Advertisement

A reduced-order method for parameter identification of a crystal plasticity model considering crystal symmetry

  • ShiWei Han
  • XiaoGuang Yang
  • DuoQi ShiEmail author
  • Jia Huang
Article
  • 14 Downloads

Abstract

The focus of this paper is to identify the material parameters of a crystal plasticity model for Ni-base single crystal superalloys. To facilitate the stepwise calibration of the multistage flow rules, further decoupling and simplification are implemented without compromising its simulating capability. Reduced-order kinematics in crystal plasticity, which only comprise scalar components instead of their original tensors, are derived by considering the crystal symmetry and uniaxial loading condition. The relationships between components in elastic and plastic deformation gradient are established by explicitly accounting the control quantities, which is overall load in stress-controlled creep tests or displacement of gauge section in strain-controlled experiments, respectively. In addition, their approximate forms are also given by neglecting both elastic changes in volume and section area. A new objective function based on the shortest distance was introduced to correlate data from the simulations and experiments, and an integrated optimization process without finite element computation was developed into a commercial software package. Parameters in the crystal plasticity model are successfully calibrated by the efficient reduced-order method from the experimental data in such a sequence as: elastic, plastic, primary stage and secondary to tertiary stages creep laws. The multistage weak coupling flow rules can significantly reduce the non-uniqueness of the optimal solution under the circumstance of excessive parameters but insufficient experimental data. Finally, the optimized results with the reduced-order method have been validated by the finite element method.

