# Influence of Pre-Stress Magnitude on Fatigue Crack Growth Behavior of Al-Alloy

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## Abstract

**:**

## 1. Introduction

^{9}cycles), the fatigue strength of Al-alloy is increased by only 20–30% due to the application of shot peening [18]. Another problem is that the shot peening-induced residual stresses are significantly influenced by initial residual stresses distribution of materials [19], which makes their applications more complex and more uncertain. That is, shot peening technologies generate both beneficial and harmful influences on improving fatigue properties, and it is hard to balance them. For example, softer metal has a greater work-hardening capacity in comparison with harder metal [20], but has a lower capacity for generating residual stresses.

## 2. Material and Experiments

_{y}(A), approximate (1 ± 0.1)σ

_{y}(B & C), 1.2σ

_{y}(D), 1.4σ

_{y}or 0.76σ

_{UTS}(E) and σ

_{UTS}(F), respectively, which are summarized in Table 2 together with applied loads for the incorporation of pre-stresses. There are five fatigue specimens in total, of which four are pre-stressed and one is as-received.

## 3. Results

#### 3.1. Effect of Pre-Stress Magnitude on Fatigue Property

_{app}for the pre-stressed specimens, and compared with that of the as-received specimen. It is evident that, after introducing pre-stress, the da/dN decelerated significantly by showing much lower da/dN in comparison to that of the as-received specimen and then increased gradually to a corresponding normal value. This indicates that pre-stress has a significant influence on improving the fatigue resistance of Al-alloy at the beginning, and the positive influence fell gradually with the increase of fatigue cycling number and/or crack length. This is because the compressive residual stresses are partially relaxed during fatigue test [17], which gradually reduces the degree of improvement on fatigue crack growth behavior.

_{app}. The length of the pre-stress affected zone, i.e., the distance from the point of pre-stress application to the point at which da/dN recovers to a normal level, increases with increasing pre-stress magnitude. The fatigue cycles elapsed during the crack propagated through the pre-stress affected zone increases first then decrease with the increase of pre-stress magnitude, and the peak value occurs at pre-stress ≈ 158 MPa. These results for all the four pre-stressed cases are summarized in Table 3.

#### 3.2. Observations of Fatigue-Fractured Surfaces

_{app}≈ 20 MPa$\sqrt{\mathrm{m}}$, 30 MPa$\sqrt{\mathrm{m}}$, 40 MPa$\sqrt{\mathrm{m}}$ and within unstable propagation zone, respectively. For all the SEM micrographs, the fatigue crack propagated from left to right.

## 4. Discussions

_{eff}for crack growth, i.e., ΔK

_{eff}< ΔK

_{app}. As well known, higher pre-stress has a more effective influence to reduce the da/dN of a specimen. At the first stage or initial improvement stage, however, the degree of improvement in da/dN first increases then decreases along with the increasing of pre-stress magnitude, and the maximum occurs at a pre-stress of 158 MPa as shown in Figure 3 and Figure 4. This is because the excessive increase in pre-stress magnitude generates strain hardening. The reduction in ductility is harmful to fatigue resistance. Here, it should be pointed out that the residual stress or pre-stress distribution along the crack growth path in the un-cracked ligament is not absolute uniform because of the stress concentration at the fatigue pre-crack tip. The residual stress in front of the pre-crack tip is slightly higher than the calculated engineering stress. That is why the pre-stress of 120 MPa, which is lower than the yield strength of the Al alloy, still has an obvious influence on improving the fatigue performance of the specimen.

_{f-pre-stress}(number of fatigue cyclesto failure for a specimen with pre-stress) and N

_{f}(number of fatigue cycles to failure for the as-received specimen) from the same crack length. Although the specimens with pre-stresses have differently initial pre-crack (from 0.9 mm to 1.9 mm), their fatigue crack growth lives can be compared with the corresponding fatigue crack growth life of the as-received specimen because the pre-crack length in the as-received specimen is 0.9 mm. It is evident that, with an increase of the pre-stress magnitude, the degree of improvement in fatigue life increases firstly, reaches a local maximum (increases by approximate 9 times than corresponding fatigue life of the as-received specimen) at a pre-stress of 158 MPa, and then decreases. The result is consistent with the da/dN measurement discussed above. This is because the compressive residual stress is achieved at the expense of material ductility. The overall improvement in fatigue performance decreases instead if the pre-stress is excessive.

