Characterization and modeling of specific strain gradient modulus of epoxy
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Microscale sensing and actuating components are prevalent in microelectromechanical systems. Deformations of microscale components are dependent not only on the strains in the body, but also on the strain gradients. The contribution of strain gradients to plastic hardening is characterized by the specific strain gradient modulus of the material. The specific strain gradient modulus has been predicted to vary with the plastic strain. The moduli of plastically prestrained epoxy specimens were experimentally characterized in this investigation using nanoindentation. Prestraining induced softening and an energy model are developed to separate the effect of prestrain softening from the effect of strain gradient. The results indicated that the contribution of strain gradient to hardening was initially large but diminished with increased plastic deformation. A model was developed for power law material and was shown to compare well with the experimental results.
I. INTRODUCTION
Plastic deformation of material is normally size independent but can become size dependent when the strains are localized. Localization of the strains in a small region leads to the development of nonnegligible strain gradients, and the magnitude of the gradient is dependent on the dimension. In indentation, the strains are localized in the indentation. The localization leads to the development of strong strain gradients when the indentation is small. The normally size-independent hardness becomes size dependent when the hardening contribution of the strain gradients becomes nonnegligible in nanoindentation.1,2 This size effect is also observed in torsion of small metal wire3 and in bending of thin metal films.4 In torsion, strain varies from zero at the axis to a maximum at the wire surface. When the wire diameter is large, strain gradients are negligible, and the deformation behavior is well described by conventional plasticity theory. When the wire diameter is small, the strain gradients are significant, and conventional plasticity theories, which ignore strain gradients, are no longer adequate. Plasticity theories with strain gradients have been developed for metals and polymers.1,5,6 In polymers, the hardness of the polymer was observed to increase with strain gradient.6 The increase was attributed to a corresponding increase in kink density and a strain gradient plasticity law for polymer Eq. (1) was developed.6 = 558
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公Mg + o
,
(1)
J. Mater. Res., Vol. 16, No. 2, Feb 2001 Downloaded: 16 Mar 2015
where is the yield stress, 0 is the yield stress without strain gradient, is the strain gradient, and Mg is the specific strain gradient modulus. Mg can be ascertained directly from indentation data through Eq. (2): Mg =
冋 册
2 Ho ho 3 tan
(2)
,
where H0 is the hardness for large indents without strain gradient effect (i.e., no depth dependence), and is the indenter tip angle. At small indent depth, hardness is a function of the indent depth. The variation is characterized by the parameter ho. Detai
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