Extrusion constitutive equations

An important aspect relating to the ability to predict extrusion behaviour is the recognition that all commercial polymers must be characterised by a spectrum of relaxation times. A single relaxation time constitutive equation is inadequate to capture all necessary features. The detailed form of the nonlinear component within the constitutive equation is also important and decisive in terms of accurate prediction and again much work has been done refining these parameters. ... 

Work on designing profile extrusion dies is complicated by the effect known as die swell. In capillary flow, elastic effects cause the diameter of the extrudate to be greater than the capillary diameter. This effect depends on the length of the capillary as well as the processing conditions and must be taken into account when designing extrusion dies. To model such an effect requires a viscoelastic constitutive equation. There is a lack of appropriate models for which data is readily available and this has hindered the use of computer simulation in this field. Nevertheless, a great deal of literature exists on simulation. ... 

Interface stability in co-extrusion has been the subject of extensive analysis. There is an elastic driving force for encapsulation caused by the second normal stress difference (56), but this is probably not an important mechanism in most coprocessing instabilities. Linear growth of interfacial disturbances followed by dramatic breaking wave patterns is observed experimentally. Interfacial instabilities in creeping multilayer flows have been studied for several simple constitutive equations (57-59). Instability modes can be traced to differences in viscosity and normal stresses across the interface, and relative layer thickness is important. 

Melt Viscosity. The study of the viscosity of poljmier melts (47-62) is important for the manufacturer who must supply suitable materials and for the fabrication engineer who must select polymers and fabrication methods. Thus, melt viscosity as a fimction of temperature, pressure, rate of flow, and poljmier molecular weight and structure is of considerable practical importance. Polymer melts exhibit elastic as well as viscous properties. This is evident in the swell of the polymer melt upon emergence from an extrusion die, a behavior that results from the recovery of stored elastic energy plus normal stress effects. Theoretical developments include a constitutive equation that correctly captures nonlinear behavior in both elongation and shear (63,64). 

Helical flow involves the steady laminar motion of a fluid in an annulus, when one (or both) of two coaxial cylinders is rotated and an axial pressure gradient is simultaneously imposed (Fig. 8). It occurs in mechanical equipment like deep well drilling and in production lines for extrusion of artificial casings [16]. Theoretical studies on the helical flow of general fluids have been done by Rivlin [17] and Coleman and Noll [18]. The work of Tanner [19,20] and Savins and Wallick [21] on helical flows emphasizes the Oldroyd type of constitutive equation. Dierckes and Schowalter [22] as well... 

One of the interesting applications where the influence of flow on transport coefficients and on the constitutive and state equation is relevant, is the nucleation process. The effect of flow on crystallization is important because it often occurs in the presence of mechanical processing of the melt, such as extrusion, shearing, or injection, all these factors may affect the process drastically. 

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