_{f-pre-stress}and N

_{f}.

_{app}(20, 30 and 40 MPa) found that: (1) Pre-stress does not change the fracture mechanism of Al-alloy, which is basic fatigue striation. (2) Before the turning point (e.g., at ΔK

_{app}≈ 20 MPa), the fatigue striation spacing in each pre-stressed specimen is narrower than the corresponding striation spacing of the as-received specimen. (3) At the stage of initial improvement, the specimen with a pre-stress of 158 MPa has the narrowest striation spacing than those of both the as-received specimen and other pre-stressed specimens. (4) After the respective turning point, the striation spacing and unstable propagation through micro-void coalescence in the pre-stressed specimens are similar to those of the as-received specimen. The results are consistent with the da/dN measurements.

## 5. Conclusions

- (1)
- The fatigue crack growth property of the Al-alloy after the introduction of pre-stress subjected to cycle loading was developed by two stages: the initial improvement stage and subsequent normal stage.
- (2)
- Various pre-stress significantly improved the fatigue performance of Al-alloy, and no adverse factor was observed for increasing fatigue property. Pre-stress does not change the fatigue fracture characteristic (i.e., fatigue striation), but obviously reduces the fatigue striations spacing.
- (3)
- At the stage of initial improvement, the fatigue life and crack growth resistance of a specimen increases firstly, reaches a peak value at a pre-stress of approximate 158 MPa, and then decreases, with the increasing pre-stress magnitude. This is because excessive pre-stress generates the phenomenon of strain hardening.
- (4)
- Paris curves of the as-received and each pre-stress specimen intersect at a point, which is the turning point from the improvement stage to normal stage. The occurrence of the normal stage after incorporation of pre-stress is due to the relaxation of pre-stress with the increasing number of fatigue cycling and/or crack length.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**(

**a**) The geometry and detailed dimensions of the Al-alloy specimen for measuring the stress–strain curve (in mm); and (

**b**) the experimental result.

**Figure 2.**The fabrication of a pre-stressed specimen for fatigue testing: (

**a**) E-CT specimen (in mm); (

**b**) specimen with a fatigue pre-crack; and (

**c**) application of pre-stress.

**Figure 3.**The da/dN-ΔK

_{app}curves for the comparison between the diverse pre-stress specimens and the as-received specimen: (

