# Assessment of the Impact of Shot-Peening on the Fatigue Life of a Compressor Blade Subjected to Resonance Vibrations

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Analysis

#### 2.1. Analysis Assumptions

^{3}, tensile strength UTS = 1200 MPa, yield strength ${\sigma}_{Y}$ = 1000 MPa, and Poisson coefficient $\vartheta $ = 0.3 [5,18]. The aforementioned values are necessary in order to perform the numerical modal analysis, as well as to estimate the fatigue constants for this alloy.

#### 2.2. Numerical Analysis

## 3. Metallography

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_{4}) were used while undergoing electrolysis etching for 20 s for each sample. The samples prepared with the typical metallography techniques were observed under an optical microscope. Using the image analysis software, a series of photographs were taken showing the grain size at different points within the blade profile (Figure 6). The size of a single grain was measured, as well as the thickness of the layer plasticized as a result of surface treatment—shot-peening (Figure 7). The measurement was made on both sides of the blade profile, at six characteristic points (at the leading edge, in the middle part, and at the trailing edge—on the inner and outer sides of the profile), as well as at two points inside the profile. The locations of the points are presented in Figure 3. It should be remembered that the inner side of the blade is the working side that is most exposed to erosive action, and that the leading edge is most exposed to collision with hard elements sucked into the engine. The obtained grain measurement results are presented in Figure 8, Figure 9 and Figure 10.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**A sketch of a magnified cross-section with the marked measurement locations and geometrical terms for the analyzed blade.

**Figure 4.**Equivalent stress ${\sigma}_{EQV}$ (MPa) distribution at the bottom of the notch, in the case of a resonance vibration with an amplitude equal to 1.8 mm.

**Figure 5.**A plot of equivalent stress ${\sigma}_{EQV}$ (MPa) at the bottom of the notch, in the case of a resonance vibration with an amplitude equal to 1.8 mm.

**Figure 6.**Picture of a cross-section of the blade with a magnified grain image from the center to the outer side of the blade.

**Figure 7.**View of the microstructure of the seventh cross-section, on the inner side of the blade with marked representative dimensions (grain size and depth of the plasticized layer).

**Figure 8.**Plots of the grain size (in the layer plasticized by shot-peening) as a function of the height of the blade for different measurement locations.

**Figure 9.**Plots of plasticized layer thickness (by shot-peening) as a function of the height of the blade for different measurement location.

**Figure 10.**Plots of plasticized layer thickness (by shot-peening) as a function of the chord of the blade for a different side of the blade, for different cross-sections.

**Table 1.**Results of the numerical fatigue analysis based on the equivalent stress at the notched edge, with an amplitude of resonant vibrations of 1.8 mm.

Assumed Value of Residual/Initial Stresses Created by Shot-Peening | ||||||
---|---|---|---|---|---|---|

$0\mathbf{M}\mathbf{P}\mathbf{a}$ | $-100\mathbf{M}\mathbf{P}\mathbf{a}$ | $-200\mathbf{M}\mathbf{P}\mathbf{a}$ | $-300\mathbf{M}\mathbf{P}\mathbf{a}$ | $-400\mathbf{M}\mathbf{P}\mathbf{a}$ | $-500\mathbf{M}\mathbf{P}\mathbf{a}$ | |

Eqv. Stress on the Edge of the Notch${\sigma}_{EQV}=955MPa$ | $117$ | $405$ | $1.89\xb7{10}^{3}$ | $17\xb7{10}^{3}$ | $875\xb7{10}^{3}$ | $259\xb7{10}^{6}$ |

**Table 2.**Results of the numerical fatigue analysis based on the maximum value of the equivalent stress, with amplitude of resonance vibrations of 1.8 mm.

Assumed Value of Residual/Initial Stresses Created by Shot-Peening | ||||||
---|---|---|---|---|---|---|

$0\mathbf{M}\mathbf{P}\mathbf{a}$ | $-100\mathbf{M}\mathbf{P}\mathbf{a}$ | $-200\mathbf{M}\mathbf{P}\mathbf{a}$ | $-300\mathbf{M}\mathbf{P}\mathbf{a}$ | $-400\mathbf{M}\mathbf{P}\mathbf{a}$ | $-500\mathbf{M}\mathbf{P}\mathbf{a}$ | |

Max. Value of Eqv. Stress${\sigma}_{EQV}=1194MPa$ | $11$ | $28$ | $76$ | $243$ | $987$ | $6.39\xb7{10}^{3}$ |

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**MDPI and ACS Style**

Bednarz, A.; Misiolek, W.Z. Assessment of the Impact of Shot-Peening on the Fatigue Life of a Compressor Blade Subjected to Resonance Vibrations. *Materials* **2020**, *13*, 5726.
https://doi.org/10.3390/ma13245726

**AMA Style**

Bednarz A, Misiolek WZ. Assessment of the Impact of Shot-Peening on the Fatigue Life of a Compressor Blade Subjected to Resonance Vibrations. *Materials*. 2020; 13(24):5726.
https://doi.org/10.3390/ma13245726

**Chicago/Turabian Style**

Bednarz, Arkadiusz, and Wojciech Z. Misiolek. 2020. "Assessment of the Impact of Shot-Peening on the Fatigue Life of a Compressor Blade Subjected to Resonance Vibrations" *Materials* 13, no. 24: 5726.
https://doi.org/10.3390/ma13245726