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Understanding the physics of non-linear unloading-reloading behavior of metal for springback prediction

Abstract

Finite element simulation technique is extensively useful nowadays for die designing by optimizing the springback from the formed state of sheet metal panel. The magnitude of springback is normally calculated in finite element simulation by assuming a completely elastic recovery in non-linear kinematic hardening law. Constant values of elastic modulus and Poisson’s ratio are required to estimate the elastic recovery by non-linear kinematic hardening law. Cleveland and Ghosh (Int J Plast 18:769–785, 2002), Li and Wagoner (Int J Plast 1827:1126–1144, 2011), and many other research groups have reported that inelastic strain release during unloading is the main source of extra strain recovery and as a result poor springback prediction by commercial finite element software. In this regard, many theoretical postulates have been proposed to explain such inelastic strain release during unloading. In this work, we show from atomistic simulation that irreversible movement of dislocation, i.e., microplasticity, is the source of inelastic strain release during unloading.

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References

  1. Sun L, Wagoner RH (2011) Complex unloading behavior: nature of the deformation and its consistent constitutive representation. Int. J. Plast. 1827:1126–1144

    Article  Google Scholar 

  2. Wagoner RH, Wang JF, Li M (2006) “Springback,” Chapter in ASM handbook. 14B: Metalworking: sheet forming, pp. 14:733–755

  3. Cleveland RM, Ghosh AK (2002) Inelastic effects on springback in metals. Int. J. Plast. 18:769–785

    CAS  Article  Google Scholar 

  4. Pourboghrat F, Chung K, Richmond O (1998) A hybrid membrane/shell method for rapid estimation of springback in anisotropic sheet metals. J Appl Mech–T ASME 6:671–684

    Article  Google Scholar 

  5. Morestin F, Boivin M (1996) On the necessity of taking into account the variation in the young modulus with plastic strain in elastic-plastic software. Nucl. Eng. Des. 162:107–116

    CAS  Article  Google Scholar 

  6. Yoshida F, Uemori T (2002) A model of large-strain cyclic plasticity describing the Bauschinger effect and workhardening stagnation. Int. J. Plast. 18:661–686

    CAS  Article  Google Scholar 

  7. Eggertsen PA, Mattiasson K (2010) On constitutive modeling for springback analysis. Int. J. Mech. Sci. 52:804–818

    Article  Google Scholar 

  8. Fei DY, Hodgson P (2006) Experimental and numerical studies of springback in air v-bending process for cold rolled TRIP steels. Nucl Eng and Des 236:1847–1851

    CAS  Article  Google Scholar 

  9. Yu HY (2009) Variation of elastic modulus during plastic deformation and its influence on springback. Mater Desi 30:846–850

    CAS  Article  Google Scholar 

  10. Murnaghan FD (1967) Finite deformation of an elastic solid. Dover, New York

    Google Scholar 

  11. Ghosh AK (1980) A physically-based constitutive model for metal deformation. Acta Metall. 28:1443–1465

    Article  Google Scholar 

  12. Zhou H, Xian Y, Wu R, Hu G, Xia R (2017) Formation of gold composite nanowires using cold welding: a structure-based molecular dynamics simulation. CrystEngComm 19:6347

    CAS  Article  Google Scholar 

  13. Li J, Lu B, Zhou H, Tian C, Xian Y, Hu G, Xia R (2019) Molecular dynamics simulation of mechanical properties of nanocrystalline platinum: grain size and temperature effects. Phys. Lett. A 383:1922–1928

    CAS  Article  Google Scholar 

  14. Li J, Tian C, Lu B, Xian Y, Wu R, Hu G, Xia R (2019) Deformation behavior of nanoporos gold based composite in compression: a finite element analysis. Compos. Struct. 211:229–235

    Article  Google Scholar 

  15. Hirel P (2015)Atomsk: a tool for manipulating and converting atomic data files. Comput. Phys Commun 197:212–219

    CAS  Article  Google Scholar 

  16. Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117:1–19

    CAS  Article  Google Scholar 

  17. Stukowski A (2010) Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool. Model. Simul. Mater. Sci. Eng. 18

  18. Nathanson M, Kanhaiya K, Pryor A, Miao J, Heinz H (2018) Atomic-scale structure and stress release mechanism in core-shell nanoparticles. ACS Nano 12:12296–12304

    CAS  Article  Google Scholar 

  19. Luo LM, Ghosh AK (2003) Elastic and inelastic recovery after plastic deformation of DQSK steel sheet. J Eng Mater-T ASME 125:237–246

    CAS  Article  Google Scholar 

  20. Andar MO, Kuwabara T, Yonemura S, Uenishi A (2010) Elastic-plastic and inelastic characteristics of high strength steel sheets under biaxial loading and unloading. ISIJ Int. 50:613–619

