# A Simulation Study on the Crack Propagation Behavior of Nanostructured Thermal Barrier Coatings with Tailored Microstructure

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}Zr

_{2}O

_{7}, fluorite-structured La

_{2}Ce

_{2}O

_{7}, magnetoplumbite-type LnMgAl

_{11}O

_{19}(Ln: La, Gd, Nd et al.) and perovskite-type BaZrO

_{3}or SrZrO

_{3}, yttria stabilized zirconia (YSZ) is still an irreplaceable material for TBCs due to its good mechanical and thermal properties [5,6,7,8,9]. In particular, the nanostructured YSZ coatings showed superior strain tolerance and thermal insulation performance owing to their typical bimodal structure, in which many unmelted nano-particles (UNPs) were randomly distributed [10,11]. The bimodal structure of nanostructured coatings contributes to approximately 2–3 times or even more of a rise in thermal cycling life compared to their traditional counterparts [12,13,14].

## 2. Experimental Procedure

#### 2.1. Materials and Plasma Spraying Process

_{2}-8 wt.% Y

_{2}O

_{3}powder with 10–85 µm was selected to fabricate the top coat (TC). The morphological structure details of YSZ powder are in our previous paper [19]. The TC with 200 μm thickness was sprayed by the supersonic atmospheric plasma spraying (SAPS) system. The specimen had a disc shape with a diameter of 25 mm. The specimens were stacked on the substrate alloy GH3030 (25 mm × 6 mm) on one side. The thermal cycling test was performed by a home-made burner rig apparatus (Xi’an Jiaotong University, Xi’an, China). The coating surface was heated to 1250 ± 20 °C in 40 s by the propane-oxygen gas flame. The two sides of sample were cooled by compressed air (40 L min

^{−1}) simultaneously, and then held for 300 s. Finally, the backside (alloy substrate) was cooled rapidly to ambient temperature by compressed air. The surface (ceramic coating) and backside (alloy substrate) temperatures were measured by two infrared thermometers (MI3, Raytek, Washington, WA, USA), continuously. The thermal cycling test was maintained at ambient temperature and normal atmosphere. The detailed information of test equipment and processes can be found in our previous work [19,20]. Four different operating conditions, described as NC1–NC4, represent the coating with different unmelted nano-particle contents (UNCs) of 11%, 15%, 22% and 34%, respectively. The spray parameters and other more details can also be found in our previous work [19].

#### 2.2. Finite Element Model

#### 2.2.1. Calculation Domain

#### 2.2.2. Material Properties

#### 2.2.3. Thermal Loads and Cracking Behavior

_{n}and G

_{s}are the critical strain energy release rate (SERR) in modes I and II, respectively [31]. The predefined cracks will propagate when α

_{m}and α

_{n}reaches 1.0. The tensile strength of the TC is set as 200 MPa [32]. The critical maximum principal stress is considered to be 15 MPa and the critical fracture energy release rate is set as 15 J·m

^{−2}[28,30]. The displacement vector function u is as follows:

_{I}(x) is conventional shape function; N

_{I}is the usual nodal displacement vector related to the continuous part of F

_{α}solution; α is the products of the nodal enriched degrees of freedom (DOFs); H(x) is the discontinuous jump function; F

_{α}(x) is the crack tip asymptotic function. More details are in reference [33]. The model with a detailed predefined crack setting is shown in Figure 3. For simplifying the analysis process, a circular particle with diameter of 10 µm was introduced into the model. The cracks in different directions were marked as shown in Figure 3a. The two cracks parallel to the x-axis are marked as a and b; the four cracks 45° from the x-axis are named c–f; and two cracks parallel to the y-axis are labeled A and B. According to the distribution of UNPs in TBCs, one particle, three particles and five particles were set respectively in the XFEM models, as shown in Figure 3b.

## 3. Results and Discussion

#### 3.1. Analysis of Stress Field Distribution

_{22}and shear stress σ

_{12}distribution of TC in NC1–NC4 coatings are in Figure 4. From Figure 4, all the types of stresses are highly dependent on the surface roughness of BC/TC interface or UNP/crystalline region’s interface. For the mises stress in Figure 4a, due to the loose distribution structure, low elastic modulus and low density, thermal stress inside the UNPs presented the lowest value, thermal stress inside the UNPs presented the lowest value (blue area, 150–317 MPa) and the stress in the vicinity of the unmelted nano-particle was higher (green area, 317–483 MPa), whereas the stress in the crystalline regions was the highest (yellow and red areas, >483 MPa). The above results suggested that the increase of unmelted nano-particle content (UNCs) played a decisive role in reducing the overall thermal stress. The tangential stress σ in plane can be expressed thusly [34]:

