Internal Friction Study of a Composite with a Negative Stiffness Constituent
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D. Stonea) Materials Science Program and Department of Materials Science, University of Wisconsin—Madison, Madison, Wisconsin 53706-1687
R.S. Lakesb) Department of Engineering Physics, Engineering Mechanics Program, Biomedical Engineering Department, Materials Science Program, and Rheology Research Center, University of Wisconsin—Madison, Madison, Wisconsin 53706-1687 (Received 24 February 2005; accepted 31 May 2005)
Composites with negative stiffness constituents can exhibit material properties that exceed conventional bounds. Composites with VO2 as negative stiffness inclusions and tin as the stabilizing matrix were prepared via powder metallurgy. Specimens were tested over a range of temperature in torsion using broadband viscoelastic spectroscopy. Composites processed via powder metallurgy exhibited internal friction anomalies over a broad range of temperatures, in contrast to the single, sharp anomalies reported previously from cast specimens. The detailed material behavior encompassed a variety of responses, which were also dependent on the number of thermal cycles. Composite theory predictions assuming a distribution of negative shear moduli can account for peak broadening.
I. INTRODUCTION
Most composite morphologies utilize inclusion shapes such as particles, fibers, or platelets etc., to stiffen or strengthen a matrix material. As a consequence of the specific microstructure chosen, the resulting composite material has effective properties intermediate between the base constituents. In the search for novel materials to enhance technological applications over traditional materials, utilization of the negative stiffness concept is one avenue to exceed the usual theoretical bounds placed upon linear, isotropic composites. Composites which contain a negative stiffness phase can theoretically possess properties, specifically modulus and mechanical damping, in excess of those of the base constituents as a result of balance between elements of positive and negative stiffness. Negative stiffness is manifested by the reversal of the usual directional relationship between causal forces and ensuing deformations and is unstable unless constrained. Negative stiffness differs from negative Poisson’s ratio,1 which refers to the transverse deformation of a material Address all correspondence to these authors. a) e-mail: [email protected] b) e-mail: [email protected] DOI: 10.1557/JMR.2005.0316 J. Mater. Res., Vol. 20, No. 9, Sep 2005
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due to a longitudinal load. The concept of negative stiffness can be illustrated by a set of linear elastic springs, all of which have positive stiffness, arranged into the geometry shown in Fig. 1. In the unloaded, unstretched condition of Fig. 1(a), all applied displacements and subsequent forces to point a will be resisted by the two springs marked k1 and the third spring marked k2. A negative stiffness situation can be obtained by applying enough displacement to point a, forcing the springs into the unstable equilibrium config
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