Representation of Polymer Chain Shape in Injection Moulding Simulation
September 18th, 1988
Paper to the Polymer Processing Society Regional Meeting, Brunel University, UK, 18th-19th September 1988.
S F Bush
Summary
As is well known, a particular feature of the injection moulding of thermoplastic polymers is the very wide range of strain rates developed at different parts of the flow field. Furthermore, the effects of high strain rates at the gate for instance are felt at points in the moulding remote from their point of origin. These effects show up principally in two ways, (a) in the fluid state and (b) in the subsequent solid state.
In the fluid state, the wide range of strain rates across the flow field means that the mean chain shape at a particular point is a function not only of the local strain rate, but also of the chains convected to the point from other parts of the flow. The chain shape determines the number of entanglements which in turn is a major determinant of the resistance to flow. Representing the flow resistance by means of a local viscosity, even if introduced as a function of local strain rate, will thus potentially give rise to significant error.
In the solid state, the incidence of high strain rates and the rapid cooling necessary for economic production give rise to substantial anisotropy and potentially damaging distortion as strained chains gradually relax.
To allow for these effects in a complex moulding simulation, chain shape has been set up as a primary dependent variable like the velocities and the temperature. The net rate of change of shape at any point and instant is thus the sum of convection terms and a local rate of change. To embed this treatment within a general two or three dimensional moulding or extrusion simulation entails a considerably simpler approach to the description of the chain shape than that adopted by other workers whose objective has been to derive point or equilibrium viscosity strain rate relations.
Using the present approach, attention is focussed on the processes of entanglement and disentanglement. The kinetic or non-equilibrium treatment adopted is suitable for a finite cell modelling system and also allows estimates to be made of the viscosity under special-case steady flow conditions. Furthermore, because of the strong dependence of crystal growth rates on local chain shape or orientation, the approach allows a prediction of the space variation of crystallinity developed in a solid moulding.
See also the section on Polymer Morphology & Fibre Reinforcement Mechanisms.