A New Nonlinear Viscoelastic Constitutive Equation for Predicting Yield in Amorphous Solid Polymers
作者:
R. M. Shay,
J. M. Caruthers,
期刊:
Journal of Rheology
(AIP Available online 1986)
卷期:
Volume 30,
issue 4
页码: 781-827
ISSN:0148-6055
年代: 1986
DOI:10.1122/1.549869
出版商: The Society of Rheology
数据来源: AIP
摘要:
A new constitutive equation has been developed for describing the nonlinear viscoelastic properties, including yield, of polymer solids. The nonlinear viscoelastic constitutive equation is the logical extension of the standard three‐dimensional linear viscoelastic constitutive equation to include the effects of deformation‐induced changes in the thermodynamic state of the polymer on the rate of viscoelastic relaxation. The rate of viscoelastic relaxation depends upon the fraction of unoccupied lattice sites (i.e., holes) in the Simha‐Somcynsky statistical thermodynamic equation of state, and the hole fraction is a known function of the temperature, pressure, and specific volume. The nonlinear viscoelastic yield and postyield behavior are a direct consequence of the deformation‐induced dilation. All material constants contained in the constitutive equation can be determined from independent elastic, linear viscoelastic, and pressure‐volume‐temperature measurements—there are no adjustable constants. The constitutive equation has been solved for model viscoelastic materials in uniaxial extension and shear deformations where the applied strain rate is constant. It is shown that an experimentally realizable “shear” deformation is only isochoric in the linear viscoelastic limit. Yield and postyield softening are predicted in both uniaxial extension and experimental shear, and the predicted yield stress exhibits the appropriate strain rate and temperature dependence. The effects of using various finite strains measures in the nonlinear viscoelastic constitutive equation are analyzed.
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