# Stiffness of Plasma Sprayed Thermal Barrier Coatings

## Abstract

**:**

## 1. Introduction

#### 1.1. Background

_{2}(stabilised with 6–8 wt % Y

_{2}O

_{3}, also called YSZ) ceramic top coat about 100–500 μm in thickness, deposited either by air plasma spray (APS) or electron beam physical vapour deposition (EB-PVD), over a metallic bond coat that has been vacuum plasma sprayed onto a superalloy substrate. Since these ceramic TBC top coats are applied onto metallic components, low macroscopic stiffness favors stability, by limiting the stresses from differential thermal contraction during production and in service. The main driving force for the spallation of the ceramic TBC top coat is the release of the stored strain energy in the layers comprising the TBC system. The stored energy within the top coat depends linearly on the in-plane Young’s modulus, but this parameter is often difficult to define. The difficulty is often related to the techniques available for measuring the Young’s modulus. In the following section, an overview is presented of the literature available on the stiffness of plasma sprayed (PS) TBCs, along with a brief description of some of the existing techniques to predict such properties and interpretation of the reported data.

#### 1.2. Reported Young’s Modulus Values of Plasma Sprayed TBC Top Coats

#### 1.2.1. General Remarks

#### 1.2.2. Indentation

^{2}at a load of 10 mN [3]. However, very little difference was observed between the stiffness values obtained at different loads (300–500 N) by indentation of TBC top coats with a large sphere of radius ~1.5 mm [10]. Wallace et al. [11] reported values for the Young’s modulus in the range of 22–38 GPa for as-sprayed YSZ top coats measured using a spherical indenter. One advantage of using indentation is that it can be performed on very small samples. This was used to reveal the elastic anisotropy in PS coatings [11,12,13,14]. Higher Young’s modulus was observed in the direction perpendicular to the surface [15]. Duan et al [13] reported the in-plane Young’s modulus value of attached YSZ coatings to be ~30 GPa, and out of plane value to be ~61 GPa. This anisotropy in plasma sprayed ceramic coatings is often attributed to the fact that the planar crack-like defects have a preferred orientation and that the relative amount of surface area of cracks and pores are different in different directions [11,14]. The surface area of the pores aligned parallel to the substrate is greater than the area of the cracks [16].

#### 1.2.3. Beam Bending

#### 1.2.4. Behaviour in Tension and Compression

_{2}-8 wt % Y

_{2}O

_{3}top coat was determined in pure tension and compression by Choi et al. [4]. The TBC top coats did not exhibit any idealized linear stress–strain behavior in both loading and unloading sequences, thus resulting in an appreciable to moderate hysteresis. In order to rationalise the nonlinear elastic behavior, especially for as-sprayed samples, Choi et al. [2,4,20] introduced the concept of an “instantaneous” elastic modulus and attributed the higher “instantaneous” modulus in compression to the porous, microcracked nature of TBCs. Harok and Neufuss [25] attributed this behavior to “internal friction”, analogous to the behavior found in rocks, which show inelastic effects under uniaxial compression. It was observed that the hysteresis in the loading and unloading plots is less marked for samples that have been annealed at high temperatures [1,2,20,26].

#### 1.3. Sintering Effects on Young’s Modulus Values of Plasma Sprayed TBCs

#### 1.4. Scope of the Paper

## 2. Materials and Methods

#### 2.1. Sample Preparation

_{2}O

_{3}) onto mild steel substrates of 1.5 mm thickness. Details of the spraying conditions can be found elsewhere [32]. Samples for mechanical testing were prepared by debonding the top coats from their substrates by treatment in a 1:1 HCl bath. The coatings had thicknesses ranging 0.5–1.5 mm. One set of coating was left attached to the substrate for measuring the stiffness of the composite beam. The porosity levels (φ) in material of this type have been measured previously and are typically around 10–15% [27]. The thicknesses of the coatings used for the different tests are given in Table 1.

^{−1}. The dwell times at these temperatures were between 1 and 20 h. After heat treatment, the samples were air cooled.

#### 2.2. Microstructural and Pore Architectural Characterisation

#### 2.3. Measurement of Coating Stiffness

#### 2.3.1. General Remarks

#### 2.3.2. Indentation

_{i}) WC spherical microindenter (load range 0.1–20 mN) were used. A typical experiment consisted of controlled loading and unloading of a diamond indenter against a specimen surface, whilst simultaneously measuring the penetration depth. Analysis was performed according to the Oliver and Pharr method [35]. This assumes that, while loading involves both elastic and plastic deformation of the specimen, recovery of the specimen upon unloading is purely elastic.

_{r}) can be calculated, which is determined from the compliance of the indenter frame (C

_{f}) and the initial gradient of the unloading curve (Figure 1), using Equation (1):

_{s}) can then be extracted from this according to the Equation (2):

_{i}and v

_{s}are the respective Poisson ratios for the diamond of the indenter and for the specimen, and E

_{i}is the Young’s modulus of diamond.

