#
Application of a
area
-Approach for Fatigue Assessment of Cast Aluminum Alloys at Elevated Temperature

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- Investigation of the fatigue strength of Al-Si cast materials at an elevated temperature of 150 ${}^{\circ}$C
- Assessment of statistically defect distribution regarding spatial extent and shape
- Investigation of damage mechanisms at enhanced operating temperatures
- Evaluation of the material constants ${C}_{1}$, ${C}_{2}$ and m of Murakami’s $\sqrt{area}$ concept for elevated temperatures

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. sDAS and Metallographic Analysis

#### 2.3. Quasi-Static and Fatigue Testing

#### 2.4. X-ray Computed Tomography

## 3. Results

#### 3.1. Tensile Tests

#### 3.2. Hardness Measurements

#### 3.3. Fatigue Tests

#### 3.4. Fatigue Assessment Model

## 4. Discussion

## 5. Conclusions

- The statistically evaluated fatigue strength of all tested alloys drops when being exposed at elevated temperatures compared to fatigue lifetime at room temperature.
- A significant change in damage mechanism at elevated temperatures is observed. A major part of the specimens taken from both EN AC-46200 Pos #1, as well as EN AC-45500 Pos #1, maintain slipping areas as crack origins.
- While the original $\sqrt{area}$ model proposed by Murakami provides a sound fit for room temperature with a slope of $m=3$, the slope changes at elevated temperature. The estimated slope ${m}_{T}\approx 4$ suggests an increased long crack threshold at elevated temperature, caused by more pronounced plasticity-induced crack closure effects. Therefore, the impact of increasing defect sizes on the anticipated fatigue resistance generally declines at elevated temperatures.
- Comparing the fatigue strength of the introduced extension of Murakami’s model for higher operating temperatures, the experiments reveal a proper relationship. The mean value of the suggested model turns out to be slightly conservative.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Abbreviations

RT | Room temperature |

ET | Elevated temperature |

$\lambda $ | Location parameter of the Gumbel distribution |

$\delta $ | Scale parameter of the Gumbel distribution |

GEV | Generalized Extreme Value distribution |

$\xi ,\sigma ,\mu $ | Shape, scale, and location parameter of the GEV |

${\sigma}_{f,1\times {10}^{7}}$ | Long-life fatigue strength amplitude at $1\times 10{}^{7}$ load cycles |

$\Delta {\sigma}_{1\times {10}^{7}}$ | Long-life fatigue strength range at $1\times 10{}^{7}$ load cycles |

${\sigma}_{a}$ | Fatigue strength amplitude |

HV | Vickers hardness |

${C}_{1}$, ${C}_{2}$,m | Constants of the $\sqrt{area}$ approach by Murakami |

sDAS | Secondary dendrite arm spacing |

YS | Yield strength |

UTS | Ultimate tensile strength |

HCF | High-cycle fatigue |

E | Young’s modulus |

A | Fracture elongation |

${N}_{D}$ | Number of load cycles at transition knee point of S/N-curve |

N | Number of load cycles until failure |

${k}_{1}$ | Slope in the finite life region of S/N-curve |

${T}_{S}$ | Scatter band of S/N-curve in the HCF region |

BHN | Brinell hardness number |

SEM | Scanning-electron-microscopy |

XCT | X-ray computed tomography |

${d}_{eq}$ | Equivalent circle diameter |

${d}_{max}$ | Maximal spatial extent of an inhomogeneity |

$\varphi $ | Shape factor |

n | Number of defects |

${C}_{1,T}$, ${C}_{2,T}$,${m}_{T}$ | Parameters of the extended $\sqrt{area}$ approach for elevated temperatures |

${K}_{}$ | Stress intensity factor |

${K}_{max}$ | Maximal stress intensity factor |

$\Delta {K}_{th,lc}$ | Long crack threshold |

$\Delta {K}_{eff}$ | Effective crack threshold |

Y | Geometry factor |

$\Delta {r}_{pl}$ | Cyclic plastic zone |

${r}_{pl}$ | Monotonic plastic zone |

${T}_{m}$ | Scatter band of the validation of the fatigue assessment model |

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**Figure 9.**Defect size measurement methodology and representative fracture-initiating micropore at Pos#3.

