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Modeling the powder compaction process using the finite element method and inverse optimization

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Abstract

This paper focuses on studying and adapting modeling techniques using the finite element method to simulate the rigid die compaction of metal powders. First, it presents the implementation of the cap constitutive model into ABAQUS FE software using the closest point projection algorithm. Then, an inverse modeling procedure was proposed to alleviate the problems raised by the interpretation of the experimental tests and to more accurately determine the material parameters. The objective function is formed, based on the discrepancy in density data between the numerical model prediction and the experiment. Minimization of the objective function with respect to the material parameters was performed using an in-house optimization software shell built on a modified Levenberg–Marquardt method. Thus, an integrated simulation module consisting of an inverse optimization method and a finite element method was developed for modeling the powder compaction process as a whole. The simulation and identification module developed was applied to simulate the compaction of some industrial parts. The results reveal that the maximum absolute error between densities is 2.3%. It corresponds to the precision of the experimental method.

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References

  1. German RM (1994) Powder metallurgy science. Metal Powder Industries Federation, Princeton, NJ

    Google Scholar 

  2. Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth. Part I. Yield criteria and flow rules for porous ductile media. Transactions of the ASME. J Eng Mat Technol 99:2–15

    Article  Google Scholar 

  3. Shima S, Oyane M (1976) Plasticity theory for porous materials. Int J Mech Sci 18:285–291

    Article  Google Scholar 

  4. Gurson AL, McCabe J (1992) Experimental determination of yield functions for compaction of blended metal powder. Adv Powder Metall Part Mater 2:133–147

    Google Scholar 

  5. Abou-Chedid G, Brown S (1992) On the mechanical behavior of metal powder compaction. Adv Powder Metall Part Mater 2:1–10

    Google Scholar 

  6. Drucker D, Prager W (1952) Soil mechanics and plastic analysis on limit design. Quart J Applied Math 10:157–175

    MathSciNet  MATH  Google Scholar 

  7. Schofield AN, Wroth CP (1968) Critical state solid mechanics. McGraw Hill, New York

    Google Scholar 

  8. DiMaggio, FL, Sandler, IS (1971) Material model for granular soils. J Eng Mech Div 97:935–950

    Google Scholar 

  9. Sandler IS, Rubin D (1979) An algorithm and a modular subroutine for the Cap model. Int J Numer Anal Methods Geomech 3:173–186

    Article  MATH  Google Scholar 

  10. Falgon D, Vidal-Salle E, Boyer JC, Peczalski R, Andrieu J (2005) Identification procedure of a hardening law for powder compaction. Powder Technol 157:183–190

    Article  Google Scholar 

  11. Michrafy A, Ringenbacher D, Tchoreloff P (2002) Modeling the compaction behavior of powders: application to pharmaceutical powders. Powder Technol 127:257–266

    Article  Google Scholar 

  12. Cunningham JC, Sinka IC, Zavaliangos A (2004) Analysis of tablet compaction. I. Characterization of mechanical behavior of powder and powder/tooling friction. J Pharm Sci 93:2022–2039

    Article  Google Scholar 

  13. Wu CY, Ruddy OM, Bentham AC, Hancock BC, Best SM, Elliott JA (2005) Modeling the mechanical behavior of pharmaceutical powders during compaction. Powder Technol 152:107–117

    Article  Google Scholar 

  14. Wu CY, Hancock BC, Mills A, Bentham AC, Best SM, Elliott JA (2008) Numerical and experimental investigation of capping mechanisms during pharmaceutical tablet compaction. Powder Technol 181:121–129

    Article  Google Scholar 

  15. Frenning G (2007) Analysis of pharmaceutical powder compaction using multiplicative hyperelasto-plastic theory. Powder Technol 172:102–112

    Article  Google Scholar 

  16. Gurson AL, Posteraro RA (1992) Yield functions for metal powders for use in the numerical simulation of powder compaction. TMS Conference, San Diego, CA

