Skip to main content
Log in

A new thermo-elasto-plasticity constitutive equation for crystals

  • Article
  • Solid Mechanics
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

Based on the crystal plasticity theory and interatomic potential, in this paper a new thermo-elasto-plasticity constitutive model is proposed to study the behavior of metal crystals at finite temperature. By applying the present constitutive model, the stress-strain curves under uniaxial tension at different temperatures are calculated for the typical crystal Al, and the calculated results are compared with the experimental results. From the comparisons, it can be seen that the present theory has the capability to describe the thermo-elasto-plastic behavior of metal crystals at finite temperature through a concise and explicit calculation process.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Boas W, Schmid E. Über die Temperaturabhängigkeit der Kristallplastizität. Zeitschrift für Physik, 1930, 61: 767–781

    Article  ADS  Google Scholar 

  2. Boas W, Schmid E. Über die Temperaturabhängigkeit der Kristallplastizität III Aluminium. Zeitschrift für Physik, 1931, 71: 703–714

    Article  ADS  Google Scholar 

  3. Schmid E. Beiträge zur Physik und Metallographie des Magnesiums. Zeitschrift für Elektrochemie und angewandte physikalische Chemie, 1931, 37: 447–459

    Google Scholar 

  4. Cottrell A, Stokes R. Effects of temperature on the plastic properties of aluminium crystals. Math Phys Sci, 1955, 233: 17–34

    Article  Google Scholar 

  5. Hoge K G, Mukherjee A K. The temperature and strain rate dependence of the flow stress of tantalum. J Mater Sci, 1977, 12: 1666–1672

    Article  ADS  Google Scholar 

  6. Huang S. Direct Disc Impact Investigation of Dynamic Large Finite Plastic Behavior of 1100 Aluminum. Dissertation for Doctoral Degree. Norman: University of Oklahoma, 1990

    Google Scholar 

  7. Frenkel D, Ladd A J C. New Monte Carlo method to compute the free energy of arbitrary solids. Applicaton to the fcc and hcp phases of hard spheres. J Chem Phys, 1984, 81: 3188–3193

    Article  ADS  Google Scholar 

  8. Huang Z, Dui G, Yang S. A new interpretation of internal-variable theory in finite thermo-viscoelasticity. Sci China-Phys Mech Astron, 2013, 56: 610–616

    Article  ADS  Google Scholar 

  9. Jiang H, Huang Y, Hwang K C. A finite-temperature continuum theory based on interatomic potentials. J Eng Mater Technol, 2005, 127: 408–416

    Article  Google Scholar 

  10. Li X, E W N. Multiscale modeling of the dynamics of solids at finite temperature. J Mech Phys Solids, 2005, 53: 1650–1685

    Article  ADS  MATH  MathSciNet  Google Scholar 

  11. LeSar R, Najafabadi R, Srolovitz D J. Finite-temperature defect properties from free-energy minimization. Phys Rev Lett, 1989, 63: 624–627

    Article  ADS  Google Scholar 

  12. Miller R E, Tadmor E B. The quasicontinuum method: Overview, applications and current directions. J Comput Aided Mater, 2002, 9: 203–239

    Article  Google Scholar 

  13. Dupuy L M, Tadmor E B, Miller R E, et al. Finite-temperature quasicontinuum: Molecular dynamics without all the atoms. Phys Rev Lett, 2005, 95: 060202

    Article  ADS  Google Scholar 

  14. Miller R, Ortiz M, Phillips R, et al. Quasicontinuum models of fracture and plasticity. Eng Fra Mech, 1998, 61: 427–444

    Article  Google Scholar 

  15. Miller R, Tadmor E B, Phillips R, et al. Quasicontinuum simulation of fracture at the atomic scale. Modell. Simul Mater Sci Eng, 1998, 6: 607–638

    Article  ADS  Google Scholar 

  16. Khan A S, Huang S. Experimental and theoretical study of mechanical behavior of 1100 aluminum in the strain rate range 10−5–104 s−1. Int J Plast, 1992, 8: 397–424

    Article  Google Scholar 

  17. Khan A S, Liang R. Behaviors of three BCC metal over a wide range of strain rates and temperatures: Experiments and modeling. Int J Plast, 1999, 15: 1089–1109

