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Research Papers

Vibration Damping of Thermal Barrier Coatings Containing Ductile Metallic Layers

[+] Author and Article Information
Filippo Casadei

Postdoctoral Fellow
Harvard University (SEAS),
Cambridge, MA 02138
e-mail: fcasadei@seas.harvard.edu

Katia Bertoldi

Professor
School of Engineering
and Applied Sciences (SEAS),
and Kavli Institute for Bionano Science,
Harvard University,
Cambridge, MA 02138
e-mail: bertoldi@seas.harvard.edu

David R. Clarke

Professor
School of Engineering
and Applied Sciences (SEAS),
Harvard University,
Cambridge, MA 02138
e-mail: clarke@seas.harvard.edu

1Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 22, 2014; final manuscript received July 8, 2014; accepted manuscript posted July 18, 2014; published online August 5, 2014. Editor: Yonggang Huang.

J. Appl. Mech 81(10), 101001 (Aug 05, 2014) (10 pages) Paper No: JAM-14-1223; doi: 10.1115/1.4028031 History: Received May 22, 2014; Revised July 08, 2014; Accepted July 18, 2014

This paper explores the vibration damping properties of thermal barrier coatings (TBCs) containing thin plastically deformable metallic layers embedded in an elastic ceramic matrix. We develop an elastic–plastic dynamical model to study how work hardening, yield strain, and elastic modulus of the metal affect the macroscopic damping behavior of the coating. Finite element (FE) simulations validate the model and are used to estimate the damping capacity under axial and flexural vibration conditions. The model also provides an explanation for the widely observed nonlinear variation of the loss factor with strain in plasma-spayed TBCs. Furthermore, it facilitates the identification of multilayer configurations that maximize energy dissipation.

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References

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Griffin, J. H., 1990, “A Review of Friction Damping of Turbine Blade Vibration,” Int. J. Turbo Jet Engines, 7(3–4), pp. 297–308. [CrossRef]
Limarga, A., Duong, T., Gregori, G., and Clarke, D., 2007, “High-Temperature Vibration Damping of Thermal Barrier Coating Materials,” Surf. Coat. Technol., 202(4), pp. 693–697. [CrossRef]
Gregori, G., Lì, L., Nychka, J., and Clarke, D., 2007, “Vibration Damping of Superalloys and Thermal Barrier Coatings at High-Temperatures,” Mater. Sci. Eng., A, 466(1), pp. 256–264. [CrossRef]
Patsias, S., Saxton, C., and Shipton, M., 2004, “Hard Damping Coatings: An Experimental Procedure for Extraction of Damping Characteristics and Modulus of Elasticity,” Mater. Sci. Eng., A, 370(1), pp. 412–416. [CrossRef]
Patsias, S., Tassini, N., and Lambrinou, K., 2006, “Ceramic Coatings: Effect of Deposition Method on Damping and Modulus of Elasticity for Yttria-Stabilized Zirconia,” Mater. Sci. Eng., A, 442(1), pp. 504–508. [CrossRef]
Abu Al-Rub, R. K., and Palazotto, A. N., 2010, “Micromechanical Theoretical and Computational Modeling of Energy Dissipation Due to Nonlinear Vibration of Hard Ceramic Coatings With Microstructural Recursive Faults,” Int. J. Solids Struct., 47(16), pp. 2131–2142. [CrossRef]
Casadei, F., Bertoldi, K., and Clarke, D., 2013, “Finite Element Study of Multi-Modal Vibration Damping for Thermal Barrier Coating Applications,” Comput. Mater. Sci., 79, pp. 908–917. [CrossRef]
Yu, Z., Zhao, H., and Wadley, H. N., 2011, “The Vapor Deposition and Oxidation of Platinum- and Yttria-Stabilized Zirconia Multilayers,” J. Am. Ceram. Soc., 94(8), pp. 2671–2679. [CrossRef]
Begley, M. R., and Wadley, H. N., 2011, “Delamination of Ceramic Coatings With Embedded Metal Layers,” J. Am. Ceram. Soc., 94(s1), pp. s96–s103. [CrossRef]
Begley, M. R., and Wadley, H. N., 2012, “Delamination Resistance of Thermal Barrier Coatings Containing Embedded Ductile Layers,” Acta Mater., 60(6), pp. 2497–2508. [CrossRef]
den Hartog, J. P., 1956, Mechanical Vibrations, Dover Publications, New York.
Hudson, D. E., 1965, “Equivalent Viscous Friction for Hysteretic Systems With Earthquake-Like Excitations,” 3rd World Conference on Earthquake Engineering, Auckland/Wellington, New Zealand, January 22–February 1, Vol. 2, pp. 185–201.
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Figures

