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Micromechanical modeling of intrinsic and specimen size effects in microforming

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Abstract

Size effect is a crucial phenomenon in the microforming processes of metallic alloys involving only limited amount of grains. At this scale intrinsic size effect arises due to the size of the grains and the specimen/statistical size effect occurs due to the number of grains where the properties of individual grains become decisive on the mechanical behavior of the material. This paper deals with the micromechanical modeling of the size dependent plastic response of polycrystalline metallic materials at micron scale through a strain gradient crystal plasticity framework. The model is implemented into a Finite Element software as a coupled implicit user element subroutine where the plastic slip and displacement fields are taken as global variables. Uniaxial tensile tests are conducted for microstructures having different number of grains with random orientations in plane strain setting. The influence of the grain size and number on both local and macroscopic behavior of the material is investigated. The attention is focussed on the effect of the grain boundary conditions, deformation rate and the grain size on the mechanical behavior of micron sized specimens. The model is intrinsically capable of capturing both experimentally observed phenomena thanks to the incorporated internal length scale and the crystallographic orientation definition of each grain.

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References

  1. Barbe F, Decker L, Jeulin D, Cailletaud G (2001) Intergranular and intragranular behavior of polycrystalline aggregates. part 1: F.e. model. Int J Plast 17:513–536

    Article  MATH  Google Scholar 

  2. Barbier C, Thibaud S, Richard F, Picart P (2009) Size effects on material behavior in microforming. Int J Mater Form 2:625–662

    Article  Google Scholar 

  3. Borg U (2007) A strain gradient crystal plasticity analysis of grain size effects in polycrystals. Eur J Mech A Solids 26:313–324

    Article  MATH  Google Scholar 

  4. Chan WL, Fu MW (2011) Experimental studies and numerical modeling of the specimen and grain size effects on the flow stress of sheet metal in microforming. Mat Sci Eng A 528:7674–7683

    Article  Google Scholar 

  5. Chan WL, Fu MW, Lu J, Liu JG (2010) Modeling of grain size effect on micro deformation behavior in micro-forming of pure copper. Mat Sci Eng A 527:6638–6648

    Article  Google Scholar 

  6. Chen F, Tsai J (2006) A study of size effect in micro-forming with micro-hardness tests. J Mater Process Technol 177:146–149

    Article  Google Scholar 

  7. Delannay L, Beringhier M, Chastel Y, Loge RE (2005) Simulation of cup-drawing based on crystal plasticity applied to reduced grain samplings. Mater Sci Forum 495-497:1639–1644

    Article  Google Scholar 

  8. Diard O, Leclercq S, Rousselier G, Cailletaud G (2005) Evaluation of finite element based analysis of 3d multicrystalline aggregates plasticity: application to crystal plasticity model identification and the study of stress and strain fields near grain boundaries. Int J Plast 21:691–722

    Article  MATH  Google Scholar 

  9. Ekh M, Bargmann S, Grymer M (2011) Influence of grain boundary conditions on modeling of size-dependence in polycrystals. Acta Mech 218:103–113

    Article  MATH  Google Scholar 

  10. Ekh M, Grymer M, Runesson K, Svedberg T (2007) Gradient crystal plasticity as part of the computational modelling of polycrystals. Int J Numer Meth Engng 72:197–220

    Article  MathSciNet  MATH  Google Scholar 

  11. Fu MW, Chan WL (2014) Micro-scaled products development via microforming. Springer, London

    Book  Google Scholar 

  12. Fulop T, Brekelmans WAM, Geers MGD (2006) Size effects from grain statistics in ultra-thin metal sheets. J Mater Process Technol 174:233–238

    Article  Google Scholar 

  13. Gau J, Principe C, Wang J (2007) An experimental study on size effects on flow stress and formability of aluminum and brass for microforming. J Mater Process Technol 184:42–46

    Article  Google Scholar 

  14. Geiger M, Kleinerb M, Eckstein R, Tiesler N, Engel U (2001) Microforming. CIRP Ann Manuf Technol 50:445–462

    Article  Google Scholar 

  15. Gottschalk D, McBride A, Reddy BD, Javili A, Wriggers P, Hirschberger CB (2016) Computational and theoretical aspects of a grain-bundary model that accounts for grain misorientation and grain-boundary orientation. Comp Mater Sci 111:443–459

