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Measurement of Young’s Modulus and Poisson’s Ratio of Thermal Barrier Coating Based on Bending of Three-Layered Plate

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Abstract

Thermal barrier coatings (TBCs) are used to protect the hot sections of gas turbine engines and airplane engines. A TBC system comprises a substrate, bond coat, and TBC topcoat. The development of an accurate method for determining the Young’s modulus and Poisson’s ratio of TBC using a multilayered specimen is of importance. In this study, we applied the bending theory of a laminated plate to a three-layered material and proposed models to determine the Young’s modulus and Poisson’s ratio of the TBC layer using the bending strain of the TBC system specimen. Three methods were developed by utilizing (i) the coating biaxial strain, (ii) substrate biaxial strain, or (iii) coating and substrate biaxial strains. Subsequently, we determined appropriate dimensions of the specimen and span by using three-dimensional finite element analysis, and numerically verified the usefulness of the three proposed methods. However, the Young’s modulus and Poisson’s ratio determined using the multilayered specimen with a substrate are sensitive to experimental errors. Therefore, we evaluated the sensitivity of the three proposed methods to experimental error, and we determined the most insensitive method among them. Finally, we experimentally demonstrated the usefulness of this method.

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References

  1. S.R. Choi, D. Zhu, and R.A. Miller, Mechanical Properties/Database of Plasma-Sprayed ZrO2-8wt% Y2O3 Thermal Barrier Coatings, Int. J. Appl. Ceram. Technol., 2004, 1(4), p 330-342

    Article  Google Scholar 

  2. W.Z. Wang, C.J. Li, and Y.Y. Wang, Effect of Spray Distance on the Mechanical Properties of Plasma Sprayed Ni-45Cr Coatings, Mater. Trans., 2006, 47(7), p 1643-1648

    Article  Google Scholar 

  3. Y. Itoh, M. Saitoh, M. Miyazaki, and K. Honda, Mechanical Properties of Low-Pressure-Plasma Sprayed MCrAlY Coatings, J. Soc. Mater. Sci., Jpn., 1994, 43(489), p 690-695 (in Japanese)

  4. H. Waki, S. Kubo, H. Ogi, and A. Kobayashi, Measurement of Anisotropic Young’s Modulus of Heat Resistant Coating by Resonance Ultrasound Spectroscopy, Trans. Jpn. Soc. Mech. Eng. A, 2010, 76(762), p 151-157 (in Japanese)

  5. Y. Tan, A. Shyam, W.B. Choi, E. Laza-Curzio, and S. Sampath, Anisotropic Elastic Properties of Thermal Spray Coatings Determined via Resonant Ultrasound Spectroscopy, Acta Mater., 2010, 58, p p5305-p5315

    Article  Google Scholar 

  6. X.Q. Ma, Y. Mizutani, and M. Takemoto, Laser-Induced Surface Acoustic Waves for Evaluation of Elastic Stiffness of Plasma Sprayed Materials, J. Mater. Sci., 2001, 36, p 5633-5641

    Article  Google Scholar 

  7. Q. Wei, J. Zhu, and W. Chen, Anisotropic Mechanical Properties of Plasma-Sprayed Thermal Barrier Coatings at High Temperature Determined by Ultrasonic Method, J. Therm. Spray Technol., 2016, 25(3), p 605-612

    Article  Google Scholar 

  8. U. Schulz, K. Fritscher, and M. Peters, EB-PVD Y2O3-and CeO2/Y2O3-Stabilized Zirconia Thermal Barrier Coatings-Crystal Habit and Phase Composition, Surf. Coat. Technol., 1996, 82, p 259-269

    Article  Google Scholar 

  9. C.A. Johnson, J.A. Ruud, R. Bruce, and D. Wortman, Relationships between Residual Stresses, Microstructure and Mechanical Properties of Electron Beam-Physical Vapor Deposition Thermal Barrier Coatings, Surf. Coat. Technol., 1998, 108-109, p 80-85

