Composites Research

The Korean Society for Composite Materials (한국복합재료학회)
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Analysis of RTM Process Using the Extended Finite Element Method

확장 유한 요소 법을 적용한 RTM 공정 해석

  • Received : 2013.08.17
  • Accepted : 2013.11.05
  • Published : 2013.12.31
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Abstract

Numerical simulation for Resin Transfer Molding manufacturing process is attempted by using the eXtended Finite Element Method (XFEM) combined with the level set method. XFEM allows to obtaining a good numerical precision of the pressure near the resin flow front, where its gradient is discontinuous. The enriched shape functions of XFEM are derived by using the level set values so as to correctly describe the interpolation with the resin flow front. In addition, the level set method is used to transport the resin flow front at each time step during the mold filling. The level set values are calculated by an implicit characteristic Galerkin FEM. The multi-frontal solver of IPSAP is adopted to solve the system. This work is validated by comparing the obtained results with analytic solutions. Moreover, a localization method of XFEM and level set method is proposed to increase the computing efficiency. The computation domain is reduced to the small region near the resin flow front. Therefore, the total computing time is strongly reduced by it. The efficiency test is made with a simple channel flow model. Several application examples are analyzed to demonstrate ability of this method.

RTM (Resin Transfer Molding) 공정을 수치해석하기 위해 Level set 방법과 결합된 확장 유한 요소 법을 적용하였다. 유동 전면 부에서 비연속적인 구배를 가지는 압력을 계산하기 위해 확장 유한 요소 법을 이용하여 계산의 정밀성을 높였다. 확장 유한 요소 법에 이용되는 확장 형상 함수는 Level set 값을 이용하여 정의하였다. 이 확장 형상 함수는 요소를 통과하는 수지 유동 전면부의 위치를 반영할 수 있다. 게다가 Level set 법이 금형 충전 동안 수지 유동 전면부의 위치를 계산할 때 적용되었다. 수지 유동 전면부의 위치를 계산하는 미분방정식은 내연적 특성 Galerkin 유한 요소 법을 적용하여 풀었다. 선형 시스템 계산에서는 IPSAP의 다중 프론트 솔버를 이용한다. 본 연구에서 계산한 해석 값은 이론 값과 비교하여 검증하였다. 계산 효율을 높이기 위해 확장 유한 요소 법과 Level set 방법의 국소화 기법이 제안되었다. 이 기법은 계산 영역을 수지 유동 전면 부 근처의 영역으로 축소한다. 그러므로 전체 계산 양은 최소화될 수 있었다. 이 기법의 계산 효율은 채널 유동 모델을 이용하여 평가된다. 본 연구의 해석 능력을 보여주기 위해 몇 가지 적용 예제를 계산하였다. 첫 번째 예제를 이용해서 복잡하게 흘러가는 수지 전면부의 갈라짐과 합쳐지는 현상 해석하였다. 그리고 금형 내부의 Race-tracking 효과와 기공 생성 현상을 확인하기 위해 복잡한 모양의 구조물을 시뮬레이션 하였다.