_{TBC}is the effective elastic modulus of TC; ν

_{TBC}is poison’s ratio; α

_{TBC}and α

_{sub}are the thermal expansion coefficients of both TC and the substrate, respectively. With the increase of UNC, the compressive stress areas of TC increased, while the elastic modulus and thermal stress of TC decreased. It is well known that the σ

_{22}and σ

_{12}tend to cause mode I and mode II fractures, respectively. Additionally, the normal and shear stress were considered as the main driving force of crack propagation. As for the normal stress σ

_{22}in Figure 4b, the tensile stress existed in the yellow areas and the blue areas corresponded to the compressive stress. Due to the thermal expansion coefficient of TC being higher than that of TGO, the contraction rate of former was higher than for the latter. The maximum tensile stress is at the peak of the TC/TGO interface (>50 MPa), while the compressive stress is at the valley. For a single unmelted nano-particle, the tensile stress and compressive stress existed at the peaks of convexity and concavity, respectively. Meanwhile, the tensile stress almost generated symmetrically outside the UNPs, which easily resulted in the initiation and propagation of microcracks at the interface between the UNPs and the crystalline regions.

_{22}in NC4 along the predefined path with white line was extracted as shown in Figure 5. The positive “+” and negative “−” signs are used to visually represent the tensile and compressive stresses (see Figure 5a), respectively. There were many UNPs continually appearing along the white line, and the tensile and compressive stresses were gradually alternated. In addition, the value of stress significantly increased around the UNPs (see Figure 5b). In the crystalline region far away from the UNPs, the value of tensile stress in the crystalline region nearly stayed at 0–33 MPa, which was even lower than that of area around the UNPs, indicating that the UNPs can reduce the overall stress of TC.

_{22}and σ

_{12}stress distribution in BC. As shown in Figure 6, since the tensile stress or shear stress reached the maximum in the BC, the initiation and propagation of cracks were both prone to occurring in the vicinity of TC/TGO or TGO/BC interface, which was consistent with the previous experiment and simulation results [19,30]. The values of tensile or shear stress in the TC were relatively lower than that of BC, indicating that the addition of UNPs was helpful for relieving the thermal stress.

_{22}and σ

_{12}stress distribution in the TGO layer. As seen from Figure 7, the maximum stress of the whole TBCs concentrated in the TGO layer. During the thermal cycling, the thermal mismatch stress formed in the vicinity of TGO layer due to the differences in the thermo-mechanical properties of each layer. The tensile or shear stress of TGO layer was approximately 2–4 GPa, which is obviously larger than the value of TC or BC. The large tensile or shear stress easily resulted in the premature failure of TBCs at the TC/TGO or TGO/BC interface.

#### 3.2. Effects of Unmelted Nano-Particles and Their Content on the Cracking Propagation Behavior

_{22}. The cracking due to stress-induced was prevented by the presence of compressive stress at the inner of the UNPs. The four cracks 45° from x/y-axis gradually propagated parallel to the x-axis due to the increased tensile stress σ

_{22}from 50 s to 150 s, indicating that the time-dependent crack propagation path was mainly determined by the tensile stress σ

_{22}. Figure 8b and Figure 9b showed three UNPs per unit area, which simulated the condition with medium UNCs like NC3. Six predefined cracks, including two cracks parallel to the x-axis and the other four 45° from the x/y-axis, propagated under the stress σ

_{22}and σ

_{12}. As seen from Figure 8b and Figure 9b, two horizontal cracks propagated parallel to the x-axis at the early stage and then the propagation direction kept constant under the tensile stress. Four cracks with 45° from x/y-axis propagated slowly under the shear stress σ

_{12}. However, in the final stage their propagation direction turned parallel to the x-axis due to the expanded area of tensile stress with the increase of thermal cycle. Figure 8c and Figure 9c show five UNPs per unit area, corresponding to the condition with the high content of unmelted nano-particles such as NC4. The propagation tendencies of six cracks including those parallel to the x-axis and 45° from the x/y-axis were similar to the condition with one unmelted nano-particle. The tensile or shear stress areas were around the unmelted nano-particle I in the initial stage because a complex thermal stress area was formed by the accumulation of nano-particles [17,35]. In the final stage, both the tensile stress and shear stress coexisted inside the UNPs. Moreover, the length of the cracks with 45° from x/y-axis in the unmelted nano-particle was smaller, suggesting that firstly the mode II dominated the crack growth mode and it shifted to mixed mode until the crack propagated parallel to the x-axis. The influence of the shear stress on the longitudinal crack propagation behavior became more and more significant. Therefore, it can be predicted that the micro-cracks would enter into the nano-particles and were finally inclined to form some horizontal cracks, resulting in the spallation of TBCs.

