# Fatigue Behaviour of Aluminium Members with Different Notch Root Shapes

^{1}

^{2}

^{3}

^{4}

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Study

#### 2.1. General

#### 2.2. Material and Specimen Geometry

#### 2.3. Monotonic Testing

- LVDT-1,2,3,4 were located at the level of the application of the load.
- LVDT-1—absolute displacement at the back of the profile behind the notch in the direction of the load.
- LVDT-2—absolute displacement at the tip of the specimen in the direction of the load
- The differential of LVDT-1 − LVDT-2 measures the opening of the notch under the load.
- LVDT-3—absolute displacement at the back of the profile behind the notch perpendicular to the direction of the load.
- LVDT-4—absolute displacement at the top end of the specimen perpendicular to the direction of the load.
- The differential of LVDT-3 − LVDT-4 measures the rotation of the tip of the specimen under load.
- LVDT-5—absolute displacement of the upper support of the specimen in the direction of the load (upper angle in the steel frame).
- LVDT-6—absolute displacement of the lower support of the specimen in the direction of the load (lower angle in the steel frame).
- The displacements of LVDT-5 and LVDT-6 are used to confirm the sufficient stiffness of the supporting steel frame.
- The differential of LVDT-5 − LVDT-6 determines the rotation of the supporting steel frame in order to distinguish between movement at the tip of the specimen due to the rotation of the support and movement due to the bending of the specimen.

#### 2.4. Cyclic Testing

#### 2.4.1. Load History

_{max}of sharp notched specimens from monotonic testing (Table 2). The maximal force for specimen M_N1_1 was equal to 6.78 kN.

_{max}, corrected for the appropriate partial factor, was chosen for design load F for the load history. According to Eurocode 0 [16], the value of the partial factor for wind action, γ

_{f}, is 1.5. The design force for cyclic testing is then F = F

_{max}/γ

_{f}= 6.78/1.5 = 4.50 kN. The load history for the cyclic testing is provided in Table 4.

#### 2.4.2. Cyclic Test Specimens

_{1}and δ

_{2}(readings of LVDT_1 and LVDT_2, respectively) for each set of cycles (single Fi) in each series for the specimen with the sharp notch (C_N1_1). It can be noted that there was a slight increase in the opening of the notch (δ1-δ2) after the first series for Fi = 90% F and Fi = 40% F load cycles. This could be caused by the onset of the crack in the root of the notch, but this pattern was not observed on other specimens and there is no definite proof of that hypothesis. For subsequent series of cycle steps, it can be observed that a stable value of measured deflections and slight fluctuations were attributed to the tolerance of the applied force due to the precision limits of the hydraulic press.

## 3. Numerical Analysis

_{t}–ε

_{t}, for the material used (aluminium alloy EN AW 6063 T6 (extrusion)) were calculated from engineering values measured on dog-bone coupons (Table 5), where L

_{0}is the gauge length, L is the elongated length, A

_{0}is original cross-section area of the specimen, and A is true cross-section area of the specimen at strain ε:

- Higher stress for the Al1 true curve, which had higher stress in the plastic zone.
- Higher strains for the standardised curve, which had lower proof stress, thus yielding earlier.

## 4. Fatigue Resistance According to Eurocode 9

_{1}= 7—inverse slope constant of logΔσ-logN fatigue strength curve for

^{6}cycles

^{5}times, so the endurance, N

_{i}, could calculated as per [21], according to Annex F for low cycle fatigue range:

_{c}= 100 MPa—reference value of fatigue strength at 2 × 10

^{6}cycles

_{min}= 0 and σ

_{max}> 0

_{c(R)}is used:

_{c(R)}= f(R) Δσ

_{c}

_{c(R)}= 120 MPa

- Δσ
_{i}—stress range for the principal stresses at the detail, max hotspot stress range at the root of the notch in numerical models, [21] - γ
_{Ff}= 1.0—partial factor for fatigue loads, [21] - γ
_{Mf}= 1.0—partial factor for materials, [21] - m
_{0}= m_{1}= 7—inverse slope of logΔσ-logN curve at 10^{3}≤ N ≤ 10^{5}cycles

_{L}:

- n
_{i}—number of cycles of stress range Δσ_{i} - N
_{i}—endurance under stress range Δσ_{i}

_{i}) for each cycle, the resulting von Mises stresses from the numerical model were used to generate stress–strain curves through the polynomial regression of each notch type. Figure 24 shows the regression curve for the sharp notch. Hotspot stress ranges (Δσ

_{i}) for each cycle were assessed from the obtained curves. Models with the true stress–strain curve for dog-bone coupon Al1 were used.

