization. Given the complexity of contact deformation behavior, design of parametric constitutive models and determination of the unknown parameters is challenging. To address the need for identification of mechanical properties of viscoelastic/plastic materials from nanoindentation data, a combined numerical finite element/optimization-based indentation modeling tool was developed, fully self-contained, and capable of running on a PC as a stand-alone executable program. The approach uses inverse engineering and formulates the material characterization task as an optimization problem. The model development consists of finite element formulation, viscoelastic/plastic material models, heuristic estimation to obtain initial solution boundaries, and a gradient-based optimization algorithm for fast convergence to extract mechanical properties from the test data. A four-parameter viscoelastic/plastic model is presented, then a simplified threeparameter model with more rapid convergence. The end result is a versatile tool for indentation simulation and mechanical property analysis. I. INTRODUCTION
The nanoindentation test has become a standard method used to study the mechanical behavior of many different materials. Unlike the traditional uniaxial tension/compression test, where the deformation mechanism enables relatively straightforward extraction of true stress versus strain data, nanoindentation requires more advanced data mining procedures to deduce the material constitutive relations from the measured load versus indentation depth curve. This data mining technique, applied to nanoindentation test data, is an important part of the nanoindentation materials characterization field. The simplest case is the characterization of elastic materials. An analytical solution exists relating the indentation load, displacement, and the elastic modulus. The Oliver–Pharr method1 applies Sneddon’s theory2 and uses the unloading portion of the experimental load versus indentation depth curve to obtain the elastic modulus. In addition, for a pure linear viscoelastic material, an analytical solution may be obtained for a specific type of loading profile,3–5 such as step loading. This specialized loading method requires indentation to be performed in a specific manner, such as a relaxation or a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2009.0141 J. Mater. Res., Vol. 24, No. 3, Mar 2009
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creep test. As a material’s properties extend into the elastoplastic domain, because of the lack of analytical solutions, various modeling techniques become necessary, or experiments are used to determine an empirical relationship between the material properties and the load versus indentation depth curve.6–11 Ho
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