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Micromechanical modelling of the elastoplastic behaviour of metallic material under strain-path changes

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Abstract

A two-level homogenization approach is applied for the micromechanical modelling of the elastoplastic material behaviour during various strain-path changes. A mechanical description of the grain is developed through a micro-meso transition based on a modified elastoplastic self-consistent approach which takes into account the dislocation evolution. Next, a meso-macro transition using a self-consistent model is used to deduce the macroscopic behaviour of the polycrystal. A correct agreement is observed between the simulations and the experimental results at the mesoscopic and macroscopic levels.

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References

  1. Aguilar MTP, Cetlin PR, Valle PE, Corrêa ECS, Rezende JLL (1998) Influence of strain path in the mechanical properties of drawn aluminum alloy bars. J Mater Process Technol 80–81: 376–379

    Article  Google Scholar 

  2. Yoshida F, Uemori T, Fujiwara K (2002) Elastic–plastic behavior of steel sheets under in-plane cyclic tension–compression at large strain. Int J Plast 18: 633–659

    Article  MATH  Google Scholar 

  3. Feaugas X (1999) On the origin of the tensile flow stress in the stainless steel AISI 316L at 300 K: back stress and effective stress. Acta Mater 47: 3617–3632

    Article  Google Scholar 

  4. Vincze G, Rauch EF, Gracio SS, Barlat F, Loes AB (2005) A comparison of the mechanical behaviour of an AA1050 and a low carbon steel deformed upon strain reversal. Acta Mater 53: 1005–1013

    Article  Google Scholar 

  5. Nesterova EV, Bacroix B, Teodosiu C (2001) Microstructure and texture evolution under strain-path changes in low-carbon interstitial-free steel. Metal Mater Trans A 32A: 2527–2538

    Article  Google Scholar 

  6. Wu PD, MacEwen SR, Lloyd DJ, Jain M, Tugcu P, Neale KW (2005) On pre-straining and the evolution of material anisotropy in sheet metals. Int J Plast 21: 723–739

    Article  MATH  Google Scholar 

  7. Ungar T, Mughrabi H, Rönnpagel D, Wilkens M (1984) X-ray line-broadening study of the dislocation cell structure in deformed [001]-orientated copper single crystals. Acta Metall 32: 333–342

    Article  Google Scholar 

  8. Ungar T, Groma I (1989) Asymmetric X-ray line broadening of plastically deformed crystals, II. Evaluation procedure and application to [001]-Cu Crystals. J Appl Cryst 22: 26–34

    Article  Google Scholar 

  9. Hutchinson JW (1970) Elastic-plastic behaviour of polycrystalline metals and composites. Proc Roy Soc Lond A 319: 247–272

    Article  Google Scholar 

  10. Beradai C, Berveiller M, Lipinski P (1987) Plasticity of metallic polycrystals under complex loading paths. Int J Plast 3: 143–162

    Article  MATH  Google Scholar 

  11. Lipinski P, Berveiller M (1989) Elastoplasticity of micro-inhomogeneous metals at large strains. Int J Plast 5: 149–172

    Article  MATH  Google Scholar 

  12. Van Houtte P (1988) A comprehensive mathematical formulation of an extended Taylor–Bishop–Hill model featuring relaxed constraints, the Renouard–Wintenberger theory and a strain rate sensitivity model. Textures Microstruct 8–9:313–350

    Google Scholar 

  13. Gloaguen D, Berchi T, Girard E (2006) Guillén R. Phys Stat Sol (a) 203: R12–R14

    Article  Google Scholar 

  14. Zattarin Z, Lipinski P, Rosochowski A (2004) Numerical study of the influence of microstructure on subsequent yield surfaces of polycrystalline materials. Int J Mech Sci 4: 377–1398

    Google Scholar 

  15. Gloaguen D, François M, Guillén R (2004) Mesoscopic residual stresses of plastic origin in zirconium: interpretation of X-ray diffraction results. J Appl Crystallogr J Appl Cryst 37: 934–940

    Google Scholar 

  16. Clausen B, Lorentzen T, Leffers T (1998) Self-consistent modelling of the plastic deformation of f.c.c. polycrystals and its implications for diffraction measurements of internal stresses. Acta Mater 46: 3087–3098

    Article  Google Scholar 

  17. Castelnau O, Francillette H, Bacroix B, Lebensohn RA (2001) Texture dependent plastic behavior of Zr 702 at large strain. J Nucl Mater 297: 14–26

    Article  Google Scholar 

  18. Langlois L, Berveiller M (2003) Overall softening and anisotropy related with the formation and evolution of dislocation cell structures. Int J Plast 19: 599–624

    Article  MATH  Google Scholar 

  19. Haddag B, Balan T, Abed-Meraim F (2007) Investigation of advanced strain-path dependent material models for sheet metal forming simulations. Int J Plast 23: 951–979

    Article  MATH  Google Scholar 

  20. Hiwatashi S, Van bael A, Van Houtte P, Teodosiu C (1997) Modelling of plastic anisotropy based on texture and dislocation structure. Comp Mater Sci 9: 274–284

    Article  Google Scholar 

  21. Mahesh S, Tomé CN, MacCabe RJ, Kaschner GC, Beyerlein IJ, Misra A (2004) Application of a substructure-based hardening model to copper under loading path changes. Metal Mat Trans 35A: 3763–3774

    Article  Google Scholar 

  22. Mughrabi H (1987) The long-range internal stress field in the dislocation wall structure of persistent slip bands. Phys Stat Sol (a) 104: 107–120

