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Interaction of nonhomogeneous shear, nonlinear viscoelasticity, and yield of a solid polymer
Author(s) -
Wineman A. S.,
Waldron Jr. W. K.
Publication year - 1993
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.760331810
Subject(s) - viscoelasticity , constitutive equation , materials science , yield (engineering) , shear stress , stress relaxation , shear (geology) , yield surface , cylinder , strain (injury) , mechanics , composite material , finite element method , thermodynamics , physics , geometry , creep , mathematics , medicine
A constitutive equation for small strain viscoelastic response is considered in which stress relaxation. occurs faster as strain increases. The constitutive equation is of single integral type and has a psuedo‐ or material time function which is calculated from a strain dependent shift function. First, it is shown that such a constitutive equation can account for yield as observed in polymers for a number of different stress and strain histories. Next, the constitutive equation is used in the analysis of the problem in which a hollow cylinder is fixed at its inner surface and a moment history is applied to its outer surface. This causes the cylindrical surfaces to rotate about the central axis, thereby inducing a radial shear strain distribution. It is shown that there is a time when the material near the inner support begins to yield and a layer of large shear strain gradient begins to grow rapidly. It is also shown that the stress or strain history at a material element will generally not be one of the standard histories used to study yield.