Nonlinear Viscoelasticity

Abstract

Because Young's modulus of most polymers is relatively low compared to other structural materials such as metals, concrete, ceramics, etc., strains and deformations may be relatively large. A casual glance at the stressstrain response of polycarbonate given in Fig. 3.7 indicates that the strain at yield is about 5% and at failure is more than 60%. Further, examination of the creep response of polycarbonate (Brinson, (1973)) as discussed in Chapter 11 indicates inear behavior for strains larger than about 3% and the material begins to neck or yield (Luder's bands form) for strains larger than about 5%. Obviously, polycarbonate as well as other polymers with similar behavior cannot be considered to be linear for such circumstances. For these reasons, it is appropriate to have basic understanding of nonlinear processes in order to be able to design structures made of polymeric materials. The intent here is to give basic definitions that will assist in identifying nonlinear effects when they occur and to review several nonlinear approaches. As many nonlinear approaches are beyond the intended level and scope of this text, the focus will be on single integral mathematical models which are an outgrowth of linear viscoelastic hereditary integrals and lead to an extended superposition principle that can be used to evaluate nonlinear polymers. The emphasis will be on one-dimensional methods but these can be readily extended to three dimensions using deviatoric and dilatational stresses and strains as was the case for linear viscoelastic stress analysis as discussed in Chapters 2 and 9.