_{I}is tensile stress intensity factor in fracture mode I; K

_{II}is tensile stress intensity factor in mode II. The maximum circumferential tensile stress intensity factor (K

_{max}) can be calculated as:

_{max}is the maximum circumferential tensile stress intensity factor. The propagation of the horizontal and longitudinal cracks was viewed as the spring vibrator [36]. When the distance between two adjacent UNPs was small enough, the stress field would be overlapped, leading to the further amplification for the crack propagation. In addition, under the interaction of tensile-tensile stress field, the propagation of the crack and its length can be further promoted, while under the tensile-compressive or compressive-compressive stress field interaction, the propagation of the crack can be prevented.

- (1)
- Accumulation of thermal stress: The tensile stress is mainly distributed in the horizontal or vertical direction of the UNPs. The compressive stress distributes inside the UNPs and the shear stress presents symmetrical distribution around the UNPs.
- (2)
- Propagation of horizontal cracks: Under the tensile and shear stress, the cracks mainly propagated along the horizontal direction. The predefined cracks with 45° from the x/y-axis were a type I and II mixed-mode cracks. These cracks propagated along the direction parallel to the x-axis since the tensile stress σ
_{22}and the shear stress σ_{12}were the main driving forces for the cracks propagation. - (3)
- “Capture effect” of UNPs: Cracks tended to propagate towards the tensile stress region of the surrounding UNPs. When the crack entered into the low elastic modulus and loose porous UNPs, the crack propagation was prevented.
- (4)
- Experimental observation for spallation of TC: With the thermal cycles increasing, the ability of UNPs to prevent crack propagation decreased and the crack eventually entered into the UNPs or propagated along the interface between the UNPs and crystalline regions, resulting in the spallation of TC (Figure 11d).

## 4. Conclusions

- (1)
- During the thermal cycling, the UNPs can effectively reduce the thermal stress of TC. The tensile stress and shear stress regions outside the UNPs enhance the initiation of cracks, while the compressive stress inside the UNPs can effectively prevent the cracks propagation.
- (2)
- Arbitrarily oriented cracks mainly propagated parallel to the x-axis at the final stage of thermal cycle, indicating that tensile stress was the main driving force for the spallation failure of TBCs. Correspondingly, I and I–II mixed types of cracks are the major cracking failure patterns.
- (3)
- The UNPs that distributed in the nanostructured coating had an obvious “capture effect” on the cracks, which means that many cracks easily accumulated in the tensile stress zone of the adjacent UNPs and a complex microcrack network generated at the periphery of UNPs.
- (4)
- At the final stage of thermal cycling, the cracks eventually entered into the UNPs or propagated along the interface between the UNPs and crystalline region. Both the tensile stress and shear stress of TC were lower than those of BC. The spallation failure usually occurred at the TC/TGO interface.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Finite element model of thermal barrier coatings (TBCs) system and a detailed finite element mesh in the top coat (TC) and thermally grown oxide (TGO)/TC interface; (

**b**) cross-sectional SEM image and corresponding model of NC1 with 11% unmelted nano-particle content (UNCs); (

**c**) cross-sectional SEM image and corresponding model of NC2 with 15% UNCs; (

**d**) cross-sectional SEM image and corresponding model of NC3 with 22% UNCs; (

**e**) cross-sectional SEM image and corresponding model of NC4 with 34% UNCs, (

**f**) the detailed morphology of unmelted nano-particles in NC3.

**Figure 3.**Crack propagation model of TBCs. (

**a**) All the layers of TBCs; a detailed view of UNP with predefined cracks; TGO layer; and an SEM image of UNP with microcracks around it; (

**b**) various UNCs with predefined cracks.

**Figure 4.**(

**a**) Misses stress; (

**b**) σ

_{22}and (

**c**) σ

_{12}stress distribution of top coats in NC1, NC2, NC3 and NC4.

**Figure 5.**σ

_{22}stress distribution in the top coat (

**a**) along the specified path; (

**b**) corresponding stress distribution curve.

**Figure 8.**Crack propagation and σ

_{22}stress distribution in coatings with various UNCs, (

**a**) one UNPs; (

**b**) three UNPs; (

**c**) five UNPs.

**Figure 9.**Crack propagation state and σ

_{12}stress distribution in coatings with various UNCs, (

**a**) one UNPs; (

**b**) three UNPs; (

**c**) five UNPs.

**Figure 10.**Crack propagation path in the coatings with various UNCs, (

**a**) a single UNP; (

**b**) three UNPs; (

**c**) five UNPs.

**Figure 11.**Effect of UNPs on cracks propagation behavior. (

**a**) Horizontal propagation; (

**b**) capture effect; (

**c**) inhibition effect of cracks propagation by interface; (

**d**) change of propagation direction.

**Figure 12.**Schematic diagram of inhibiting effect of cracks propagation from UNPs: (

**a**) cracks were stopped at the UNPs and crystalline region interface; (

**b**) cracks entered the UNPs.

Materials | T/°C | E/GPa | α/10^{−6}·K^{−1} | ν | k /W·m ^{−1}·K^{−1} | C /J·kg ^{−1}·K^{−1} | ρ/kg·m^{−3} |
---|---|---|---|---|---|---|---|

