Doctoral Dissertations
Date of Award
8-1994
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Major
Polymer Engineering
Major Professor
Donald C. Bogue
Committee Members
Joseph E. Spruiell, Edward S. Clark, Marion G. Hansen
Abstract
Most polymer processing operations involve a high cooling rate in which the material is cooled from a molten state into a solid state. Non-equilibrium density builds up during such a process and relaxes inhomogeneously later. These time-dependent changes also result in residual stresses. The analysis and computer simulation of various polymer processing operations are far from satisfactory because of the lack of sufficiently general theories to deal with the non-equilibrium problem. This research is part of continuing work on the residual stresses and non-isothermal rheological behavior at the University of Tennessee, Knoxville. The present study includes experiments and analysis on time-dependent density changes in amorphous polymers; and the theoretical development and simulation of injection molding. The experimental work of the present study involved quenching bead-like polystyrene samples. The samples were subjected to air and water quenches, the average cooling rates being of the order of degrees per second by the air quench and hundreds of degree per second by the water quench. The descent of the samples in a density gradient column was measured as a function of time. Special calibration and analysis provided an estimate of the density at the end of the quench and during the subsequent aging. A rate equation and an empirical time constant equation were developed based on the data of the present work and the data of Greiner and Schwarzl. Finally, these results were used in the simulation of injection molding. The simulation of injection molding was done on an idealized rectangular slab—taken to be homogeneous in the flat (x-y) plane, with gradients present only in the thin (z) dimension. This is only an approximation of the actual situation in injection molding, in which there are gradients in the flow direction as well. The simulation started with an imposed z-dependent temperature distribution and an imposed time-dependent pressure distribution, simulating the end of the filling step. An imposed packing pressure is maintained by imagining that a small amount of material is added during the packing step. In the cooling step, one presumes the volume and mass to be constant. While in the post-ejection step the volume changes and the mass remains constant. The predictions are, finally, the "total stress" (pressure in the ordinary sense) as a function of time; and residual stresses and density distributions at various times. A new concept in the theoretical framework has to do with a kind of pressure (an isotropic stress) that is used in the PVT equation—not, however, pressure in the ordinary sense. This "pressure", which is here given the symbol P, was introduced by Ko and Bogue to generalize the framework of existing constitutive theory. Temperature and hydrostatic pressure necessarily affect the volume; but certain normal loadings (for example, tensile or compressive stresses) can affect it also. The generalized isotropic stress (-P) can be of either sign. This becomes important in the constrained (residual stress) problem: through the thin dimension z, where the total stress ωzz is a constant, one can have gradients in both P and the anisotropic stresses, often with a change of sign. These new results are discussed in detail. Three cases were simulated in detail, approximating experimental data from groups at Cornell University, the Delft University of Technology and the Eindhoven University of Technology. In cases where "total pressure" versus time data are available, it was found that the time-dependent PVT formulation of the present work is necessary to obtain reasonable fits to the data. The predictions for residual stresses and densities cannot be tested directly because the present formulation predicts values for an undisturbed sample. In practice the sample must be cut up for testing, which releases part of the stresses. An alternate simulation was therefore done, in an attempt to simulate what was done experimentally. This alternate simulation predicts the measured residual stresses quite well. Some features of the density distribution could be predicted qualitatively, although not quantitatively.
Recommended Citation
He, Xinhua, "Experiments on time-dependent density changes in amorphous polymers and simulation of injection molding. " PhD diss., University of Tennessee, 1994.
https://trace.tennessee.edu/utk_graddiss/10367