A dislocation density based material model to simulate the anisotropic creep behavior of single-phase and two-phase single crystals

International Journal of Plasticity

Volumn 25, Issue 5, 2009, Pages 973-994

  Preussner J ^a   Rudnik, Y ^b   Brehm, H ^c   Volkl R ^a   Glatzel, U ^a  

^a UNIVERSITY OF BAYREUTH   (Germany)

^b FRAUNHOFER INSTITUTE FOR MANUFACTURING TECHNOLOGY AND ADVANCED MATERIALS IFAM   (Germany)

^c Behr GmbH   (Germany)

Author keywords

Anisotropic material; Constitutive equations; Creep; Dislocations; Finite elements

Indexed keywords

CONSTITUTIVE EQUATIONS; CREEP; CRYSTAL MICROSTRUCTURE; CRYSTAL ORIENTATION; DIFFERENTIAL EQUATIONS; DISLOCATIONS (CRYSTALS); FINITE ELEMENT METHOD; MATERIALS; OPTICAL ANISOTROPY; SUPERALLOYS;

ANISOTROPIC CREEPS; ANISOTROPIC MATERIAL; BODY-CENTERED-CUBIC; CREEP BEHAVIORS; DEFORMATION PROCESS; DISLOCATION DENSITIES; DISLOCATIONS; EVOLUTION EQUATIONS; FACE-CENTERED CUBIC; FINITE ELEMENT MODELS; FINITE ELEMENTS; HEXAGONAL CLOSED PACKED (HCP); INTERACTION MATRICES; LATTICE STRUCTURES; MATERIAL MODELS; NICKEL-BASE SUPERALLOYS; ORIENTATION DEPENDENTS; SECONDARY CREEPS; SLIP SYSTEMS;

SINGLE CRYSTALS;

EID: 61849091512     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2008.04.006     Document Type: Article

References (67)

