5.1 Introduction

In this chapter we discuss then on-Newtonian effect in flow problems. Innon-Newtonian flow cases, the viscosity of the material is dependent on non-linear relations of the stress and/or strain rate. Several models are available for non-Newtonian fluids, the simplest and widely used among these is the one based on a power law. We start with such a formulation for metal and polymer forming in Sec. 5.2. Fluids that partially return to their original form when applied stress is released are called viscoelastic. The models for viscoelastic fluids can be quite complicated. In Sec. 5.3 we present some simplified model forms and discuss their numerical solution using the CBS procedure described in Chapter 3. In Sec. 5.4 we briefly discuss a direct displacement method based on the CBS approach to solve impact problems.

5.2 Non-Newtonian flows metal and polymer forming

5.2.1 Non-Newtonian flows including viscoplasticity and plasticity

In many fluids the viscosity, though isotropic, may be dependent on the rate of strain as well as on the state variables such as temperature or total deformation. Typical here is, for instance, the behaviour of many polymers, hot metals, etc., where a power law of the type

with

governs the viscosity strain rate dependence where m is a physical constant. In the above is the second invariant of the deviatoric strain rate tensor defined from Eq.(3.35), T is the (absolute) temperature and is a total strain invariant.

This secant viscosity can of course be...