# Correlation between Thermal Behaviour of AA5754-H111 during Fatigue Loading and Fatigue Strength at Fixed Number of Cycles

^{*}

## Abstract

**:**

## 1. Introduction

^{6}cycles, and the achievement of real fatigue limit in correspondence of which “cracks growth” at roughly 10

^{7}–10

^{8}cycles, depending on grain dimensions as well as the specific microstructure [5]. However, the absence of “knee” point or the presence of different sloping trends in S-N curves [1,5,6,7,8,9,10,11] makes the assessment of fatigue life difficult, but the interest in this non-ferrous metal is growing due to the fact that it represents a good options for structural applications, particularly in the aerospace, aeronautic, naval, and automotive industries, due to their high strength to weight ratio and excellent resistance to atmospheric corrosion [12].

^{7}cycles corresponds to the stress level that experiences the first significant heat dissipation in terms of temperature increase. So, this paper is the first approach to answer to the questions: “Does it exist a significant temperature variation in the thermal behaviour of aluminium?”, and by the way, “What does represent the significant temperature increase for materials such as aluminium alloys that do not present a horizontal asymptote in S-N curve?”. In this regard, a specific data assessment and a processing procedure will be presented capable of both determining estimation of the fatigue strength at a specific number of loading cycles and obtaining an “S-N curve” by thermal data.

## 2. Theory

## 3. Material and Setup

^{7}, as suggested by the Eurocode EN 1999-1-3. The result in terms of the fatigue life at 10

^{7}was 148.30 MPa, the prediction fitting line was calculated by using α = 0.1, as reported in Figure 5.

## 4. Data Processing

^{®}that provides not only quantitative values for each parameter, but also the related maps, which are the matrixes of pixels whose values are specific for each thermal component. The overall procedure, for the generic samples that is loaded at specific Δσ is represented in Figure 6. Further, Figure 6 depicts the three maps of signal that is related to the temperature signal components of interest. An important observation that is possible to make by observing Figure 6, is such that each map provides different information that contributes to understand the behaviour of the material during fatigue loadings. Specifically, both S

_{1}and S

_{2}highlight very localized phenomena in the gage length, while S

_{0}provides an overall map of the temperature in the gage length.

_{0}parameter, which represents the total temperature variation.

_{0}signal presents a double-sloped trend due to different disturbing heat sources, such as the heating from convection and conduction. The first contribute is represented by the temperature of environment, while the second one can be determined by the heating from moving grip of loading machine that is in contact with hot oil. The influence of these disturbing heat sources was discussed in [23], however this particular temperature signal behaviour can be totally filtered out by using the procedure that was adopted for estimating fatigue strength, as will be explained in further paragraph.

_{1}parameter data. As shown in the theory, this component of the temperature is related to the thermoelastic first order effect that is influenced by the mean stress and the stress amplitude.

^{2}dependence, as shown by Equation (1), so that the curve fitting is represented by a polynomial second order curve. Particularly for the S

_{2}parameter, the study of the fatigue behaviour can be difficult since it includes both dissipative and thermoelastic effects, in other words, it includes both reversible and irreversible temperature variations. So, to discern these two effects, a filtering procedure is needed as will be explained in further paragraphs.

## 5. Results and Discussion

#### 5.1. Assessment of Significant Thermal Signal Variations by Using the Threshold Method

_{1}, S

_{2}, S

_{0}, the data were addressed to a specific procedure, as applied on ferrous metals [23] as well as on composites [31].

_{0}data. In the present work, an extension of the procedure to the signals S

_{1}and S

_{2}is presented.

_{1}and S

_{0}, while it is polynomial (the grade of interpolating polynomial is 2) for S

_{2}. The difference between two methods (linear and polynomial) is due the square stress amplitude dependence of the second order temperature variations parameter with respect S

_{1}. However, this procedure allows for processing the data in order to eliminate both thermoelastic influences on S

_{1}, S

_{2}, and the influence of “disturbing heat sources” on S

_{0}.

_{0}and S

_{2}parameters is slightly the same (approximately 145 MPa), while the results that are provided by the application of the method on the S

_{1}parameter indicate a higher value with a higher scatter of data.

_{2}data, it is possible to obtain a “thermographic S-N curve” that allows for reducing the testing time and the costs of the experimental campaign, as will be detailed explained in the further paragraph.

