# Measurement of the Elastic Modulus and Residual Stress of Thermal Barrier Coatings Using a Digital Image Correlation Technique

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Analysis

_{R}, as shown in Figure 1. The sign direction is specified, and whether the curvature is positive or negative depends on the sign of the moment M and residual stress σ

_{R}. A right-handed coordinate system with the neutral layer as the x-axis and the positive y-axis pointing downward is established. The M direction shown in Figure 1 is positive, that is, the upper side of the neutral axis is compressed, and the lower side is tensioned. Residual stress is negative for compression and positive for tension. Therefore, positive bending moments or negative residual stresses provide the system with positive curvature, while negative bending moments or positive residual stresses cause the system to produce negative curvature.

_{c}and ${A}_{\mathrm{s}}$ are the cross-sectional areas of the deposited coating and substrate, respectively; and ${\sigma}_{c}$ and ${\sigma}_{s}$ are axial stresses in the cross section of coating and substrate, respectively. Assuming small strain and neglecting residual stress in the substrate, the normal stresses in the cross section are [18,22]:

_{1}is the distance from the neutral surface to the interface; and ${h}_{0}$ is the distance from the neutral surface to the bottom of the substrate.

## 3. Experimental

#### 3.1. Specimen Preparation

_{2}O

_{3}powder (BGRIMM Advanced Materials Science & Technology Co., Ltd., Beijing, China) with a particle size distribution of 45−106 μm was selected as the bond-coat material and yttrium oxide stabilized zirconia (8 wt.% Y

_{2}O

_{3}, 8YSZ, 38−75 μm, Precursor Plasma Powders Co., Ltd., China) was used as the feedstock to deposit the topcoat. A HVOF spraying system (JP8000, Praxair Surface Technologies, Inc., Bury, CT, USA) with a torch (TAFA 8220) and an atmospheric plasma spraying system (3710, Praxair Surface Technologies, Inc., Bury, CT, USA) with a high energy plasma gun (SG-100) were used for bond coating and top coating deposition, respectively. The thickness of the bond-coat and topcoat was about 150 μm and 330 μμm, respectively. The spraying parameters and material parameters are listed in Table 1.

^{3}. Four of the comb-shaped TBC specimens were subjected to high temperature loading with homogeneous temperature distribution in a furnace. The four comb-shaped specimens were dwelling in the highest temperature of 1000 °C for 2, 5, 10 and 20 h, respectively. The high temperature loading is presented in Figure 3. The specimens after different high temperature loading are shown in Figure 4.

#### 3.2. Digital Image Correction

^{2}and a step size of 10 pixels were selected in the calculation. The initial curvatures of the TBC specimens were finally extracted with polynomial fitting using least square method according to the 3D contours of the DIC measurement.

^{2}was selected in the calculation. Note that the CCD cameras began to record images before loading. During the experiment, a corresponding deformed image was captured immediately when the load increased. For instance, when the load increased to 3 N, an image was taken and named as 3 N. Since the loading speed is very low, there was sufficient time for image capture without breaking off the machine. In this way, the captured images for DIC calculation can be guaranteed to be synchronized with the testing set-up. The tested specimen was topcoat-upward loaded so that the topcoat was in a compressed stress state, or topcoat-downward loaded so that the topcoat was in a tensile stress state. Figure 6 shows that the specimen is in a topcoat-upward loading state. After the tests, the microstructures of the TBC specimens were measured using a scanning electron microscope (SEM, ZEISS Merlin Compact, Jena, Germany).

## 4. Experimental Results and Discussion

#### 4.1. Microstructure

#### 4.2. Curvature Measurement with DIC

#### 4.3. Elastic Modulus and Residual Stress

## 5. Conclusions

- The formula to determine the elastic modulus and residual stress of TBCs was deduced based on the composite beam bending theory. According to the formula, the elastic modulus and residual stress of TBCs can be experimentally determined.
- The experimental method to simultaneously determine the elastic modulus and residual stress of TBCs using a 3D digital image correlation technique combined with bending test is effective and reliable.
- The results show that the elastic modulus of the ceramic layer measured under com-pression is greater than that under tension, and the elastic modulus of the ceramic layer increases first and then tends to be stable as the heat treatment time increases. In addition, the residual stress of the TBCs ceramic layer quickly changes from compressive stress to tensile stress with heat treatment, and the tensile stress increases with the increase in thermal exposure time.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 6.**Schematic diagram of a 3D DIC system for cross sectional profile measurement of four-point bending TBCs.