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Fig. 4

Schematic of the equivalent SDOF model of the system. The substrate and ceramic elastic moduli, although different, are combined into a single elastic stiffness term Ee, while Em is the linear stiffness of the metal. Also, ET  and σY denote the hardening modulus and yield stress of the metal, respectively.

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Fig. 5

Functional variation of the effective loss factor on the deformation (μ) for different values of the kinematic hardening parameter γ. Analytical solution (solid lines) and numerical solution (○ markers).

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Fig. 6

Schematic of three cross sections (labeled A, B, and C, respectively) used to estimate the damping of the system in bending ((a)–(c)). Comparison between the loss factor of the three sections computed with the exact and approximate damping models (d).

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Fig. 7

Variation of the maximum damping capacity of a coating comprising two ductile layers as a function of the substrate thickness (Hs) and metal volume fraction (Φm)

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Fig. 8

Variation of the damping peak for different values of the substrate thickness (Hs). This study compares results for different volume fractions obtained by increasing either the number of layers from one to four as shown on the side (dashed lines) or the thickness of a single layer (solid lines).

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Fig. 9

FE discretization of an elastic superalloy coated on both sides by a 7YSZ ceramic containing a ductile metal layer (a) and detail of the applied axial and bending loads (b)

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Fig. 3

Schematic of the beam undergoing axial (a) and flexural deformations (b), and its cross section (c)

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Fig. 2

Elastic–plastic constitutive law of the ductile metal (a) and schematic of the cyclic behavior (b)

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Fig. 1

Schematic of a coating comprising a planar stack of discrete ductile metal layers embedded in a ceramic matrix on an elastic substrate

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Fig. 10

Comparison between analytical and FE predictions of the energy dissipation in the coating for different values of the hardening parameter γ(Φm=10%) (a) and metal volume fraction Φm(γ = 0.0) (b)

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Fig. 11

Steady state axial stress distribution (S11) in the beam without distributed mass (a) and with distributed mass (b)

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Fig. 12

Variation of the relative damping peak (Q-1/Q-1(Hs = 0)) as a function of the substrate thickness (Hs) (Φm=10%)

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Fig. 13

Variation of the effective loss factor on the bending displacement parameter μ, for different values of the hardening parameter γ (coating only)

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Fig. 14

Comparison of the steady state axial stress distribution (S11) in the beam with mass concentrated at the tip (a) and with distributed mass (b)

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Fig. 15

Variation of the relative damping peak (Q-1/Q-1(Hs = 0)) as a function of the substrate thickness (Hs) (Φm = 10%)

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Fig. 16

Variation of the elastic modulus and yield stress of a Pt-10%Rh alloy with temperature

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Fig. 17

Variation the coating damping capacity with temperature for different values of the applied axial strain (i.e., Eq. (8))

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Fig. 18

Influence of the metal modulus (a) and yield stress (b) of a coating with 10% metal on the variation of damping with temperature for a given deformation (ε = 0.11%)

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Fig. 19

Influence of the metal modulus (a) and yield stress (b) on the variation of damping efficiency ηT (see Eq. (18)) with strain

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Fig. 20

Variation of the loss factor associated with the Dahl frictional law computed for different values of the parameter α

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Fig. 21

Numerical response of the equivalent SDOF system (see Sec. 2) (a) and detail of the steady state amplitude used to numerically estimate the energy dissipated per cycle (b)

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