Doctoral Dissertations

Wen-Chien Ko

Date of Award

8-1989

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Polymer Engineering

Major Professor

Donald C. Bogue

Committee Members

John F. Fellers, Joseph E. Spruiell, Hui Pih

Abstract

Time-dependent volume changes are important in polymer processing because the material almost always cools rapidly from a rubbery melt into a nonequilibrium solid. The present work is part of a continuing study on the development and use a new constitutive equation which includes volume (compressibility) effects in amorphous polymers. Experiments and analysis involving simultaneous pulling and cooling were done for testing the theory and for specifying the parameters in the equations. Applications of the theory to certain practical volume-related problems were then carried out: first, the cooling step in injection molding and, second, the development of residual stresses in free, quenched samples.

The theoretical framework for coupling volume changes with stress changes (prior work at the University of Tennessee) has been restated in a more tractable and slightly modified form in the present work. The new theory reduces naturally to the existing theories of linear elasticity, large-deformation viscoelasticity, and to equilibrium and rate-dependent PVT equations.

The data of the present work came from measuring the force build-up in fiber-like polystyrene samples, which were subjected to simultaneous pulling and cooling, with cooling rates up to 3.3 °C/sec. In the analysis a set of two moduli and two time constants (with accompanying shift factors) are needed for the volume changes and stress changes, respectively. The time constants and associated shift factors were obtained from fitting the dilatometry data of Greiner and Schwarzl and melt shear data of Racin. The modulus G(T) as a function of temperature was estimated from literature data. Satisfactory fits with reasonable parameters were obtained, although the results depended strongly on the choice of the G(T) function. The experiments were not definitive because the volume change data were not measured. Further testing on the theory is being continued in separate work.

The cooling step in injection molding was simulated by using the simple geometry of a thin slab and assuming that there were no temperature and pressure gradients in the plane along the flow direction. Before the cooling step, the gapwise temperature profile at the end of mold filling was approximated from the C-FLOW mold filling program, while the build-up of packing pressure was introduced as a forcing function, similar to the data of the Cornell group. Two cases were studied as regards the compressibility (PVT) behavior: an equilibrium case, and a time-dependent case. While both could be fit to the data, the time-dependent case allowed one to use a more reasonable PVT equation.

The problem of inducing residual stresses in rapidly quenched slabs is a classical one, with the basic theory being that of Lee, Rogers and Woo (LRW), and special cases of it. The result of the LRW theory is an integral, which is not easily modified to change the inherent rheological assumptions. In the present work the problem is reformulated on a layer-by-layer basis, such that the computer simulation is directly connected to the physical problem. In the cases studied the PVT behavior was taken as time-dependent (unlike the equilibrium assumption of the LRW theory), with a discontinuous assumption for the modulus (like the special case of the LRW theory due to Aggarwala and Saibel). In this latter case the modulus is taken to be either zero (completely "fluid") or finite (completely "solid" with a modulus Gg), depending on the temperature relative to the glass transition. With the modulus Gg as an adjustable parameter, good fits to residual stress data from the literature can be made, but the numerical value of Gg is more reasonable when the PVT behavior is time-dependent. There are also literature data for the density profile across the slab and these are in qualitative agreement with the analysis. The inability to measure densities in situ precludes a direct quantitative comparison.

The complexity of the problems, involving time-dependent behavior in the rubbery, transition and glassy states, means that a large amount of independent data are needed. In the absence of such data simplified cases with adjustable parameters must be treated. These cases illustrate, however, the usefulness and tractability of the generalized theory in problems of practical interest.

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