Physics-assisted machine-learning approach for modeling the temperature-dependent ultimate strengths of superalloys, with comparison to medium- and high-entropy alloys

B. Steingrimsson; X. Fan; B. M. Adam; P. K. Liaw

doi:10.1016/j.matchemphys.2025.130618

Physics-assisted machine-learning approach for modeling the temperature-dependent ultimate strengths of superalloys, with comparison to medium- and high-entropy alloys

B. Steingrimsson
, X. Fan
, B. M. Adam
, P. K. Liaw

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In the pursuit of developing high-temperature alloys with superior ability to fulfill the performance requirements of next-generation energy and aerospace demands, integrated computational materials engineering (ICME) has played a key role. A physics-assisted machine-learning (ML) approach, utilizing a bilinear-log model together with its extensions, is presented, in this paper. The bilinear-log model and the associated trilinear-log model are capable of predicting the temperature-dependent ultimate strengths of superalloys, medium-entropy alloys (MEAs), and high-entropy alloys (HEAs). In these models, the parameter break temperature, T_break, is introduced. The break temperature serves as an upper boundary for operating conditions, ensuring acceptable mechanical performance. In contrast to conventional black-box ML approaches, the underlying fundamental physics are built directly into the bilinear- and the trilinear-log models. These models are here being further extended such as to analytically account for dependence on the strain rate and composition parameters, in addition to the analytical dependence on the temperature. The results presented extend the authors‘ earlier work on MEAs and HEAs and offer further support for the bilinear- and trilinear-log models and their applicability for modeling the temperature-dependent strength behavior of superalloys as well as of MEAs and HEAs.

Original language	English
Article number	130618
Journal	Materials Chemistry and Physics
Volume	340
DOIs	https://doi.org/10.1016/j.matchemphys.2025.130618
State	Published - Aug 1 2025
Externally published	Yes

Funding

PKL very much appreciates the support of (1) the U.S. Army Research Office Project (W911NF-13-1-0438 and W911NF-19-2-0049) with the program managers, Drs. J. C. Marx, A. D. Brown, M. P. Bakas, S. N. Mathaudhu, and D. M. Stepp, (2) the National Science Foundation (DMR-1611180, 1809640, and 2226508) with the program managers, Drs. J. Madison, J. Yang, G. Shiflet, and D. Farkas, (3) the Department of Energy (DOE DE-EE0011185) with the program manager of J. R. Terneus, and (4) the Air Force Office of Scientific Research (AF AFOSR-FA9550-23-1-0503) with the program manager of Dr. D. P. Cole. PKL very much appreciates the support from the Bunch Fellowship. XF and PKL very much appreciate the support of (1) the U.S. Army Research Office Project (W911NF-13-1-0438 and W911NF-19-2-0049), (2) the National Science Foundation (DMR-1611180, 1809640, and 2226508), (3) the Department of Energy (DOE DE-EE0011185), (4) the Air Force Office of Scientific Research (AF AFOSR-FA9550-23-1-0503), and (5) the State of Tennessee and Tennessee Higher Education Commission (THEC) through their support of the Center for Materials Processing (CMP). BS very much appreciates the support from the National Science Foundation (IIP-1447395 and IIP-1632408), with the program managers, Drs. G. Larsen and R. Mehta, from the U.S. Air Force (FA864921P0754), with J. Evans as the program manager, and from the U.S. Navy (N6833521C0420), with Drs. D. Shifler and J. Wolk as the program managers. The trilinear log model may be suitable for analysis of an anomalous yield stress phenomenon in select superalloys, such as Inconel 903 (notch bar) or Monel 400 (annealed) from the supplementary manuscript. As articulated in Supplementary Note 7 of [7], and as supported by the Supplementary Tables S2 and S3 of [9], a practical approach to model selection assumes one stops increasing the model order, once the mean squared error (MSE) tapers off. This practical approach assumes the model selected is the one yielding MSE corresponding to the on-set of the tapering.XF and PKL very much appreciate the support of (1) the U.S. Army Research Office Project (W911NF-13-1-0438 and W911NF-19-2-0049) with the program managers, Drs. J. C. Marx, A. D. Brown, M. P. Bakas, S. N. Mathaudhu, and D. M. Stepp, (2) the National Science Foundation (DMR-1611180, 1809640, and 2226508) with the program managers, Drs. J. D. Madison, J. C. Yang, G. J. Shiflet, and D. Farkas, (3) the Department of Energy (DOE DE-EE0011185) with the program manager of J. R. Terneus, and (4) the Air Force Office of Scientific Research (AF AFOSR-FA9550-23-1-0503) with the program manager of Dr. D. P. Cole. PKL very much appreciates the support from the Bunch Fellowship. XF and PKL very much appreciate the support of the State of Tennessee and Tennessee Higher Education Commission (THEC) through their support of the Center for Materials Processing (CMP) with Prof. C. J. Rawn and P. D. Rack as the Directors at The University of Tennessee. BS very much appreciates the support from the National Science Foundation (IIP-1447395 and IIP-1632408), with the program managers, Drs. G. Larsen and R. Mehta, from the U.S. Air Force (FA864921P0754), with J. Evans as the program manager, and from the U.S. Navy (N6833521C0420), with Drs. D. Shifler and J. Wolk as the program managers. The authors also want to thank Dr. Guofeng Wang for educating them on the use of DFT for prediction of the mechanical properties of high-entropy alloys, and related fundamental concepts, summarized in the supplementary manuscript. The authors, furthermore, want to thank Dr. William Curtin for referring the authors to his recent papers on short-range ordering, and precipitation strengthening in Al–Mg–Si alloys, and for educating the authors on the specifics of his models (especially on the underlying assumptions). The authors want to thank Dr. Yanfei Gao for valuable perspectives on mechanisms behind precipitation strengthening and ordered strengthening, both in aluminum alloys and superalloys, and on associated modeling approaches. In addition, B.S. thanks Dr. L. Arnadottir for assistance with overall planning and coordination.