Keywords

References

  1. Kang, M.K., Jung, J.J., and Lee, W.I., "Analysis of Resin Transfer Moulding Process with Controlled Multiple Gates Resin Injection," Composites Part A, Vol. 31, No. 5, 2000, pp. 407-422. https://doi.org/10.1016/S1359-835X(99)00086-X
  2. Bruschke, M.V., and Advani ,S.G., "A Finite-Element Control Volume Approach to Mold Filling in Anisotropic Porous- Media," Polymer Composites, Vol. 11, No. 6, 1990, pp. 398-405. https://doi.org/10.1002/pc.750110613
  3. Shojaei, A. and Ghaffarian, S.R., "Modeling and Simulation Approaches in the Resin Transfer Molding Process: A Review," Polymer Composites, Vol. 24, No. 4, 2003, pp. 525-544. https://doi.org/10.1002/pc.10050
  4. Young, W.B., Rupel, K., Han, K., Lee, L.J., and Liou, M.J., "Analysis of Resin Injection-Molding in Molds with Preplaced Fiber Mats. 2. Numerical-Simulation and Experiments of Mold Filling," Polymer Composites, Vol. 12, No. 1, 1991, pp. 30-38. https://doi.org/10.1002/pc.750120106
  5. Trochu, F., Gauvin, R., and Gao, D.M., "Numerical-Analysis of the Resin Transfer Molding Process by the Finite-Element Method," Advances in Polymer Technology, Vol. 12, No. 4, 1993, pp. 329-342. https://doi.org/10.1002/adv.1993.060120401
  6. Trochu, F., Ruiz, E., Achim, V., and Soukane, S., "Advanced Numerical Simulation of Liquid Composite Molding for Process Analysis and Optimization," Composites Part A, Vol. 37, No. 6, 2006, pp. 890-902. https://doi.org/10.1016/j.compositesa.2005.06.003
  7. Shojaei, A., Ghaffarian, S.R., and Karimian, S.M.H., "Numerical Simulation of Three-Dimensional Mold Filling Process in Resin Transfer Molding Using Quasi-Steady State and Partial Saturation Formulations," Composites Science and Technology, Vol. 62, No. 6, 2002, pp. 861-879. https://doi.org/10.1016/S0266-3538(02)00020-9
  8. Liu, X.L., "Isothermal Flow Simulation of Liquid Composite Molding," Composites Part A, Vol. 31, No. 12, 2000, pp.1295-1302. https://doi.org/10.1016/S1359-835X(00)00007-5
  9. Kang, M.K., and Lee, W.I., "A Flow-Front Refinement Technique for the Numerical Simulation of the Resin-Transfer Molding Process," Composites Science and Technology, Vol. 59, No. 11, 1999, pp. 1663-1674. https://doi.org/10.1016/S0266-3538(99)00029-9
  10. Dong, C.S., "A Modified Rule of Mixture for the Vacuum- Assisted Resin Transfer Moulding Process Simulation," Composites Science and Technology, Vol. 68, No. 9, 2008, pp. 2125-2133. https://doi.org/10.1016/j.compscitech.2008.03.019
  11. Phelan, F.R., "Simulation of the Injection Process in Resin Transfer Molding," Polymer Composites, Vol. 18, No. 4, 1997, pp. 460-476. https://doi.org/10.1002/pc.10298
  12. Jiang, S.F., Yang, L., Alsoliby, S.L., and Zhou, G.F., "PCG Solver and its Computational Complexity for Implicit Control-Volume Finite-Element Method of RTM Mold Filling Simulation," Composites Science and Technology, Vol. 67, No. 15-1, 2007, pp. 3316-3322. https://doi.org/10.1016/j.compscitech.2007.03.030
  13. Chessa, J., Smolinski, P., and Belytschko, T., "The Extended Finite Element Method (XFEM) for Solidification Problems," International Journal for Numerical Methods in Engineering, Vol. 53, No. 8, 2002, pp. 1959-1977. https://doi.org/10.1002/nme.386
  14. Chessa, J., and Belytschko, T., "An Extended Finite Element Method for Two-Phase Fluids," Journal of Applied Mechanics, Vol. 70, No. 1, 2003, pp. 10-17. https://doi.org/10.1115/1.1526599
  15. Chessa, J., and Belytschko, T., "An Enriched Finite Element Method and Level Sets for Axisymmetric Two-Phase Flow with Surface Tension," International Journal for Numerical Methods in Engineering, Vol. 58, No. 13, 2003, pp. 2041-2064. https://doi.org/10.1002/nme.946
  16. Belytschko, T., Gracie, R., and Ventura, G., "A Review of Extended/Generalized Finite Element Methods for Material Modelinga," Modeling and Simulation in Materials Science and Engineering, Vol. 17, No. 4, 2009, pp. 1-24.
  17. Ji, H., Chopp, D., and Dolbow, J.E., "A Hybrid Extended Finite Element/Level Set Method for Modeling Phase Transformations," International Journal for Numerical Method in Engineering, Vol. 54, No. 8, 2002, pp.1209-1233. https://doi.org/10.1002/nme.468
