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Mathematical Problems in Engineering
Volume 2015, Article ID 486346, 16 pages
http://dx.doi.org/10.1155/2015/486346
Research Article

A Robust Numerical Procedure for the Thermomechanical Flow Simulation of Friction Stir Welding Process Using an Adaptive Element-Free Galerkin Method

1Livermore Software Technology Corporation, 7374 Las Positas Road, Livermore, CA 94551, USA
2General Motors, 30500 Mound Road, Warren, MI 48090, USA
3Hengstar Technology Corporation, Shanghai 201203, China

Received 24 March 2015; Revised 21 June 2015; Accepted 23 June 2015

Academic Editor: Vladimir Turetsky

Copyright © 2015 C. T. Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. C. J. Dawes and W. M. Thomas, “Friction stir process welds in aluminum alloys,” Welding Journal, vol. 75, no. 3, pp. 41–45, 1996. View at Google Scholar
  2. O. Lorrain, J. Serri, V. Favier, H. Zahrouni, and M. El-Hadrouz, “A contribution to a critical review of friction stir welding numerical simulation,” Journal of Mechanics of Materials and Structures, vol. 4, no. 2, pp. 351–369, 2009. View at Publisher · View at Google Scholar · View at Scopus
  3. D. M. Neto and P. Neto, “Numerical modeling of friction stir welding process: a literature review,” The International Journal of Advanced Manufacturing Technology, vol. 65, no. 1–4, pp. 115–126, 2013. View at Publisher · View at Google Scholar · View at Scopus
  4. H. Pashazadeh, A. Masoumi, and J. Teimournezhad, “A 3D numerical model to investigate mechanical, thermal and material flow characteristics in friction stir welding of copper sheets,” International Journal of Automotive Engineering, vol. 3, no. 1, pp. 328–342, 2013. View at Google Scholar
  5. P. Ulysse, “Three-dimensional modeling of the friction stir-welding process,” International Journal of Machine Tools and Manufacture, vol. 42, no. 14, pp. 1549–1557, 2002. View at Publisher · View at Google Scholar · View at Scopus
  6. P. A. Colegrove and H. R. Shercliff, “3-Dimensional CFD modelling of flow round a threaded friction stir welding tool profile,” Journal of Materials Processing Technology, vol. 169, no. 2, pp. 320–327, 2005. View at Publisher · View at Google Scholar · View at Scopus
  7. D. Jacquin, B. de-Meester, A. Simar, D. Deloison, F. Montheillet, and C. Desrayaud, “A simple Eulerian thermo-mechanical modeling of friction stir welding,” Journal of Materials Processing Technology, vol. 211, no. 1, pp. 57–65, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. R. Nandan, G. G. Roy, and T. Debroy, “Numerical simulation of three-dimensional heat transfer and plastic flow during friction stir welding,” Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, vol. 37, no. 4, pp. 1247–1259, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Bastier, M. H. Maitournam, F. Roger, and K. Dang-Van, “Modelling of the residual state of friction stir welded plates,” Journal of Materials Processing Technology, vol. 200, no. 1–3, pp. 25–37, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. M. Song and R. Kovacevic, “Thermal modeling of friction stir welding in a moving coordinate system, and its validation,” International Journal of Machine Tools and Manufacture, vol. 43, no. 6, pp. 605–615, 2003. View at Publisher · View at Google Scholar · View at Scopus
  11. M. Z. H. Khandkar, J. A. Khan, and A. P. Reynolds, “Prediction of temperature distribution and thermal history during friction stir welding: input torque based model,” Science and Technology of Welding and Joining, vol. 8, no. 3, pp. 165–174, 2003. View at Publisher · View at Google Scholar · View at Scopus
  12. P. A. Colegrove and H. R. Shercliff, “Experimental and numerical analysis of aluminium alloy 7075-T7351 friction stir welds,” Science and Technology of Welding and Joining, vol. 8, no. 5, pp. 360–368, 2003. View at Publisher · View at Google Scholar · View at Scopus
  13. Z. Zhang and H. W. Zhang, “Solid mechanics-based Eulerian model of friction stir welding,” The International Journal of Advanced Manufacturing Technology, vol. 72, no. 9–12, pp. 1647–1653, 2014. View at Publisher · View at Google Scholar · View at Scopus
  14. D. H. Santiago, G. Lombera, S. Urquiza, A. Cassanelli, and L. A. Vedia, “Numerical modeling of welded joints by the ‘Friction Stir Welding’ process,” Materials Research, vol. 7, no. 4, pp. 569–574, 2004. View at Publisher · View at Google Scholar
  15. H. Schmidt and J. Hattel, “A local model for the thermomechanical conditions in friction stir welding,” Modelling and Simulation in Materials Science and Engineering, vol. 13, no. 1, pp. 77–93, 2005. View at Publisher · View at Google Scholar · View at Scopus