Keywords

High temperature
High-entropy alloys
Machine learning
Medium-entropy alloys
Physics-assisted modeling
Structural materials
Superalloys
Ultimate strength

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10.1016/j.matchemphys.2025.130618

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title = "Physics-assisted machine-learning approach for modeling the temperature-dependent ultimate strengths of superalloys, with comparison to medium- and high-entropy alloys",

abstract = "In the pursuit of developing high-temperature alloys with superior ability to fulfill the performance requirements of next-generation energy and aerospace demands, integrated computational materials engineering (ICME) has played a key role. A physics-assisted machine-learning (ML) approach, utilizing a bilinear-log model together with its extensions, is presented, in this paper. The bilinear-log model and the associated trilinear-log model are capable of predicting the temperature-dependent ultimate strengths of superalloys, medium-entropy alloys (MEAs), and high-entropy alloys (HEAs). In these models, the parameter break temperature, Tbreak, is introduced. The break temperature serves as an upper boundary for operating conditions, ensuring acceptable mechanical performance. In contrast to conventional black-box ML approaches, the underlying fundamental physics are built directly into the bilinear- and the trilinear-log models. These models are here being further extended such as to analytically account for dependence on the strain rate and composition parameters, in addition to the analytical dependence on the temperature. The results presented extend the authors{\textquoteleft} earlier work on MEAs and HEAs and offer further support for the bilinear- and trilinear-log models and their applicability for modeling the temperature-dependent strength behavior of superalloys as well as of MEAs and HEAs.",

keywords = "High temperature, High-entropy alloys, Machine learning, Medium-entropy alloys, Physics-assisted modeling, Structural materials, Superalloys, Ultimate strength",

author = "B. Steingrimsson and X. Fan and Adam, \{B. M.\} and Liaw, \{P. K.\}",

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AU - Steingrimsson, B.

AU - Fan, X.

AU - Adam, B. M.

AU - Liaw, P. K.

PY - 2025/8/1

Y1 - 2025/8/1

N2 - In the pursuit of developing high-temperature alloys with superior ability to fulfill the performance requirements of next-generation energy and aerospace demands, integrated computational materials engineering (ICME) has played a key role. A physics-assisted machine-learning (ML) approach, utilizing a bilinear-log model together with its extensions, is presented, in this paper. The bilinear-log model and the associated trilinear-log model are capable of predicting the temperature-dependent ultimate strengths of superalloys, medium-entropy alloys (MEAs), and high-entropy alloys (HEAs). In these models, the parameter break temperature, Tbreak, is introduced. The break temperature serves as an upper boundary for operating conditions, ensuring acceptable mechanical performance. In contrast to conventional black-box ML approaches, the underlying fundamental physics are built directly into the bilinear- and the trilinear-log models. These models are here being further extended such as to analytically account for dependence on the strain rate and composition parameters, in addition to the analytical dependence on the temperature. The results presented extend the authors‘ earlier work on MEAs and HEAs and offer further support for the bilinear- and trilinear-log models and their applicability for modeling the temperature-dependent strength behavior of superalloys as well as of MEAs and HEAs.

AB - In the pursuit of developing high-temperature alloys with superior ability to fulfill the performance requirements of next-generation energy and aerospace demands, integrated computational materials engineering (ICME) has played a key role. A physics-assisted machine-learning (ML) approach, utilizing a bilinear-log model together with its extensions, is presented, in this paper. The bilinear-log model and the associated trilinear-log model are capable of predicting the temperature-dependent ultimate strengths of superalloys, medium-entropy alloys (MEAs), and high-entropy alloys (HEAs). In these models, the parameter break temperature, Tbreak, is introduced. The break temperature serves as an upper boundary for operating conditions, ensuring acceptable mechanical performance. In contrast to conventional black-box ML approaches, the underlying fundamental physics are built directly into the bilinear- and the trilinear-log models. These models are here being further extended such as to analytically account for dependence on the strain rate and composition parameters, in addition to the analytical dependence on the temperature. The results presented extend the authors‘ earlier work on MEAs and HEAs and offer further support for the bilinear- and trilinear-log models and their applicability for modeling the temperature-dependent strength behavior of superalloys as well as of MEAs and HEAs.

KW - High temperature

KW - High-entropy alloys

KW - Machine learning

KW - Medium-entropy alloys

KW - Physics-assisted modeling

KW - Structural materials

KW - Superalloys

KW - Ultimate strength

UR - https://www.scopus.com/pages/publications/105001688445

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DO - 10.1016/j.matchemphys.2025.130618

M3 - Article

AN - SCOPUS:105001688445

SN - 0254-0584

VL - 340

JO - Materials Chemistry and Physics

JF - Materials Chemistry and Physics

M1 - 130618

ER -

Physics-assisted machine-learning approach for modeling the temperature-dependent ultimate strengths of superalloys, with comparison to medium- and high-entropy alloys

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Keywords

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