Abstract
Taking into account the effects that the components of tension stresses couple with components of torsion stresses when off-axis loads are applied to orthotropic materials, Hill’s yield criterion for plastically orthotropic solids is modified by adding an invariant that is composed of the product item of quadratic components of the deviatoric stress tensor, and a new yield criterion is put forward in terms of the characteristics of the face-centered cubic (FCC) single-crystal material. The correlation of prediction and experiments is very good, and the new criterion is used to predict the yield stresses of an internal single-crystal, Nickel-based superalloy, DD3, which is more accurate than that of Hill’s at 760°C. Equivalent stress and strain that adapt to the new criterion are defined. Thinking of the yield function as a plastic potential function from the associated flow rule, the elastic-plastic constitutive model for the FCC single-crystal material is constructed, and the corresponding elastic-plastic matrix is educed. The new yield criterion and its equivalent stress and strain will be reduced to Von Mises’ yield criterion and corresponding equivalent stress and strain for isotropic materials.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hill R., A theory of the yielding and plastic flow of anisotropic metals, Proc. R. Soc. Lond., A, 1948, 193–281
Liu C, Huang Y. and Stout M. G., On the asymmetric yield surface of plastically orthotropic materials: a phenomenological study. Acta Mater., 1997, 45(6): 2397–2406
Tsai S. W. and Wu E. M., A general theory of strength for anisotropic material, J. Compos. Mater., 1971, 5: 58
Zhou B., Yang S. and Nie J., Study of yield criterion for orthotropic material, The 8th CSAA Academic Conference Symposium on Structural Strength and Vibration of Engine, **an, China, 1996, 10, 44–48
Yue Z. and Zheng C., The mechanical study of the tension/compression flow asymmetry of Nickel base turbine blade alloys, J. Mech. Strength, 1993, 15(4): 53–58 (in Chinese)
Yue Z. and Zheng C., Study of the tension/compression yield behavior of single crystal blade superalloys, Acta Aeronaut. Astronaut. Sin., 1993, 14(9): A556–A559 (in Chinese)
Swanson G. A., Linask I., Nissley D. M. et al, Life Prediction and Constitutive Models for Engine Hot Section Anisotropic Materials, NASACR-179594, 1987
Meric L., Poubanne P. and Cailletaud G., Single crystal modeling for structural calculations: part 1—model presentation, J. Eng. Mater. Technol., 1991, 113: 162–170
Yin Z., Cheng X., Yang Z. et al, Study on strength and life of anisotropic single crystal blade—part 1: crystallographic constitutive models and applications, Chin. J. Aeronaut., 2001, 14: 18–23
Yue Z., Lu H., Zheng C. et al, A viscoplastic crystallographic analysis of a nickel-based single crystal blade, J. Propuls. Technol., 1996, 17(3): 50–55 (in Chinese)
Yue Z., Zheng C., Yin Z. et al, The study of the creep constitutive equation and the life predictive model of single crystal nickel-based superalloys, J. Mech. Strength, 1994, 16(4): 2–5 (in Chinese)
Zhou B., Zhang X. and Luo Y., A unified viscoplastic constitutive model of orthogonal anisotropic material, J. Propuls. Technol., 1998, 1: 89–93 (in Chinese)
Yue Z. and Lu Z., A model of multiaxial low cycle fatigue life time of a nickel-based single crystal, Rare Met. Mater. Eng., 2000, 29(1): 28–31 (in Chinese)
Kanda M., Sakane M. and Ohnami M., High temperature multiaxial low cycle fatigue of CMSX-2 Ni-base single crystal superalloy, J. Eng. Mater. Technol., 1997, 119: 153–160
MacLachlan D. W. and Knowles D. M., Fatigue behaviour and lifting of two single crystal superalloys, Fatigue Fract. Eng. Mater. Struct., 2001, 24: 503–521
Tao X., Yin Z. and Gao D., Study on damage-coupled viscoplastic constitutive model for DD3 single crystal, Acta Aeronaut. Astronaut. Sin., 1998, 19(1): 35–40 (in Chinese)
Committee to Edit China Aeronautical Materials Handbook, China Aeronautical Material Handbook (2nd edn.) vol. 2, Bei**g: China Standard Publishing Company, 2002, 5 (in Chinese)
Zhang Z., Zhang K. and Yang N., Mechanics of Structure for Composite Materials, Bei**g: Publishing Company of Bei**g University of Aeronautics and Astronautics, 1993, 9 (in Chinese)