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.
Similar content being viewed by others
References
MacLachlan D W, Knowles D M. Modelling and prediction of the stress rupture behaviour of single crystal superalloys. Mater Sci Eng- A, 2001, 302: 275–285
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: 129–141
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: 441–467
Lemaitre L, Chaboche J L. Mechanics of Solid Materials. Cambridge: Cambridge University Press, 1994
Chaboche J L. A review of some plasticity and viscoplasticity constitutive theories. Int J Plast, 2008, 24: 1642–1693
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: 937–948
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: 251–266
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: 267–282
Meric L, Poubanne P, Cailletaud G. Single crystal modeling for structural calculations: Part 1—model presentation. J Eng Mater Technol, 1991, 113: 162
Meric L, Cailletaud G. Single crystal modeling for structural calculations: Part 2—finite element implementation. J Eng Mater Technol, 1991, 113: 171
Hill R. Generalized constitutive relations for incremental deformation of metal crystals by multislip. J Mech Phys Solids, 1966, 14: 95–102
Hill R. The essential structure of constitutive laws for metal composites and polycrystals. J Mech Phys Solids, 1967, 15: 79–95
Rice J R. On the structure of stress-strain relations for time-dependent plastic deformation in metals. J Appl Mech, 1970, 37: 728–737
Rice J R. Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity. J Mech Phys Solids, 1971, 19: 433–455
Peirce D, Asaro R J, Needleman A. An analysis of nonuniform and localized deformation in ductile single crystals. Acta Metall, 1982, 30: 1087–1119
Asaro R J. Micromechanics of crystals and polycrystals. Adv Appl Mech, 1983, 23: 1–115
Peirce D, Asaro R J, Needleman A. Material rate dependence and localized deformation in crystalline solids. Acta Metall, 1983, 31: 1951–1976
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. 707–716
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: 289–298
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: 223–237
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: 372–394
Staroselsky A, Cassenti B N. Combined rate-independent plasticity and creep model for single crystal. Mech Mater, 2010, 42: 945–959
Staroselsky A, Cassenti B N. Creep, plasticity, and fatigue of single crystal superalloy. Int J Solids Struct, 2011, 48: 2060–2075
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: 5697–5711
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: 042501
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: 2235–2260
Li B, Lin J, Yao X. A novel evolutionary algorithm for determining unified creep damage constitutive equations. Int J Mech Sci, 2002, 44: 987–1002
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: 325–336
Shenoy M M. Constitutive Modeling and Life Prediction in Ni-base Superalloys. Dissertation for Dcotoral Degree. Atlanta: Georgia Institute of Technology, 2006
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: 443–477
Anand L. Single-crystal elasto-viscoplasticity: Application to texture evolution in polycrystalline metals at large strains. Comput Methods Appl Mech Eng, 2004, 193: 5359–5383
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: 1–15
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: 544–552
Muñoz-Rojas P A, Cardoso E L, Vaz M. Parameter identification of damage models using genetic algorithms. Exp Mech, 2010, 50: 627–634
Grédiac M, Pierron F. Applying the virtual fields method to the identification of elasto-plastic constitutive parameters. Int J Plast, 2006, 22: 602–627
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: 451–464
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: 73–85
Lin J, Yang J. GA-based multiple objective optimisation for determining viscoplastic constitutive equations for superplastic alloys. Int J Plast, 1999, 15: 1181–1196
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: 339–346
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: 254–265
Kröner E. Allgemeine kontinuumstheorie der versetzungen und eigenspannungen. Arch Rational Mech Anal, 1959, 4: 273–334
Lee E H. Elastic-plastic deformation at finite strains. J Appl Mech, 1969, 36: 1–6
Eringen A C. Mechanics of Continua. Huntington: Robert E. Krieger Publishing Co., 1980. 606
Mackay R A, Maier R D. The influence of orientation on the stress rupture properties of nickel-base superalloy single crystals. MTA, 1982, 13: 1747–1754
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Han, S., Yang, X., Shi, D. et al. A reduced-order method for parameter identification of a crystal plasticity model considering crystal symmetry. Sci. China Technol. Sci. 62, 373–387 (2019). https://doi.org/10.1007/s11431-018-9353-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-018-9353-2