    CAS  Article  Google Scholar 

  21. Kim H, Kim C, Barlat F, Pavlina E, Lee MG (2013) Nonlinear elastic behaviors of low and high strength steels in unloading and reloading. Mater Sci Eng-A 562:161–171

    CAS  Article  Google Scholar 

  22. Chen Z, Bong HJ, Li D, Wagoner RH (2016) The elasticeplastic transition of metals. Int. J. Plast. 83:178–201

    CAS  Article  Google Scholar 

  23. Cottrell AH (1961) Dislocations and plastic flow in crystals. Clarendon Press, Oxford

    Google Scholar 

  24. Frank FC, Read WT (1950) Multiplication processes for slow moving dislocations. Phys. Rev. 79:722

    CAS  Article  Google Scholar 

  25. Mott NF (1946) Atomic physics and strength of metals. J. Inst. Met. 72:367

    CAS  Google Scholar 

  26. Yamakov V, Wolf D, Salazar M, Phillpot SR, Gleiter H (2001) Length-scale effects in the nucleation of extended dislocations in nanocrystalline Al by molecular-dynamics simulation. Acta Mater. 49:2713–2722

    CAS  Article  Google Scholar 

  27. Jiang B, Tu A, Wang H, Duan H, He S, Ye H, Du K (2018) Direct observation of deformation twinning under stress gradient in body-centered cubic metals. Acta Mater. 155:56–68

    CAS  Article  Google Scholar 

  28. George E. Deiter (2016) Mecanical Metallurgy, pp 35–36

  29. Wael A, Huseyin S (2017) Critical resolved shear stress for slip and twin nucleation in single crystalline FeNiCoCrMn high entropy alloy. Mater Charac. 129:288–299

    Article  Google Scholar 

  30. Aral G, Wang YJ, Ogata S, Van Duin CT (2016) A effects of oxidation on tensile deformation of iron nanowires: insights from reactive molecular dynamics simulations. J Appl Phy 135104:1–14

    Google Scholar 

  31. Shimizu F, Ogata S, Li J (2007) Theory of shear banding in metallic glasses and molecular dynamics calculations. Mater. Trans. 48:2923–2927

    CAS  Article  Google Scholar 

  32. Sha ZD, Pei QX, Liu ZS, Zhang YW, Wang TJ (2015) Necking and notch strengthening in metallic glass with symmetric sharp-and-deep notches. Sci. Rep. 5:1–7

    Google Scholar 

  33. Rajut A, Ghosal P, Kumar A, Paul SK (2019) Monotonic and cyclic plastic deformation behavior of nanocrystalline gold: atomistic simulations. J. Mol. Model. 25:153

    Article  Google Scholar 

  34. Paul SK (2018) Effect of twist boundary angle on deformation behavior of 〈1 0 0〉 FCC copper nanowires. Comput. Mater. Sci. 150:24–32

    CAS  Article  Google Scholar 

  35. Gianola DS, Van Petegem S, Legros M, Brandstetter S, Van SH (2006) Stress-assisted discontinuous grain growth and its effect on the deformation behavior of nanocrystalline aluminum thin films. Acta Mater. 54:2253–2263

    CAS  Article  Google Scholar 

  36. Rupert TJ, Gianola DS, Gan Y, Hemker KJ (2009) Experimental observations of stress- driven grain boundary migration. Sci 326:1686–1690

    CAS  Article  Google Scholar 

  37. Schiotz J, Di Tolla FD, Jacobsen KW (1998) Softening of nanocrystalline metals at very small grain sizes. Nature 39:561

    Article  Google Scholar 

  38. Schiotz J, Di Tolla FD, Jacobsen KW (1999) Atomic-scale simulations of the mechanical deformation of nanocrystalline metals. Phys. Rev. B 60:11971

    CAS  Article  Google Scholar 

  39. Swygenhoven HV, Spaczer M, Caro A (1999) A microscopic description of plasticity in computer generated metallic nanophase samples: a comparison between Cu and Ni. Acta Mater. 47:3117

    Article  Google Scholar 

  40. Keblinski P, Wolf D, Gleiter H (1998) Molecular-dynamics simulation of grain-boundary diffusion creep. Interface Sci 6:205

    CAS  Article  Google Scholar 

  41. Yamakov V, Phillpot S R, Wolf D, Gleiter H (2000) Computer simulations in condensed matter physics, Vol. XIII, ed. D. P. Landau, S. P. Lewis and H. -B. Schu¨ttler. Springer, New York, p. 195

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Correspondence to Surajit Kumar Paul.

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Rajput, A., Paul, S.K. Understanding the physics of non-linear unloading-reloading behavior of metal for springback prediction. J Mol Model 25, 321 (2019). https://doi.org/10.1007/s00894-019-4203-4

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  • DOI: https://doi.org/10.1007/s00894-019-4203-4

Keywords

  • Uniaxial tensile deformation
  • Unloading-reloading
  • Springback
  • Nanocrystalline gold
  • Molecular dynamics simulation