  16. M. Chiumenti, M. Cervera, C. Agelet-de-Saracibar, and N. Dialami, “Numerical modeling of friction stir welding processes,” Computer Methods in Applied Mechanics and Engineering, vol. 254, pp. 353–369, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. Y. J. Chao, X. Qi, and W. Tang, “Heat transfer in friction stir welding—experimental and numerical studies,” Journal of Manufacturing Science and Engineering, vol. 125, no. 1, pp. 138–145, 2003. View at Publisher · View at Google Scholar · View at Scopus
  18. H. Askes and A. Rodríguez-Ferran, “A combined rh-adaptive scheme based on domain subdivision. Formulation and linear examples,” International Journal for Numerical Methods in Engineering, vol. 51, no. 3, pp. 253–273, 2001. View at Publisher · View at Google Scholar · View at Scopus
  19. G. Buffa, J. Hua, R. Shivpuri, and L. Fratini, “A continuum based fem model for friction stir welding—model development,” Materials Science and Engineering A, vol. 419, no. 1-2, pp. 389–396, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. H. Si, “Constrained Delaunay tetrahedral mesh generation and refinement,” Finite Elements in Analysis and Design, vol. 46, no. 1-2, pp. 33–46, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. J.-S. Chen, C. Pan, C.-T. Wu, and W. K. Liu, “Reproducing kernel particle methods for large deformation analysis of non-linear structures,” Computer Methods in Applied Mechanics and Engineering, vol. 139, no. 1–4, pp. 195–227, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. C.-T. Wu, J.-S. Chen, L. Chi, and F. Huck, “Lagrangian meshfree formulation for analysis of geotechnical materials,” Journal of Engineering Mechanics, vol. 127, no. 5, pp. 440–449, 2001. View at Publisher · View at Google Scholar · View at Scopus
  23. S. Li and W. K. Liu, Meshfree Particle Method, Springer, Berlin, Germany, 2004. View at MathSciNet
  24. D. C. Simkins and S. Li, “Meshfree simulations of thermo-mechanical ductile fracture,” Computational Mechanics, vol. 38, no. 3, pp. 235–249, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  25. T. Belytschko, Y. Y. Lu, and L. Gu, “Element-free Galerkin methods,” International Journal for Numerical Methods in Engineering, vol. 37, no. 2, pp. 229–256, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  26. W. K. Liu, S. Jun, and Y. F. Zhang, “Reproducing kernel particle methods,” International Journal for Numerical Methods in Fluids, vol. 20, no. 8-9, pp. 1081–1106, 1995. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. L. B. Lucy, “A numerical approach to the testing of the fission hypothesis,” The Astronomical Journal, vol. 82, pp. 1013–1024, 1977. View at Publisher · View at Google Scholar
  28. C. T. Wu and M. Koishi, “A meshfree procedure for the microscopic analysis of particle-reinforced rubber compounds,” Interaction and Multi-Scale Mechanics, vol. 2, no. 2, pp. 147–169, 2009. View at Google Scholar
  29. C. T. Wu, C. K. Park, and J. S. Chen, “A generalized approximation for the meshfree analysis of solids,” International Journal for Numerical Methods in Engineering, vol. 85, no. 6, pp. 693–722, 2011. View at Publisher · View at Google Scholar · View at Scopus
  30. H.-P. Wang, C.-T. Wu, Y. Guo, and M. E. Botkin, “A coupled meshfree/finite element method for automotive crashworthiness simulations,” International Journal of Impact Engineering, vol. 36, no. 10-11, pp. 1210–1222, 2009. View at Publisher · View at Google Scholar · View at Scopus
  31. C. K. Park, C. T. Wu, and C. D. Kan, “On the analysis of dispersion property and stable time step in meshfree method using the generalized meshfree approximation,” Finite Elements in Analysis and Design, vol. 47, no. 7, pp. 683–697, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. C. T. Wu, W. Hu, and J. S. Chen, “A meshfree-enriched finite element method for compressible and near-incompressible elasticity,” International Journal for Numerical Methods in Engineering, vol. 90, no. 7, pp. 882–914, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. C. T. Wu and M. Koishi, “Three-dimensional meshfree-enriched finite element formulation for micromechanical hyperelastic modeling of particulate rubber composites,” International Journal for Numerical Methods in Engineering, vol. 91, no. 11, pp. 1137–1157, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. C. T. Wu, Y. Guo, and E. Askari, “Numerical modeling of composite solids using an immersed meshfree Galerkin method,” Composites Part B: Engineering, vol. 45, no. 1, pp. 1397–1413, 2013. View at Publisher · View at Google Scholar · View at Scopus
