Load-Displacement Behavior During Sharp Indentation of Viscous-Elastic-Plastic Materials
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Load-Displacement Behavior During Sharp Indentation of Viscous-Elastic-Plastic Materials Michelle Oyen-Tiesma, Yvete A. Toivola, and Robert F. Cook Department of Chemical Engineering and Materials Science University of Minnesota Minneapolis, MN 55455
ABSTRACT: A constitutive equation is developed for geometrically-similar sharp indentation of a material capable of elastic, viscous, and plastic deformation. The equation is based on a series of elements consisting of a quadratic (reversible) spring, a quadratic (time-dependent, reversible) dashpot, and a quadratic (time-independent, irreversible) slider—essentially modifying a model for an elastic-perfectly plastic material by incorporating a creeping component. Loaddisplacement solutions to the constitutive equation are obtained for load-controlled indentation during constant loading-rate testing. A characteristic of the responses is the appearance of a forward-displacing “nose” during unloading of load-controlled systems (e.g., magnetic-coildriven “nanoindentation” systems). Even in the absence of this nose, and the associated initial negative unloading tangent, load-displacement traces (and hence inferred modulus and hardness values) are significantly perturbed on the addition of the viscous component. The viscouselastic-plastic (VEP) model shows promise for obtaining material properties (elastic modulus, hardness, time-dependence) of time-dependent materials during indentation experiments. INTRODUCTION: Instrumented indentation techniques have been developed for mechanically probing engineering materials and structures [1]. These techniques have been utilized for measuring mechanical properties of both bulk materials and thin films, with an emphasis on the latter due to nanometer displacement resolution. Deconvolution of load-displacement, P-h, responses allows determination of elastic modulus (E) and hardness (H) for materials with minimal timedependence [1], once probe shape and probe and instrument stiffness are known. Time-dependent materials exhibit an altered shape of the indentation load-displacement response with a forward-creeping “nose” on unloading under load-control [2]. The increasing displacement with decreasing load prohibits meaningful calculation of the modulus by measuring unloading stiffness. This problem has been avoided by permitting 10 seconds of creep at peak load until unloading curves do not show the forward-creeping nose, and then proceeding with standard E-H deconvolution techniques [2]. This method does not allow the experimenter to gain information about the time-dependence of the material, which is an integral part of the mechanical response. Here we develop a model for sharp, geometrically-similar indentation of time-dependent materials. The three-parameter series model incorporates independent elastic, plastic, and viscous contributions to the total displacement.
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MODEL: The three-element series model consists of independent elastic, viscous, and plastic elements. Elastic and plastic constitutive responses were taken from
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