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Acta Metall Sin  2025, Vol. 61 Issue (12): 1911-1924    DOI: 10.11900/0412.1961.2024.00121
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Phase Field Simulation of γ' Phase Rafting in Single Crystal Superalloys Under Applied Stress
ZHANG Jinhu, XU Haisheng, GUO Hui, LI Xuexiong, XU Dongsheng(), YANG Rui
Shi-changxu Innovation Center for Advanced Materials, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
Cite this article: 

ZHANG Jinhu, XU Haisheng, GUO Hui, LI Xuexiong, XU Dongsheng, YANG Rui. Phase Field Simulation of γ' Phase Rafting in Single Crystal Superalloys Under Applied Stress. Acta Metall Sin, 2025, 61(12): 1911-1924.

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Abstract  

Nickel-based single crystal superalloys are critical materials for manufacturing advanced aircraft engine blades. During operation, microstructural changes in alloys under the applied stress significantly influence their fatigue and creep performances. However, relying solely on experimental methods poses challenges in capturing the dynamic processes by which the applied stress affects the alloy microstructure. Utilizing computational simulations to study the impact of the applied stress on the rafted γ' phase in single crystal superalloys offers distinct advantages. In this study, specific slip systems activated within the γ matrix are identified based on the type of the applied stress and their intrinsic plastic strain is calculated. The simulation models the formation of rafting under the applied stress and investigates the evolution of the microstructure during the rafting process in nickel-based single crystal superalloys. This study focuses on the effect of plastic strain within γ channels on the formation of the rafting morphology during the early stages of creep formation. Plastic strain generated under externally applied tensile stress promotes the preferential growth of γ′ precipitates along specific directions, which is the primary cause of γ′ phase rafting. Moreover, the lattice misfit directly determines the type of rafting (N-type or P-type). The spacing of dislocations at the γ′/γ interfaces, such as along {001} planes, significantly affects the morphology (aspect ratio) of γ′ precipitates but does not influence the growth kinetics or volume of γ′ precipitates at a given time step. In contrast to tensile stress, shear stress induces rafting microstructure coarsening at angles of approximately 30° or 60° relative to the horizontal direction, closely associated with activated slip systems. Additionally, different combinations of slip systems can result in the distortion of γ channels.

Key words:  applied stress      superalloy      rafting      phase field method      elastoplasticity     
Received:  25 April 2024     
ZTFLH:  TG132.3  
Fund: National Key Research and Development Program of China(2021YFA1600601)
Corresponding Authors:  XU Dongsheng, professor, Tel: (024)23971946, E-mail: dsxu@imr.ac.cn

URL: 

https://www.ams.org.cn/EN/10.11900/0412.1961.2024.00121     OR     https://www.ams.org.cn/EN/Y2025/V61/I12/1911

Fig.1  Phase diagram of the Ni-Al binary alloy (T—temperature) (a) and Gibbs free energy curves for γ and γ' phases (b)
Fig.2  Growth processes of the γ' phase at {001} plane with dislocation spacings of 200 nm (a1-e1), 400 nm (a2-e2), and 800 nm (a3-e3) when the misfit is -0.3% (t—time)
(a1-a3) t = 0.049 h (b1-b3) t = 0.098 h (c1-c3) t = 0.148 h (d1-d3) t = 0.197 h (e1-e3) t = 0.246 h
Fig.3  Growth processes of the γ' phase at {001} plane with dislocation spacings of 200 nm (a1-e1), 400 nm (a2-e2), and 800 nm (a3-e3) when the misfit is +0.3%
(a1-a3) t = 0.049 h (b1-b3) t = 0.098 h (c1-c3) t = 0.148 h (d1-d3) t = 0.197 h (e1-e3) t = 0.246 h
Fig.4  Volume fractions of the γ' phase at different time steps under -0.3% (a) and +0.3% (b) misfits
Fig.5  Nucleations and growth processes of the γ' phase in nickel-based superalloys after experiencing noise disturbances without external stress
(a-e) microstructure morphologies at t = 0.098 h (a), t = 0.197 h (b), t = 0.295 h (c), t = 0.393 h (d), and t = 0.492 h (e) (Deep blue color represents the γ phase matrix. V1-V4 represent different variants of the γ' phase)
(f) distribution of Al element composition field at t = 0.492 h
Fig.6  Evolution processes of γ' phase rafting in nickel-based superalloys under a tensile stress of 152 MPa along [001] direction with a misfit of -0.3%
(a-e) microstructure morphologies at t = 0.098 h (a), t = 0.197 h (b), t = 0.295 h (c), t = 0.393 h (d), and t = 0.492 h (e)
(f) distribution of Al element composition field at t = 0.492 h
Fig.7  Distributions of plastic strain in the γ phase channels in nickel-based superalloys under a tensile stress of 152 MPa along the [001] orientation with a misfit of -0.3% at t = 0.492 h (η1-η8—field variables of plastic strain corresponding to slip systems 1-8, respectively)
(a) slip system 1 (b) slip system 2 (c) slip system 3 (d) slip system 4
(e) slip system 5 (f) slip system 6 (g) slip system 7 (h) slip system 8
Fig.8  Evolution of the macroscopic plastic strain component (ε33) over time step
Fig.9  Evolution processes of γ' phase rafting in nickel-based superalloys under a tensile stress of 152 MPa along [001] oren-tation with a misfit of +0.3%
(a-e) microstructure morphologies at t = 0.098 h (a), t = 0.197 h (b), t = 0.295 h (c), t = 0.393 h (d), and t = 0.492 h (e)
(f) distribution of Al element composition field at t = 0.492 h
Fig.10  Distributions of plastic strain in the γ phase channels in nickel-based superalloys under a tensile stress of 152 MPa along the [001] orientation with a misfit of +0.3% at t = 0.492 h
(a) slip system 1 (b) slip system 2 (c) slip system 3 (d) slip system 4
(e) slip system 5 (f) slip system 6 (g) slip system 6 (h) slip system 8
Fig.11  Evolution of the ε33 over time step
Fig.12  Initial input configuration (a); γ' rafting 3D microstructures and corresponding view along the X direction at t = 0.492 h when only slip systems 2 and 8 (b), slip systems 4 and 6 (c), slip systems 9 and 11 (d), slip systems 10 and 12 (e), slip systems 2, 8, 10, and 12 (f) are activated
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