YSZ | 25 | 48 | 7.9 | 0.25 | 1.5 | 500 | 5280 |

200 | 47 | 8.7 | 0.25 | 1.2 | 535 | 5280 | |

400 | 43 | 9.4 | 0.25 | 1.2 | 576 | 5280 | |

800 | 39 | 16 | 0.25 | 1.2 | 637 | 5280 | |

1100 | 25 | 16 | 0.25 | 1.1 | 637 | 5280 | |

Unmelted nano-particle | 25 | 10 | 7.9 | 0.25 | 0.5 | 300 | 3580 |

BC | 25 | 152 | 12.3 | 0.3 | 4.3 | 501 | 7320 |

200 | 143 | 13.2 | 0.31 | 5.2 | 546 | 7320 | |

400 | 133 | 15.2 | 0.31 | 6.4 | 592 | 7320 | |

800 | 118 | 16.3 | 0.32 | 10.2 | 781 | 7320 | |

1000 | 74 | 17.2 | 0.33 | 16.5 | 781 | 7320 | |

1100 | 41 | 17.7 | 0.33 | - | 781 | 7320 | |

TGOs | 25 | 400 | 7.1 | 0.27 | 5.8 | 600 | 4200 |

200 | 390 | 7.5 | 0.27 | 5.8 | 600 | 4200 | |

400 | - | - | 0.27 | 5.8 | 600 | 4200 | |

800 | 355 | 9.0 | 0.27 | 5.8 | 600 | 4200 | |

1000 | 325 | 9.5 | 0.27 | 5.8 | 600 | 4200 | |

1100 | 315 | 9.7 | 0.27 | 5.8 | 600 | 4200 | |

Sub | 25 | 204 | 12.6 | 0.32 | 11.5 | 431 | 8110 |

200 | 195 | 14 | 0.32 | 14.6 | 465 | 8110 | |

400 | 179 | 14.4 | 0.33 | 17.5 | 494 | 8110 | |

800 | 149 | 15.4 | 0.34 | 23.8 | 682 | 8110 | |

1000 | 137 | 16.3 | 0.34 | 33.1 | 833 | 8110 |

T/°C | Stress/MPa | Plastic Strain |
---|---|---|

25 | 1000 | 0 |

400 | 2500 | 0.23 |

600 | 2200 | 0.30 |

800 | 375 | 0.02 |

900 | 60 | 0.02 |

1000 | 19 | 0.01 |

B/s^{−1} MPa^{−n} | n | T/°C | |
---|---|---|---|

TC | 1.8 × 10^{−10} | 1 | 1000 |

TGOs | 7.3 × 10^{−8} | 1 | 1000 |

BC | 6.5 × 10^{−19} | 4.6 | ≤600 |

BC | 2.2 × 10^{−12} | 3.0 | 700 |

BC | 1.8 × 10^{−7} | 1.6 | ≥800 |

Samples | T/°C |
---|---|

NC1 | 1115 |

NC2 | 1110 |

NC3 | 1090 |

NC4 | 1080 |

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**MDPI and ACS Style**

Zhang, L.; Wang, Y.; Fan, W.; Gao, Y.; Sun, Y.; Bai, Y.
A Simulation Study on the Crack Propagation Behavior of Nanostructured Thermal Barrier Coatings with Tailored Microstructure. *Coatings* **2020**, *10*, 722.
https://doi.org/10.3390/coatings10080722

**AMA Style**

Zhang L, Wang Y, Fan W, Gao Y, Sun Y, Bai Y.
A Simulation Study on the Crack Propagation Behavior of Nanostructured Thermal Barrier Coatings with Tailored Microstructure. *Coatings*. 2020; 10(8):722.
https://doi.org/10.3390/coatings10080722

**Chicago/Turabian Style**

Zhang, Lei, Yu Wang, Wei Fan, Yuan Gao, Yiwen Sun, and Yu Bai.
2020. "A Simulation Study on the Crack Propagation Behavior of Nanostructured Thermal Barrier Coatings with Tailored Microstructure" *Coatings* 10, no. 8: 722.
https://doi.org/10.3390/coatings10080722