    Article  Google Scholar 

  16. Greer JR, De Hosson JTM (2011) Plasticity in small-sized metallic systems: intrinsic versus extrinsic size effect. Prog Mater Sci 56:654–724

    Article  Google Scholar 

  17. Gurtin ME (2008) A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation. J Mech Phys Solids 56:640–662

    Article  MathSciNet  MATH  Google Scholar 

  18. Kim G, Ni J, Koc M (2006) Modeling of the size effects on the behavior of metals in microscale deformation processes. ASME J Manuf Sci Eng 129:470–476

    Article  Google Scholar 

  19. Kim HS, Lee YS (2011) Size dependence of flow stress and plastic behaviour in microforming of polycrystalline metallic materials. Proc Inst Mech Eng C J Mech Eng Sci 226:403–412

    Article  Google Scholar 

  20. Klusemann B, Yalçinkaya T (2013) Plastic deformation induced microstructure evolution through gradient enhanced crystal plasticity based on a non-convex helmholtz energy. Int J Plast 48:168–188

    Article  Google Scholar 

  21. Klusemann B, Yalçinkaya T, Geers MGD, Svendsen B (2013) Application of non-convex rate dependent gradient plasticity to the modeling and simulation of inelastic microstructure development and inhomogeneous material behavior. Comp Mater Sci 80:51– 60

    Article  Google Scholar 

  22. Kruzel P, Madej L, Perzynski K, Banas K (2014) Development of three-dimensional adaptive mesh generation for multiscale applications. Int J Multiscale Eng 12:257–269

    Article  Google Scholar 

  23. Lu HN, Wei DB, Jiang ZY, Liu XH, Manabe K (2013) Modelling of size effects in microforming process with consideration of grained heterogeneity. Comput Mater Sci 77:44–52

    Article  Google Scholar 

  24. Madej L, Kruzel P, Cybulka P, Perzynski K, Banas K (2012) Generation of dedicated finite element meshes for multiscale applications with delaunay triangulation and adaptive finite element - cellular automata algorithms. Comput Meth Mater Sci 12:85–96

    Google Scholar 

  25. Melchior MA, Delannay L (2006) A texture discretization technique adapted to polycrystalline aggregates with non-uniform grain size. Comp Mater Sci 37:557–564

    Article  Google Scholar 

  26. Nix WD, Gao H (1998) Indentation size effects in crystalline materials: a law for strain gradient plasticity. J Mech Phys Solids 46:411–425

    Article  MATH  Google Scholar 

  27. Ozdemir I (2014) Grain statistics induced size effect in the expansion of metallic micro rings. Int J Mech Sci 87:52–59

    Article  Google Scholar 

  28. Ozdemir I, Yalcinkaya T (2014) Modeling of dislocation–grain boundary interactions in a strain gradient crystal plasticity framework. Comput Mech 54:255–268

    Article  MathSciNet  MATH  Google Scholar 

  29. Ozdemir I, Yalcinkaya T (2017) Strain gradient crystal plasticity: intragranular microstructure formation. Handbook of Nonlocal Continuum Mechanics for Materials and Structures, pp 1–29

  30. Prakash A, Lebensohn RA (2009) Simulation of micromechanical behavior of polycrystals: finite elements versus fast fourier transforms. Modelling Simul Mater Sci Eng 17:064010

    Article  Google Scholar 

  31. Prakash A, Weygand SM, Riedel H (2009) Modeling the evolution of texture and grain shape in mg alloy az31 using the crystal plasticity finite element method. Comp Mater Sci 45:744–750

    Article  Google Scholar 

  32. Quey R, Dawson PR, Barbe F (2011) Large-scale 3d random polycrystals for the finite element method: generation, meshing and remeshing. Comput Methods Appl Mech Eng 200:1729–1745

    Article  MATH  Google Scholar 

  33. Szyndler J, Madej L (2015) Numerical analysis of the influence of number of grains, fe mesh density and friction coefficient on representativeness aspects of the polycrystalline digital material representation plane strain deformation case study. Comp Mater Sci 96:200–2013