**a**) the as-received specimen and the specimen with pre-stress = 120 MPa; (

**b**) the as-received specimen and the specimen with pre-stress = 137 MPa; (

**c**) the as-received specimen and the specimen with pre-stress = 158 MPa; and (

**d**) the as-received specimen and the specimen with pre-stress = 183 MPa.

**Figure 4.**The da/dN-ΔK

_{app}curves for direct comparison (

**a**) between the four pre-stressed specimens and the as-received specimen; and (

**b**) between 158 MPa pre-stress and 183 MPa pre-stress.

**Figure 5.**The as-received specimen: (

**a**) macrograph showing the detailed SEM locations; (

**b**) ΔK

_{app}≈ 20 MPa$\sqrt{\mathrm{m}}$; (

**c**) ΔK

_{app}≈ 30 MPa$\sqrt{\mathrm{m}}$ (striation spacing ≈ 1.7 μm); (

**d**) ΔK

_{app}≈ 40 MPa$\sqrt{\mathrm{m}}$ (striation spacing ≈ 3.2 μm); and (

**e**) unstable propagation zone.

**Figure 6.**The pre-stressed specimen with pre-stress of 137 MPa: (

**a**) macrograph showing the detailed SEM locations; (

**b**) ΔK

_{app}≈ 20 MPa$\sqrt{\mathrm{m}}$ (striation spacing ≈ 0.3 μm); (

**c**) ΔK

_{app}≈ 30 MPa$\sqrt{\mathrm{m}}$ (striation spacing ≈ 1.7 μm); (

**d**) ΔK

_{app}≈ 40 MPa$\sqrt{\mathrm{m}}$ (striation spacing ≈ 3.8 μm); and (

**e**) unstable propagation zone (striation spacing ≈ 4.7 μm).

**Figure 7.**The pre-stressed specimen with pre-stress of 158 MPa: (

**a**) macrograph showing the detailed SEM locations; (

**b**) ΔK

_{app}≈ 20 MPa$\sqrt{\mathrm{m}}$ (striation spacing ≈ 0.2 μm); (

**c**) ΔK

_{app}≈ 30 MPa$\sqrt{\mathrm{m}}$ (striation spacing ≈ 1.4 μm); (

**d**) ΔK

_{app}≈ 40 MPa$\sqrt{\mathrm{m}}$ (striation spacing ≈ 3.2 μm); and (

**e**) unstable propagation zone.

**Figure 8.**The pre-stressed specimen with pre-stress of 183 MPa: (

**a**) macrograph showing the detailed SEM locations; (

**b**) ΔK

_{app}≈ 20 MPa$\sqrt{\mathrm{m}}$; (

**c**) ΔK

_{app}≈ 30 MPa$\sqrt{\mathrm{m}}$ (striation spacing ≈ 2.6 μm); (

**d**) ΔK

_{app}≈ 40 MPa$\sqrt{\mathrm{m}}$ (striation spacing ≈ 4.9 μm); and (

**e**) unstable propagation zone.

**Figure 9.**The relationship between the pre-stress magnitude and the ratio of N

_{f-pre-stress}and N

_{f}.

Material | State | Yield Strength σ_{y} | Ultimate Tensile Strength σ_{UTS} | Young Modulus |
---|---|---|---|---|

Al5052 | H32 | 132 MPa | 243 MPa | 69.3–70.7 GPa |

Sample | Fatigue Pre-Crack (mm) | Ligament (mm^{2}) (Length × Thickness) | Applied Load (kN) | Pre-Stress (MPa) (Point in Figure 2b) |
---|---|---|---|---|

1 | 0.9 | 42.3 × 10 | - | - |

2 | 1.4 | 41.8 × 10 | 50 | 120 (B) |

3 | 1 | 42.2 × 10 | 58 | 137 (C) |

4 | 1.9 | 41.3 × 10 | 65.2 | 158 (D) |

5 | 0.9 | 42.3 × 10 | 77.3 | 183 (E) |

Pre-Stress (MPa) | 120 | 137 | 158 | 183 |
---|---|---|---|---|

Length of pre-stress affected zone (mm) | 4.9 | 5.5 | 9.9 | 10.1 |

Fatigue pre-crack (mm) | 1.4 | 1.0 | 1.9 | 0.9 |

Crack length recovering to normal da/dN | 6.3 | 6.5 | 11.8 | 11.0 |

Number of fatigue cycles elapsed | 109,055 | 209,857 | 333,650 | 242,905 |

ΔK_{app} ($\mathrm{MPa}\sqrt{\mathrm{m}}$) ↔ normal da/dN | 22.0 | 23.2 | 31.5 | 28.4 |

The applied maximum load P_{max} (kN) | 12.0 | 12.0 | 12.5 | 12.0 |

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**MDPI and ACS Style**

Zhang, C.; Song, W.; Wang, Q.; Liu, W.
Influence of Pre-Stress Magnitude on Fatigue Crack Growth Behavior of Al-Alloy. *Materials* **2018**, *11*, 1267.
https://doi.org/10.3390/ma11081267

**AMA Style**

Zhang C, Song W, Wang Q, Liu W.
Influence of Pre-Stress Magnitude on Fatigue Crack Growth Behavior of Al-Alloy. *Materials*. 2018; 11(8):1267.
https://doi.org/10.3390/ma11081267

**Chicago/Turabian Style**

Zhang, Chunguo, Weizhen Song, Qitao Wang, and Wen Liu.
2018. "Influence of Pre-Stress Magnitude on Fatigue Crack Growth Behavior of Al-Alloy" *Materials* 11, no. 8: 1267.
https://doi.org/10.3390/ma11081267