    Article  MATH  Google Scholar 

  18. Khan A S, Sung Suh Y, Kazmi R. Quasi-static and dynamic loading responses and constitutive modeling of titanium alloys. Int J Plast, 2004, 20: 2233–2248

    Article  MATH  Google Scholar 

  19. Beyerlein I, Tomé C. A dislocation-based constitutive law for pure Zr including temperature effects. Int J Plast, 2008, 24: 867–895

    Article  MATH  Google Scholar 

  20. Stainier L, Cuitiño A M, Ortiz M. A micromechanical model of hardening, rate sensitivity and thermal softening in bcc single crystals. J Mech Phys Solids, 2002, 50: 1511–1545

    Article  ADS  MATH  Google Scholar 

  21. Johnson G R, Cook W H. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: The Proceedings of the 7th International Symposium on Ballistics. Hague: Netherlands International Ballistics Committee, 1983

    Google Scholar 

  22. Zerilli F J, Armstrong R W. Dislocation-mechanics-based constitutive relations for material dynamics calculations. J Appl Phys, 1987, 61: 1816–1825

    Article  ADS  Google Scholar 

  23. Baig M, Khan A S, Choi S H, et al. Shear and multiaxial responses of oxygen free high conductivity (OFHC) copper over wide range of strain-rates and temperatures and constitutive modeling. Int J Plast, 2013, 40: 65–80

    Article  Google Scholar 

  24. Liang R, Khan A S. A critical review of experimental results and constitutive models for BCC and FCC metals over a wide range of strain rates and temperatures. Int J Plast, 1999, 15: 963–980

    Article  MATH  Google Scholar 

  25. Khan A S, Kazmi R, Farrokh B. Multiaxial and non-proportional loading responses, anisotropy and modeling of Ti-6Al-4V titanium alloy over wide ranges of strain rates and temperatures. Int J Plast, 2007, 23: 931–950

    Article  MATH  Google Scholar 

  26. Khan A S, Yu S. Deformation induced anisotropic responses of Ti-6Al-4V alloy. Part I: Experiments. Int J Plast, 2012, 38: 1–13

    Article  Google Scholar 

  27. Khan A S, Yu S, Liu H. Deformation induced anisotropic responses of Ti-6Al-4V alloy Part II: A strain rate and temperature dependent anisotropic yield criterion. Int J Plast, 2012, 38: 14–26

    Article  Google Scholar 

  28. Tang Q, Wang T, Shang B, et al. Thermodynamic properties and constitutive relations of crystals at finite temperature. Sci China-Phys Mech Astron, 2012, 55: 918–926

    Article  ADS  Google Scholar 

  29. Tang Q H, Wang T C. Lattice wave theory of molecular dynamics (in Chinese). Sci Sin-Phys Mech Astron, 2011, 41: 214–220

    Article  Google Scholar 

  30. Zbib H M, Diaz de la Rubia T. A multiscale model of plasticity. Int J Plast, 2002, 18: 1133–1163

    Article  MATH  Google Scholar 

  31. Roters F, Eisenlohr P, Hantcherli L, et al. Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications. Acta Mater, 2010, 58: 1152–1211

    Article  Google Scholar 

  32. Kim J H, Kim D, Lee Y S, et al. A temperature-dependent elastoplastic constitutive model for magnesium alloy AZ31 sheets. Int J Plast, 2013, 50: 66–93

    Article  Google Scholar 

  33. Li Z C, Jia H S, Ma H A, et al. FEM analysis on the effect of cobalt content on thermal residual stress in polycrystalline diamond compact (PDC). Sci China-Phys Mech Astron, 2012, 55: 639–643

    Article  ADS  Google Scholar 

  34. Agarwal S, Briant C L, Krajewski P E, et al. Experimental validation of two-dimensional finite element method for simulating constitutive response of polycrystals during high temperature plastic deformation. J Mater Eng Perform, 2007, 16: 170–178

    Article  Google Scholar 

  35. Ma A, Roters F. A constitutive model for fcc single crystals based on dislocation densities and its application to uniaxial compression of aluminium single crystals. Acta Mater, 2004, 52: 3603–3612