_{i}) for each cycle was assessed from the respective regression curve. The endurance (N

_{i}) for each cycle was calculated using Formula (7), and the total damage for each cycle was calculated using Formula (8). The results of this procedure for the sharp notch are shown in Table 9.

_{L}, was 0.259, which is lower than 1.0; therefore, the safe life design was achieved, and it can be assumed that the element was not likely to fail due to fatigue during its design life (T

_{L}) of 50 years. The expected safe life (T

_{S}) is:

_{S}= T

_{L}/D

_{L}= 193 years

## 5. Discussion

## 6. Conclusions

- Specimens were first tested in the monotonic regime until failure in order to assess their maximal load capacity. As expected, specimens with a sharp root had a substantially lower failure load, roughly 20% lower than that of the other specimens.
- Specimens were then tested in the cyclic regime in order to assess their fatigue resistance. The applied variable load history is typical for a 50-year exposure to wind in the UK, which was the actual in-use condition of the original profiles. The selected magnitude of the load history was derived from the lowest monotonic failure load of the specimen with the sharp root, reduced by the partial factor for the wind load.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**(

**a**) Cross-section of the profile, (

**b**) semi-circular notch in the profile, (

**c**) view of the profile.

**Figure 6.**Geometry of the (

**a**) sharp notch, N1, (

**b**) rounded notch, N2, and (

**c**) semi-circular notch (mm).

**Figure 10.**Fracture in monotonic tests: (

**a**) Sharp notch specimen M_N1_1; (

**b**) Semi-circular specimen M_N3.

**Figure 13.**Microcracking of the surface of specimens with the rounded and semi-circular root: (

**a**) C_N2_1; (

**b**) C_N3_1.

**Figure 15.**Element mesh: (

**a**) entire model, (

**b**) upper part, and (

**c**) mesh around the root of the notch.

**Figure 17.**Strain in the model of the sharp notch: (

**a**) True stress–strain curve (coupon Al1), load 5.5 kN; (

**b**) standardised stress–strain curve (alloy EN AW 6063 T6), load 5.0 kN.

**Figure 18.**Strain in the model of the rounded notch: (

**a**) True stress–strain curve (coupon Al1), load 5.5 kN; (

**b**) nominal stress–strain curve (alloy EN AW 6063 T6), load 5.0 kN.

**Figure 19.**Strain in the model of the semi-circular notch 55 mm: (

**a**) True stress–strain curve (coupon Al1), load 5.5 kN; (

**b**) nominal stress–strain curve (alloy EN AW 6063 T6), load 5.0 kN.

**Figure 20.**Strain in the model of the semi-circular notch 67.5 mm: (

**a**) True stress–strain curve (coupon Al1), load 5.0 kN; (

**b**) nominal stress–strain curve (alloy EN AW 6063 T6), load 4.5 kN.

Coupon/Source | R_{p0,2} | R_{m} | A |
---|---|---|---|

[MPa] | [MPa] | [%] | |

Coupon Al1 | 207.7 | 229.8 | 10.1 |

Coupon Al2 | 211.0 | 233.7 | 8.0 |

Coupon Al3 | 222.1 | 241.9 | 9.7 |

EN 755-2 [6] | 170.0 | 215.0 | 8.0 |

Supplier’s certificate | 216.6 | 235.7 | 11.8 |

Specimen | Shape of Notch N | Width of Notch (mm) | Depth of Notch (mm) | Radius at the Root of Notch (mm) | |
---|---|---|---|---|---|

Monotonic Test | Cyclic Test | ||||

M_N1_1 | C_N1_1 | Sharp (N1) | 25 | 55 | 0 |

M_N1_2 | C_N1_2 | ||||

- | C_N1_3 | ||||

M_N2_1 | C_N2_1 | Rounded (N2) | 55 | 3.5 | |

M_N2_2 | C_N2_2 | ||||

M_N3 | C_N3_1 | Semi-circular (N3) | 67.5 | 12.5 | |

- | C_N3_2 |

Specimen | Ultimate Load | Opening of the Notch LVDT-1 − LVDT-2, Figure 8. |
---|---|---|

