# Comparative Multi-Modal, Multi-Scale Residual Stress Evaluation in SLM 3D-Printed Al-Si-Mg Alloy (RS-300) Parts

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Sample Manufacturing and Preparations

#### 2.2. Contour Method

#### 2.3. Hole Drilling and Laser Speckle Interferometry Method

^{−3}. Holes a few millimeters in diameter generate displacements of several micrometers that can be measured with sufficient accuracy. Electronic laser speckle-pattern interferometry technique applied for this purpose visualizes the interference fringe patterns generated by in-plane displacements. The corresponding interferograms were recorded by two symmetrical side detectors (digital cameras) when a diode laser of wavelength 532 nm was directed at the surface containing the drilled hole. The phase shift between the two surface states before and after drilling forms alternating dark and light interference patterns known as fringes. Typical interference fringe patterns used for residual stress determination at the point of drilling are shown in Figure 4. The number of fringes is linearly related with the diameter increment or decrement. These quantities are related by the multiplication factor $\frac{\lambda}{2\mathrm{sin}\theta}$, where $\lambda $ is the incident illumination light wavelength and 2$\theta $ is the angle between the incident and reflected beams [33]. Drilling was conducted on the cut plane as well as on the outer faces of the cut-in-half double tower specimens using a drill bit diameter of from 1.9 to 2.5 mm. The drilling depth was set equal to the drill bit diameter. The values of the hole diameter increment in the principal stress directions were used as the initial experimental information for further calculation of the principal residual stress components. The typical uncertainty inherent in the determination of the maximum in-plane principal residual stress component is in the order of 5%. The approach is thought to be valid for residual stress values that do not exceed 60% of the material yield stress.

#### 2.4. X-ray Diffraction Method

#### 2.5. Xe pFIB-DIC Micro-Ring-Core Drilling Method

^{2}was scanned using a 1024 × 1024 pixel matrix, corresponding to the scanning step of 0.5 µm.

^{−4}to 10

^{−2}using image datasets of up to 60 images for the ring-core diameters of 70 μm.

## 3. Results and Discussion

#### 3.1. Residual Stress Evaluation by the Contour Method

#### 3.2. Residual Stress Evolution by Hole Drilling and Laser Speckle Interferometry Method

#### 3.3. Residual Stress Evolution by X-ray Diffraction Method

^{2}typical for laboratory X-rays) in the middle of cut plane gives no spatial resolution, which potentially can be improved with dedicated setups utilizing fine focus tubes and advanced sample positioning systems. We consider these results as elective.

#### 3.4. Residual Stress Evolution by Xe pFIB Ring-Core Drilling Method

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

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**Figure 1.**The appearance of the double tower shape sample in the as-printed state: (

**a**) front view, (

**b**) side view, (

**c**) dimensions.

**Figure 2.**The appearance of the double tower sample (

**a**) before and (

**b**,

**c**) after EDM cutting: (

**b**) top view with the indicated cut plane (red line) and (

**c**) sectional view.

**Figure 3.**The appearance of double tower shaped sample as 3D models: (

**a**) before and (

**b**) after EDM cutting in half with the indicated primary coordinate system according to which all used methods are aligned.

**Figure 4.**(

**a**) general view of vertical outer face of the half-cut double tower perpendicular to the sectioning plane with the drill hole, and (