**Figure 14.**Defect correlated fatigue lifetime model with evaluated coefficient m at elevated temperature.

Alloy | Si [%] | Cu [%] | Fe [%] | Mn [%] | Mg [%] | Ti [%] | Al [-] |
---|---|---|---|---|---|---|---|

EN AC-46200 | 7.5–8.5 | 2.0–3.5 | 0.8 | 0.15–0.65 | 0.05–0.55 | 0.25 | balance |

EN AC-45500 | 6.5–7.5 | 0.2-0.7 | 0.25 | 0.15 5 | 0.45 | 0.20 | balance |

Part | Position | Alloy | Modifier | Heat Treatment | sDAS [μm] | |
---|---|---|---|---|---|---|

CH | Pos #1 | EN AC-46200 | Sr | T5 | 24 ± 4.8 | |

CC | Pos #2 | EN AC-46200 | Sr | T6 | 30 ± 7.3 | |

CC | Pos #3 | EN AC-46200 | Sr | T6 | 72 ± 24.9 | |

CH | Pos #1 | EN AC-45500 | Sr | T6 | 27 ± 6.6 |

Abbreviation | Temperature | UTS [MPa] | YS [MPa] | A [%] | |
---|---|---|---|---|---|

EN AC-46200 Pos #2 | RT | 326 | 277 | 1.58 | |

EN AC-46200 Pos #2 | ET | 265 | 245 | 2.96 | |

EN AC-46200 Pos #3 | RT | 208 | 207 | 0.18 | |

EN AC-46200 Pos #3 | ET | 187 | 187 | 0.19 | |

EN AC-46200 Pos #1 | RT | 287 | 198 | 2.31 | |

EN AC-46200 Pos #1 | ET | 234 | 184 | 5.25 | |

EN AC-45500 Pos #1 | RT | 334 | 273 | 6.78 | |

EN AC-45500 Pos #1 | ET | 259 | 233 | 9.55 |

Abbreviation | Temperature | ${\mathit{\sigma}}_{1\times {10}^{7},\mathit{norm}}$ | ${\mathit{N}}_{\mathit{D}}$ | ${\mathit{k}}_{1}$ | $\frac{1}{{\mathit{T}}_{\mathit{s}}}$ |
---|---|---|---|---|---|

EN AC-46200 Pos#2 | RT | 0.245 | $5.71\times {10}^{5}$ | 3.58 | 1.256 |

EN AC-46200 Pos#2 | ET | 0.241 | $1.75\times {10}^{6}$ | 5.85 | 1.391 |

EN AC-46200 Pos#3 | RT | 0.176 | $3.92\times {10}^{6}$ | 5.13 | 1.278 |

EN AC-46200 Pos#3 | ET | 0.172 | $2.68\times {10}^{6}$ | 6.41 | 1.210 |

EN AC-46200 Pos#1 | RT | 0.332 | $5.29\times {10}^{5}$ | 7.40 | 1.147 |

EN AC-46200 Pos#1 | ET | 0.244 | $6.16\times {10}^{6}$ | 10.65 | 1.115 |

EN AC-45500 Pos#1 | RT | 0.348 | $9.99\times {10}^{5}$ | 6.22 | 1.140 |

EN AC-45500 Pos#1 | ET | 0.291 | $4.27\times {10}^{6}$ | 7.48 | 1.206 |

Abbreviation | $\mathit{\xi}$ | $\mathit{\sigma}$ | $\mathit{\mu}$ | $\mathit{\varphi}$ | |
---|---|---|---|---|---|

EN AC-46200 Pos #1 | 0.03 | 39.03 | 104.60 | 0.52 | |

EN AC-46200 Pos #2 | −0.12 | 29.83 | 85.10 | 0.48 | |

EN AC-46200 Pos #3 | −0.19 | 168.57 | 444.88 | 0.60 | |

EN AC-45500 Pos #1 | 0.06 | 14.50 | 36.08 | 0.49 |

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**MDPI and ACS Style**

Aigner, R.; Garb, C.; Leitner, M.; Stoschka, M.; Grün, F.
Application of a *Metals* **2018**, *8*, 1033.
https://doi.org/10.3390/met8121033

**AMA Style**

Aigner R, Garb C, Leitner M, Stoschka M, Grün F.
Application of a *Metals*. 2018; 8(12):1033.
https://doi.org/10.3390/met8121033

**Chicago/Turabian Style**

Aigner, Roman, Christian Garb, Martin Leitner, Michael Stoschka, and Florian Grün.
2018. "Application of a *Metals* 8, no. 12: 1033.
https://doi.org/10.3390/met8121033