  35. C. T. Wu and W. Hu, “Multi-scale finite element analysis of acoustic waves using global residual-free meshfree enrichments,” Interaction and Multi-scale Mechanics, vol. 6, no. 2, pp. 83–105, 2013. View at Publisher · View at Google Scholar
  36. W. Pan, D. Li, A. M. Tartakovsky, S. Ahzi, M. Khraisheh, and M. Khaleel, “A new smoothed particle hydrodynamics non-newtonian model for friction stir welding: process modeling and simulation of microstructure evolution in a magnesium alloy,” International Journal of Plasticity, vol. 48, pp. 189–204, 2013. View at Publisher · View at Google Scholar · View at Scopus
  37. C. T. Dyka, P. W. Randles, and R. P. Ingel, “Stress points for tension instability in SPH,” International Journal for Numerical Methods in Engineering, vol. 40, no. 13, pp. 2325–2341, 1997. View at Google Scholar · View at Scopus
  38. T. Belytschko, Y. Guo, W. K. Liu, and S. P. Xiao, “A unified stability analysis of meshless particle methods,” International Journal for Numerical Methods in Engineering, vol. 48, no. 9, pp. 1359–1400, 2000. View at Google Scholar · View at MathSciNet · View at Scopus
  39. T. J. R. Hughes, The Finite Element Method, Prentice Hall, Englewood Cliffs, NJ, USA, 2000. View at MathSciNet
  40. T. D. Marusich and M. Ortiz, “Modelling and simulation of high-speed machining,” International Journal for Numerical Methods in Engineering, vol. 38, no. 21, pp. 3675–3694, 1995. View at Publisher · View at Google Scholar · View at Scopus
  41. M. A. Puso and T. A. Laursen, “A mortar segment-to-segment contact method for large deformation solid mechanics,” Computer Methods in Applied Mechanics and Engineering, vol. 193, pp. 601–629, 2004. View at Google Scholar
  42. W. Hu and C. T. Wu, “Metal forming analysis using meshfree-enriched finite element method and mortar contact algorithm,” Interaction and Multi-Scale Mechanics, vol. 6, no. 2, pp. 237–255, 2013. View at Google Scholar
  43. N. Kikuchi and J. T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia, Pa, USA, 1988.
  44. S. Koric, L. C. Hibbeler, and B. G. Thomas, “Explicit coupled thermo-mechanical finite element model of steel solidification,” International Journal for Numerical Methods in Engineering, vol. 78, no. 1, pp. 1–31, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  45. P. C. Guan, S. W. Chi, J. S. Chen, T. R. Slawson, and M. J. Roth, “Semi-Lagrangian reproducing kernel particle method for fragment-impact problems,” International Journal of Impact Engineering, vol. 38, no. 12, pp. 1033–1047, 2011. View at Publisher · View at Google Scholar · View at Scopus
  46. C. T. Wu and B. Ren, “A stabilized non-ordinary state-based peridynamics for the nonlocal ductile material failure analysis in metal machining process,” Computer Methods in Applied Mechanics and Engineering, vol. 291, pp. 197–215, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  47. O. C. Zienkiewicz and J. Z. Zhu, “A simple error estimator and adaptive procedure for practical engineering analysis,” International Journal for Numerical Methods in Engineering, vol. 24, no. 2, pp. 337–357, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  48. P. George and H. Borouchaki, Delaunay Triangulation and Meshing: Application to Finite Elements, Hermes, Paris, France, 1998. View at MathSciNet
  49. R. Lohner and P. Parikh, “Generation of three-dimensional unstructured grids by the advanced-front method,” International Journal for Numerical Methods in Fluids, vol. 8, no. 10, pp. 1135–1149, 1988. View at Publisher · View at Google Scholar · View at Scopus
  50. A. Bucher, A. Meyer, U.-J. Görke, and R. Kreißig, “A comparison of mapping algorithms for hierarchical adaptive FEM in finite elasto-plasticity,” Computational Mechanics, vol. 39, no. 4, pp. 521–536, 2007. View at Publisher · View at Google Scholar · View at Scopus
  51. G. Farin, “Triangular Bernstein-Bézier patches,” Computer Aided Geometric Design, vol. 3, no. 2, pp. 83–127, 1986. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  52. P. Moller and P. Hansbo, “On advancing front mesh generation in three dimensions,” International Journal for Numerical Methods in Engineering, vol. 38, no. 21, pp. 3551–3569, 1995. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  53. H. Samet, The Design and Analysis of Spatial Data Structures, Addison-Wesley, Reading, Pa, USA, 1990.
  54. LS-DYNA, Keyword User's Manual, LS-DYNA, 2015.