    Article  Google Scholar 

  10. H.B. Guo, R. Vaβen, and D. Stöver, Atmospheric Plasma Sprayed Thick Thermal Barrier Coatings with High Segmentation Crack Density, Surf. Coat. Technol., 2004, 186, p 353-363

    Article  Google Scholar 

  11. H.B. Guo, S. Kuroda, and H. Murakami, Segmented Thermal Barrier Coatings Produced by Atmospheric Plasma Spraying Hollow Powders, Thin Solid Films, 2006, 506-507, p 136-139

    Article  Google Scholar 

  12. A. Valarezo, G. Dwivedi, S. Sampath, R. Musalek, and J. Matejicek, Elastic and Anelastic Behavior of TBCs Sprayed at High-Deposition Rates, J. Therm. Spray Technol., 2015, 24(1-2), p 160-167

    Google Scholar 

  13. X. Zhang, M. Watanabe, and S. Kuroda, Effects of Processing Conditions on the Mechanical Properties and Deformation Behaviors of Plasma-Sprayed Thermal Barrier Coatings: Evaluation of Residual Stresses and Mechanical Properties of Thermal Barrier Coatings on the Basis of in situ Curvature Measurement under a Wide Range of Spray Parameters, Acta Mater., 2013, 61, p 1037-1047

    Article  Google Scholar 

  14. J. Matejicek and S. Sampath, In situ Measurements of Residual Stresses and Elastic Moduli in Thermal Sprayed Coatings Part 1: Apparatus and Analysis, Acta Mater., 2003, 51, p 863-872

    Article  Google Scholar 

  15. Y.C. Tsui and T.W. Clyne, An Analytical Model for Predicting Residual Stresses in Progressively Deposited Coatings Part1: Planar Geometry, Thin Solid Films, 1997, 306, p 23-33

    Article  Google Scholar 

  16. Y. Liu, T. Nakamura, V. Srinivasan, A. Vaidya, A. Gouldstone, and S. Sampath, Non-linear elastic properties of plasma-sprayed zirconia coatings and associated relationship with processing conditions, Acta Mater., 2007, 55, p 4667-4678

    Article  Google Scholar 

  17. G. Dwivedi, T. Nakamura, and S. Sampath, Determination of Thermal Spray Coating Property with Curvature Measurement, J. Therm. Spray Technol., 2013, 22(8), p 1337-1347

    Article  Google Scholar 

  18. H. Waki, H. Fujioka, Y. Harada, M. Okazaki, and A. Kawasaki, Young’s Modulus of Thermal Barrier Coating and Oxidation Resistant Coating Bonded to Stainless Substrate by Four-Point Bending, J. Solid Mech. Mater. Eng., 2010, 4(2), p 274-285

    Article  Google Scholar 

  19. H. Waki, A. Oikawa, M. Kato, S. Takahashi, Y. Kojima, and F. Ono, Evaluation of the Accuracy of Young’s moduli of Thermal Barrier Coatings Determined on the Basis of Composite Beam Theory, J. Therm. Spray Technol., 2014, 23(8), p 1291-1301

    Article  Google Scholar 

  20. H. Waki, K. Takizawa, K. Masahiko, and S. Takahashi, Accuracy of Young’s Modulus of Thermal Barrier Coating Layer Determined by Bending Resonance of a Multilayered Specimen, J. Therm. Spray Technol., 2016, 25(4), p 684-693

    Article  Google Scholar 

  21. E.F. Rybicki, J.R. Shadley, Y. Xiong, and D.J. Greving, A Cantilever Beam Method for Evaluating Young’s modulus and Poisson’s Ratio of Thermal Spray Coatings, J. Therm. Spray Technol., 1995, 4(4), p 377-383

    Article  Google Scholar 

  22. M. Beghini, L. Bertini, and F. Frendo, Measurement of Coatings’ Elastic Properties by Mechanical Methods: Part1. Consideration on Experimental Errors, Exp. Mech., 2001, 41(4), p 293-304

