ULTRASONIC WELDING OF THERMOPLASTIC COMPOSITES: MODELING OF THE PROCESS USING TIME HOMOGENIZATION

The process of ultrasonic welding allows to assemble thermoplastic composite parts. A high frequency vibration imposed to the processing zone induces self heating and melting of the polymer. The main feature of this process is the existence of phenomena that occur on two very different time scales: the vibration (about 10−5 s) and the flow of molten polymer (about 1s). In order to simulate accurately these phenomena without the use of a very fine time discretization over the whole process, we apply a time homogenization technique. First, the thermo-mechanical problem is formulated using a Maxwell viscoelastic constitutive law and then, it is homogenized using asymptotic expansion. This leads to three coupled problems: a micro-chronological mechanical problem, a macro-chronological mechanical problem and a macro-chronological thermal problem. This coupled formulation is actually simpler because the macro-chronological problems do not depend on the micro time scale and its associated fast variations. Lastly, a uniform simple test case is proposed to compare the homogenized solution to a direct calculation. It shows that the method gives good results provided that the vibration is fast enough compared to the duration of the process. Moreover, the time saving appears to be highly reduced down to one thousand times less.