#### 5.2. Correlation between S_{2} Thermal Signal Variations and Experimental Data to Obtain “Thermal S-N Curve”

^{7}cycles, is indicated.

_{1}, S

_{2}, and S

_{0}, will be correlated to the thermographic S-N curve in order to better understand what the value that was obtained by applying the threshold value corresponds to.

#### 5.3. Estimation of the Fatigue Life at Specific Loading Cycles by Using the “Thermal S-N Curves”

_{0}, S

_{1}, and S

_{2}thermographic data and in Figure 12 the correlation between thermographic S-N curve data and the stresses resulting from the application of the threshold method are shown.

_{2}and S

_{0}(respectively, 146.67 MPa and 145 MPa) is higher (2 × 10

^{7}) than the one in correspondence of the runout 10

^{7}cycles (148.30 MPa).

_{1}data provides a consistently higher value of stress in correspondence of a fatigue life of 9.69 × 10

^{5}cycles.

_{0}and S

_{2}appear to be different from the one that is provided by S

_{1}, it is worth noting that it can be related to different aspect of the fatigue life of material. In fact, together with the absence of horizontal asymptote in the High Cycle Fatigue (HCF) regime, as reported in Figure 5 and Figure 11, accordingly with the literature [5,6,7,8,9], the S-N curve presents a double sloped trend at approximately 10

^{6}cycles. Even if in literature, on the presented alloy, there are few information on fatigue behaviour, several authors [1,2,3,4,5] discussed of the double slope variation of the curve in sight of the absence of a fatigue limit, especially in the High Cycle Fatigue (HCF) regime, where the fatigue limit of several type of steels lies. In particular, on alloys 7075-T6 and 2024-T3, Newman [8] observed a slope variation at approximately 8 × 10

^{5}loading cycles.

^{6}cycles. This change in slope, as stated by [6], corresponds to the achievement of persistent slip band limit that determines the increase in deformation and in turn the onset of damage phenomena. The persistent slip band limit separates the Low Cycle Fatigue (LCF) where the stress values are correlated to the necessary energy to move dislocations and creating the persistent slip bands structures [5].

_{1}seems to be a good estimator of the stress condition at which the regime switches from LCF to HCF, since the fatigue life seems to be very similar to the point of inversion of the S-N trend that is found for present alloy at 7 × 10

^{5}cycles.

_{0}, S

_{2}seem to be providing an estimation of the fatigue life in very high cycle regime at higher values than 10

^{7}cycles.

## 6. Conclusions

_{0}has been presented that can eliminate the disturbing heat contributions due to influence of environment or conduction throughout the material. The procedure also allows for filtering out thermoelastic mean stress or square stress amplitude dependences from the thermal component related to first order S

_{1}and second order S

_{2}temperature variations.

_{0}and S

_{2}estimate a stress value over the conventional run-out of 10

^{7}cycles, while the S

_{1}provides values that are similar to the first slope variation, which corresponds to the transition between LCF and HCF limit in correspondence of the critical stress to which a generic damage process growth.

_{2}, in order to obtain a thermographic S-N curve that allows for exploring the different aspects of the fatigue life of the materials with less time and less cost in comparison to the traditional experimental campaign.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 3.**Sample geometry and dimensions expressed in mm [37].

**Figure 4.**Equipment and setup: (

**a**) strain gage applied on sample surface; (

**b**) IR detector monitoring the test.

**Figure 9.**Linear Residuals of S

_{0}(

**a**) and S

_{1}(

**b**) parameters, and polynomial residuals of S

_{2}parameter (

**c**), example of the polynomial fit line adopted for analysing sample 1 (

**d**).

**Figure 10.**Polynomial residuals of S

_{2}parameter in relation to the number of cycles of a classical S-N curve.

**Figure 12.**Assessment of the fatigue strength of AA5754-H111 by using the data from threshold method and thermographic S-N curve.