1. Alexander H., and Haasen P. Dislocations and plastic flow in the diamond structure. Solid State Phys. 22 (1968) 27-158
2. Basoalto H., Sondhi S.K., Dyson B.F., and McLean M. A generic microstructure-explicit model of creep. In: Green K.A., et al. (Ed). Superalloys 2004 (2004), TMS, Warrendale, PA 907-916
3. Blum W., Eisenlohr P., and Breutinger F. Understanding creep - a review. Metall. Mater. Trans. A33 (2002) 291-303
4. Brehm H. Modellierung des orientierungsabhängigen Kriechverhaltens einkristalliner Strukturen (2000), Shaker Verlag, Aachen
5. Brehm H., and Glatzel U. Material model describing the orientation dependent creep behavior of single crystals based on dislocation densities of slip systems. Int. J. Plasticity 15 3 (1998) 285-298
6. Busso E.P., Meissonnier F.T., and O'Dowd N.P. Gradient-dependent deformation of two-phase single crystals. J. Mech. Phys. Solids 48 (2000) 2333-2361
7. Caillard D., and Martin J.L. Thermally activated mechanisms in crystal plasticity (2003), Pergamon Materials Series, Elsevier Science Ltd., Cambridge
8. Carry C., Dermarkar S., Strudel J.L., and Wonsiewicz B.C. Internal stresses due to dislocation walls around second phase particles. Metall. Trans. A 10 (1979) 855-860
9. Chaboche J.-L. Cyclic viscoplastic constitutive equations, Part I: A thermodynamically consistent formulation. J. Appl. Mech. 60 December (1993) 813-821
10. Devincre B. Three dimensional stress field expressions for straight dislocation segments. Solid State Commun. 93 11 (1995) 875-878
11. Dunlop J.W., Bréchet Y.J.M., Legras L., and Estrin Y. Dislocation density-based modelling of plastic deformation of Zircaloy-4. Mater. Sci. Eng. A443 1-2 (2007) 77-86
12. Dyson B.F., and Gibbons T.B. Tertiary creep in nickel-base superalloys: analysis of experimental data and theoretical synthesis. Acta Metall. 35 9 (1987) 2355-2369
13. El-Azab A., Zaiser M., and Busso E. Special issue: density-based modelling of dislocations. Philos. Mag. 87 8-9 (2007) 1159-1160
14. Estrin Y. Constitutive modelling of creep of metallic materials: Some simple recipes. Mater. Sci. Eng. A463 1-2 (2007) 171-176
15. Feller-Kniepmeier M., Hemmersmeier U., Kuttner T., and Link T. Analysis of interfacial dislocations in a single crystal nickel-base superalloy after [0 0 1] creep at 1033 K. Evolution of internal stresses. Scripta Metall. Mater. 30 10 (1994) 1275-1280
16. Fikar J., Dupas C., Kruml T., Jacques A., and Martin J.L. Dislocation multiplication rate in the early stage of germanium plasticity. Mater. Sci. Eng. A400 (2005) 431-434
17. Forest S. Modeling slip, kink and shear banding in classical and generalized single crystal plasticity. Acta Mater. 46 9 (1998) 3265-3281
18. Frasier D.J., Whetstone J.R., Harris K., Erickson G.L., and Schwer R.E. Process and alloy optimization for CMSX-4 superalloy single crystal airfoils. In: Bachelet E. (Ed). Proceedings of the Conference on High Temperature Material Power Engineering vol. 2 (1990), Allison Gas Turbine, Indianapolis (IN) 1281
19. Gao H., Huang Y., and Nix W.D. Modeling plasticity at the micrometer scale. Naturwissenschaften 86 11 (1999) 507-515
20. Glatzel U. Microstructure and internal strains of undeformed and creep deformed samples of a nickel-base-superalloy (1994), Verlag Dr. Köster, Berlin
21. Glatzel U., and Feller-Kniepmeier M. Calculations of internal stresses in the γ/γ′ microstructure of a nickel-base superalloy with high volume fraction of γ′-phase. Scripta Metall. 23 (1989) 1839-1844
22. Haasen P. Dislocation dynamics in the diamond structure. In: Rosenfield A.R., Hahn G.T., Bement A.L., and Jaffee R.I. (Eds). Dislocation Dynamics (1968), McGraw-Hill Book Co., New York p. 701
23. 3Al at temperatures above the flow stress peak. Acta Metall. 37 12 (1989) 3235-3244
24. Heilmaier M., Kestler H., and Gibeling J.C. A unified description of creep in pure and dispersion-strengthened copper. Int. J. Mat. Res. (formerly Z. Metallkd.) 93 7 (2002) 666-671