    Google Scholar 

  17. Chtourou H, Gakwaya A, Guillot M (2002) Modeling of the metal powder compaction process using the cap model. Part II: numerical implementation and practical applications. Int J Solids Struct 39:1077–1096

    Article  Google Scholar 

  18. Erhart T, Wall WA, Ramm E (2005) A robust computational approach for dry powders under quasi-static and transient impact loadings. Comput Meth Appl Mech Eng 194:4115–4134

    Article  MATH  Google Scholar 

  19. Rossi R, Alves MK, Al-Qureshi HA (2007) A model for the simulation of powder compaction processes. J Mater Process Technol 182:286–296

    Article  Google Scholar 

  20. Khoei AR, Azami AR, Azizi S (2007) Computational modeling of 3D powder compaction processes. J Mater Process Technol 185:166–172

    Article  Google Scholar 

  21. Lee SC, Kim KT (2007) A study on the Cap model for metal and ceramic powder under cold compaction. Mater Sci Eng, A 445–446:163–169

    Google Scholar 

  22. Szantoa M, Bierb W, Fragec N, Hartmannb S, Yosibash Z (2008) Experimental based finite element simulation of cold isostatic pressing of metal powders. Int J Mech Sci 50:405–421

    Google Scholar 

  23. Pizette P, Martin CL, Delette G, Sornay P, Sans F (2010) Compaction of aggregated ceramic powders: from contact laws to fracture and yield surfaces. Powder Technol 198:240–250

    Article  Google Scholar 

  24. Andersson DC, Larsson PL, Cadario A, Lindskog P (2010) On the influence from punch geometry on the stress distribution at powder compaction. Powder Tech 202(1–3):78–88

    Article  Google Scholar 

  25. Peric D (1992) On consistent stress rates in solid mechanics: computational implications. Int J Numer Methods Eng 33:799–817

    Article  MATH  Google Scholar 

  26. Peric D, Owen DRJ, Honnor ME (1992) A model for finite strain elasto-plasticity based on logarithmic strains: computational issues. Comput Meth Appl Mech Eng 94:35–61

    Article  MATH  Google Scholar 

  27. Chtourou H, Gakwaya A, Guillot M, Hrairi M (1995) Implementing a cap material model for the simulation of metal powder compaction. Net Shape Processing of Powder Materials, AMD-vol. 216, ASME, San Fransisco, CA, pp. 19–27

  28. Alm O (1983) Mechanical testing of powders and powder compacts. Scand J Metall 12:302–311

    Google Scholar 

  29. Weber GG, Brown SB (1989) Simulation of the compaction of powder components. Adv Powder Metall Part Mater 1:105–118

    Google Scholar 

  30. Simo JC, Ortiz M (1985) A unified approach to finite deformation elastoplasticity based on the use of hyperelastic constitutive equations. Comput Meth Appl Mech Eng 49:222–245

    Google Scholar 

  31. Simo JC, Taylor RL (1986) A return mapping algorithm for plane stress elastoplasticity. Int J Numer Methods Eng 22:649–670

    Article  MathSciNet  MATH  Google Scholar 

  32. Simo JC, Ju JW, Pister KS, Taylor RL (1988) Assessment of Cap model: consistent return algorithms and rate-dependent extension. J Eng Mech 114:191–218

    Article  Google Scholar 

  33. Hofstetter G, Simo JC, Taylor RL (1993) A modified Cap model: closest point solution algorithms. Comput Struct 46(2):203–214

    Article  MATH  Google Scholar 

  34. Chtourou H, Gakwaya A, Guillot M (2002) Modeling of the metal powder compaction process using the cap model. Part I: experimental material characterization and validation. Int J Solids Struct 39:1059–1075

