Multi-Variate Process Models for Predicting Site-Specific Microstructure and Properties of Inconel 706 Forgings

The performance of superalloy forgings hinges on the careful design of the thermomechanical history to promote distributions of oft-dependent microstructural features. Establishing predictive process-structure-property (PSP) models to tailor manufacturing routes requires immense cost due to the time-consuming tasks of quantifying statistically significant observations of different predictors and performance metrics across multiple lengthscales [1]. Power analysis indicates that for a simple multivariate linear model of one performance metric, P, dependent on six input process predictors (k = 6) (i.e., P = f(k₁, k₂, …k₆)) with 80% predictive power would require over 120 observations; to predict n performance metrics (P₁, P₂, ...P_n), a statistical study protocol would require 120n observations (ANOVA would require 175n). Measuring a statistical number of observations of predictors and metrics is challenging at both ends of the lengthscale spectra. Nanoscale precipitates, like the distribution of the ��′ and ��′′ precipitates in Inconel 706 have required transmission electron microscopy which does not readily lend itself to transition from qualitative analysis to statistical measures [3]. While conventional mechanical testing, on the other hand, requires relatively large volumes of material for a single observation. In both cases, these predictors and metrics are observed destructively resulting in development efforts that take many years to establish the database necessary for PSP models. Since PSP models benefit from an iterative design paradigm, this motivates the development of high-throughput measurements, both experimental approaches [4, 5] and physics-based predictions [6] if the dramatic design paradigm shift predicted by the Materials Genome Initiative.<br/>In this paper, high-throughput measures of the precipitation distributions in Inconel 706 from experimental observations and physics-based simulations are used to reduce the necessary “physical” observation space necessary to predict PSP models. Heritage data from five years of development work conducted by Howmet Aerospace Forgings were used to demonstrate the method. DEFORM simulations of thermal history were used to supply time-temperature boundary conditions to CALPHAD simulations in ThermoCalc/PRISMA of the resulting ��′ and ��′′ precipitate distributions at discrete locations within thermomechanically processed Inconel 706. Computer vision algorithms were developed to observe features in scanning electron micrographs. These features were used to tailor the CALPHAD interfacial energy and predict features from other processing conditions. In this manner, the number of physical observations of ��′ the ��′′ distributions is reduced by 25x (100’s to 4); and it relies on more readily available experimental and computational approaches allowing for industrial use with limited available technical resources. When combined within the heritage data frame, gradient boost machine learning PSP models were trained following a 4:1 train-split procedure. The predictive power of many models was 80% or higher, estimated by ��² value on the test data.<br/><br/>1. Li S, Kattner UR, Campbell CE (2017) Integrating Mater Manuf Innov 6:229–248. https://doi.org/10.1007/s40192-017-0101-8<br/>2. Jones SR, Carley S, Harrison M (2003) Emerg Med J 20:453. https://doi.org/10.1136/emj.20.5.453<br/>3. Zhang S, Zeng L, Zhao D, et al (2022) Mater Sci Eng A 839:142836. https://doi.org/10.1016/j.msea.2022.142836<br/>4. Senanayake NM, Carter JLW (2020) Integrating Mater Manuf Innov 9:446–458. https://doi.org/10.1007/s40192-020-00195-z<br/>5. Senanayake N, Mukhopadhyay, S, Carter JLW (2020) Superalloys 2020. Seven Springs, PA, p 10<br/>6. Kuehmann CJ, Olson GB (2009) Mater Sci Technol 25:472–478. https://doi.org/10.1179/174328408X371967