# Numerical Investigation of the Influence of Fatigue Testing Frequency on the Fracture and Crack Propagation Rate of Additive-Manufactured AlSi10Mg and Ti-6Al-4V Alloys

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials Processing and Characterization

_{t}the hatch distance, and t the layer thickness. High-quality components with a relative density of more than 99.5% for both alloys were produced using an improved scanning approach and settings. The authors investigated with secondary exposure experiments, which led to significant improvements in relative density as well as modification of microstructure and mechanical properties. The corresponding parameters can be found in [11]. On Schenck PC63M (45 kN) and Instron 8872 (10 kN) servohydraulic systems, low-frequency experiments were carried out for Ti-6Al-4V at 5 Hz and AlSi10Mg at 20 Hz. Nikon X TH 160 X-ray microcomputed tomography (µ-CT) was used to scan the specimens in the gauge length volume at 160 kV. The mean pore size for AlSi10Mg is 43.45 µm, and the standard deviation is 24.42 µm. Corresponding values for Ti-6Al-4V were 68.91 µm and 36.26 µm, respectively. The relative densities for AlSi10Mg and Ti-6Al-4V were 99.94% and 99.97%, respectively, in a specimen with a gauge section diameter of 5 mm. To manage the high-strain rate cyclic deformation temperature caused by deformation, high-frequency tests were performed on a Shimadzu USF-2000A ultrasonic system using pressurized dry air and a pulse:pause ratio of 1:1 [12,13]. More information on specimen shapes and experimental settings are provided in [11,14,15].

^{3}GPa and a Poisson’s ratio of 0.07 to demonstrate an example of elastic modulus determination (Figure 1). Equation (7) specifies a fixed 68° semi-apex angle. First, unloading’s maximum depth of 1.893 µm was taken into account in the calculation of ${h}_{c}$. The elastic modulus for AlSi10Mg in Figure 1a is ~83 GPa since $P$ is equal to the highest load after the first unloading. Figure 1b show that the elastic modulus of Ti-6Al-4V is ~112 GPa. The elastic modulus obtained from the conventional tensile test was greater in the case of Ti-6Al-4V but lower in the case of AlSi10Mg [11,21]. The same procedure was used to measure mechanical characteristics for functionally graded binary alloys with second exposure treatments [11]. The benefit of this method was the speed and efficiency with which the effect of process parameters on mechanical qualities could be monitored [22]. The elastoplastic properties of metals and alloys were extracted from the obtained data using an instrumented indentation method in deep neural networks [23]. In order to convert hardness into yield strength, a constraint factor was also utilized [24]. Microstructure flow characteristics may be determined via instrumented indentation, which isolates the effects of defects from process factors.

#### 2.2. The Extended Finite Element Method

## 3. Results

## 4. Discussion

## 5. Summary

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Sample Availability

## References

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**Figure 2.**XFEM model 2D mesh with enhanced nodes and radius [25].

**Figure 5.**Crack portion of a triangular crack portion of a triangular crack: (

**a**) fractured element; (

**b**) intersection points.

**Figure 6.**Crack length and width in a four-cornered crack segment: (

**a**) fractured element; (

**b**) intersection points.

**Figure 8.**Influence of loading amplitude on the crack area evolution during low-frequency fatigue loading: (

**a**) AlSi10Mg and (

**b**) Ti-6Al-4V.

**Figure 9.**At 20 kHz, the loading amplitude has a significant impact on the propagation of cracks: (

**a**) AlSi10Mg and (

**b**) Ti-6Al-4V are available.

**Figure 12.**The geometry of the crack during its fatigue propagation as obtained numerically of Ti-6Al-4V at 800 MPa of 5 Hz.

**Figure 13.**Fractographich morphology of fatigue cracking showing crack geometry: (

**a**,

**b**) AlSi10Mg —120 MPa; (

**c**,

**d**) Ti-6Al-4V—800 MPa.

**Table 1.**Laser scanning parameters used to construct AlSi10Mg and Ti-6Al-4V alloy specimens in a single exposure procedure.

Power | Scanning Speed | Spot Size | Hatching Distance | Layer Thickness | |
---|---|---|---|---|---|

P (W) | vs (mm/s) | D (mm) | h_{t}(mm) | t (mm) | |

AlSi10Mg | 350 | 1200 | 0.083 | 0.190 | 0.050 |

Ti-6Al-4V | 240 | 1200 | 0.082 | 0.105 | 0.060 |

mm/Cycle | ${\mathit{c}}_{3}\text{}[{\mathbf{Cycle}}^{-1}\xb7{\mathbf{J}}^{-1}]$ | ${\mathit{c}}_{4}$ [-] |
---|---|---|

AlSi10Mg (20 Hz) | 4.2 × 10^{−5} | 1.2 |

(20 kHz) | 7.6 × 10^{−7} | 1.2 |

Ti-6Al-4V (5 Hz) | 2.1 × 10^{−6} | 1.685 |

(20 kHz) | 1.22 × 10^{−8} | 1.685 |

Experimental | Numerical | |
---|---|---|

AlSi10Mg | 41,288 | 51,463 |

140 MPa | ||

100 MPa | 220,475 | 234,895 |

Ti-6Al-4V | ||

800 MPa | 13,113 | 12,316 |

500 MPa | 51,159,835 | 76,693,033 |

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**MDPI and ACS Style**

Awd, M.; Walther, F.
Numerical Investigation of the Influence of Fatigue Testing Frequency on the Fracture and Crack Propagation Rate of Additive-Manufactured AlSi10Mg and Ti-6Al-4V Alloys. *Solids* **2022**, *3*, 430-446.
https://doi.org/10.3390/solids3030030

**AMA Style**

Awd M, Walther F.
Numerical Investigation of the Influence of Fatigue Testing Frequency on the Fracture and Crack Propagation Rate of Additive-Manufactured AlSi10Mg and Ti-6Al-4V Alloys. *Solids*. 2022; 3(3):430-446.
https://doi.org/10.3390/solids3030030

**Chicago/Turabian Style**

Awd, Mustafa, and Frank Walther.
2022. "Numerical Investigation of the Influence of Fatigue Testing Frequency on the Fracture and Crack Propagation Rate of Additive-Manufactured AlSi10Mg and Ti-6Al-4V Alloys" *Solids* 3, no. 3: 430-446.
https://doi.org/10.3390/solids3030030