Keywords

reduced-order crystal plasticity parameter identification finite deformation single crystal crystal symmetry 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    MacLachlan D W, Knowles D M. Modelling and prediction of the stress rupture behaviour of single crystal superalloys. Mater Sci Eng- A, 2001, 302: 275–285CrossRefGoogle Scholar
  2. 2.
    MacLachlan D W, Gunturi G S K, Knowles D M. Modelling the uniaxial creep anisotropy of nickel base single crystal superalloys CMSX-4 and RR2000 at 1023 K using a slip system based finite element approach. Comput Mater Sci, 2002, 25: 129–141CrossRefGoogle Scholar
  3. 3.
    MacLachlan D W, Wright L W, Gunturi S, et al. Constitutive modelling of anisotropic creep deformation in single crystal blade alloys SRR99 and CMSX-4. Int J Plast, 2001, 17: 441–467CrossRefzbMATHGoogle Scholar
  4. 4.
    Lemaitre L, Chaboche J L. Mechanics of Solid Materials. Cambridge: Cambridge University Press, 1994zbMATHGoogle Scholar
  5. 5.
    Chaboche J L. A review of some plasticity and viscoplasticity constitutive theories. Int J Plast, 2008, 24: 1642–1693CrossRefzbMATHGoogle Scholar
  6. 6.
    Li S X, Smith D J. Development of an anisotropic constitutive model for single-crystal superalloy for combined fatigue and creep loading. Int J Mech Sci, 1998, 40: 937–948CrossRefzbMATHGoogle Scholar
  7. 7.
    Han S, Li S, Smith D J. Comparison of phenomenological and crystallographic models for single crystal nickel base superalloys. I. Analytical identification. Mech Mater, 2001, 33: 251–266Google Scholar
  8. 8.
    Han S, Li S, Smith D J. Comparison of phenomenological and crystallographic models for single crystal nickel base superalloys. II. Numerical simulations. Mech Mater, 2001, 33: 267–282Google Scholar
  9. 9.
    Meric L, Poubanne P, Cailletaud G. Single crystal modeling for structural calculations: Part 1—model presentation. J Eng Mater Technol, 1991, 113: 162CrossRefGoogle Scholar
  10. 10.
    Meric L, Cailletaud G. Single crystal modeling for structural calculations: Part 2—finite element implementation. J Eng Mater Technol, 1991, 113: 171CrossRefGoogle Scholar
  11. 11.
    Hill R. Generalized constitutive relations for incremental deformation of metal crystals by multislip. J Mech Phys Solids, 1966, 14: 95–102CrossRefGoogle Scholar
  12. 12.
    Hill R. The essential structure of constitutive laws for metal composites and polycrystals. J Mech Phys Solids, 1967, 15: 79–95CrossRefGoogle Scholar
  13. 13.
    Rice J R. On the structure of stress-strain relations for time-dependent plastic deformation in metals. J Appl Mech, 1970, 37: 728–737CrossRefGoogle Scholar
  14. 14.
    Rice J R. Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity. J Mech Phys Solids, 1971, 19: 433–455CrossRefzbMATHGoogle Scholar
  15. 15.
    Peirce D, Asaro R J, Needleman A. An analysis of nonuniform and localized deformation in ductile single crystals. Acta Metall, 1982, 30: 1087–1119CrossRefGoogle Scholar
  16. 16.
    Asaro R J. Micromechanics of crystals and polycrystals. Adv Appl Mech, 1983, 23: 1–115CrossRefGoogle Scholar
  17. 17.
    Peirce D, Asaro R J, Needleman A. Material rate dependence and localized deformation in crystalline solids. Acta Metall, 1983, 31: 1951–1976CrossRefGoogle Scholar
  18. 18.
    MacLachlan D W, Williams S, Knowles D. A damage mechanics approach to stress rupture and creep of single crystal blade alloys. In: Proceedings of 7 th International Conference on Creep and Fracture of Engineering Materials and Structures. Irvine, 1997. 707–716Google Scholar
  19. 19.
    Gunturi S S K, MacLachlan D W, Knowles D M. Anisotropic creep in CMSX-4 in orientations distant from 001. Mater Sci Eng-A, 2000, 289: 289–298CrossRefGoogle Scholar
  20. 20.
    Knowles D M, Gunturi S. The role of 112111 slip in the asymmetric nature of creep of single crystal superalloy CMSX-4. Mater Sci Eng-A, 2002, 328: 223–237CrossRefGoogle Scholar
  21. 21.
    Przybyla C P, McDowell D L. Microstructure-sensitive extreme value probabilities for high cycle fatigue of Ni-base superalloy IN100. Int J Plast, 2010, 26: 372–394CrossRefzbMATHGoogle Scholar
  22. 22.
    Staroselsky A, Cassenti B N. Combined rate-independent plasticity and creep model for single crystal. Mech Mater, 2010, 42: 945–959CrossRefGoogle Scholar
  23. 23.
    Staroselsky A, Cassenti B N. Creep, plasticity, and fatigue of single crystal superalloy. Int J Solids Struct, 2011, 48: 2060–2075CrossRefGoogle Scholar
  24. 24.
