# A Novel Ultrasonic Fatigue Test and Application in Bending Fatigue of TC4 Titanium Alloy

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## Abstract

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## 1. Introduction

^{7}to 10

^{9}cycles, which involves the problem of VHCF [1,2]. In fact, aviation components such as engine blades are vulnerable to the combined action of high frequency and low load, which means their failure forms also have VHCF characteristics [3]. At the same time, the revised national military standard “General Specification for Aeronautical Turbojet and Turbofan Engines” (GJB241A-2010) also clearly stipulates that “all components of the aero-engine must have a life of not less than 10

^{9}cycles”. Therefore, due to the higher requirements for long life and reliability of aviation components, the research on VHCF has received special attention in the aerospace field.

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## 2. Specimen Design for Very High Cycle Bending Fatigue

_{0}), the coefficient of displacement to stress (${C}_{s}$) needs to be calculated before the experiment [29]. Therefore, the bending vibration mode of the specimen as well as the distribution of stresses in the gauge section need to be considered.

#### 2.1. Specimen Design and Analysis

#### 2.2. Stress Calibration

_{0}) of the system; i.e.:

## 3. Experiment Materials and Methods

#### 3.1. Materials

#### 3.2. Ultrasonic Fatigue Test

_{0}) of the ultrasonic fatigue system. Figure 6c shows that the test point of the sensor was located at point M.

^{9}, the fatigue test was stopped and the specimen was considered to be undamaged.

#### 3.3. Comparison Fatigue Test

^{7}cycles. In order to investigate the difference between axial loading fatigue and bending loading fatigue in the VHCF regime, a set of ultrasonic axial loading tests on a plate were conducted for comparison. Figure 7 shows the geometry of the axially loaded specimens.

## 4. Results and Discussion

#### 4.1. S-N Curve

^{9}cycles, which was consistent with the traditional view of “infinite life” [38]. In addition, under bending loading, there were two typical types of crack initiation; namely, surface crack initiation and internal crack initiation. This was consistent with the results of conventional axial fatigue loading. Finally, the ultrasonic bending fatigue test and the ultrasonic axial fatigue test obtained 19 and 14 valid data, respectively, as shown in Table 2.

^{8}cycles. Previous studies have shown that under high stress amplitude, the bending load can show better fatigue resistance than the axial load. However, the difference will gradually decrease with the increase of cycle times, and even show the trend of intersection [16,21,43].

#### 4.2. Fracture Morphology

## 5. Conclusions

- A new bending fatigue model in the resonant state under ultrasonic loading was developed in which the accelerated bending frequency reached 20 kHz and the symmetrical stress distribution at the gauge section was optimized compared with the conventional cantilever model.
- The S-N curve for the studied material showed that the fatigue data of the bending loading and axial loading intended to have an intersection point when the cycles went beyond 10
^{8}. Re-discussion of the conservative design strategy may be required regarding bending loading and axial loading in the VHCF regime. - There were two types of bending fatigue loading—surface crack initiation and internal crack initiation. As the cycle life increased, the possibility of an internal crack occurring also increased.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

R | Stress ratio (minimum stress/maximum stress) |

${\sigma}_{a}$ | Stress amplitude |

${\sigma}_{0},a,b$ | Material constants |

${N}_{f}$ | Number of cycles to failure |

${C}_{s}$ | Coefficient of displacement to stress |

A_{0} | Excitation displacement of the system |

R^{2} | Coefficient of determination |

HCF | High cycle fatigue (${N}_{f}$ > 10^{5}) |

VHCF | Very high cycle fatigue (${N}_{f}$ > 10^{7}) |

FEA | Finite element analysis |

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**Figure 3.**The stress distribution on the bent specimen: (