**Figure 7.**Scanning electron microscope diagrams of thermal barrier coatings under high temperature exposure: (

**a**–

**e**) are surface morphologies for 0, 2, 5, 10 and 20 h, respectively; (

**f**–

**j**) are cross sectional morphologies for 0, 2, 5, 10 and 20 h, respectively.

**Figure 8.**(

**a**) Porosity distribution based on image analysis; and (

**b**) curve between porosity and thermal exposure time.

**Figure 9.**Morphology contours of TBC specimens: (

**a**) before topcoat deposition; (

**b**) as received; (

**c**) high temperature exposure for 2 h; (

**d**) high temperature exposure for 5 h; (

**e**) high temperature exposure for 10 h; (

**f**) high temperature exposure for 20 h.

**Figure 10.**Vertical deformation of the topcoat-upward specimens under four-point bending measured by 3D DIC. The loading P is equal to 5 N. (

**a**–

**e**) are vertical deformation fields of specimens with high temperature exposure for 0, 2, 5, 10 and 20 h, respectively, and (

**f**–

**j**) are their corresponding fitting curves.

**Figure 12.**Relation curves of (

**a**) elastic modulus; and (

**b**) residual stress with high temperature exposure time.

Parameter | Bond Coat | Top Coat |
---|---|---|

Spraying process | HVOF | APS |

Kerosene flow rate (GPH) | 5.9 | \ |

Oxygen flow rate (SCFH) | 2000 | \ |

Primary gas flow rate (SCFH) | \ | 70 (Ar) |

Secondary gas flow rate (SCFH) | \ | 2.5 (H_{2}) |

Plasma arc power (kW) | \ | 30 |

Powder feed rate (r·min^{−1}) | 45 | 50 |

Spray distance (mm) | 380 | 60 |

Gun traverse speed (mm·s^{−1}) | 500 | 500 |

Curvature before Top Coat Deposition ${\mathit{\kappa}}_{1}$ $\left({\mathit{m}}^{-1}\right)$ | −0.98 | ||||
---|---|---|---|---|---|

High Temperature Exposure (h) | |||||

0 | 2 | 5 | 10 | 20 | |

Curvature after thermal exposure ${\kappa}_{2}$ $({m}^{-1}$) | -1.56 | 0.81 | 1.02 | 1.25 | 1.50 |

$Initial\text{}curvature\text{}{\kappa}_{0}$$({m}^{-1}$) | -0.58 | 1.79 | 2.00 | 2.23 | 2.48 |

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**MDPI and ACS Style**

Zhu, Q.; Zeng, Y.; Yang, D.; Zhu, J.; Zhuo, L.; Li, J.; Xie, W.
Measurement of the Elastic Modulus and Residual Stress of Thermal Barrier Coatings Using a Digital Image Correlation Technique. *Coatings* **2021**, *11*, 245.
https://doi.org/10.3390/coatings11020245

**AMA Style**

Zhu Q, Zeng Y, Yang D, Zhu J, Zhuo L, Li J, Xie W.
Measurement of the Elastic Modulus and Residual Stress of Thermal Barrier Coatings Using a Digital Image Correlation Technique. *Coatings*. 2021; 11(2):245.
https://doi.org/10.3390/coatings11020245

**Chicago/Turabian Style**

Zhu, Qi, Yuchun Zeng, Dong Yang, Jianguo Zhu, Lijun Zhuo, Jian Li, and Weihua Xie.
2021. "Measurement of the Elastic Modulus and Residual Stress of Thermal Barrier Coatings Using a Digital Image Correlation Technique" *Coatings* 11, no. 2: 245.
https://doi.org/10.3390/coatings11020245