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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v9.i1.50
pages 53-72

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

Arthur Levy
GeM - Ecole Centrale Nantes, Universite de Nantes - 1 rue de la Noe 44321 Nantes, France
Steven Le Corre
GeM - Ecole Centrale Nantes, Universite de Nantes - 1 rue de la Noe 44321 Nantes, France
Arnaud Poitou
GeM - Ecole Centrale Nantes, Universite de Nantes - 1 rue de la Noe 44321 Nantes, France
Eric Soccard
EADS IW - Technocampus, 1 rue de la Noe 44321 Nantes, France

ABSTRACT

The 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 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 savings appears to be highly reduced, to 1,000 times less.

REFERENCES

  1. Ageorges, C., Ye, L., and Hou, M., Avdances in fusion bonding techniques for joining thermoplastic matrix composites: A review. DOI: 10.1016/S1359-835X(00)00166-4

  2. Benatar, A. and Gutowski, T. G., Ultrasonic welding of peek graphite apc-2 composites. DOI: 10.1002/pen.760292313

  3. Benssousan, A., Lions, J. L., and Papanicoulau, G., Asymptotic Analysis for Periodic Structures.

  4. Boutin, C. and Auriault, J., Dynamic behaviour of porous media saturated by a viscoelastic fluid. Application to bituminous concretes.

  5. Boutin, C. and Wong, H., Study of thermosensitive heterogeneous media via space-time homogenisation. DOI: 10.1016/S0997-7538(98)90503-4

  6. Cojocaru, D. and Karlsson, A. M., A simple numerical method of cycle jumps for cyclically loaded structures. DOI: 10.1016/j.ijfatigue.2006.01.010

  7. Francfort, G. and Suquet, P., Homogenization and mechanical dissipation in thermoviscoelasticity. DOI: 10.1007/BF00251909

  8. Geindreau, C. and Auriault, J., Investigation of the viscoplastic behaviour of alloys in the semi-solid state by homogenization. DOI: 10.1016/S0167-6636(99)00012-5

  9. Goyal, R., Tiwari, A. N., Mulik, U. P., and Negi, Y. S., Dynamic mechanical properties of Al<sub>2</sub>O<sub>3</sub>/poly(ether ether ketone) composites. DOI: 10.1002/app.25607

  10. Guennouni, T., Sur une m&#233;thode de calcul de structures soumises &#225; des chargements cycliques: L’Homog&#233;n&#233;isation en temps.

  11. Le Corre, S., Dumont, P., Orgeas, L., and Favier, D., Une approche multi-&#233;chelle de la rh&#233;ologie des suspensions concentr&#233;es de fibres. DOI: 10.3166/rcma.15.355-369

  12. Li, R., Time-temperature superposition method for glass transition temperature of plastic materials. DOI: 10.1016/S0921-5093(99)00602-4

  13. Oskay, C. and Fish, J., Fatigue life prediction using 2-scale temporal asymptotic homogenization. DOI: 10.1002/nme.1069

  14. Sanchez-Palencia, E., Non-homogeneous media and vibration theory. DOI: 10.1007/3-540-10000-8

  15. Suresh, K., Rani, M., Prakasan, K., and Rudramoorthy, R., Modeling of temperature distribution in ultrasonic welding of thermoplastics for various joint designs. DOI: 10.1016/j.jmatprotec.2006.12.028

  16. Tolunay, M., Heating and bonding mechanisms in ultrasonic welding of thermoplastics. DOI: 10.1002/pen.760231307

  17. Van Paepegem, W., Degrieck, J., and De Baets, P., Finite element approach for modelling fatigue damage in fibre-reinforced composite materials. DOI: 10.1016/S1359-8368(01)00038-5

  18. Wang, X., Yan, J., Li, R., and Yang, S., FEM investigation of the temperature field of energy director during ultrasonic welding of peek composites. DOI: 10.1177/0892705706067479

  19. Yu, Q. and Fish, J., Multiscale asymptotic homogenization for multiphysics problems with multiple spatial and temporal scales: A coupled thermo-viscoelastic example problem.


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