**a**) finite element analysis (FEA) solved dis-tribution of displacement and stress; (

**b**) paths of stress collecting at the gauge section; (

**c**) stress profile along the longitudinal direction; (

**d**) stress profile along the transversal direction.

**Figure 4.**Strain measurement: (

**a**) diagram of strain gages; (

**b**) waveform of excitation displacement; (

**c**) waveform of measured strain; (

**d**) relationship between measured stress and FEA stress.

**Figure 6.**Bending test based on ultrasonic fatigue system: (

**a**) full view of the system; (

**b**) details of the constraint; (

**c**) composition of the bending constraint method.

**Figure 10.**Typical fracture morphology in the HCF: (

**a**–

**c**) ${\sigma}_{a}=390.14$ MPa, ${N}_{f}=3.39\times {10}^{5}$ cycles; (

**d**–

**f**) ${\sigma}_{a}=220.01$ MPa, ${N}_{f}=6.05\times {10}^{6}$ cycles.

**Figure 11.**Typical fracture morphology in the VHCF: (

**a**,

**b**) ${\sigma}_{a}=246.66$ MPa, ${N}_{f}=9.91\times {10}^{7}$; (

**c**,

**d**) ${\sigma}_{a}=213.1$ MPa, ${N}_{f}=2.53\times {10}^{8}$ cycles.

Young’s Modulus (GPa) | Yield Strength (MPa) | Tensile Strength (MPa) | Poisson’s Ratio | Hardness (Hv) |
---|---|---|---|---|

113 | 915 | 954 | 0.33 | 330 |

Bending Load | Axial Load | ||||
---|---|---|---|---|---|

Specimen No. | Stress Level (MPa) | Fatigue Cycle (Cycles) | Specimen No. | Stress Level (MPa) | Fatigue Cycle (Cycles) |

1 | 390.14 | 3.39 × 10^{5} | 1 | 278.29 | 4.38 × 10^{5} |

2 | 335.41 | 4.78 × 10^{7} | 2 | 259.49 | 2.61× 10^{6} |

3 | 335.41 | 7.96 × 10^{5} | 3 | 246.96 | 1.79 × 10^{7} |

4 | 320.00 | 1.20 × 10^{6} | 4 | 246.96 | 4.90 × 10^{7} |

5 | 320.00 | 2.82 × 10^{6} | 5 | 246.96 | 4.84 × 10^{7} |

6 | 310.00 | 2.29 × 10^{6} | 6 | 234.43 | 1.49 × 10^{6} |

7 | 299.75 | 2.39 × 10^{6} | 7 | 234.43 | 5.35 × 10^{7} |

8 | 294.25 | 5.20 × 10^{6} | 8 | 234.43 | 7.36 × 10^{7} |

9 | 287.07 | 2.23 × 10^{7} | 9 | 228.16 | 6.80 × 10^{7} |

10 | 280.50 | 4.25 × 10^{6} | 10 | 221.90 | 1.17 × 10^{8} |

11 | 262.10 | 1.05 × 10^{7} | 11 | 221.90 | 2.16 × 10^{7} |

12 | 246.77 | 2.07 × 10^{8} | 12 | 221.90 | 2.20 × 10^{8} |

13 | 246.66 | 9.91 × 10^{7} | 13 | 221.90 | 1.98 × 10^{8} |

14 | 243.02 | 5.26 × 10^{7} | 14 | 215.00 | 1.00 × 10^{9} |

15 | 238.03 | 4.35 × 10^{7} | |||

16 | 222.01 | 6.05 × 10^{6} | |||

17 | 213.10 | 2.53 × 10^{8} | |||

18 | 208.59 | 5.06 × 10^{7} | |||

19 | 200.00 | 1.00 × 10^{9} |

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## Share and Cite

**MDPI and ACS Style**

Tang, S.; Wang, X.; Huang, B.; Yang, D.; Li, L.; He, C.; Xu, B.; Liu, Y.; Wang, C.; Wang, Q.
A Novel Ultrasonic Fatigue Test and Application in Bending Fatigue of TC4 Titanium Alloy. *Materials* **2023**, *16*, 5.
https://doi.org/10.3390/ma16010005

**AMA Style**

Tang S, Wang X, Huang B, Yang D, Li L, He C, Xu B, Liu Y, Wang C, Wang Q.
A Novel Ultrasonic Fatigue Test and Application in Bending Fatigue of TC4 Titanium Alloy. *Materials*. 2023; 16(1):5.
https://doi.org/10.3390/ma16010005

**Chicago/Turabian Style**

Tang, Sen, Xinyu Wang, Beihai Huang, Dongtong Yang, Lang Li, Chao He, Bo Xu, Yongjie Liu, Chong Wang, and Qingyuan Wang.
2023. "A Novel Ultrasonic Fatigue Test and Application in Bending Fatigue of TC4 Titanium Alloy" *Materials* 16, no. 1: 5.
https://doi.org/10.3390/ma16010005