# Thermal Stress Analysis of Environmental Barrier Coatings Considering Interfacial Roughness

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## Abstract

**:**

## 1. Introduction

_{2}Zr

_{2}O

_{7}/8YSZ coating system deposited on the surface of the superalloy (GH4169) using the birth and death element technology. They simulated the thermal stress under the typical service conditions for the turbine and discussed the mechanism of crack initiation and propagation. Yu et al. [11] used the finite element method to simulate the effect of the thickness of thermally grown oxides (TGO) on the stress distribution in TBCs. Abir et al. [12] established an analytical method for thermal residual stress in functionally graded coatings and discussed the influence of layers’ properties on the distribution of thermal residual stress. Their results showed that the thermal expansion mismatch between the components and the stress concentration caused by the microstructure (such as the uneven interface between the layers) are the main sources of the damage. Therefore, a lot of studies [13,14,15] had been carried out to analyze the failure mechanism by simulating the effect of rough interface on stress distribution in the different coated systems.

_{2}SiO

_{5}coating on the surface of SiC/SiC composites and investigated the relations between the properties and microstructures of the coating. However, there are still few modeling studies on the coatings of CMCs comparing to the coating systems for superalloy. Abdul-Aziz et al. [20] developed a finite element model for the residual stress of Si/mullite/BSAS coating on SiC/SiC composites was analyzed by the finite element method. Heveran et al. [21] carried out a finite element simulation of residual stresses in various coating systems for SiC/SiC composites. It should be noted that the interface between each coating layer is simplified as a flat interface in all the mentioned models.

## 2. Modeling Methodology

#### 2.1. Coating System and Material Propperties

_{2}Zr

_{2}O

_{7}and Gd

_{2}Zr

_{2}O

_{7}. It works as a thermal barrier; (2) Under the TBC is an EBC layer which is usually composed of the rare earth silicate with excellent water oxygen corrosion resistance and phase stability, such as ReSiO

_{5}and Re

_{2}Si

_{2}O

_{7}. This layer mainly provides protections from environmental degradations such as oxidation and corrosion. (3) Between the EBC and substrate is a bonding layer (BC) which should have good thermal expansion matching and chemical compatibility with EBC and CMCs. The Si layer is the most popular one. This T/EBC coating system is chosen as the investigative object here. The coating consists of three layers: La

_{2}Zr

_{2}O

_{7}is used for TBC, Yb

_{2}Si

_{2}O

_{7}for EBC, and Si for BC. The coatings are usually deposited by air plasma spray (APS) process and usually contain a lot of pores. Thus, their properties may be very different from those of the dense materials. Referring to the literatures [10,19,21,24], the thermal-mechanical properties of the coating layers were listed in Table 1.

#### 2.2. Model Geometry and Boundary Conditions

_{a}and R

_{sm}refer to the amplitude and spacing parameters of roughness for the studied interfaces. They can be obtained through measurement. The definitions of surface roughness parameters and related information can be found in the literature [27]. A and λ refer to the amplitude and wavelength of the sine function, respectively.

_{x}and u

_{y}are displacements in the x- and y-directions, respectively. ε

_{x}is the average strain in the x-direction of RVE. In this paper, the equation interaction in ABAQUS was used to carry out the PBC. A piece of Python code was written for this end.

#### 2.3. Simulation Procedure

- (1)
- Before the EBCs was deposited on the surface of CMCs at 1000 °C, all the constituents were assumed to be stress free;
- (2)
- After the preparation the coated system was cooled down to 0 °C, thermal residual stress is introduced;
- (3)
- At last, the coated system was analyzed under a typical operating condition. The top surface was heated by 1700 °C high-temperature gas; the convective heat transfer coefficient is 8000 W/(m
^{2}·°C). While the bottom surface of CMCs was cooled by 500 °C air, and the convective heat transfer coefficient is 8000 W/(m^{2}·°C).

