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Strain localization at the crack tip in single crystal CT specimens under monotonous loading: 3D Finite Element analyses and application to nickel-base superalloys

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Abstract

Three-dimensional Finite Element simulations of mode I crack tip fields in Compact Tension specimens are presented for elastic ideally-plastic F.C.C. single crystals. The computations are carried out within the framework of classical continuum crystal plasticity for three crack orientations: (001)[110],(110)[001] and (001)[100]. The attention is drawn on the strong differences between the plastic strain field obtained at the free surface and in the mid-section of the specimens. The results are compared, on the one hand, to analytical solutions for stationary cracks in single crystals under plane strain conditions and, on the other hand, to experimental tests on a single crystal nickel-based superalloy at room temperature. For this material, both octahedral and cube slip must be taken into account. A good agreement between experimental observations and numerical results is found in the structure of the strain localization bands observed at the free surface of (110)[001] cracked specimens. In particular, the evidence of kink banding near the crack tip is provided, confirmed by EBSD orientation mapping. The measured values of local lattice rotation are in agreement with the Finite Element prediction.

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References

  • Arakere, N. and Swanson, G. (2002). Effect of orientation on fatigue failure of single crystal nickel base turbine blade superalloys. J. Eng. Mat. for Gas Turbines and Power 134(1), 161-176.

    Google Scholar 

  • Asaro, R. (1983). Crystal plasticity. J. Appl. Mech. 50, 921-934.

    Google Scholar 

  • Aswath, P. (1994). Effect of orientation on crystallographic cracking in notched nickel-base superalloy single crystal subjected to far-field cyclic compression. Met. Mat. Trans 25A, 287-297.

    Google Scholar 

  • Besson, J. Cailletaud, G., Chaboche, J.-L. and Forest, S. (2001). Mécanique non linéaire des matériaux, Hermès, France, 445 p.

    Google Scholar 

  • Bettge, D. and Osterle, W. (1999). Cube slip in near [111] oriented speciments of single crystal nickel-base superalloys. Scripta Mat. 40(4), 389-395.

    Google Scholar 

  • Cho, J. and Yu, J. (1991). Near-crack-tip deformation in copper single crystals. Phil. Mag. Letters 64(4), 175-182.

    Google Scholar 

  • Crompton, J. and Martin, J. (1984a). Crack growth in a single-crystal superalloy at elevated temperatures. Metall. Trans. 15A, 1711-1719.

    Google Scholar 

  • Crone, W. and Drugan, W. (2001). Comparison of experiment and theory for crack tip fields in ductile single crystals. In: Proceedings of the ICF 10 International Congress on Fracture (Edited by K.K. Ravi-Chander, B. Karihaloo, T. Kishi, R. Ritchie, A. Yokobori Jr. and T. Yokobori).

  • Crone, W. and Shield, T. (2001). Experimental study of the deformation near a notch tip in copper and copperberyllium single crystals. J. Mech. Phys. Solids 49, 2819-2838.

    Google Scholar 

  • Cuitiño, A. and Ortiz, M. (1992). Computational modeling of single crystals. Modelling Simul. Mater. Sci. Eng. 1, 225-263.

    Google Scholar 

  • Cuitiño, A. and Ortiz, M. (1996). Three-dimensional crack-tip fields in four-point-bending copper single-crystal specimens. J. Mech. Phys. Solids 44, 863-904.

    Google Scholar 

  • Defresne, A. and Rémy, L. (1990). Fatigue behavior of CMSX2 superalloy [001] single crystals at high temperature II: Fatigue crack growth. Mat. Sci. and Eng. A129, 55-64.

    Google Scholar 

  • Deshpande, V., Needleman, A. and Van Der Giessen, E. (2001). A discrete dislocation analysis of near threshold fatigue crack growth. Acta Mater. 49, 3189-3203.

    Google Scholar 

  • Drugan, W. (2001). Asymptotic solutions for tensile crack tip fields without kink-type bands in elastic-ideally plastic single crystals. J. Mech. Phys. Phys. Solids 49, 2155-2176.

    Google Scholar 

  • Drugan, W. and Rice, J. (1984). Restrictions on quasi-statically moving surfaces of strong discontinuity in elastoplastic solids. In: Mechanics of Material Behavior (Edited by G. Dvorak and R. Shield), Elsevier, Amsterdam, 59-73.

    Google Scholar 

  • Farhat, C. and Roux, F.-X. (1991). A Method of Finite Element Tearing and Interconnecting and its Parallel Solution Algorithm. Int. J. for Numerical Methods in Engineering 32, 1205-1227.

    Google Scholar 

  • Fleury, E. (1991). Endommagement du superalliage monocristallin AM1 en fatigue isotherme et anisotherme. Ph.D. thesis, Ecole Nationale Supérieure des Mines de Paris.

  • Flouriot, S., Forest, S. and Rémy, L. (2003). Strain localization phenomena under cyclic loading: Application to fatigue of single crystals. Computational Materials Science 26, 61-70.

    Google Scholar 

  • Forest, S. (1998). Modeling Slip, Kink and Shear Banding in Classical and Generalized Single Crystal Plasticity. Acta Materialia 46(9), 3265-3281.

    Google Scholar 

  • Forest, S., Boubidi, P. and Sievert, R. (2001). Strain localization patterns at a crack tip in generalized single crystal plasticity. Scripta Mat. 44, 953-958.

    Google Scholar 

  • Forest, S., Olschewski, J., Ziebs, J. Kühn, H.-J., Meersmann, J. and Frenz, H. (1996). The elastic/plastic deformation behaviour of various oriented SC16 single crystals under combined tension/torsion fatigue loading. In: Sixth International Fatigue Congress (Edited by G. Lütjering and H. Nowack), ASME, STP, 139-150.