Alloy | Si | Fe | Cu | Mn | Mg | Cr | Ni | Zn | Ti | Other Elements |
---|---|---|---|---|---|---|---|---|---|---|

AA5754-H111 | 0.40 | 0.40 | 0.10 | 0.50 | 2.60–3.60 | 0.30 | 0.05 | 0.20 | 0.15 | 0.05 |

Loading Levels | |||||
---|---|---|---|---|---|

Step | Δσ | σ_{max} | Step | Δσ | σ_{max} |

(MPa) | (MPa) | (MPa) | (MPa) | ||

1 | 36.0 | 40.0 | 8 | 135.0 | 150.0 |

2 | 54.0 | 60.0 | 9 | 139.5 | 155.0 |

3 | 72.0 | 80.0 | 10 | 144.0 | 160.0 |

4 | 90.0 | 100.0 | 11 | 148.5 | 165.0 |

5 | 108.0 | 120.0 | 12 | 153.0 | 170.0 |

6 | 126.0 | 140.0 | 13 | 166.5 | 185.0 |

7 | 130.5 | 145.0 | 14 | 175.5 | 195.0 |

Sample | σ_{max} (MPa) | Number of Cycles | Sample | σ_{max} (MPa) | Number of Cycles |
---|---|---|---|---|---|

1 | 70.0 | 1 × 10^{7} | 5 | 170.0 | 242,637 |

2 | 100.0 | 1 × 10^{7} | 6 | 185.0 | 286,216 |

3 | 177.0 | 444,272 | 7 | 165.0 | 835,571 |

4 | 160.0 | 4,323,679 | 8 | 162.5 | 626,212 |

- | - | - | 9 | 195.0 | 207,560 |

Samples | Fatigue Strength Assessment: Threshold Method Applied on Different Thermal Indexes (Values in MPa) | |||
---|---|---|---|---|

S_{0} | S_{1} | S_{2} | CLASSICAL S-N CURVE | |

SAMPLE 1 | 150.00 | 190.00 | 140.00 | - |

SAMPLE 2 | 140.00 | 160.00 | 145.00 | |

SAMPLE 3 | 145.00 | 150.00 | 155.00 | |

Mean (MPa) | 145.00 | 166.67 | 146.67 | Mean (MPa) 148.30 |

Std. Dev (MPa) | 5.00 | 20.82 | 7.64 | Prediction Interval. 90% (MPa) 11.89 |

**Table 5.**Evaluation of number of cycles of thermographic S-N curve by using the model of Equation (5).

Residuals of ${\mathit{S}}_{2}$ of Sample 1 (Signal Units) | ${\mathit{\sigma}}_{\mathit{m}\mathit{a}\mathit{x}}$ (MPa) | Number of Cycles |
---|---|---|

0.04 | 145 | 2.41 × 10^{7} |

0.05 | 150 | 9.77 × 10^{6} |

0.06 | 155 | 4.01 × 10^{6} |

0.07 | 160 | 1.47 × 10^{6} |

0.09 | 165 | 6.67 × 10^{5} |

0.09 | 170 | 4.63 × 10^{5} |

0.11 | 185 | 2.24 × 10^{5} |

0.14 | 195 | 5.19 × 10^{4} |

Parameter | Fatigue Strength Provided by Threshold Method (MPa) | Fatigue Life Estimated (Number of Cycles) | Fatigue Life Estimated at 10^{7} by Classical SN Curve (MPa) |
---|---|---|---|

S_{0} | 145.00 | >10^{7} | 148.30 |

S_{1} | 166.67 | <10^{7}; ~10^{6} | |

S_{2} | 146.67 | >10^{7} |

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**MDPI and ACS Style**

De Finis, R.; Palumbo, D.; Serio, L.M.; De Filippis, L.A.C.; Galietti, U.
Correlation between Thermal Behaviour of AA5754-H111 during Fatigue Loading and Fatigue Strength at Fixed Number of Cycles. *Materials* **2018**, *11*, 719.
https://doi.org/10.3390/ma11050719

**AMA Style**

De Finis R, Palumbo D, Serio LM, De Filippis LAC, Galietti U.
Correlation between Thermal Behaviour of AA5754-H111 during Fatigue Loading and Fatigue Strength at Fixed Number of Cycles. *Materials*. 2018; 11(5):719.
https://doi.org/10.3390/ma11050719

**Chicago/Turabian Style**

De Finis, Rosa, Davide Palumbo, Livia Maria Serio, Luigi A. C. De Filippis, and Umberto Galietti.
2018. "Correlation between Thermal Behaviour of AA5754-H111 during Fatigue Loading and Fatigue Strength at Fixed Number of Cycles" *Materials* 11, no. 5: 719.
https://doi.org/10.3390/ma11050719