    Article  Google Scholar 

  23. Peeters B, Seefeldt M, Teodosiu C, Kalidindi SR, Van Houtte P, Aernoudt E (2001) Work-hardening/softening behaviour of b.c.c. polycrystals during changing strain paths: I. An integrated model based on substructure and texture evolution, and its prediction of the stress–strain behaviour of an IF steel during two-stage strain paths. Acta Mater 19: 1607–1619

    Article  Google Scholar 

  24. Karaman I, Sehitoglu H, Beaudoin AJ, Chumlyakov YI, Maier HJ, Tome CN (2000) Modeling the deformation behavior of Hadfield steel single and polycrystals due to twinning and slip. Acta Mater 18: 2031–2047

    Article  Google Scholar 

  25. Viatkina EM, Brekelmans WAM, Geers MGD (2008) Numerical analysis of strain path dependency in FCC metals. Comp Mech 41: 391–405

    Article  MATH  Google Scholar 

  26. Muller D, Lemoine X, Berveiller M (1994) Nonlocal behavior of elastoplastic metals: theory and results. J Eng Mat Tech 116: 378–383

    Article  Google Scholar 

  27. Lemoine X, Berveiller M, Muller D (1994) Texture of microstructure in BCG metals for various loading paths. Mat Sci Forum 157–162: 1821–1826

    Article  Google Scholar 

  28. David F, Aubert I, Lemoine X, Berveiller M (1997) Modelling of elastoplastic polycrystals and aspects of applications. Comp Mat Sci 9: 188–198

    Article  Google Scholar 

  29. Gloaguen D, François M (2006) Prediction of intragranular strains in metallic polycrystals with two-level homogenisation approach: Influence of dislocations microstructure on the mechanical behaviour. Phys Stat Sol (a) 203: 1940–1953

    Article  Google Scholar 

  30. Kröner E (1961) On the plastic deformation of polycrystals. Acta Metall 9: 155–161

    Article  Google Scholar 

  31. Berveiller M, Zaoui A (1979) An extension of the self-consistent scheme to plastically-flowing polycrystals. J Mech Phys Sol 26: 325–344

    Article  Google Scholar 

  32. Schmitt C, Lipinski P, Berveiller M (1997) Micromechanical modelling of the elastoplastic behavior of polycrystals containing precipitates— Application to hypo- and hyper-eutectoid steels. Int J Plast 13: 183–199

    Article  MATH  Google Scholar 

  33. Hill R (1965) Continuum micro-mechanics of elastoplastic polycrystals. J Mech Phys Solids 13: 89–101

    Article  MATH  Google Scholar 

  34. Nes E (1998) Modelling of work hardening and stress saturation in FCC metals. Prog Mater Sci 41: 129–193

    Article  Google Scholar 

  35. Essmann U, Mughrabi H (1979) Annihilation of dislocations during tensile and cyclic deformation and limits of dislocation densities. Phil Mag 40: 731–756

    Article  Google Scholar 

  36. Franciosi P (1985) The concepts of latent hardening and strain hardening in metallic single crystals. Acta Metall 33: 1601–1612

    Article  Google Scholar 

  37. Ben Zineb T, Arbab Chirani S, Berveiller M (2001) Nouvelle formulation de la plasticité crystalline utilisant une contrainte de reference avec écrouissage. In: Sixteen french conference of mechanic, Nancy, France

  38. Lorrain JP, Ben Zineb T, Abd Meriam F, Berveiller M (2005) Ductility loss modelling fo BCC single crystals. Int J Proc 8: 135–158

    Google Scholar 

  39. Gloaguen D, Berchi T, Girard E, Guillén R (2007) Measurement and prediction of residual stresses and crystallographic texture development in rolled Zircaloy-4 plates: X-ray diffraction and the self-consistent model. Acta Mat 55: 4369–4379

    Article  Google Scholar 

  40. Pollnow D, Penelle R, Lacombe P (1973) Etude des propriétés mécaniques et du taux de consolidation des monocristaux de fer déformés par traction à température ambiante. Lxx 4010: 703–714

    Google Scholar 

  41. Keh AS, Nakada Y (1967) Plasticity of iron single crystals. Can J Phys 45: 1101–1120

    Google Scholar 

  42. Choteau M, Quaegebeur P, Degallaix S (2005) Modelling of Bauschinger effect by various constitutive relations derived from thermodynamical formulation. Mech Mat 37: 1143–1152

    Article  Google Scholar 

  43. Orlans-Joliet B (1989) PhD thesis, Déformation plastique de monocristaux de structure cubique centrée en compression plane, Ecole National des Mines de Paris et de Saint-Etienne

  44. Rauch EF (1998) Plastic anisotropy of sheet metals determined by simple shear tests. Mat Sci Eng A241: 179–183

    Google Scholar 

  45. Hori M, Nemat-Nasser S (1999) On two micromechanics theories for determining micro–macro relations in heterogeneous solids. Mech Mate 31: 667–682

    Article  Google Scholar 

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Authors and Affiliations

  1. GeM, Institut de Recherche en Génie Civil et Mécanique,, Université de Nantes, Ecole Centrale de Nantes, CNRS UMR 6183, 37 Boulevard de l’Université, BP 406, 44602, Saint-Nazaire, France

    Jamal Fajoui, David Gloaguen, Bruno Courant & Ronald Guillén

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  1. Jamal Fajoui
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  2. David Gloaguen
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  3. Bruno Courant
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  4. Ronald Guillén
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Correspondence to Jamal Fajoui.

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Fajoui, J., Gloaguen, D., Courant, B. et al. Micromechanical modelling of the elastoplastic behaviour of metallic material under strain-path changes. Comput Mech 44, 285–296 (2009). https://doi.org/10.1007/s00466-009-0374-7

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  • DOI: https://doi.org/10.1007/s00466-009-0374-7

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