# Onset Frequency of Fatigue Effects in Pure Aluminum and 7075 (AlZnMg) and 2024 (AlCuMg) Alloys

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## Abstract

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## 1. Introduction

#### 1.1. Influence of the Loading Frequency on the Fatigue Response of Metals

#### 1.2. Influence of Temperature on the Fatigue Response of Al Alloys

#### 1.3. Influence of the Microstructure on the Fatigue Response of Al Alloys

## 2. Materials and Methods

_{2}atmosphere. Namely, the DMA measured the storage modulus E’ (i.e., the elastic-real-component of the dynamic tensile modulus, accounting for the deformation energy stored by the material), the loss modulus E” (i.e., the viscous-imaginary component of the dynamic tensile modulus, accounting for the energy dissipation due to internal friction during relaxation processes) and the loss tangent (also termed mechanical damping or tanδ) [7]. The 3-point bending clamp was used, and the DMA was set to sequentially apply dynamic loading with frequencies ranging from 1–100 Hz, at temperatures from RT to 723 K in step increments of 5 K. More details on the procedure, as well as the viscoelastic data of AA 7075-T6 and 2024-T3 used in this work, can be found in [5,6].

## 3. Results and Discussion

#### 3.1. Storage Modulus

#### 3.2. Loss Modulus

#### 3.3. Temperature Dependence of the Storage Modulus

_{0}’. Finally, it is important to note that the larger decrease of E’ for low frequencies is typically explained by the Arrhenius-type behavior of the relaxation rate. That is, the mechanical relaxation time decreases with temperature [7], so that, at low frequencies, the shorter relaxation times lead to responses with larger values of E” and smaller values of E’.

#### 3.4. Effect of Internal Friction on Fatigue Strength

#### 3.5. Onset Frequency of Fatigue Effects

_{0}’. The procedure is illustrated in Figure 3, which shows E

_{0}’ as a function of the loading frequency for pure Al in the H24 temper and pure Al, as obtained from linear regression of DMA data, and for AA 7075-T6 and 2024-T3, as obtained in [5,6]. These values of E

_{0}’ are compared to average values of the rate of loss of static elastic modulus with temperature, as obtained by linear regression of data in the literature for pure Al [36] and AA 2024 [35]. To calculate these averages, data from Kamm and Alers [37] and from Varshni [38] were disregarded, as they correspond to temperatures below RT. Data from Wolfenden and Wolla [39] were also disregarded, since these data are too scattered in a broad temperature range, and thus, the computable slope is probably not representative.

_{0}’ should become equal to the rate of loss of the elastic modulus with temperature under static loading conditions, this threshold frequency may be estimated by the intersection of the latter rate with a tendency line extrapolating the behavior of E

_{0}’ measured experimentally to lower frequencies. In the example shown in Figure 3, the intersection of a logarithmic tendency line with the rate of loss of the static elastic modulus for pure Al in the H24 temper and pure Al gives a threshold frequency of around 0.001 and 0.005 Hz, respectively. For AA 2024-T3, the threshold frequency obtained with the same procedure would be about 0.006 Hz. For AA 7075-T6, no data on the variation of the elastic stiffness constants with temperature were found in the literature, but using the data available for AA 2024 and pure Al, a threshold frequency of 0.075 and 0.350 Hz would be obtained, respectively. These results are similar to those in the literature: Henaff et al. [26] reported a critical frequency of 0.020 Hz for AA 2650-T6, and Nikbin and Radon [25] reported that the transition region is 0.100–1 Hz for cast Al alloy RR58 at 423 K. However, to better assess the performance of the proposed procedure, further comparison with experimental data on fatigue response at very low frequencies is necessary. Unfortunately, there is a lack of this type of test data [26], due to the extremely long testing time. It is interesting to note that, on one side, according to our results, fatigue effects would seem to appear at lower loading frequencies for pure Al, compared to the alloys. Thus, apparently, the precipitation structure in the alloys would cause not only hardening, but would also enable the alloys to be loaded at a wider range of low frequencies without experiencing fatigue. On the other side, fatigue would appear already at lower frequencies for pure Al in the H24 temper compared to pure Al. In this case, the reason may be the lower ductility (and, thus, lower resistance to FCG) associated with the H24 temper.

## 4. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

AA | Aluminum alloy(s) |

bcc | Body-centered cubic |

CFCG | Creep-fatigue crack growth |

CCG | Creep crack growth |

DMA | Dynamic-mechanical analyzer |

fcc | Face-centered cubic |

FCG | Fatigue crack growth |

GPBZ | Guinier–Preston–Bagariastkij zones |

GPZ | Guinier–Preston zones |

HCF | High cycle fatigue |

RT | Room temperature |

VHCF | Very high cycle fatigue |

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**Figure 1.**Storage modulus E’ vs. temperature T from dynamic-mechanical analyzer tests at frequencies ranging from 1–100 Hz: (

**a**) for pure Al in the H24 temper, from room temperature (RT) to 648 K; (

**b**) for pure Al, from RT to 723 K.

**Figure 2.**Loss modulus E” vs. temperature T from dynamic-mechanical analyzer tests at frequencies ranging from 1–100 Hz: (

**a**) for pure Al in the H24 temper, from room temperature (RT) to 648 K; (

**b**) for pure Al, from RT to 723 K.

**Figure 3.**Temperature softening coefficient E

_{0}’ vs. frequency f for pure Al in the H24 temper, pure Al, Al alloy (AA) 7075-T6 and AA 2024-T3, as obtained from linear regression of test data from the dynamic-mechanical analyzer. Logarithmic tendency lines fitted to the data to extrapolate them to lower frequencies are also shown, as well as the rates of loss of static elastic modulus with temperature, as obtained by linear regression of data in the literature for pure Al [36] and AA 2024 [35].

**Table 1.**Temperature softening coefficient E

_{0}’, for pure Al in the H24 temper and for pure Al, as obtained from linear regression of dynamic-mechanical analyzer test data.

Loading Frequency (Hz) | E_{0}’ (Pure Al in H24 Temper) (MPa·K^{−1}) | E_{0}’ (Pure Al) (MPa·K^{−1}) |
---|---|---|

100 | −23.1 | −26.4 |

30 | −25.2 | −27.7 |

10 | −26.4 | −29.1 |

3 | −27.9 | −31.0 |

1 | −29.7 | −32.2 |

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**MDPI and ACS Style**

Rojas, J.I.; Crespo, D.
Onset Frequency of Fatigue Effects in Pure Aluminum and 7075 (AlZnMg) and 2024 (AlCuMg) Alloys. *Metals* **2016**, *6*, 50.
https://doi.org/10.3390/met6030050

**AMA Style**

Rojas JI, Crespo D.
Onset Frequency of Fatigue Effects in Pure Aluminum and 7075 (AlZnMg) and 2024 (AlCuMg) Alloys. *Metals*. 2016; 6(3):50.
https://doi.org/10.3390/met6030050

**Chicago/Turabian Style**

Rojas, Jose I., and Daniel Crespo.
2016. "Onset Frequency of Fatigue Effects in Pure Aluminum and 7075 (AlZnMg) and 2024 (AlCuMg) Alloys" *Metals* 6, no. 3: 50.
https://doi.org/10.3390/met6030050