Metallurgical and Materials Transactions A

, Volume 49, Issue 6, pp 2324–2339 | Cite as

Elastic Properties of Novel Co- and CoNi-Based Superalloys Determined through Bayesian Inference and Resonant Ultrasound Spectroscopy

  • Brent R. GoodletEmail author
  • Leah Mills
  • Ben Bales
  • Marie-Agathe Charpagne
  • Sean P. Murray
  • William C. Lenthe
  • Linda Petzold
  • Tresa M. Pollock


Bayesian inference is employed to precisely evaluate single crystal elastic properties of novel \(\gamma -\gamma '\) Co- and CoNi-based superalloys from simple and non-destructive resonant ultrasound spectroscopy (RUS) measurements. Nine alloys from three Co-, CoNi-, and Ni-based alloy classes were evaluated in the fully aged condition, with one alloy per class also evaluated in the solution heat-treated condition. Comparisons are made between the elastic properties of the three alloy classes and among the alloys of a single class, with the following trends observed. A monotonic rise in the \(c_{44}\) (shear) elastic constant by a total of 12 pct is observed between the three alloy classes as Co is substituted for Ni. Elastic anisotropy (A) is also increased, with a large majority of the nearly 13 pct increase occurring after Co becomes the dominant constituent. Together the five CoNi alloys, with Co:Ni ratios from 1:1 to 1.5:1, exhibited remarkably similar properties with an average A 1.8 pct greater than the Ni-based alloy CMSX-4. Custom code demonstrating a substantial advance over previously reported methods for RUS inversion is also reported here for the first time. CmdStan-RUS is built upon the open-source probabilistic programing language of Stan and formulates the inverse problem using Bayesian methods. Bayesian posterior distributions are efficiently computed with Hamiltonian Monte Carlo (HMC), while initial parameterization is randomly generated from weakly informative prior distributions. Remarkably robust convergence behavior is demonstrated across multiple independent HMC chains in spite of initial parameterization often very far from actual parameter values. Experimental procedures are substantially simplified by allowing any arbitrary misorientation between the specimen and crystal axes, as elastic properties and misorientation are estimated simultaneously.



This research was funded by the U.S. Air Force Research Laboratory (AFRL) through BAA Contract FA8650-15-M-5208, SBIR Contract FA8650-15-M-5074. Vibrant Corporation provided the RUS measurement equipment and many helpful discussions. This paper was cleared for public release by the AFRL, Case Number 88ABW-2017-6331


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Copyright information

© The Minerals, Metals & Materials Society and ASM International 2018

Authors and Affiliations

  • Brent R. Goodlet
    • 1
    Email author
  • Leah Mills
    • 2
  • Ben Bales
    • 3
  • Marie-Agathe Charpagne
    • 1
  • Sean P. Murray
    • 1
  • William C. Lenthe
    • 1
  • Linda Petzold
    • 3
  • Tresa M. Pollock
    • 1
  1. 1.Materials DepartmentUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Department of Materials Science and EngineeringThe Ohio State UniversityColumbusUSA
  3. 3.Department of Mechanical EngineeringUniversity of CaliforniaSanta BarbaraUSA

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