# Experimental Investigation on the Fatigue Life of Ti-6Al-4V Treated by Vibratory Stress Relief

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experiments

#### 2.1. Dynamic Stress Measurement Tests

_{a}, ε

_{b}, and ε

_{c}are the measured strains at the 0°, 45°, and 90° directions, respectively; σ

_{1}, σ

_{2}, and σ

_{3}are the first, second, and third principal stresses, respectively (σ

_{3}is zero in the plane problems); σ

_{eqv}is the equivalent stress (von Mises stress); E is the elastic modulus; and μ is Poisson’s ratio. Thus, the generated dynamic stresses under different amplitudes can be obtained.

#### 2.2. VSR Tests

#### 2.3. Residual Stress Measurement Tests

#### 2.4. Uniaxial Tension-Compression Fatigue Experiments

^{7}cycle times for the first time with the decrease in the cyclic stress amplitude. The first appearance of the no-fractured specimen and its previous fractured specimen are considered as effective specimens. If two specimens have the opposite fracture results (i.e., one is fractured, whereas the other is unfractured) and adjacent cyclic stress amplitude (±10 MPa), then both are regarded as effective specimens. The fatigue limit can then be calculated by Equation (4):

_{i}is the ith cyclic stress amplitude; and v

_{i}is the number of specimens at σ

_{i}cyclic stress amplitude.

## 3. Results and Discussion

#### 3.1. Dynamic Stress Measurement Tests

#### 3.2. Residual Stress Measurement Tests

#### 3.3. Uniaxial Tension-Compression Fatigue Experiments

_{d}+ σ

_{r}(σ

_{r}is the residual stress, whereas σ

_{d}is the dynamic stress in the VSR) is larger than the yield limit of the material in the local position, micro-plastic deformation occurs, and the internal residual stress is redistributed. The residual stress magnitude then decreases with the formation of a new stress equilibrium [42]. Therefore, micro-plastic deformation and stress redistribution that occur during the VSR process are the main reasons for the decrease and homogenization of residual stress.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Finite element (FE) modal analysis and sticking position of the strain rosette: (

**a**) FE model and first-order vibration mode result; and (

**b**) sticking position of the strain rosette.

**Figure 8.**Dynamic stress and strain under different amplitudes: (

**a**) dynamic strain; and (

**b**) dynamic stress.

**Figure 9.**Measured stresses of Groups A to F after the VSR tests: (

**a**) first principal stresses along the depth direction; and (

**b**) comparison of the measured stress among the different groups (i.e., σ

_{surf}, σ

_{max}, and σ

_{ave}denote the stresses at 0.02 mm depth, absolute value of the peak stress, and average stress along the depth direction, respectively).

**Figure 10.**Fatigue limits under different amplitudes (−0.05 mm amplitude stands for the annealing treatment).

**Figure 11.**Cyclic stress amplitude-logarithm of cycle numbers (S-lgN) curves for Ti-6Al-4V titanium alloy.

Density/kg·m^{3} | Elastic Modulus/GPa | Poisson’s Ratio | Yield Strength/MPa |
---|---|---|---|

4440 | 110 | 0.33 | 980 |

Results | Group A | Group B | Group C | Group D | Group E | Group F |
---|---|---|---|---|---|---|

Fatigue limit (MPa) | 481 | 475 | 475 | 472 | 430 | 440 |

Percentage change | / | −1.25% | −1.25% | −1.87% | −10.60% | −8.52% |

Surface stress(MPa) | 217 | 86.7 | 108 | 34.1 | 21.3 | 5.91 |

Percentage change | / | −60.05% | −50.23% | −84.29% | −90.18% | −97.28% |

Average stress (MPa) | 13.55 | 1.22 | 4.47 | 3.43 | 4.24 | 8.15 |

Percentage change | / | −90.99% | −67.02% | −74.68% | −68.68% | −39.87% |

Dynamic stress (MPa) | / | 8.68 | 14.43 | 28.76 | 57.22 | / |

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**MDPI and ACS Style**

Gao, H.-J.; Zhang, Y.-D.; Wu, Q.; Song, J.
Experimental Investigation on the Fatigue Life of Ti-6Al-4V Treated by Vibratory Stress Relief. *Metals* **2017**, *7*, 158.
https://doi.org/10.3390/met7050158

**AMA Style**

Gao H-J, Zhang Y-D, Wu Q, Song J.
Experimental Investigation on the Fatigue Life of Ti-6Al-4V Treated by Vibratory Stress Relief. *Metals*. 2017; 7(5):158.
https://doi.org/10.3390/met7050158

**Chicago/Turabian Style**

Gao, Han-Jun, Yi-Du Zhang, Qiong Wu, and Jing Song.
2017. "Experimental Investigation on the Fatigue Life of Ti-6Al-4V Treated by Vibratory Stress Relief" *Metals* 7, no. 5: 158.
https://doi.org/10.3390/met7050158