25. Johnston W.G., and Gilman J.J. Dislocation velocities, dislocation densities, and plastic flow in lithium fluoride crystals. J. Appl. Phys. 30 2 (1959) 129-144
26. Kassner M.E., and Hayes T.A. Creep cavitation in metals. Int. J. Plasticity 19 10 (2003) 1715-1748
27. Kocks U.F., and Brown T.J. Latent hardening in aluminum. Acta Metall. 14 2 (1966) 87-98
28. Kubin L.P., Canova G., Condat M., Devincre E., Pontikis V., and Bréchet Y. Dislocation microstructures and plastic flow: a 3D simulation. In: Martin G., and Kubin L.P. (Eds). Non Linear Phenomena in Materials Science II (1992), Trans Tech Publications 455
29. Kuttner T. Mechanismen des Hochtemperaturkriechens einkristalliner Nickelbasissuperlegierungen in [0 1 1]-Orientierung (1993), VDI Verlag, Berlin
30. Ma A., Roters F., and Raabe D. A dislocation density based constitutive model for crystal plasticity FEM including geometrically necessary dislocations. Acta Mater. 54 8 (2006) 2169-2179
31. MacLachlan D.W., Wright L.W., Gunturi S., and Knowles D.M. Constitutive modelling of anisotropic creep deformation in single crystal blade alloys SRR99 and CMSX-4. Int. J. Plasticity 17 4 (2001) 441-467
32. McLean M. Resistant superalloys. In: Buschow J., et al. (Ed). Encyclopedia of Materials: Science and Technology (2001), Elsevier Science Ltd. p. 1845
33. Meagher S., Borch R.S., Groza J., Mukherjee A.K., and Green H.W. Activation parameters of high-temperature creep in polycrystalline nickel at ambient and high pressures. Acta Metall. Mater. 40 (1992) 159-166
34. Meric L., Poubanne P., and Cailletaud G. Single crystal modeling for structural calculations: Part 1 Model presentation. J. Eng. Mater. - Trans. ASME 113 1 (1991) 162-170
35. Müller L., and Feller-Kniepmeier M. Finite element modelling of the morphology and orientation dependence of the creep behavior in nickel-base superalloys. Scripta Metall. Mater. 29 (1993) 81-84
36. Müller L., Glatzel U., and Feller-Kniepmeier M. Calculation of the internal stresses and strains in the microstructure of a single-crystal nickel-base superalloy during creep. Acta Metall. Mater. 41 (1993) 3401-3411
37. Nabarro F.R.N. The superiority of superalloys. Mater. Sci. Eng. A184 2 (1994) 167-171
38. Pollock T., and Argon A. Intermediate temperature creep deformation in CMSX-3 single crystals. In: Reichman S., Duhl D., Maurer G., Antolovich S., and Lund C. (Eds). Superalloys 1988 (1988), TMS 285
39. Prasad S.C., Rajagopal K.R., and Rao I.J. A continuum model for the anisotropic creep of single crystal nickel-based superalloys. Acta Mater. 54 (2006) 1487-1500
40. Preußner J., Rudnik Y., Völkl R., and Glatzel U. Finite element modeling of anisotropic single crystal superalloy creep deformation based on dislocation densities of individual slip systems. Z Metallkd 6 (2005) 595-601
41. Probst-Hein M., Dlouhy A., and Eggeler G. Interface dislocations in superalloy single crystals. Acta Mater. 47 8 (1999) 2497-2510
42. Qi W., and Bertram A. Damage modeling of the single crystal superalloy SRR99 under monotonous creep. Comput. Mater. Sci. 13 (1998) 132-141
43. Raabe D., Roters F., Barlat F., and Chen L.-Q. Continuum Scale Simulation of Engineering Materials: Fundamentals - Microstructures - Process Applications (2004), Wiley-VCH, Weinheim
44. Rao S.I., Parthasarathy T.A., Dimiduk D.M., and Hazzledine P.M. Discrete dislocation simulations of precipitation hardening in superalloys. Phil. Mag. 84 30 (2004) 3195-3215
45. Rodary E., Rodney D., Proville L., Bréchet Y., and Martin G. Dislocation glide in model Ni(Al) solid solutions by molecular dynamics. Phys. Rev. B 70 (2004) 054111
46. Rösler J., Mukherji D., and Baranski T. Co-Re-based alloys: a new class of high temperature materials?. Adv. Eng. Mater. 9 10 (2007) 876-881
