Estimation of melt film variables during the steady‐state penetration phase of thermoplastic vibration welding using a generalized newtonian fluid model

Abstract

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.

A simple analytical model for estimation of melt film variables in thermoplastic vibration welding

“…It is clear from Fig. 6, that for all the resins, h 0 decreases with increases in p 0 , a trend that is consistent with earlier predictions [3,16,17,18,20]. It is notable that the decrease in h 0 with increase in weld pressure is larger in case of PP-1105, and PP-1042 especially at the lower weld pressure range.…”

“…On the other hand, the estimates of melt film thicknesses are underestimated due to the lack of two‐way coupling between the heat transfer and momentum balance. For both melt film variables, the analytical model reveals exactly the same trends as the comprehensive numerical model with respect to the sensitivity of the variables to changes in welding conditions. Therefore, with an optimal choice of the viscosity curve, the analytical model provides a significantly faster and inexpensive method of estimating the melt film variables during vibration welding, while incorporating the details of resin rheology.…”

“…However, Patham and Foss [20] observed that the contribution to II 2D is dominated by the vibration direction shear rates: qw/qy .. qu/qy, qv/qx, qu/qx, qv/qy. Therefore, to simplify the analysis without losing much accuracy, only qw/qy is considered for evaluation of viscosity and viscous heating terms.…”

“…The steady state penetration phase (Phase III) of vibration welding has received considerable attention in modeling studies [1][2][3][16][17][18][19][20]. Figure 2 shows the geometry and boundary conditions typically used for modeling of steady state flow and heat transfer within the melt film during longitudinal vibration welding.…”

Thermoplastic vibration welding: Review of process phenomenology and processing–structure–property interrelationships

“…Therefore, in the strictest sense, these approaches cannot be considered to be full‐fledged nonNewtonian solutions. More recently, Patham and Foss [36] have developed an iterative finite element approach that accounts for both the shear‐rate and temperature dependence of viscosity in a fundamental fashion by incorporating the Cross‐WLF dependence of viscosity in the formulation of the momentum balance as well as in the viscous heating term in the heat balance. An alternative modeling approach by Lee et al [32] employs the measurement of shear‐force amplitude to directly calculate the shear stresses (ratio of shear‐force and sheared area) in the melt‐film; the input of these measured shear stresses, in addition to the penetration transient measurements, into the model can enable the direct calculation of the shear‐rate dependent melt‐film viscosities and viscous dissipation functions, without resorting to an iterative approach.…”