_{i}= 0.07 and E

_{i}= 1147 GPa were assumed for the diamond indenter [35]. The modulus and Poisson’s ratio for the WC spherical indenter were taken as ~773 GPa and 0.24 respectively. Frame compliance, C

_{f}, was found to be between 0.48 and 0.50 nm/mN, and v

_{s}is reported to be ~0.23 [36,37].

_{p}, immediately before unloading can be obtained by [35]

#### 2.3.3. Beam Bending

_{b}, is given by:

_{r}) could then be identified, and the modulus is given by:

_{1}is a correction factor, which depends on the L/h ratio and on the Poisson ratio. For our specimens, this was found to be ~1 [38].

_{r}can be determined with a repeatability in the order of 1 Hz. This variation is too small to affect the accuracy of the calculated elastic modulus, which is dominated by the accuracy of the measured sample dimensions, especially by its thickness.

## 3. Results

#### 3.1. Indentation

^{−1}was used. Typical load-displacement curves are shown in Figure 2. Young’s modulus of the top coat was obtained by using the unloading part of the load displacement curve following Oliver and Pharr’s method [35] as described earlier (Section 3.2.2). During loading, some ‘kinks’ were sometimes observed. These were not included in the analysis as they often indicate cracking of the material tested.

_{a}~ 200 nm) is also small (10% of indentation depth), but not negligible compared to the indentation depth. Thus, one would expect some effect on the indentation values, but this effect is unlikely to be significant.

#### 3.2. Beam Bending

#### 3.2.1. Attached Coatings

#### 3.2.2. Detached or Free-Standing TBC Top Coats

#### 3.3. Effect of Heat Treatment

#### 3.3.1. Stiffness of Detached or Free-Standing Coatings

#### 3.3.2. Pore Architecture in Detached or Free-Standing Coatings

## 4. Discussion

#### 4.1. Local Stiffness

#### 4.2. Global Stiffness

^{2}, while, for similar indentation depth, the spherical microindenter probes an area exceeding 7000 μm

^{2}(Figure 10). The scatter in the modulus for larger indents is also smaller than that of nanoindentation, due to the fact that the local stiffness depends on the proximity of the indent to a flaw.

#### 4.3. Effect of Service Conditions

^{3+}ions replace Zr

^{4+}in the cationic sublattice, thereby generating oxygen vacancies to maintain charge neutrality. These oxygen vacancies play an important role in the diffusion process within YSZ. The slowest (rate-controlling) diffusional process in YSZ is suggested to be the transport of cations [43], since the oxygen vacancies have far lower activation energy for diffusion than the solute cations. The diffusion coefficients of Zr

^{4+}and O

^{2−}in ZrO

_{2}are reported to be 10

^{−19}and 2 × 10

^{−13}m

^{2}·s

^{−1}[44].

_{0}) and the activation energy barrier ΔE are generally extracted using Equation (9):

_{gb}and d

_{grain}, respectively. Plasma sprayed zirconia have columnar grains with the column size in the order of 1–3 μm and width in the order of a few hundred nanometres. A grain size of 1 μm and grain boundary thickness of 1 nm was assumed in the following calculations. Incorporation of these values into Equation (10) and using the simple expression $x=\text{}\sqrt{Dt}$ the diffusion distance (x) was calculated (Figure 12).

_{2}O

_{3}-ZrO

_{2}system, which is slightly different from the system studied here (4 mol % Y

_{2}O

_{3}-ZrO

_{2}system). As such, these comparisons are of largely qualitative nature, but it is useful to note that diffusion distances are often of the order of the defect size. The plot suggests that, for typical heating time and temperatures used, only fine scale pores are likely to be sintered. For healing of large globular pores (≥1 μm), longer heat treatment times (>100 h) at high temperatures (≥1400 °C) would be required.