    Srivastava A, Gopagoni S, Needleman A, et al. Effect of specimen thickness on the creep response of a Ni-based single-crystal superalloy. Acta Mater, 2012, 60: 5697–5711CrossRefGoogle Scholar
  25. 25.
    Staroselsky A, Martin T J, Cassenti B. Transient thermal analysis and viscoplastic damage model for life prediction of turbine components. J Eng Gas Turbines Power, 2015, 137: 042501CrossRefGoogle Scholar
  26. 26.
    Furukawa T, Sugata T, Yoshimura S, et al. An automated system for simulation and parameter identification of inelastic constitutive models. Comput Methods Appl Mech Eng, 2002, 191: 2235–2260CrossRefzbMATHGoogle Scholar
  27. 27.
    Li B, Lin J, Yao X. A novel evolutionary algorithm for determining unified creep damage constitutive equations. Int J Mech Sci, 2002, 44: 987–1002CrossRefzbMATHGoogle Scholar
  28. 28.
    Shenoy M M, Gordon A P, McDowell D L, et al. Thermomechanical fatigue behavior of a directionally solidified Ni-base superalloy. J Eng Mater Technol, 2005, 127: 325–336CrossRefGoogle Scholar
  29. 29.
    Shenoy M M. Constitutive Modeling and Life Prediction in Ni-base Superalloys. Dissertation for Dcotoral Degree. Atlanta: Georgia Institute of Technology, 2006Google Scholar
  30. 30.
    Bronkhorst C A, Kalidindi S R, Anand L. Polycrystalline plasticity and the evolution of crystallographic texture in FCC metals. Phil Trans R Soc Lond A, 1992, 341: 443–477CrossRefGoogle Scholar
  31. 31.
    Anand L. Single-crystal elasto-viscoplasticity: Application to texture evolution in polycrystalline metals at large strains. Comput Methods Appl Mech Eng, 2004, 193: 5359–5383MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Herrera-Solaz V, LLorca J, Dogan E, et al. An inverse optimization strategy to determine single crystal mechanical behavior from polycrystal tests: Application to AZ31 Mg alloy. Int J Plast, 2014, 57: 1–15CrossRefGoogle Scholar
  33. 33.
    Springmann M, Kuna M. Identification of material parameters of the Gurson-Tvergaard-Needleman model by combined experimental and numerical techniques. Comput Mater Sci, 2005, 32: 544–552CrossRefGoogle Scholar
  34. 34.
    Muñoz-Rojas P A, Cardoso E L, Vaz M. Parameter identification of damage models using genetic algorithms. Exp Mech, 2010, 50: 627–634CrossRefGoogle Scholar
  35. 35.
    Grédiac M, Pierron F. Applying the virtual fields method to the identification of elasto-plastic constitutive parameters. Int J Plast, 2006, 22: 602–627CrossRefzbMATHGoogle Scholar
  36. 36.
    Sutton M A, Yan J H, Avril S, et al. Identification of heterogeneous constitutive parameters in a welded specimen: Uniform stress and virtual fields methods for material property estimation. Exp Mech, 2008, 48: 451–464CrossRefGoogle Scholar
  37. 37.
    Réthoré J, Muhibullah J, Elguedj T, et al. Robust identification of elasto-plastic constitutive law parameters from digital images using 3D kinematics. Int J Solids Struct, 2013, 50: 73–85CrossRefGoogle Scholar
  38. 38.
    Lin J, Yang J. GA-based multiple objective optimisation for determining viscoplastic constitutive equations for superplastic alloys. Int J Plast, 1999, 15: 1181–1196CrossRefzbMATHGoogle Scholar
  39. 39.
    Chaparro B M, Thuillier S, Menezes L F, et al. Material parameters identification: Gradient-based, genetic and hybrid optimization algorithms. Comput Mater Sci, 2008, 44: 339–346CrossRefGoogle Scholar
  40. 40.
    Vaz Jr. M, Muñoz-Rojas P A, Cardoso E L, et al. Considerations on parameter identification and material response for Gurson-type and Lemaitre-type constitutive models. Int J Mech Sci, 2016, 106: 254–265Google Scholar
  41. 41.
    Kröner E. Allgemeine kontinuumstheorie der versetzungen und eigenspannungen. Arch Rational Mech Anal, 1959, 4: 273–334MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Lee E H. Elastic-plastic deformation at finite strains. J Appl Mech, 1969, 36: 1–6CrossRefzbMATHGoogle Scholar
  43. 43.
    Eringen A C. Mechanics of Continua. Huntington: Robert E. Krieger Publishing Co., 1980. 606Google Scholar
  44. 44.
    Mackay R A, Maier R D. The influence of orientation on the stress rupture properties of nickel-base superalloy single crystals. MTA, 1982, 13: 1747–1754CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • ShiWei Han
    • 1
  • XiaoGuang Yang
    • 1
    • 2
  • DuoQi Shi
    • 1
    • 2
    Email author
  • Jia Huang
    • 3
  1. 1.School of Energy and Power EngineeringBeihang UniversityBeijingChina
  2. 2.Beijing Key Laboratory of Aero-Engine Structure and StrengthBeijingChina
  3. 3.Shijiazhuang Flying CollegeShijiazhuangChina

Personalised recommendations