#### 2.4. Numerical Implementation

## 3. Results and Discussions

#### 3.1. The Effect of Rough Interface on Thermal Residual Stress

_{2}SiO

_{5}coating system deposited on SiC/SiC composites. No crack in the Si coating (BC layer) was found, while considerable microcracks were found in mullite (EBC layer) and Yb

_{2}SiO

_{5}(TBC layer). Additionally, the cracking inside the mullite coating was the most serious.

#### 3.2. The Effect of Rough Interface On Thermal Stress under Service Conditions

#### 3.3. Analysis of Possible Failure Mode

## 4. Conclusions

- During the processing, considerable thermal residual stress is induced in coatings. Large in-plane and through-thickness residual stress may cause vertical cracks in the EBC layer and delamination cracks at the interface between the EBC and BC layer. The rough interface plays an important role in the distribution of thermal residual stress. Stress concentration occurs near the peak and valley of the rough interface. The range of stress variation increases with the amplitude while decreases with the wavelength.
- Under the typical service conditions for SiC/SiC composites, the thermal residual stress in the T/EBC coating system can be eliminated to some extent. However, large thermal stress may be induced at the surface layer of TBC due to the thermal gradient. This stress tends to cause surface cracks. Thus, the surface roughness has a significant impact on the thermal stress distribution. The magnitude and range of thermal stress increase with the roughness level.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**Variation of thermal residual stress S11 in CMCs coatings along the depth direction: the effect of amplitude at (

**a**) peak path and (

**b**) valley path; the effect of wavelength at (

**c**) peak path and (

**d**) valley path.

**Figure 6.**Variations of normal thermal residual stress along the EBC/BC interface of CMCs coatings with different (

**a**) amplitude; (

**b**) wavelength.

**Figure 7.**Variations of tangential thermal residual stress along the EBC/BC interface of CMCs coatings with different (

**a**) amplitude; (

**b**) wavelength.

**Figure 8.**Variation of temperature versus depth of CMCs coatings under service conditions with different (

**a**) amplitude; (

**b**) wavelength.

**Figure 10.**Mises stress along the length of the surface of CMCs coatings with different (

**a**) amplitude; (

**b**) wavelength.

**Figure 11.**Analysis of possible failure mode for the investigated coatings induced by (

**a**) thermal residual stress and (

**b**) operating thermal stress.

Constituents | E/GPa | v | k/(W·m^{−1}·K^{−1}) | α/(×10^{−6}K^{−1}) |
---|---|---|---|---|

TBC (La_{2}Zr_{2}O_{7}) | 63 | 0.25 | 0.87 | 4.25 |

EBC (Yb_{2}Si_{2}O_{7}) | 150 | 0.28 | 3.5 | 5.5 |

BC (Si) | 97 | 0.21 | 14.23 | 3.5 |

E_{1}/GPa | E_{2}/GPa | v_{12} | G_{12}/GPa | k_{1}/(W·m^{−1}·K^{−1}) | k_{2}/(W·m^{−1}·K^{−1}) | α_{1}/(×10^{−6}K^{−1}) | α_{2}/(×10^{−6}K^{−1}) |
---|---|---|---|---|---|---|---|

238.37 | 81.40 | 0.20 | 96.92 | 12.1 | 8.83 | 4.36 | 3.80 |

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**MDPI and ACS Style**

Fang, G.; Ren, J.; Shi, J.; Gao, X.; Song, Y.
Thermal Stress Analysis of Environmental Barrier Coatings Considering Interfacial Roughness. *Coatings* **2020**, *10*, 947.
https://doi.org/10.3390/coatings10100947

**AMA Style**

Fang G, Ren J, Shi J, Gao X, Song Y.
Thermal Stress Analysis of Environmental Barrier Coatings Considering Interfacial Roughness. *Coatings*. 2020; 10(10):947.
https://doi.org/10.3390/coatings10100947

**Chicago/Turabian Style**

Fang, Guangwu, Jiacheng Ren, Jian Shi, Xiguang Gao, and Yingdong Song.
2020. "Thermal Stress Analysis of Environmental Barrier Coatings Considering Interfacial Roughness" *Coatings* 10, no. 10: 947.
https://doi.org/10.3390/coatings10100947