    Article  Google Scholar 

  34. van Beers PRM, McShane GJ, Kouznetsova VG, Geers MGD (2013) Grain boundary interface mechanics in strain gradient crystal plasticity. J Mech Phys Solids 61:2659–2679

    Article  MathSciNet  Google Scholar 

  35. Van Houtte P, Kanjarla AK, Van Bael A, Seefeldt M, Delannay L (2006) Multiscale modelling of the plastic anisotropy and deformation texture of polycrystalline materials. Eur J Mech A Solids 25:634–648

    Article  MathSciNet  MATH  Google Scholar 

  36. Vollertsen F, Biermann D, Hansen HN, Jawahir IS, Kuzman K (2009) Size effects in manufacturing of metallic components. CIRP Ann Manuf Techn 58:566–587

    Article  Google Scholar 

  37. Vollertsen F, Schulze Niehoff H, Hu Z (2006) State of the art in micro forming. Int J Mach Tool Manu 46:1172–1179

    Article  Google Scholar 

  38. Voyiadjis GZ, Abu Al-Rub RK (2005) Gradient plasticity theory with a variable length scale parameter. Int J Solids Struct 42:3998–4029

    Article  MATH  Google Scholar 

  39. Yalcinkaya T (2011) Microstructure evolution in crystal plasticity : strain path effects and dislocation slip patterning. Ph.D thesis. Eindhoven University of Technology, The Netherlands

    Google Scholar 

  40. Yalcinkaya T (2017) Strain gradient crystal plasticity: Thermodynamics and implementation. Handbook of Nonlocal Continuum Mechanics for Materials and Structures, pp 1–32

  41. Yalcinkaya T, Brekelmans WAM, Geers MGD (2008) Bcc single crystal plasticity modeling and its experimental identification. Modelling Simul Mater Sci Eng 16:085007

    Article  Google Scholar 

  42. Yalcinkaya T, Brekelmans WAM, Geers MGD (2011) Deformation patterning driven by rate dependent non-convex strain gradient plasticity. J Mech Phys Solids 59:1–17

    Article  MathSciNet  MATH  Google Scholar 

  43. Yalcinkaya T, Brekelmans WAM, Geers MGD (2012) Non-convex rate dependent strain gradient crystal plasticity and deformation patterning. Int J Solids Struct 49:2625–2636

    Article  Google Scholar 

  44. Yalcinkaya T, Demirci A, Simonovski I, Ozdemir I (2017) Intrinsic and statistical size effects in microforming. AIP Conf Proc 1896:160013

    Article  Google Scholar 

  45. Yalcinkaya T, Demirci A, Simonovski I, Ozdemir I (2017) Micromechanical modelling of size effects in microforming. Procedia Eng 207:998–1003

    Article  Google Scholar 

  46. Yalcinkaya T, Simonovski I, Ozdemir I (2016) Strain gradient polycrystal plasticity for micro-forming. AIP Conf Proc 1769(1):160003

    Article  Google Scholar 

  47. Zhang H, Dong X (2015) Physically based crystal plasticity FEM including geometrically necessary dislocations: numerical implementation and applications in micro-forming. Comput Mater Sci 110:308–320

    Article  Google Scholar 

  48. Zhang H, Dong X (2016) Experimental and numerical studies of coupling size effects on material behaviors of polycrystalline metallic foils in microscale plastic deformation. Mat Sci Eng A-Struct 658:450–462

    Article  Google Scholar 

Download references

Acknowledgments

Tuncay Yalçinkaya gratefully acknowledges the support by the Scientific and Technological Research Council of Turkey (TÜBİTAK) under the 3001 Program (Grant No. 215M381).

Funding

This study was funded by Scientific and Technological Research Council of Turkey (TÜBİTAK) (grant number 215M381).

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Correspondence to T. Yalçinkaya.

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Yalçinkaya, T., Özdemir, İ. & Simonovski, I. Micromechanical modeling of intrinsic and specimen size effects in microforming. Int J Mater Form 11, 729–741 (2018). https://doi.org/10.1007/s12289-017-1390-3

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  • DOI: https://doi.org/10.1007/s12289-017-1390-3

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