    Article  MATH  Google Scholar 

  35. Pavier E, Doremus P (1996) Mechanical behaviour of a lubricated iron powder. In: Cadle TM, Narasimhan KS (eds) Advances in powder metallurgy and particulate materials—1996. Metal Powder Industries Federation, USA, pp 6–40

    Google Scholar 

  36. Mosbah P (1995) Modeling and experimental study of metal powders behaviour during comaction in closed die. Ph.D. thesis, University Joseph Fourier-Grenoble I, Grenoble, France

  37. Gelin JC, Ghouati O (1995) An inverse method for material parameters estimation in the inelastic range. Comput Mech 16(3):143–150

    Article  MATH  Google Scholar 

  38. Mahnken R, Stein E (1996) A unified approach for parameter identification of inelastic material models in the frame of the finite element method. Comput Meth Appl Mech Eng 136:225–258

    Article  MATH  Google Scholar 

  39. Levenberg K (1944) A method for the solution of certain nonlinear problems in least squares. Quart Appl Math 2:164–168

    MathSciNet  MATH  Google Scholar 

  40. Marquardt DW (1963) An algorithm for least squares estimation of nonlinear parameters. SIAM J Appl Math 11:431–441

    Article  MathSciNet  MATH  Google Scholar 

  41. Hrairi M (1999) Modélisation Numérique et Identification Directe et Inverse du Comportement des Poudres Métalliques lors du Procédé du Compactage. Ph.D. Thesis, Laval University, Québec

  42. Abaqus (1995) Theory Manual Version 5.5. Hibbit, Karlsson and Sorenson, Inc., Rhode Island

  43. Samuelson P, Bolin B (1983) Experimental studies of frictional behavior of hard metal powders sliding on cemented carbide walls. Scand J Metall 12:315–322

    Google Scholar 

  44. Khoei AR, Biabanaki SOR, Vafa AR, Taheri-Mousavi SM (2009) A new computational algorithm for 3D contact modeling of large plastic deformation in powder forming processes. Comput Mater Sci 46:203–220

    Article  Google Scholar 

  45. Guillot M, Chtourou H (1996) Generalization of the Vickers hardness local density measurement technique to different powder materials. Proceedings of the World Congress on Powder Metallurgy and Particulate Materials, vol. 1, part 4, pp.31–40

  46. SDRC Corporation (1994) Ideas Master Series Student Guide

  47. Hibbitt K (1997) ABAQUS theory manual, Version 5.7, Sorensen, Inc., Boston, USA

  48. Hibbitt K (1997) ABAQUS-post user guide, Version 5.7, Sorensen, Inc., Boston, USA

  49. Chtourou H, Gakwaya A, Guillot M, Hrairi M (1996) Finite element simulation of the rigid die compaction of metal powder components. Proceedings of the Canadian Societyof Mechanical Engineers Forum. McMaster University, Hamilton, Canada

  50. ASTM E92-82 (1987) Standard test method for Vickers hardness of metallic materials

  51. MPIF Standard 43 (1991). Method for determination of hardness of powder metallurgy products, Princeton, NJ

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Authors and Affiliations

  1. Mechanical Engineering Department, International Islamic University Malaysia, Gombak, Malaysia

    Meftah Hrairi

  2. Department of Technology, IPEIS, Sfax University, Sfax, Tunisia

    Hedi Chtourou

  3. Mechanical Engineering Department, Laval University, Quebec City, Canada

    Augustin Gakwaya & Michel Guillot

Authors
  1. Meftah Hrairi
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  2. Hedi Chtourou
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  3. Augustin Gakwaya
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  4. Michel Guillot
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Correspondence to Meftah Hrairi.

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Hrairi, M., Chtourou, H., Gakwaya, A. et al. Modeling the powder compaction process using the finite element method and inverse optimization. Int J Adv Manuf Technol 56, 631–647 (2011). https://doi.org/10.1007/s00170-011-3211-z

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  • DOI: https://doi.org/10.1007/s00170-011-3211-z

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