Characterization of the Linear Viscoelastic Properties of Materials by the Results of Nanoindentation Test

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Department of Mechanical Engineering of Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran.

Abstract

In this paper, the linear viscoelastic properties of materials are calculated using results from the nanoindentation test. The generalized standard linear solid (GSLS) viscoelastic models describe the material behavior, with the mechanical properties (model parameters) obtained by minimizing the error between the GSLS response and the experimental results under the same loading conditions. Since the test data are in the force-displacement not the stress-strain form, obtaining the material properties is less straightforward than the conventional tests (e.g., the tensile test) and requires analytical solutions. Specifically, the Hertzian contact theory and its closed-form solution for spherical indentation into a semi-infinite medium are employed. We fit the experimental results to the closed-form solutions, with error minimized via the least squares. This leads to a non-linear, constrained, and non-convex optimization problem, necessitating robust global optimization strategies beyond conventional local methods. Considering these challenges, the model coefficients meaningful in the experiment time span are computed using a genetic algorithm (GA) suited for the optimization. Several examples demonstrate ability of the method to accurately characterize the viscoelastic responses from nanoindentation test results, showing up to 50% difference compared with the values reported in the open literature.

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