We present a finite element method for predicting the fiber orientation patterns in 3-D injection molded features, and compare the predictions to experiments. The predictions solve the full balance equations of mass, momentum, and energy for a generalized Newtonian fluid. A second-order tensor is used to describe and calculate the local fiber orientation state. A standard Hele-Shaw molding filling simulation is used to provide inlet boundary conditions for the detailed finite element models, which are limited to the local geometry of each feature. The experiments use automated image analysis of polished cross-sections to determine fiber orientation as a function of position. Predictions compare well with experiments on a transverse rib, where the detailed calculation can be 2-D. Results of a 3-D calculation for a flow-direction rib also show generally good agreement with experiments. Some errors in this latter calculation are caused by not simulating the initial filling of the rib, due to computational limits.
The thickness of the melt film and the temperature profiles within the melt film in the weld zone are key process variables governing the development of weldzone microstructures and the resulting development of weld strengths, during vibration welding of thermoplastics. The mathematical model described in this report is aimed at investigating the role of the rheology of the melt-specifically the magnitude and shear-rate as well as temperature dependence of the melt viscosity-in governing the process variables such as the molten film thickness and the viscosities, stresses, and the temperatures within the melt film during vibration welding. The analysis is focused on the steady-state penetration phase (phase III) of vibration welding. The coupled steady-state momentum balance and heat transfer within the melt film, formulated using the Cross-WLF (Williams-Landel-Ferry) relationship for viscosity, are solved in an iterative finite element framework. The model has been implemented for two different polymers displaying significant differences in viscosities and shear thinning behaviors. An attempt has been made to correlate the trends in the estimated melt film variables with the experimentally measured weld quality. FIG. 2. Geometry employed for analysis of steady state flow and heat transfer in the vibration welding melt film (grey colored portion), and the boundary conditions for (a) momentum balance and (b) energy balance.
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