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Load–displacement behavior during sharp indentation of viscous–elastic–plastic materials

Published online by Cambridge University Press:  31 January 2011

Michelle L. Oyen  and
Robert F. Cook
Michelle L. Oyen
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
Robert F. Cook
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
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Abstract

A model is developed that describes the sharp indentation behavior of time-dependent materials. The model constitutive equation is constructed from a series of quadratic mechanical elements, with independent viscous (dashpot), elastic (spring), and plastic (slider) responses. Solutions to this equation describe features observed under load-controlled indentation of polymers, including creep, negative unloading tangents, and loading-rate dependence. The model describes a full range of viscous–elastic–plastic responses and includes as bounding behaviors time-independent elastic–plastic indentation (appropriate to metals and ceramics) and time-dependent viscous–elastic indentation (appropriate to elastomers). Experimental indentation traces for a range of olymers with different material properties (elastic modulus, hardness, viscosity) are econvoluted and ranked by calculated time constant. Material properties for these polymers, deconvoluted from single load–unload cycles, are used to predict the indentation load–displacement behavior at loading rates three times slower and faster, as well as the steady-state creep rate under fixed load.

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Articles
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Journal of Materials Research , Volume 18 , Issue 1 , January 2003 , pp. 139 - 150
Copyright
Copyright © Materials Research Society 2003

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