    Article  Google Scholar 

  23. M. Beghini, G. Benamati, L. Bertini, and F. Frendo, Measurement of Coatings’ Elastic Properties by Mechanical Methods: Part2. Application to Thermal Barrier Coatings, Exp. Mech., 2001, 41(4), p 305-311

    Article  Google Scholar 

  24. S. Parthasarathi, B.R. Tittmann, K. Sampath, and E.J. Onesto, Ultrasonic Characterization of Elastic Anisotropy in Plasma-Sprayed Alumina Coatings, J. Therm. Spray Technol., 1995, 4(4), p 367-373

    Article  Google Scholar 

  25. N. Margadant, J. Neuenschwander, S. Stauss, H. Kaps, A. Kulkarni, J. Matejicek, and G. Rössler, Impact of probing volume from different mechanical measurement methods on elastic properties of thermally sprayed Ni-based coatings on a mesoscopic scale, Surf. Coat. Technol., 2006, 200, p 2805-2820

    Article  Google Scholar 

  26. S.P. Timoshenko and S. W. Krieger, Theory of Plates and Shells, 2nd ed., McGraw-Hill, Inc., New York, 1959, p 72, 113-124

  27. J.M. Whitney, Cylindrical Bending versus Beam Theory in the Analysis of Composite Laminates, Composites, 1995, 26(5), p 395-398

    Article  Google Scholar 

  28. S. Timoshenko, Strength of Materials: Part II, Advanced Theory and Problems, 3rd ed., D. Van Nostrand Company Inc, New York, 1966, p 76-78

    Google Scholar 

  29. Y. Negishi and K. Hirashima, General Higher-Order Beam Theory Including Effects of Transverse and Lateral Components, Trans. Jpn. Soc. Mech. Eng. A, 1994, 60(576), p 1821-1828 (in Japanese)

  30. R.B. Pipes and J.W. Dalley, On the Birefringent-Coating Method of Stress Analysis for Fiber-reinforced Laminated Composites, Exp. Mech., 1972, 12(6), p 272-277

    Article  Google Scholar 

  31. A.E. Bogdanovich and C.M. Pastore, Material-Smart Analysis of Textile-Reinforced Structures, Compos. Sci. Technol., 1996, 56, p 291-309

    Article  Google Scholar 

  32. A. Kulkarni, A. Vaidya, A. Goland, S. Sampath, and H. Herman, Processing effects on porosity-property correlations in plasma sprayed yttria-stabilized zirconia coatings, Mater. Sci. Eng. A, 2003, 359, p 100-111

    Article  Google Scholar 

  33. Y. Yamazaki, T. Kinebuchi, H. Fukanuma, N. Ohno, and K. Kaise, Deformation and Fracture Behaviors in the Freestanding APS-TBC—Effects of Process Parameters and Thermal Exposure, Key Eng. Mater., 2007, 353-358, p 1935-1938

    Article  Google Scholar 

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Acknowledgment

We wish to thank Prof. S. Takahashi (Tokyo Metropolitan University) for the preparation of the specimens. This research was supported by JSPS KAKENHI Grant Number 17K06039.

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Authors and Affiliations

  1. Graduate School of Engineering, Iwate University, 4-3-5 Ueda, Morioka, Iwate, 020-8551, Japan

    Tomoyuki Hayase

  2. Department of Systems Innovation Engineering, Iwate University, 4-3-5 Ueda, Morioka, Iwate, 020-8551, Japan

    Hiroyuki Waki

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  1. Tomoyuki Hayase
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Correspondence to Hiroyuki Waki.

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Hayase, T., Waki, H. Measurement of Young’s Modulus and Poisson’s Ratio of Thermal Barrier Coating Based on Bending of Three-Layered Plate. J Therm Spray Tech 27, 983–998 (2018). https://doi.org/10.1007/s11666-018-0741-z

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  • DOI: https://doi.org/10.1007/s11666-018-0741-z

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