# Ratcheting–Fatigue Damage Assessment of Additively Manufactured SS304L and AlSi10Mg Samples under Asymmetric Stress Cycles

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Fatigue Damage Assessment

#### 2.2. Ratcheting Damage Assessment

#### 2.2.1. Isotropic Hardening Description

#### 2.2.2. Ahmadzadeh–Varvani (A–V) Kinematic Hardening Rule

#### 2.2.3. Chaboche Hardening Rule

#### 2.3. Fatigue–Ratcheting Interaction

## 3. Results and Discussion

#### 3.1. Materials, Tests, and Ratcheting Data

#### 3.2. Backstress and Yield Surface Translation

#### 3.3. Finite Element Analysis

#### 3.4. Ratcheting–Fatigue Damage Curves

#### Contribution of Fatigue and Ratcheting Damage

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Stress range versus number of cycles to failure for horizontal (H) and vertical (V) AM samples of (

**a**) SS304L and (

**b**) AlSi10Mg.

**Figure 4.**Measured and predicted stress-controlled stress–strain hysteresis loops for (

**a**) SS304L and (

**b**) AlSi10Mg alloys.

**Figure 5.**Yield surface evolution of vertical (V) and horizontal (H) samples made of AlSi10Mg alloy.

**Figure 6.**Backstress evolution through the A–V and Chaboche hardening rules for vertical (V) and horizontal (H) AM samples made of AlSi10Mg.

**Figure 8.**Predicted and simulated damage upper curves and predicted fatigue damage lower curve for vertical and horizontal samples of (

**a**,

**b**) SS304L and (

**c**,

**d**) AlSi10Mg.

**Figure 9.**Bar charts to partition fatigue and ratcheting damage values at different stress levels and AM specimen directions for (

**a**,

**b**) SS304L and (

**c**,

**d**) AlSi10Mg.

Material | Fatigue Coefficients | Models | Parameters and Coefficients |
---|---|---|---|

${\sigma}_{f}^{,}=4000$ | Isotropic | $Q\left(\mathrm{MPa}\right)=90$, $b=13.5$ | |

304L Stainless Steel (Horizontal samples) | ${\epsilon}_{f}^{,}=$ 0.016 | A–V | $C\left(\mathrm{GPa}\right)=16$, ${\gamma}_{1}=195$, ${\gamma}_{2}=20$ |

$b=$ −0.06 $c=$ −0.3 | Chaboche | ${C}_{1-3}\left(\mathrm{GPa}\right)=44,37,25$, ${\gamma}_{1-3}^{\prime}=110,115,0$ | |

${\sigma}_{f}^{,}=$ 4200 | Isotropic | $Q\left(\mathrm{MPa}\right)=79$, $b=12.5$ | |

304L Stainless Steel (Vertical samples) | ${\epsilon}_{f}^{,}=$ 0.026 | A–V | $C\left(\mathrm{GPa}\right)=17$, ${\gamma}_{1}=187.5$, ${\gamma}_{2}=10$ |

$b=$ −0.184 $c=$ −0.2 | Chaboche | ${C}_{1-3}\left(\mathrm{GPa}\right)=50,35,25$, ${\gamma}_{1-3}^{\prime}=100,120,0$ | |

${\sigma}_{f}^{,}=$ 330 | Isotropic | $Q\left(\mathrm{MPa}\right)=260$, $b=3.5$ | |

AlSi10Mg (Horizontal samples) | ${\epsilon}_{f}^{,}=$ 0.024 | A–V | $C\left(\mathrm{GPa}\right)=15$, ${\gamma}_{1}=90$, ${\gamma}_{2}=40$ |

$b=$ −0.005 −0.2 | Chaboche | ${C}_{1-3}\left(\mathrm{GPa}\right)=180,120,33$, ${\gamma}_{1-3}^{\prime}=1200,600,0$ | |

${\sigma}_{f}^{,}=$ 320 | Isotropic | $Q\left(\mathrm{GPa}\right)=250$, $b=2.5$ | |

AlSi10Mg (Vertical samples) | ${\epsilon}_{f}^{,}=$ 0.01 | A–V | $C\left(\mathrm{GPa}\right)=12$, ${\gamma}_{1}=96$, ${\gamma}_{2}=30$ |

$b=$ −0.005 $c=$ −0.2 | Chaboche | ${C}_{1-3}\left(\mathrm{GPa}\right)=140,100,28$, ${\gamma}_{1-3}^{\prime}=1500,800,0$ |

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**MDPI and ACS Style**

Servatan, M.; Hashemi, S.M.; Varvani-Farahani, A.
Ratcheting–Fatigue Damage Assessment of Additively Manufactured SS304L and AlSi10Mg Samples under Asymmetric Stress Cycles. *Metals* **2023**, *13*, 1534.
https://doi.org/10.3390/met13091534

**AMA Style**

Servatan M, Hashemi SM, Varvani-Farahani A.
Ratcheting–Fatigue Damage Assessment of Additively Manufactured SS304L and AlSi10Mg Samples under Asymmetric Stress Cycles. *Metals*. 2023; 13(9):1534.
https://doi.org/10.3390/met13091534

**Chicago/Turabian Style**

Servatan, M., S. M. Hashemi, and A. Varvani-Farahani.
2023. "Ratcheting–Fatigue Damage Assessment of Additively Manufactured SS304L and AlSi10Mg Samples under Asymmetric Stress Cycles" *Metals* 13, no. 9: 1534.
https://doi.org/10.3390/met13091534