  • Garrett, G. and Knott, J. (1975). Crytallographic fatigue crack growth in aluminium alloys. Acta Metall. 23, 841-848.

    Google Scholar 

  • Gilman, J. (1955). Structure and polygonization of bent zinc monocrystals. Acta Metall. 3, 277-288.

    Google Scholar 

  • Gupta, V. (1993). Tensile crack-tip fields in elastic-ideally plastic hexagonal crystals and layered materials. Acta Metall. 16, 553-561.

    Google Scholar 

  • Hanriot, F., Cailletaud, G. and Rémy, L. (1991). Mechanical behavior of a nickel-base superalloy single crystal. In: Proc. of Int. Conf. on High Temperature Constitutive Modeling (Edited by A. Freed and K. Walker), ASME, STP, 139-150.

  • Henderson, M. and Martin, J. (1996). The influence of crystal orientation on high temperature fatigue crack growth of a Ni-based single crystal superalloy. Acta Mat. 44(1), 111-126.

    Google Scholar 

  • Köster, A. and Rémy, L. (2000). An oxidation creep-fatigue damage model for fatigue at high temperature and under thermal transients. In: Fatigue'99 (Edited by H. Sehitoglu and H. Maier), Elsevier, pp. 2139-2144.

  • Kysar, J. and Briant, C. (2002). Crack tip deformation fields in ductile single crystals. Acta Mat. 50(9), 2367-2380.

    Google Scholar 

  • Lerch, B. and Antolovich, S. (1990). Fatigue crack propagation behavior of a single crystalline superalloy. Metall. Trans. A 21A, 2169-2177.

    Google Scholar 

  • Leverant, G. and Gell, M. (1975). The influence of temperature and cyclic frequency on the fatigue fracture of cube oriented nickel-base superalloy single crystals. Metall. Trans. A 6A, 367-371.

    Google Scholar 

  • Mandel, J. (1973). Equations constitutives et directeurs dans les milieux plastiques et viscoplastiques. Int. J. Solids Structures 9, 725-740.

    Google Scholar 

  • Méric, L., Poubanne, P. and Cailletaud, G. (1991). Single crystal modeling for structural calculations: Part 1-Model presentation. J. Eng. Mat. Techn. 113, 162-170.

    Google Scholar 

  • Mohan, R., Ortiz, M. and Shih, C. (1992). An analysis of cracks in ductile single crystals-II Mode I loading. J. Mech. Phys. Solids 40(2), 315-337.

    Google Scholar 

  • Neumann, P. (1974). New experiments concerning the slip process at propagating fatigue cracks-I. Acta Met. 22, 1155-1165.

    Google Scholar 

  • Nouailhas, D. and Cailletaud, G. (1995). Tension-torsion behavior of single-crystal superalloys: experiment and finite element analysis. International Journal of Plasticity 11(4), 451-470.

    Google Scholar 

  • Nouailhas, D., Pacou, D., Cailletaud, G. Hanriot, F. and Rémy, L. (1993). Experimental study of the anisotropic behaviour of the CMSX2 single crystal superalloy under tension-torsion loadings. In: Advances in Multiaxial Fatigue (Edited by D. McDowell and R. Ellis), 244-258.

  • Pan, J. (1986). Plain strain crack-tip stress field for anisotropic perfectly-plastic materials. J. Mech. Phys. Solids 34, 617-635.

    Google Scholar 

  • Rémy, L. and Skelton, R. (1992). In: High Temperature Structural Design, ESIS 12 (Edited by M. Larsson), Mechanical Engineering Publications, London, 283-315.

    Google Scholar 

  • Rice, J. (1987). Tensile crack tip fields in elastic-ideally plastic crystals. Mechanics of Materials 6, 317-335.

    Google Scholar 

  • Rice, J., Hawk, D. and Asaro, R. (1990). Crack tip fields in ductile single crystals. Int. J. Fracture 42, 301-321.

    Google Scholar 

  • Saeedvafa, M. and Rice, J. (1989). Crack tip singular fields in ductile crystals with Taylor power-law hardening; II: Plane strain. J. Mech. Phys. Solids 37(6), 673-691.

    Google Scholar 

  • Shield, T. (1996). An experimental study of the plastic strain fields near a notch tip in a copper single crystal, during loading. Acta Mater. 44(4), 1547-1561.

    Google Scholar 

  • Shield, T. and Kim, K.-S. (1994). Experimental measurement of the near tip strain field in an Iron-silicon single crystal. J. Mech. Phys. Solids 42(5), 845-873.

    Google Scholar 

  • Simo, J. and Hughes, T. (1997). Computational Inelasticity, Springer-Verlag, Berlin.

    Google Scholar 

  • Van der Giessen, E., Deshpande, V., Cleveringa, H. and Needleman, A. (2001). Discrete dislocation plasticity and crack tip fields in single crystals. J. Mech. Phys. Solids 49, 2133-2153.

    Google Scholar 

  • Xia, Z. and Hutchinson, J. (1996). Crack tip fields in strain gradient plasticity. J. Mech. Phys. Solids 44, 1621.

    Google Scholar 

  • Z-set package (1996). www.nwnumerics.com, www.mat.ensmp.fr.

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Flouriot, S., Forest, S., Cailletaud, G. et al. Strain localization at the crack tip in single crystal CT specimens under monotonous loading: 3D Finite Element analyses and application to nickel-base superalloys. International Journal of Fracture 124, 43–77 (2003). https://doi.org/10.1023/B:FRAC.0000009300.70477.ba

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  • DOI: https://doi.org/10.1023/B:FRAC.0000009300.70477.ba

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