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The polycrystalline plasticity due to slip and twinning during magnesium alloy forming

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Abstract

In order to simulate the magnesium alloy-forming processes accurately, it is necessary to consider the plastic anisotropy. In this paper, a new rate-independent constitutive model for polycrystalline plastic deformation by slip and twinning has been formulated, and then introduced into a FEM program. Metal flow is assumed to occur by crystallographic slip on given slip and twinning systems within each crystal. Each integration point represents a single crystal. Then uniaxial compression and cup drawing of Mg alloy are studied by using a rate-independent polycrystalline plasticity finite element analysis. In this paper, the ear distributions of the polycrystal are predicted for different typical initial orientation cases. The values of the twinning factors associated with slip system deformation are deduced. It is found that the twinning factors vary with the value of the stress. The basal slip and twinning system plays the dominant role in the deformation of magnesium alloy, which might be the most important contribution to strain hardening.

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References

  1. Michael, M., Avedesian, H.B.: ASM Specialty Handbook-Magnesium and Magnesium Alloys. ASM International, Materials Park, Ohio (1999)

  2. Parks D.M., Ahzi S.: Polycrystalline plastic deformation and texture evolution for crystals lacking five independent slip systems. J. Mech. Phys. Solids 38, 701–724 (1990)

    Article  MATH  Google Scholar 

  3. Balasubramanian, S.: Polycrystalline plasticity: application to deformation processing of lightweight metals, PhD thesis, MIT (1998)

  4. Taylor G.I.: Plastic strain in metal. J. Inst. Metals 62, 307–324 (1938)

    Google Scholar 

  5. Myagchilov S., Dawson P.R.: Evolution of texture in aggregates of crystals exhibiting both slip and twinning. Model. Simul. Mater. Sci. Eng. 7, 975–1004 (1999)

    Article  Google Scholar 

  6. Schoenfeld S.E., Kad B.: Texture effects on shear response in Ti-6Al-4V plates. Int. J. Plast. 18, 461–486 (2002)

    Article  MATH  Google Scholar 

  7. Jain A., Agnew S.R.: Modeling the temperature dependent effect of twinning on the behavior of magnesium alloy AZ31B sheet. Mater. Sci. Eng. A 462, 29–36 (2007)

    Article  Google Scholar 

  8. Walde T., Riedel H.: Simulation of earing during deep drawing of magnesium alloy AZ31. Acta Mater. 55, 867–874 (2007)

    Article  Google Scholar 

  9. Lee E.H.: Elastic–plastic deformation at finite strains. J. Appl. Mech. 136, 1–21 (1969)

    Google Scholar 

  10. Staroselsky A., Anand L.: A constitutive model for hcp materials deforming by slip and twinning: application to magnesium alloy AZ31B. Int. J. Plast. 19, 1843–1864 (2003)

    Article  MATH  Google Scholar 

  11. Yi S.-B., Davies C.H.J., Brokmeier H.-G. et al.: Deformation and texture evolution in AZ31 magnesium alloy during uniaxial loading. Acta Mater. 54, 549–562 (2006)

    Article  Google Scholar 

  12. Pitteri M.: On type-2 twins in crystals. Int. J. Plast. 2, 99–106 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  13. Zanzotto G.: The cauchy-born hypothesis, nonlinear elasticity and mechanical twinning in crystals. Acta Crystallograph. Sect. A A52, 839–849 (1996)

    Article  MathSciNet  Google Scholar 

  14. Hosford W.G.: The Mechanics of Crystals and Textured Polycrystals. Oxford University Press, New York (1993)

    Google Scholar 

  15. Jin Y.M., Weng G.J.: A direct method for the crystallography of martensitic transformation and its application to TiNi and AuCd. Acta Mater. 50, 2967–2987 (2002)

    Article  Google Scholar 

  16. Khachaturyan A.G.: Theory of Structural Transformations in Solids. Wiley, New York (1983)

    Google Scholar 

  17. Jin Y.M., Weng G.J.: A relaxed constraint model for the tensile behavior of polycrystal shape-memory alloy wires. Metallurg. Mater. Trans. A 32A, 305–313 (2001)

    Article  Google Scholar 

  18. Akahashi H.: Stress–strain relations of polycrystalline metals: 3. Proportional loading of FCC Metals. Bull. J. Soc. Mech. Eng. 19, 1115 (1976)

    Google Scholar 

  19. Pierce D., Asaro R.J., Needleman A.: Material rate dependent and localized deformation in crystalline solids. Acta Metall. 31, 1951–1972 (1983)

    Article  Google Scholar 

  20. Walde T., Riede H.: Mater. Sci. Eng. 443, 277–284 (2007)

    Article  Google Scholar 

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Correspondence to Yinghong Peng.

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Zhang, S., Peng, Y., Tang, W. et al. The polycrystalline plasticity due to slip and twinning during magnesium alloy forming. Acta Mech 212, 293–303 (2010). https://doi.org/10.1007/s00707-009-0260-6

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  • DOI: https://doi.org/10.1007/s00707-009-0260-6

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