Ultrasonic Welding of Thermoplastic Composites, Modeling of the Process Using Time Homogenization.

International audienceThe process of ultrasonic welding allows assembly of 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 1 s). In order to accurately simulate these phenomena without the use of a very fine time discretization over the whole process, we apply a time homogenization technique. First, the thermomechanical problem is formulated using a Maxwell viscoelastic constitutive law, and then it is homogenized using asymptotic expansion. This leads to three coupled problems: a microchronological mechanical problem, a macrochronological mechanical problem, and a macrochronological thermal problem. This coupled formulation is actually simpler because the macrochronological problems do not depend on the micro time scale and its associated fist 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 savings appears to be highly reduced, to 1,000 times less