Mapping Multivariate Influence of Alloying Elements on Creep Behavior for Design of New Martensitic Steels

Abstract

Heritage data for the class of 9 to 12 wt pct Cr steels are studied using data science to quantify the statistically significant relationships among multiple processing/microstructure and performance variables. The effort is undertaken to find new martensitic steels for creep life of \(10^5{{\text { hours}}}\) or greater at 650 °C and 100 MPa using machine learning. Linear regression and lasso regression were utilized to identify alloying elements that contribute towards better creep strength. Visualization techniques such as t-distributed stochastic neighbor embedding and pair-wire element specific comparisons were utilized to explore information gaps that exist within the data and are in conflict with existing domain knowledge. Combining all results suggest that the next alloy design to be explored should be 9 wt pct Cr with high W (2 to 3 wt pct) and high Co (2 to 3 wt pct) for creep life of \(10^5\,\,{\text { hours}}\) or greater at 650 °C, 100 MPa.

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Acknowledgments

This work made use of the High Performance Computing Resource in the Core Facility for Advanced Research Computing at Case Western Reserve University. This project was funded by the Department of Energy (Grant DE-FE0028685), National Energy Technology Laboratory, an agency of the United States Government.

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This project was funded by the Department of Energy, National Energy Technology Laboratory, an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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Appendix A: Regression Coefficients

Appendix A: Regression Coefficients

The rank-ordered contributors presented in Tables II through V represents the fitted equations, minus the magnitude of regression coefficients. For example, rupture time (RT) model in Table III can be translated to:

$$\begin{aligned} \log_{10} (RT) = \beta _0 - \beta _1 \log_{10} (\sigma ) - \beta _2 Temp + \beta _3 {{\text{Nb}}} + \beta _4 {{\text{W}}} + \beta _5 {{\text{Mo}}} + \beta _6 {{\text{Ni}}} + \beta _7 {{\text{B}}} \end{aligned}$$

The magnitude of regression coefficients are a function of magnitude of the associated variable. For example, change in B at ppm level may bring about small changes in response, although being the changes at ppm level will push the magnitude of regression coefficient to a very high value. This might appear to a reader at first glance that changes in B might bring about better results than W or Co. As the focus is on inference throughout the paper, except for Section III–C, the positive and negative signs served the purpose for the results, and avoided the unwanted confusion. Here, we present regression coefficients and their scaled counterparts to show the complete breadth of the fitted models. The scaling was done by subtracting the mean and dividing by the standard deviation of a variable (Table AI through AIV).

Table AI Rank-Ordered Contributors for Yield Strength (YS) at Low and High Temperature Regions with Regression Coefficients and Their Scaled Counterparts
Table AII Rank-Ordered Contributors for Larson–Miller Parameter (LMP) and Rupture Time (RT) for All Creep Data with Regression Coefficients and Their Scaled Counterparts
Table AIII Temperature (Temp) Specific Rank-Ordered Contributors for Rupture Time (\({\text {log}}_{10}\)(RT)) with Regression Coefficients and Their Scaled Counterparts
Table AIV Temperature Specific Rank-Ordered Contributors for Rupture Time After Correction with Lasso Regression Along with Regression Coefficients and Their Scaled Counterparts

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Verma, A.K., Hawk, J.A., Bruckman, L.S. et al. Mapping Multivariate Influence of Alloying Elements on Creep Behavior for Design of New Martensitic Steels. Metall Mater Trans A 50, 3106–3120 (2019). https://doi.org/10.1007/s11661-019-05234-9

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