47. Rudnik Y. Modellierung des anisotropen Kriechverhaltens von Nickelbasis-Superlegierungen und Untersuchung festigkeitsrelevanter Eigenschaften von Platinlegierungen bei hohen Temperaturen (2006), Verlag Dr. Köster, Berlin
48. Saß V. Untersuchung der Anisotropie im Kriechverhalten der einkrostallinen Nickelbasis-Superlegierung CMSX-4 (1997), Verlag Dr. Köster, Berlin
49. Saß V., and Feller-Kniepmeier M. Orientation dependence of dislocation structures and deformation mechanisms in creep deformed CMSX-4 single crystals. Mater. Sci. Eng. A245 1 (1998) 19-28
50. Saß V., Glatzel U., and Feller-Kniepmeier M. Creep anisotropy in the monocrystalline nickel-base superalloy CMSX-4. In: Kissinger R.D., Deye D.J., Anton D.L., and Cetel A.D. (Eds). Superalloys 1996 (1996), TMS 283
51. Saß, V., Siebörger, D., Knobloch, C., Glatzel, U., 1997. Anisotropic creep behavior of a nickel-based superalloy compared with single phase nickel solid solution and γ′ phase single crystals. In: Earthman, J.C., Mohamed, F.A. (Eds.), Proceedings of the 11th International Conference on the Strength of Materials, Prague, pp. 687-696.
52. Schall P., Feuerbacher M., Bartsch M., and Messerschmidt U. Dislocation density evolution upon plastic deformation of Al-Pd-Mn single quasicrystals. Philos. Mag. Lett. 79 10 (1999) 785-796
53. 3Al). Scripta Metall. 17 8 (1983) 997-1002
54. Shah D.M., and Cetel A. Creep anisotropy in nickel base γ, γ′ and γ/γ′ superalloy single crystals. In: Kissinger R.D., Deye D.J., Anton D.L., and Cetel A.D. (Eds). Superalloys 1996 (1996), TMS 273
55. Siebörger D., and Glatzel U. Orientation dependent creep behavior and microstructure of nickel solid solution single crystals. Acta Mater. 47 (1999) 397-406
56. Siebörger D., Knake H., and Glatzel U. Temperature dependence of the elastic moduli of the nickel-base superalloy CMSX-4 and its isolated phases. Mater. Sci. Eng.-Struct. A298 (2001) 26-33
57. Tschopp M.A., and McDowell D.L. Dislocation nucleation in Σ3 asymmetric tilt grain boundaries. Int. J. Plasticity 24 2 (2008) 191-217
58. Völkl R., Glatzel U., and Feller-Kniepmeier M. Analysis of matrix and interfacial dislocations in the nickel base superalloy CMSX-4 after creep in [over(1, ̄) 1 1] direction. Scripta Metall. Mater. 31 11 (1994) 1481-1486
59. Völkl R., Glatzel U., and Feller-Kniepmeier M. Measurement of the lattice misfit in the single crystal nickelbase superalloys CMSX-4, SRR 99 and SC 16 by convergent beam electron diffraction. Acta Mater. 46 (1998) 4395-4404
60. Von Blanckenhagen B., Arzt E., and Gumbsch P. Discrete dislocation simulation of plastic deformation in metal thin films. Acta Mater. 52 3 (2004) 773-784
61. Wang S., and Pirouz P. Mechanical properties of undoped GaAs. Part I: Yield stress measurements. Acta Mater. 55 (2007) 5500-5514
62. Wang Y.U., Jin Y.M., Cuitino A.M., and Khachaturyan A.G. Phase field microelasticity theory and modeling of multiple dislocation dynamics. Appl. Phys. Lett. 78 16 (2001) 2324-2326
63. Weygand D., Friedman L.H., Van der Giessen E., and Needleman A. Aspects of boundary-value problem solutions with three-dimensional dislocation dynamics. Model. Simulat. Mater. Sci. 10 4 (2002) 437-468
64. Yaguchi M., Yamamoto M., and Ogata T. A viscoplastic constitutive model for nickel-base superalloy, Part 2: modeling under an isothermal conditions. Int. J. Plasticity 18 8 (2002) 1111-1131
65. Yamakov V., Wolf D., Phillpot S.R., and Gleiter H. Dislocation-dislocation and dislocation-twin reactions in nanocrystalline Al by molecular dynamics simulation. Acta Mater. 51 14 (2003) 4135-4147
66. Yashiro K., Kurose F., Nakashima Y., Kubo K., Tomita Y., and Zbib H.M. Discrete dislocation dynamics simulation of cutting of γ′ precipitate and interfacial dislocation network in Ni-based superalloys. Int. J. Plasticity 19 9 (2006) 713-723
67. Zeghadi A., Forest S., Gourgues A.-F., and Bouaziz O. Cosserat continuum modelling of grain size effects in metal polycrystals. PAMM 5 (2005) 79-82