A flexible model for instrumented indentation of viscoelastic-plastic materials

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Research Letter

A flexible model for instrumented indentation of viscoelastic–plastic materials Robert F. Cook, Materials Measurement Science Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA Address all correspondence to Robert F. Cook at robert.coo[email protected] (Received 24 January 2018; accepted 23 February 2018)

Abstract The time-dependent pyramidal or conical indentation of viscoelastic–plastic materials, such as glassy polymers, is examined by a flexible, Kelvin-like model. The model equation is simply solved numerically for a wide range of material properties and indentation loading sequences. The flexibility of the model is demonstrated by generating typical indentation responses for a metal, a ceramic, an elastomer, and a glassy polymer. Polymer indentation is further examined under ramp, hold, and cyclic loading conditions, including adhesive effects. The model and approach should be particularly useful in identifying the various deformation components contributing to observed instrumented indentation phenomena.

In a recent work,[1] the experimental application of a timedependent indentation model was demonstrated in determining the viscous, elastic, and plastic properties of polymer and polymer-composite materials. Earlier indentation work concerned ex situ time-independent measurements, first of the plastic properties of materials via the hardness,[2] primarily metals, and later including the elastic properties via the modulus,[3] primarily of ceramics. In the last few decades, in situ timeindependent instrumented indentation methods have been developed to measure the hardness and modulus in a single test.[4] The recent work also used instrumented indentation methods and extended the testing and analysis to include the measurement of viscous properties of materials,[1] primarily polymers. Although the recent work had all the advantages of indentation testing—small sample volumes, minimal sample preparation, ability to map areas—the measurement of a third parameter (the viscous response) led to somewhat complicated testing protocols and analysis. The general complication is inevitable given the historical development in indentation testing sophistication, from single-parameter plastic properties[2] to two-parameter elastic and plastic properties[3,4] to three, or more, parameters for viscous, elastic, and plastic properties.[1] A large part of the complication of the most recent work was the development of analytical solutions to the model equations. Such solutions were necessary in order to join different experimental indentation loading segments together by boundarycondition matching and accomplish the “reverse” modeling process of fitting experimental measurements to the model. Although the methods were very successful in predicting properties and behavior, the complications obscured the

simplicity of the model and detracted from the ability of the model to explain commonly observed time-dependent indentation phenomena. Here, we redress some of the complications and use