  18. Ji, H., and Dolbow, J.E., "On Strategies for Enforcing Interfacial Constraints and Evaluating Jump Conditions with the Extended Finite Element Method," International Journal for Numerical Method in Engineering, Vol. 61, No. 14, 2004, pp. 2508-2535. https://doi.org/10.1002/nme.1167
  19. Hirt, C.W., and Nichols, B.D., "Volume of Fluid (Vof) Method for the Dynamics of Free Boundaries," Journal of Computional Physics, Vol. 39, No. 1, 1981, pp. 201-225. https://doi.org/10.1016/0021-9991(81)90145-5
  20. Kim, M.S., and Lee, W.I., "A New VOF-Based Numerical Scheme for the Simulation of Fluid Flow with Free Surface. Part I: New Free Surface-Tracking Algorithm and its Verification," International Journal for Numerical Method in Fluids, Vol. 42, No. 7, 2003, pp. 765-790. https://doi.org/10.1002/fld.553
  21. Lin, C.L., Lee, H., Lee, T., and Weber, L.J., "A Level Set Characteristic Galerkin Finite Element Method for Free Surface Flows," International Journal for Numerical Method in Fluids, Vol. 49, No. 5, 2005, pp. 521-547. https://doi.org/10.1002/fld.1006
  22. Peng, D.P., Merriman, B., Osher, S., Zhao, H.K., and Kang, M.J., "A PDE-Based Fast Local Level Set Method," Journal of Computational Physics, Vol. 155, No. 2, 1999, pp. 410-438. https://doi.org/10.1006/jcph.1999.6345
  23. Soukane, S. and Trochu, F., "Application of the Level Set Method to the Simulation of Resin Transfer Molding," Composites Science and Technology, Vol. 66, No. 7-8, 2006, pp. 1067-1080. https://doi.org/10.1016/j.compscitech.2005.03.001
  24. Gantois, R., Cantarel, A., Dusserre, G., Felices, J.N., and Schmidt, F., "Numerical Simulation of Resin Transfer Molding using BEM and Level Set Method," International Journal of Material Forming, Vol. 3, No. 1, 2010, pp. 635-638. https://doi.org/10.1007/s12289-010-0850-9
  25. Sethian, J.A., Level Set Methods and Fast Marching Methods, 2nd edition, Cambridge University Press, USA, 1999.
  26. Advani, S.G., and Sozer, E.M., Process Modeling in Composites Manufacturing, Marcel Dekker, Inc., USA, 2003.
  27. Zienkiewicz, O.C., and Taylor, R.L., The Finite Element Method Volume 3: Fluid Dynamics, 5th Edition, Butterworth Heinemann, USA, 2000.
  28. Ventura, G., "On the Elimination of Quadrature Subcells for Discontinuous Functions in the eXtended Finite-Element Method," International Journal for Numerical Method in Engineering, Vol. 66, No. 5, 2006, pp. 761-795. https://doi.org/10.1002/nme.1570
  29. Mousavi, S.E., and Sukumar, N., "Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method," Computer Methods in Applied Mechanics and Engineering, Vol. 199, No. 49-52, 2010, pp. 3237-3249. https://doi.org/10.1016/j.cma.2010.06.031
  30. Kim, J.H., Lee, C.S., and Kim, S.J., "High-Performance Domainwise Parallel Direct Solver for Large-Scale Structural Analysis," AIAA Journal, Vol. 43, No. 3, 2005, pp. 662-670. https://doi.org/10.2514/1.11171
  31. Cai, Z., "Simplified Mold Filling Simulation in Resin Transfer Molding," Journal of Composite Materials, Vol. 26, No. 17, 1992, pp. 2606-2630. https://doi.org/10.1177/002199839202601708
  32. Lin, M., Hahn, H.T., and Huh, H., "A Finite Element Simulation of Resin Transfer Molding Based on Partial Nodal Saturation and Implicit Time Integration", Composites Part A, Vol. 29, No. 5-6, 1998, pp. 541-550. https://doi.org/10.1016/S1359-835X(97)00126-7
  33. Shojaei, A., Ghaffarian, S.R., and Karimian, S.M.H., "Numerical Simulation of Three-Dimensional Mold Filling Process in Resin Transfer Molding Using Quasi-Steady State and Partial Saturation Formulations," Composites Science and Technology, Vol. 62, No. 6, 2002, pp. 861-879. https://doi.org/10.1016/S0266-3538(02)00020-9
  34. Jung, Y., Han, W.S., Vautrin, A., and Kim, S.J., "RTM Process Simulation by Using XFEM and Levelset Method," 18th International Conference on Composite Materials, Jeju, Korea, Aug. 2011, 21-26 2011, ICC Jeju, Seogipo Special Self-Governing Province, Korea, W23-1-IF1687.
  35. Jung, Y., Kim, S.J., and Han, W.S., "Numerical Simulation of RTM Process Using the Extended Finite Element Method Combined with the Level Set Method," Journal of Reinforced Plastics and Composites, Vol. 32, No. 5, 2013, pp. 308-317. https://doi.org/10.1177/0731684412474526