Lattice Misfit Predictions via the Gaussian Process Regression for Ni-Based Single Crystal Superalloys
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Lattice Misfit Predictions via the Gaussian Process Regression for Ni‑Based Single Crystal Superalloys Yun Zhang1 · Xiaojie Xu1 Received: 17 July 2020 / Accepted: 14 September 2020 © The Korean Institute of Metals and Materials 2020
Abstract Ni-based single crystal superalloys exhibit superb mechanical strength, particularly, creep resistance at elevated temperature. The unique microstructure, which is consisted of 𝛾 and 𝛾 ′ phases, is a major factor that determines the mechanical behavior of these alloys. The lattice misfit between the two phases is of particular interest in understanding and predicting the deformation mechanism. The measurement of the lattice misfit by advanced analytical instruments is costly and difficult. In current study, we develop the Gaussian process regression model to predict lattice misfits for Ni-based single crystal superalloys based on chemical composition, temperature, and two morphological indicators. The model is highly stable and accurate and promising as a fast, robust, and low-cost tool for lattice misfit estimations. Keywords Ni-based single crystal superalloys · Lattice mismatch · Lattice constant · Machine learning
1 Introduction Nickel-based single crystal superalloys (Ni-SXs) exhibit superior mechanical strength, particularly, the excellent high temperature creep strength. The high creep resistance of these alloys makes them great candidates for the manufacturing of turbines, heat exchangers, and nuclear reactors [1–10]. The superb high temperature creep resistance results from the absence of any harmful grain boundaries and the precipitation of a high-volume fraction ( ∼ 70%) of the long-range ordered L12 𝛾 ′ phase. The ordered 1 2 𝛾 ′ phase appears as cubes that are coherently embedded in a face-centered-cubic solid solution 𝛾 matrix [11]. The lattice misfit, which is a result of different partitioning behavior of alloying elements in the two phases, is closely related to the movements and interactions of dislocations and thus creep properties of the Ni-SX [12–14]. For example, elements such as Ti, Al, and Ta, prefer to partition to the 𝛾 ′ phase, while those such as Cr, Co, nad Mo, prefer to partition to the 𝛾 phase. Due to * Yun Zhang [email protected] Xiaojie Xu [email protected] 1
Department of Materials Science and Engineering, North Carolina State University, Raleigh, NC 27695, USA
different sizes of the atoms, the 𝛾 ′ phase usually has a larger lattice constant than the 𝛾 phase, which leads to a positive lattice misfit at room temperature. The natural lattice misfit a � −a is defined as: 𝛿 = 2 a𝛾 +a𝛾 , where a𝛾 ′ and a𝛾 are the free lattice 𝛾�
𝛾
parameters of 𝛾 and 𝛾 ′ phases, respectively. The directional coarsening of the 𝛾 ′ phase, a.k.a. 𝛾 ′ rafting, generally happens at temperature over 900 ◦ C. The lattice misfit is one of the driving forces for the 𝛾 ′ rafting process. The orientation of the 𝛾 ′ rafts and the distribution of internal stresses depend largely on the sign and amplitude of the lattice misfit. By increasing the 𝛾 /𝛾 ′ lattice mismatch,
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