# Morphological and Crystallographic Effects in the Laser Powder-Bed Fused Stainless Steel Microstructure

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Material Testing

## 3. Constitutive Description of the Material

#### 3.1. Principles of Continuum Mechanics

#### 3.2. Phenomenological Constitutive Law

## 4. Virtual Material Testing

#### 4.1. Voronoi Tessellation

#### 4.2. Meshing and Boundary Conditions

## 5. Results and Discussion

#### 5.1. Morphological Effects

#### 5.2. Crystallographic Effects

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Parameter sets employed for irradiation in laser powder-bed fusion for processing of the austenitic stainless steel AISI 316L/1.4404 [2]. Common to all parameter sets is a layer thickness of 30 $\mathsf{\mu}$m, mounting plate temperature of 200 ${}^{\circ}$C, nitrogen as the inert gas, and a scan vector length of 10 mm.

Parameter | Scan | Laser | Hatch | Rotation | Energy |
---|---|---|---|---|---|

Set | Speed, mm/s | Power, W | Dist., mm | Angle Inc., ${}^{\circ}$ | Density, J/mm${}^{3}$ |

Contour | 400 | 100 | 0.09 | – | 92.6 |

Core | 800 | 200 | 0.12 | 33 | 69.4 |

Final layer | 400 | 300 | 0.10 | – | 250.0 |

Support | 875 | 200 | – | – | – |

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**Figure 1.**EBSD inverse pole figure mapping showing the morphologically and crystallographically highly textured stainless steel microstructure processed by laser powder-bed fusion. The grains are elongated in the build direction (z-direction) and exhibit a preferred orientation in the <001> direction.

**Figure 2.**Flat tensile specimens with different orientations to the build direction (z-direction). The exact orientations are specified by the angles 0${}^{\circ}$, 45${}^{\circ}$, and 90${}^{\circ}$ in the x-z plane. Note that the designations for the 0${}^{\circ}$ and 90${}^{\circ}$ loading have been reversed compared to the experiment [2].

**Figure 3.**Virtual microstructures of an austenitic stainless steel consisting of 150 grains with a columnar (

**A**), a mixed columnar/equiaxial (

**B**,

**C**), and an equiaxial shape (

**D**). This is completed by a strongly regular columnar (

**E**) and an equiaxial grain shape (

**F**) with respect to grain size. Both, a columnar and an equiaxed grain, are highlighted.

**Figure 4.**Grain size distribution of the virtual stainless steel microstructures (

**A**)–(

**F**), together with the experimental data obtained from the EBSD analysis. Note that all distributions consistently range from 0 $\mathsf{\mu}$m to 80 $\mathsf{\mu}$m.

**Figure 5.**Young’s modulus for different virtual microstructures and loading directions with error bars for microstructures E and F. All microstructures feature a random crystallographic texture.

**Figure 6.**Yield strength for different virtual microstructures and loading directions considered, with error bars for microstructures E and F. All microstructures feature a random crystallographic texture.

**Figure 7.**Macroscopic stress-strain behaviour of the virtual microstructures E and F under the loading directions 0${}^{\circ}$ and 90${}^{\circ}$ with magnification of the hardening behaviour. All microstructures feature a random crystallographic texture.

**Figure 8.**Young’s modulus for different virtual microstructures and loading directions considered, with error bars for microstructures E and F. While most of the microstructures possess a <001> fibre texture, microstructures D and F are assigned a random grain orientation. Experimental results are taken from Reference [2].

**Figure 9.**Yield strength for different virtual microstructures and loading directions considered, with error bars for microstructures E and F. While most of the microstructures possess a <001> fibre texture, microstructures D and F are assigned a random grain orientation. Experimental results are taken from Reference [2].

**Figure 10.**Macroscopic stress-strain behaviour of the virtual microstructures E and F under the loading directions 0${}^{\circ}$ and 90${}^{\circ}$ with magnification of the hardening behaviour. While microstructure E possesses a <001> fibre texture, microstructure F is assigned a random grain orientation.

**Figure 11.**Experimentally determined macroscopic stress-strain behaviour for the loading directions 0${}^{\circ}$, 45${}^{\circ}$, and 90${}^{\circ}$ with magnification of the hardening behaviour. Experimental results are taken from Reference [2].

**Figure 12.**Macroscopic shear stress-strain behaviour of the virtual microstructures E and F under pure shear loading (45${}^{\circ}$) with magnification of the hardening behaviour. While microstructure E possesses a <001> fibre texture, microstructure F is assigned a random grain orientation.

**Figure 13.**Relative frequency of the von Mises stress distribution within the virtual microstructures E and F under pure shear loading (45${}^{\circ}$) at a macroscopic strain of 20%. While microstructure E possesses a <001> fibre texture, microstructure F is assigned a random grain orientation. The von Mises stresses shown in the deformed microstructure range from 0 MPa (white) to 1400 MPa (black).

**Table 1.**Chemical composition of the austenitic stainless steel AISI 316L/1.4404 in wt.-%, balance Fe.

Element | C | Cr | Ni | Mo | Mn | Si |
---|---|---|---|---|---|---|

Content, wt.-% | <0.03 | 17.6 | 11.1 | 2.3 | 1.2 | 0.6 |

**Table 2.**Constitutive parameters for the mechanical behaviour of the stainless steel 316L. The values for the elastic constants and the Hall-Petch constant are taken from Wang et al. [23].

Property | Value | Unit |
---|---|---|

${C}_{11}$ | 260 | GPa |

${C}_{12}$ | 111 | GPa |

${C}_{44}$ | 77 | GPa |

${\dot{\gamma}}_{0}$ | 0.001 | 1/s |

n | 20 | - |

a | 1.75 | - |

${h}_{0}$ | 1000 | MPa |

${\tau}_{\mathrm{c},0}$ | 178.75 | MPa |

${\tau}_{\mathrm{s},0}$ | 327.41 | MPa |

${k}_{\mathrm{c}}$ | 8.02 | $\mathrm{MPa}\sqrt{\mathrm{mm}}$ |

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**MDPI and ACS Style**

Fischer, T.; Hitzler, L.; Werner, E.
Morphological and Crystallographic Effects in the Laser Powder-Bed Fused Stainless Steel Microstructure. *Crystals* **2021**, *11*, 672.
https://doi.org/10.3390/cryst11060672

**AMA Style**

Fischer T, Hitzler L, Werner E.
Morphological and Crystallographic Effects in the Laser Powder-Bed Fused Stainless Steel Microstructure. *Crystals*. 2021; 11(6):672.
https://doi.org/10.3390/cryst11060672

**Chicago/Turabian Style**

Fischer, Tim, Leonhard Hitzler, and Ewald Werner.
2021. "Morphological and Crystallographic Effects in the Laser Powder-Bed Fused Stainless Steel Microstructure" *Crystals* 11, no. 6: 672.
https://doi.org/10.3390/cryst11060672