    Article  Google Scholar 

  36. Zamiri A, Bieler T, Pourboghrat F. Anisotropic crystal plasticity finite element modeling of the effect of crystal orientation and solder joint geometry on deformation after temperature change. J Electron Mater, 2009, 38: 231–240

    Article  ADS  Google Scholar 

  37. Asaro R J. Crystal plasticity. J Appl Mech, 1983, 50: 921–934

    Article  MATH  Google Scholar 

  38. Liu X L, Tang Q H, Wang T C. A continuum thermal stress theory for crystals based on interatomic potentials. Sci China-Phys Mech Astron, 2014, 57: 1–10

    ADS  Google Scholar 

  39. Nix F C, MacNair D. The thermal expansion of pure metals: Copper, gold, aluminum, nickel, and iron. Phys Rev, 1941, 60: 597–605

    Article  ADS  Google Scholar 

  40. Schmid E, Boas W. Plasticity of Crystals. London: F.A. Hughes & Co. Limited, 1950

    Google Scholar 

  41. Suzuki T, Kamimura Y, Kirchner H. Plastic homology of bcc metals. Philos Mag A, 1999, 79: 1629–1642

    Article  ADS  Google Scholar 

  42. Noguchi O, Oya Y, Suzuki T. The effect of nonstoichiometry on the positive temperature dependence of strength of Ni3AI and Ni3Ga. Metall Trans. A, 1981, 12: 1647–1653

    Article  Google Scholar 

  43. Suzuki T, Mishima Y, Miura S. Plastic behaviour in Ni3(Al, X) single crystal-temperature, strain-rate, orientation and composition. ISIJ Int, 1989, 29: 1–23

    Article  Google Scholar 

  44. Suzuki T, Oya Y, Wee D M. Transition from positive to negative temperature dependence of the strength in Ni3Ge-Fe3Ge solid solution. Acta Metall, 1980, 28: 301–310

    Article  Google Scholar 

  45. Wee D M, Noguchi O, Oya Y, et al. New Ll2 ordered alloys having the positive temperature dependence of strength. Trans JIM, 1980, 21: 237

    Google Scholar 

  46. Howe S, Liebmann B, Lücke K. High temperature deformation of aluminum single crystals. Acta Metall, 1961, 9: 625–631

    Article  Google Scholar 

  47. Gottstein G, Kocks U F. Dynamic recrystallization and dynamic recovery in 〈111〉 single crystals of nickel and copper. Acta Metall, 1983, 31: 175–188

    Article  Google Scholar 

  48. Anongba P, Bonneville J, Martin J. Hardening stages of [112] copper single crystals at intermediate and high temperatures-I. Mechanical behaviour. Acta Metall Mater, 1993, 41: 2897–2906

    Article  Google Scholar 

  49. Stipp M, Stünitz H, Heilbronner R, et al. Dynamic recrystallization of quartz: Correlation between natural and experimental conditions. Geol Soci London Spec Pub, 2002, 200: 171–190

    Article  ADS  Google Scholar 

  50. Mei J, Davenport J. Free-energy calculations and the melting point of Al. Phys Rev B, 1992, 46: 21–25

    Article  ADS  Google Scholar 

  51. Adams M, Cottrell A. Effect of temperature on the flow stress of work-hardened copper crystals. Philos Mag, 1955, 46: 1187–1193

    Article  Google Scholar 

  52. Takeuchi S, Kuramoto E. Temperature and orientation dependence of the yield stress in Ni{3} Ga single crystals. Acta Metall, 1973, 21: 415–425

    Article  Google Scholar 

  53. Lee M G, Lim H, Adams B L, et al. A dislocation density-based single crystal constitutive equation. Int J Plast, 2010, 26: 925–938

    Article  MATH  Google Scholar 

  54. Izadbakhsh A, Inal K, Mishra R K, et al. New crystal plasticity constitutive model for large strain deformation in single crystals of magnesium. Comp Mater Sci, 2011, 50: 2185–2202

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to TzuChiang Wang.

Additional information

Recommended by ZHAO YaPu (Associate Editor)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, C., Tang, Q. & Wang, T. A new thermo-elasto-plasticity constitutive equation for crystals. Sci. China Phys. Mech. Astron. 58, 1–10 (2015). https://doi.org/10.1007/s11433-015-5642-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11433-015-5642-2

Keywords

Navigation