Modeling of Crack Susceptibility of Ni-Based Superalloy for Additive Manufacturing via Thermodynamic Calculation and Machine Learning

doi:10.11900/0412.1961.2023.00050

Acta Metall Sin

2023, Vol. 59

Issue (8): 1075-1086 DOI: 10.11900/0412.1961.2023.00050

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Modeling of Crack Susceptibility of Ni-Based Superalloy for Additive Manufacturing via Thermodynamic Calculation and Machine Learning

MU Yahang¹^,², ZHANG Xue¹^,², CHEN Ziming³, SUN Xiaofeng¹(

), LIANG Jingjing¹(

), LI Jinguo¹, ZHOU Yizhou¹

¹Shi -changxu Innovation Center for Advanced Materials, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
²School of Materials Science and Engineering, University of Science and Technology of China, Shenyang 110016, China
³School of Intelligence Science and Technology, University of Science and Technology Beijing, Beijing 100083, China

Cite this article:

MU Yahang, ZHANG Xue, CHEN Ziming, SUN Xiaofeng, LIANG Jingjing, LI Jinguo, ZHOU Yizhou. Modeling of Crack Susceptibility of Ni-Based Superalloy for Additive Manufacturing via Thermodynamic Calculation and Machine Learning. Acta Metall Sin, 2023, 59(8): 1075-1086.

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Abstract

The rapid development of aeroengines has led to high demand heat resistant blades. As a result, fabricating techniques and designing materials have taken center stage in producing aeroengines. Additive manufacturing (AM), which integrates design and manufacturing, has advantages in preparing blades with complex cavity structures. However, commercial Ni-based superalloys have poor additive manufacturability and are prone to defects such as cracks, severely hindering the development of the AM of superalloy blades. Therefore, finding a high-performance superalloy with excellent additive manufacturability is necessary. To alleviate this problem, many crack susceptibility criteria and test methods have recently been proposed to evaluate the crack susceptibility of alloys from a compositional and/or process point of view. However, the rapid prediction of the crack susceptibility of superalloys remains a challenge, hindering the widespread screening and designing of superalloys for AM. Nevertheless, using machine learning (ML) in conjunction with thermodynamic calculation may effectively predict the properties of alloys, and this combination is anticipated to grow as an important tool for designing alloys with low crack susceptibility for AM. Based on the aforementioned context, this study reports the development of an ML prediction model after combining experimental data and thermodynamic calculations to establish a Ni-based alloy crack susceptibility database. This ML model has an excellent prediction effect (R² = 0.96 on the training set and R² = 0.81 on the validation set) and enables accurate prediction of the crack susceptibility of the experimental alloys and published alloys. It is verified that a hot crack is the most typical type of crack in Ni-based superalloys during AM. The influence of elements on crack susceptibility is also analyzed using the SHapley Additive exPlanation method. Precipitation-strengthening (Al and Ti) and trace (C and B) elements greatly influence crack susceptibility. A small amount of Re can inhibit cracks, but excessive amounts produce a topologically close-packed phase, deteriorating the crack susceptibility and mechanical properties. The influence of other alloying elements on crack susceptibility is roughly ranked as follows: Re, W, Cr, Mo, Ta, and Co, which can provide a screening method for the composition design of subsequent AMed superalloys.

Key words: Ni-based superalloy crack susceptibility additive manufacturing machine learning thermodynamic calculation

Received: 10 February 2023

ZTFLH:

TG146.1

Fund: National Science and Technology Major Project(Y2019-VII-0011-0151);National Science and Technology Major Project(P2022-C-IV-002-001)

Corresponding Authors: SUN Xiaofeng, professor, Tel:(024)23971887, E-mail: xfsun@imr.ac.cn;LIANG Jingjing, professor, Tel:(024)23971787, E-mail: jjliang@imr.ac.cn

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	MU Yahang
	ZHANG Xue
	CHEN Ziming
	SUN Xiaofeng
	LIANG Jingjing
	LI Jinguo
	ZHOU Yizhou

URL:

https://www.ams.org.cn/EN/10.11900/0412.1961.2023.00050 OR https://www.ams.org.cn/EN/Y2023/V59/I8/1075

Fig.1 Workflow for crack susceptibility prediction of Ni-based superalloy (FR—freezing range, CSC—crack susceptibility criterion, HSC—hot-tearing susceptibility criterion, SCI—solidification cracking index, SAC—strain age cracking index, M_SAC—index of strain age cracking by mass-percentage, ABR—AdaBoost regression, BR—Bagging regression, GBR—gradient boosting regression, RFR—random forest regression, KNN—K-nearest neighbors, SVR—support vector regression, LR—linear regression, R²—correlation coefficient, RMSE—root mean squared error, MAE—mean absolute error)

Table 1 Chemical compositions of Ni-based alloy and alloys designed for additive manufacturing

Type of crack	Crack susceptibility criteria	Formula	Ref.
Hot-tearing crack	FR	$F R = T l - T s$	[18]
	CSC	$C S C = t V t R = t f s = 0.99 - t f s = 0.90 t f s = 0.90 - t f s = 0.40$	[19]
	HSC	$H S C = T V T R = T f s = 0.99 - T f s = 0.90 T f s = 0.90 - T f s = 0.40$	[20]
	SCI	$S C I = d T d (f s 1 / 2) f s 1 / 2 → 1$	[4]
Solid-state crack	SAC	$S A C = d V f γ / d T, T ∈ [T γ *, T s]$	[5]
	M_SAC	$M S A C = [A l] + 0.5 [T i] + 0.3 [N b] + 0.15 [T a]$	[21]

Table 2 Crack susceptibility criteria of Ni-based superalloys^[4,5,18-21]

Fig.2 Low (a) and high (b) magnified SEM images of cracks in as-built 4# (Ni-8Co-10Cr-8W-4.5Al-1Ti-5Ta) sample, corresponding BSE image of TCP phase (c), bright field TEM image and EDS elemental maps of TCP phase (d) (TCP—topologically close-packed)

Fig.3 Crack area percentages (a) and calculated crack susceptibility criteria (b) of different superalloys

Fig.4 Sactterplot matrix and Pearson correlation map of crack area percentage and crack susceptibility criteria (The lower triangular matrix is scatterplot matrix between each pair of variables, the diagonal is the frequency distribution histogram of each variable, and the upper triangular matrix is Pearson correlation map. The red frame line part represents the scatter plot of CAP and crack sensitivity, and the arrow refers to the crack susceptibility criterion with the highest correlation with CAP. Red, green, and blue dots represent the alloys that only change the solid solution elements, the γ′ forming elements, and trace elements, respectively. CAP—crack area percentage, PCC—Pearson correlation coefficient)

Fig.5 Trend of HSC variation with single element content

Fig.6 Scatter plot of the Ni-based superalloys in the dataset, demonstrating the crack susceptibility pattern of different alloys by four criteria

Fig.7 R², RMSE,^{and MAE of machine learning models on training sets}

Fig.8 Performance of machine learning (ML) models on training and test sets for different crack susceptibility criteria
(a) FR (b) CSC (c) HSC (d) SCI

Fig.9 Performance of ML models on validation sets for different crack susceptibility criteria
(a) FR (b) CSC (c) HSC (d) SCI

Fig.10 SHAP values of ten elements for FR (a), CSC (b), HSC (c), and SCI (d) for each data; ranked mean absolute value of SHAP values of ten selected features for crack susceptibility (e) (SHAP—SHapley Additive exPlanation)

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