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Acta Metall Sin  2020, Vol. 56 Issue (6): 855-862    DOI: 10.11900/0412.1961.2019.00355
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Anisotropy of Elasticity of a Ni Base Single Crystal Superalloy
LIU Jinlai(), YE Lihua, ZHOU Yizhou, LI Jinguo, SUN Xiaofeng
Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
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The anisotropy of elasticity of single crystal superalloy is essential to understand its mechanical behavior, e.g. calculating the vibration frequency of turbine blade and avoiding resonance during operation. However, it's difficult to calculate the stiffness constants of single crystal superalloy by theory methods. In this work, one simple experimental method is employed to determine the stiffness constants. The slabs of a first generation single crystal superalloy in two orientations 〈001〉〈100〉 and 〈011〉〈110〉 are employed to measure the Young's modulus and shear modulus of this alloy. The Young's modulus and shear modulus of the first specimen and the shear modulus of the second specimen are measured by resonance method from room temperature to 1100 ℃. The three stiffness constants C11, C12 and C44 of this superalloy are calculated from the measured moduli. The Young's modulus and shear modulus in any orientation can be calculated based on the stiffness constants. Further, the 3D distribution map of Young's modulus and maximum and minimum of shear modulus related to primary orientation can be drawn, so the distribution feature of modulus in 3D space can be acquired conveniently. When the primary orientations are along 〈001〉 and 〈111〉, the shear modulus in plane is isotropy with secondary orientation. When the primary orientation is along 〈011〉, the shear modulus demonstrates significant anisotropy with secondary orientation, the shear modulus reaches minimum with secondary orientation 〈110〉, while the maximum is obtained in secondary orientation 〈100〉.

Key words:  single crystal superalloy      stiffness constant      anisotropy      modulus      crystal orientation     
Received:  21 October 2019     
ZTFLH:  TG113.25  
Fund: National Science and Technology Major Project(2017-VI-0002-0072);National Key Research and Development Program of China(2017YFA0700704);National Natural Science Foundation of China(51971214)
Corresponding Authors:  LIU Jinlai     E-mail:

Cite this article: 

LIU Jinlai, YE Lihua, ZHOU Yizhou, LI Jinguo, SUN Xiaofeng. Anisotropy of Elasticity of a Ni Base Single Crystal Superalloy. Acta Metall Sin, 2020, 56(6): 855-862.

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Fig.1  Schematics of dependence of shear modulus on orientation (l—the unit vector along primary orientation, m—the unit vector along secondary orientation, θ—the polar angle, ?—the azimuth angle, χ—the angle between m and line projected from l on horizontal plane then projected on the plane normal to l )
(a) definition of primary and secondary orientations in crystal coordinate system
(b) the relation between orientations and specimen geometry
Fig.2  OM images of slabs with three orientations in transverse section
(a) 〈001〉〈100〉 (b) 〈011〉〈110〉 (c) 〈011〉〈100〉


E / GPaG / GPaG / GPaG / GPa
Table 1  Measured moduli of specimens with three orientations
Temperature / ℃C11 / GPaC12 / GPaC44 / GPa
Table 2  Calculated stiffness constants (C11, C12, C44) of the single crystal superalloy
Fig.3  3D distribution maps of moduli of the single crystal superalloy at 800 ℃
Color online
(a) Young's modulus
(b) maximum of shear modulus (Gmax)
(c) minimum of shear modulus (Gmin)
Fig.4  The variations of shear modulus of single crystal superalloy at 800 ℃ in plane with primary orientations along 〈001〉 (a), 〈011〉 (b) and 〈111〉 (c)
Fig.5  Comparison of shear modulus in 〈011〉〈100〉 orientation of single crystal superalloy between measured and calculated values
Fig.6  The variation of anisotropy ratio of the superalloy with temperature
Fig.7  Schematics of atom arrangement in end surface of specimen with primary orientation along 〈011〉
(a) secondary orientation along 〈110〉 (specimen for test)
(b) secondary orientation along 〈100〉 (specimen for validation)
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