(kN) | (mm) | |

M_N1_1 | 6.78 | 6.18 |

M_N1_2 | 6.99 | 3.78 |

M_N2_1 | 8.08 | 9.49 |

M_N2_2 | 8.61 | 9.45 |

M_N3 | 8.45 | 20.20 |

Loading Step | Number of Cycles | Percentage of the Design Load F | Nominal Load F_{i} for Step i [kN] |
---|---|---|---|

1 | 1 | 90% | 4.05 |

2 | 960 | 40% | 1.80 |

3 | 60 | 60% | 2.70 |

4 | 240 | 50% | 2.25 |

5 | 5 | 80% | 3.60 |

6 | 14 | 70% | 3.15 |

7 | 1 | 100% | 4.50 |

Coupon | Engineering Stress R_{m} (MPa) | Corresponding True Stress σ_{t} (MPa) |
---|---|---|

Al1 | 229.8 | 243.9 |

Al2 | 233.7 | 245.9 |

Al3 | 241.9 | 258.0 |

Notch Shape | Strain [%] | |
---|---|---|

Nominal Stress–Strain Curve | True Stress–Strain Curve (Al1) | |

Sharp | 16.17 | 11.88 |

Rounded | 7.10 | 5.64 |

Semi-circular (depth 55 mm) | 2.88 | 2.42 |

Semi-circular (depth 67.5 mm) | 5.69 * | 5.62 |

Detail Type | Detail Category Δσ-m _{1} | Product Forms Constructional Detail Initiation Site | Stress Orientation | Stress Analysis | Execution Requirements | |
---|---|---|---|---|---|---|

1.6 | 100-7 | Notches, holes Surface irregularity | Parallel or normal to rolling or extrusion direction. | Account for stress concentration. | Surface free of sharp corners unless parallel to stress direction; edges free of stress raisers | No score marks transverse to stress orientation visual inspection |

Cycles | Total of Cycles n_{i} | Force (kN) |
---|---|---|

1 | 5 | 4.05 |

960 | 4800 | 1.80 |

60 | 300 | 2.70 |

240 | 1200 | 2.25 |

5 | 25 | 3.60 |

14 | 70 | 3.15 |

1 | 1 | 4.50 |

6401 |

Cycles | Force | Stress | Endurance | Damage |
---|---|---|---|---|

n_{i} | [kN] | [MPa] | N_{i} | D |

5 | 4.05 | 285.1 | 4679 | 0.00107 |

4800 | 1.80 | 221.5 | 27,410 | 0.17512 |

300 | 2.70 | 238.6 | 16,292 | 0.01841 |

1200 | 2.25 | 228.6 | 21,947 | 0.05468 |

25 | 3.60 | 267.9 | 7235 | 0.00346 |

70 | 3.15 | 252.1 | 11,083 | 0.00632 |

1 | 4.50 | 304.1 | 2981 | 0.00034 |

6401 | 0.25939 |

Notch Type | Total Damage D_{L} | Expected Safe Life T_{s} [Years] |
---|---|---|

Sharp | 0.259 | 193 |

Rounded | 0.192 | 260 |

Semi-circular 55 mm | 0.076 | 660 |

Semi-circular 67.5 mm | 0.144 | 348 |

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**MDPI and ACS Style**

Buljan, N.; Skejić, D.; Krolo, P.; Lukić, M.
Fatigue Behaviour of Aluminium Members with Different Notch Root Shapes. *Buildings* **2022**, *12*, 681.
https://doi.org/10.3390/buildings12050681

**AMA Style**

Buljan N, Skejić D, Krolo P, Lukić M.
Fatigue Behaviour of Aluminium Members with Different Notch Root Shapes. *Buildings*. 2022; 12(5):681.
https://doi.org/10.3390/buildings12050681

**Chicago/Turabian Style**

Buljan, Nebojša, Davor Skejić, Paulina Krolo, and Mladen Lukić.
2022. "Fatigue Behaviour of Aluminium Members with Different Notch Root Shapes" *Buildings* 12, no. 5: 681.
https://doi.org/10.3390/buildings12050681