**b**,

**c**) interference fringe patterns obtained as a result of 1.9 mm diameter hole drilling: (

**b**) the horizontal in-plane displacement component and (

**c**) the vertical in-plane displacement component.

**Figure 5.**Appearance of the polished half-cut double tower sample: (

**a**) mounted in conductive resin for FIB-SEM studies, (

**b**) fixed in the goniometer-like sample holder for X-ray diffraction measurements.

**Figure 6.**Illustration of the distribution of the zz-component of residual stresses (

**a**,

**c**) and z-component of displacements (

**b**,

**d**) in the real (

**a**,

**b**) and continuously processed (

**c**,

**d**) geometry models, respectively.

**Figure 7.**Illustration of distribution of xx- (

**a**,

**c**) and yy- (

**b**,

**d**) components of residual stresses in the real (

**a**,

**b**) and continuous (

**c**,

**d**) geometry models, respectively.

**Figure 8.**Line plots of xx (s11), yy (s22), and zz (s33) components of residual stress along the (

**a**) horizontal (x) and (

**b**) vertical (y) lines illustrated by the dashed lines on the sectioned surface in Figure 12 below.

**Figure 10.**Details of X-ray measurement of residual stresses at the cut plane: (

**a**) measured $I~2\theta $ plot for the specimen (highlighted red plane $\left(420\right)$ was selected for the next calculations); (

**b**) ${\epsilon}_{HKL}~{\mathrm{sin}}^{2}\phi $ plot.

**Figure 11.**Details of Xe-pFIB ring-core drilling measurements of residual stresses at the cut plane: (

**a**) combined EBSD map with the Euler’ colors and milled ring, and (

**b**) measured relief strains with the fitting curve.

**Figure 13.**Comparison of all used methods: (

**a**) the locations of the measured points and the plotting line, superimposed on the contour map of the horizontal stress component reconstructed by the contour method; (

**b**) residual stress line plot.

N | Description of Location | $\mathit{\sigma}$, MPa |
---|---|---|

1 | Vertical outer face parallel to the cut plane | $120\text{}({\sigma}_{xx}$) |

2 | $118\text{}({\sigma}_{xx}$) | |

10 | $129\text{}({\sigma}_{xx}$) | |

3 | Vertical outer face perpendicular to the cut plane | $-31\text{}({\sigma}_{zz}$) |

5 | Cut plane | $-47\text{}({\sigma}_{xx}$) |

7 | $-17\text{}({\sigma}_{xx}$) | |

9 | Bottom of the base | $11\text{}({\sigma}_{xx}$) |

N | ${\mathit{\sigma}}_{\mathit{x}\mathit{x}},\text{}\mathbf{MPa}$ |
---|---|

H1 | 62.1 |

H2 | −4.9 |

H3 | −45.8 |

H4 | 33.4 |

H5 | 22.8 |

H6 | −78.7 |

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**MDPI and ACS Style**

Statnik, E.S.; Uzun, F.; Lipovskikh, S.A.; Kan, Y.V.; Eleonsky, S.I.; Pisarev, V.S.; Somov, P.A.; Salimon, A.I.; Malakhova, Y.V.; Seferyan, A.G.;
et al. Comparative Multi-Modal, Multi-Scale Residual Stress Evaluation in SLM 3D-Printed Al-Si-Mg Alloy (RS-300) Parts. *Metals* **2021**, *11*, 2064.
https://doi.org/10.3390/met11122064

**AMA Style**

Statnik ES, Uzun F, Lipovskikh SA, Kan YV, Eleonsky SI, Pisarev VS, Somov PA, Salimon AI, Malakhova YV, Seferyan AG,
et al. Comparative Multi-Modal, Multi-Scale Residual Stress Evaluation in SLM 3D-Printed Al-Si-Mg Alloy (RS-300) Parts. *Metals*. 2021; 11(12):2064.
https://doi.org/10.3390/met11122064

**Chicago/Turabian Style**

Statnik, Eugene S., Fatih Uzun, Svetlana A. Lipovskikh, Yuliya V. Kan, Sviatoslav I. Eleonsky, Vladimir S. Pisarev, Pavel A. Somov, Alexey I. Salimon, Yuliya V. Malakhova, Aleksandr G. Seferyan,
and et al. 2021. "Comparative Multi-Modal, Multi-Scale Residual Stress Evaluation in SLM 3D-Printed Al-Si-Mg Alloy (RS-300) Parts" *Metals* 11, no. 12: 2064.
https://doi.org/10.3390/met11122064