## 5. Conclusions

## Acknowledgments

## Conflicts of Interest

## Nomenclature

## Roman Symbols

a, m | Characteristic length in beam bending |

A, m^{2} | Area |

b, m | Beam width |

C | Constant |

C_{1} | Correction factor for IET |

C_{f}, nm mN^{−1} | Frame compliance |

d_{grain}, m | Grain diameter |

D, m | Diffusion coefficient |

E, N m^{−2} (Pa) | Young’s modulus |

E_{c}, N m^{−2} (Pa) | Young’s modulus of the coating |

E_{i}, N m^{−2} (Pa) | Young’s modulus of the indenter |

E_{s}, N m^{−2} (Pa) | Young’s modulus of the substrate or specimen |

ΔE, J mol^{−1} | Activation energy |

f_{r}, Hz | Resonance frequency |

F, N | Force or Load |

h, m | Height |

h_{b}, m | Height of beam in 4-pt bending |

h_{gb}, m | Grain boundary thickness |

I, m^{4} | Second moment of area |

L, m | Length or distance |

l, m | Indentation depth |

l_{e}, m | Depth of elastic recovery during indentation |

l_{max}, m | Maximum depth attained by the indenter |

l_{p}, m | Contact depth during indentation |

l_{r}, m | Residual depth during indentation |

m, kg | Mass |

R_{i}, m | Radius of the indenter |

t, m | Thickness |

t_{c}, m | Thickness of the coating |

t_{s}, m | Thickness of the substrate |

y_{nn}, m | Position of the neutral axis |

## Greek Symbols

β | Geometrical constant (for an indenter) |

δ, m | Displacement/deflection |

ε | Strain |

φ | Porosity |

υ | Poisson’s ratio |

υ_{i} | Poisson’s ratio of the indenter |

υ_{s} | Poisson’s ratio of the sample |

## Acronyms

APS | Atmospheric (Air) Plasma Spray |

BET | Brunauer–Emmett–Teller (N_{2} adsorption isotherm) |

EB-PVD | Electron Beam Physical Vapour Deposition |

FFF | Fundamental Flexural Frequency |

HVOF | High Velocity Oxy-Fuel |

IET | Impulse Excitation Technique |

MIP | Mercury Intrusion Porosimetry |

NDT | Non-Destructive Testing |

PS | Plasma Spray |

RFDA | Resonance Frequency and Damping Analyser |

SEM | Scanning Electron Microscopy |

TWAS | Twin Wire Arc Apray |

TBC | Thermal Barrier Coating |

YSZ | Yttria Stabilised Zirconia |

## Appendix A

_{c}”, Young’s modulus “E

_{c}” on a substrate of thickness “t

_{s}” and Young’s modulus “Y

_{s}” will give a transformed section of b × (E

_{c}/E

_{s}), where “b” is the width of the non-transformed section. A schematic explanation is given in Figure A1.

**Figure A1.**Schematic showing the composite beam along with the various notations used in the derivation (

**a**), and the geometry of the transformed section (

**b**).

_{nn}is the position of the neutral axis. Substituting the width of the part in question in the above equation using the transformed section, we get:

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**Figure 1.**Schematic representation of (

**a**) typical load–displacement curve, and (

**b**) corresponding geometrical parameters for a pyramidal indenter, showing definition of key parameters. The load is in mN and the displacement is in nm.

**Figure 2.**Two examples of load-displacement curves for loading and unloading of an as-sprayed top coat under nanoindentation testing. Fifteen indentation tests were performed, but only two are shown here (with only 5% of the data points) for clarity.

**Figure 4.**Stress versus strain curve for the TBC top coat. The data was obtained from the attached coating during beam bending.

**Figure 6.**Load-unload plot for a free-standing as-sprayed YSZ (204NS) top coat during four-point bend testing. The maximum surface strain for this particular beam, as measured by strain gauging, was found to be <~55 microstrain.

**Figure 7.**Young’s Modulus data of detached YSZ top coats subjected to various prior heat treatments. Error bars represent the standard deviation of at least 15 indents.

**Figure 8.**SEM micrographs of plasma sprayed TBC top coat before (

**a**) and after (

**b**) heat treatment at 1400 °C for 10 h.

**Figure 9.**Porosity data, showing the effect of heat treatment on total porosity and fine-scale porosity for detached PS top coats.

**Figure 12.**Calculated diffusion distances for Zr

^{4+}ions in tetragonal zirconia, obtained using data in Table 2.

Test | Coating Thickness, t (mm) | Comments |
---|---|---|

Four-point bending and IET of stand-alone coatings | 0.65 | Detached coatings were used |

Four-point bending and IET of coatings on steel substrate | 1.40 | Attached coatings were used |

Microindentation | 0.30 | The samples were polished before testing |

Nanoindentation | 0.30 |

Diffusion Type | Pre-Exponential Factor, D_{0} (m^{2}·s^{−1}) | Activation Energy, ΔE (kJ·mol^{−1}) |
---|---|---|

Lattice | 5 × 10^{−4} | 515 |

Grain Boundary | 1 × 10^{−3} | 370 |

© 2017 by the author and TWI. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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Paul, S.
Stiffness of Plasma Sprayed Thermal Barrier Coatings. *Coatings* **2017**, *7*, 68.
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**AMA Style**

Paul S.
Stiffness of Plasma Sprayed Thermal Barrier Coatings. *Coatings*. 2017; 7(5):68.
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**Chicago/Turabian Style**

Paul, Shiladitya.
2017. "Stiffness of Plasma Sprayed Thermal Barrier Coatings" *Coatings* 7, no. 5: 68.
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