# Different Approaches for Manufacturing Ti-6Al-4V Alloy with Triply Periodic Minimal Surface Sheet-Based Structures by Electron Beam Melting

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. TPMS File Preparation

^{6}), thus creating a high-poly model. The design files of large size can in some cases cause memory issues of ARCAM Build Assembler software. Thus, the high-poly meshes generated with random polygon size and shape distribution required additional mesh optimization. For this purpose, the MeshLab software, an open-source Mesh Processing Tool [30], was used. The number of the vertices was steeply reduced to 10,000 for zero-thickness model and to 44,000 for 200 µm thick model, preserving the boundaries and the topology of the mesh. Topological errors, such as non-manifold faces, self-intersections, duplicate faces, etc., were also removed using the MeshLab.

#### 2.2. Finite Element Analysis

#### 2.3. Manufacturing

^{TM}mode’. In the latter case, the beam moves only through the short sector of the contour and ‘jumps’ away to melt another sector, repeating the operation many times to cover all needed contours. The main purpose for selecting single- or double- contours in continuous or Multibeam

^{TM}mode is the optimization of the process to obtain the smallest possible roughness of side surfaces of the components. It is clear that when using any mode for the manufacturing of lightweight and porous structures, careful parameter selection is needed to guarantee that the resulting element cross-sections are as close to the CAD design as possible. When the elements with a small cross-sectional area are EBM-manufactured using Melt Theme, automated file preprocessing can reduce the number of contours (in an automatic fashion) until only the hatch is left, minimizing the increase in the dimensions of the manufactured elements.

^{TM}contour mode (continuous beam path), beam current of I = 5 mA, and scanning velocity of v = 1000 mm/s. Three specimens were manufactured for each of tension and compression tests. The fixation heads for all tension specimens were manufactured using Melt Theme with default parameter settings, Figure 1f, h. Equivalent parameters of the manufactured compression specimens are given in Table 1.

_{0 =}4.43 g/cm

^{3}, the porosity P of the scaffolds in % was obtained by:

#### 2.4. X-ray Computed Tomography

#### 2.5. Mechanical Tests

_{qe}[4,39,40,41,42,43] of the porous samples is the gradient of the straight line determined within the linear deformation region at the beginning of the compressive stress-strain curve, i.e., this value is defined similarly to Young’s modulus E for bulk material. Additionally, the compressive offset stress and the first maximum compressive strength for porous specimens are defined similarly to the yield stress σ

_{y}and the compressive strength σ

_{max}for bulk specimens. Yield strain was defined as 0.2% strain, and the compressive offset stress was determined accordingly. Quasi-elastic gradient E

_{qe}, yield stress σ

_{y}, and ultimate tensile strength σ

_{max}were estimated for tensile specimens. The plateau stress σ

_{pl}is the arithmetical mean of the stress values between 20% and 40% compressive strain. The point in the stress-strain curve at which the stress is 1.3 times the plateau stress is defined as the plateau end. It can be used for the determination of energy absorption and energy absorption efficiency:

^{3}), σ is the compressive stress (MPa), e

_{0}is the upper limit of the compressive strain. The energy absorption per unit volume was calculated from the area under the stress-strain curve up to 50% strain.

## 3. Results

#### 3.1. Scanning Electron Microscopy

#### 3.2. X-ray Computed Tomography

_{a}) for vertical struts of the EBM-manufactured structures is about 40 µm, while the mean value of the maximum height of the surface profiles of vertical struts (R

_{t}) is 212 µm [28]. Comparison of a designed 3D model and as-manufactured samples performed with the standard VGStudio function named ‘Nominal/Actual Comparison’ characterizes the manufacturing accuracy and supplements the wall thickness analysis, Figure 3b. Nominal/Actual Comparison is also an alternative way to describe roughness of the manufactured specimens in qualitative terms. The value of average surface roughness is comparable with the sheet thickness that is quite typical for EBM-manufactured porous structures [49].

#### 3.3. Mechanical Properties

#### 3.3.1. Compression Tests

#### 3.3.2. Tensile Tests

#### 3.4. Finite Element Analysis

## 4. Discussion

_{0}= 110 GPa). Corresponding values are n ~ 2.3 for WT and n ~ 3.2 for MT samples. Since n = 2 corresponds to a cellular structure of compacted overlapping pores and n = 3 to a cellular structure of compacted non-overlapping pores [52], we can observe that thinning the walls not only causes an increase of porosity but also makes elastic behavior of the samples more similar to a strut-like cellular structure. The MT structure even tends to the elastic behavior of a cellular structure of overlapping spheres (n = 4).

## 5. Conclusions

- The minimum mean wall thickness, which can be achieved using standard Melt Theme in ARCAM EBM A2 machine, is around 380 µm, while the minimum mean wall thickness with Wafer Theme is 250 µm.
- Despite the difference in thickness, quasi-elastic gradient and specific energy absorption at 50% strain are approximately the same. Thus, MT and WT structures behave identically at small strains up to 5% (in the elastic range) and have similar strain tolerance.
- WT gyroids exhibit through-hole defects in the surface sections perpendicular to the building direction. They supposedly appear in each horizontal saddle point because the areas of zero-thickness 3D model are not detected by slicing software and, therefore, are not processed by the beam. Through-holes connect two separate void regions which TPMS consist of, thus, enabling better fluid transport, tissue ingrowth and differentiation.
- FEA simulation revealed that the yielding of the metal initiates in the vertical areas located parallel to the load direction and continues in the diagonally oriented surfaces. The yielding process reaches horizontally aligned saddle points only at a later stage. Therefore, the through-holes influence the mechanical behavior only in the plastic region.
- Thus, the Wafer Theme EBM-manufacturing is a promising method for TPMS-based structures.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Samples for compression tests: (

**a**) 3D model with zero thickness; (

**b**) WT specimen; (

**c**) 3D model with 200 µm thickness; (

**d**) MT specimen. Samples for tension tests: (

**e**) 3D model with zero thickness; (

**f**) WT specimen; (

**g**) 3D model with 200 µm thickness; (

**h**) MT specimen.

**Figure 3.**Evaluation of the parameters based on the XCT data analysis: (

**a**) Wall thickness distribution; (

**b**) Deviation distribution obtained from Nominal/Actual Comparison analysis.

**Figure 4.**3D rendering of the CT reconstructions for the Nominal/Actual Comparison of the MT gyroid (

**a**) and WT gyroid (

**b**). Visualization of the wall thickness for the MT gyroid (

**c**) and WT gyroid (

**d**). White arrows indicate stalactite-like structures on the horizontally oriented parts of the MT walls (areas parallel to the layers, purple color). The white circles highlight the partially melted powder particles attached to the surface of the vertical areas.

**Figure 5.**3D rendering of CT-reconstruction of WT gyroid vertical (

**a**,

**c**) and horizontal (

**b**) views (

**a**—bottom view;

**c**—top view;

**b**—side view).

**Figure 6.**Compressive stress-strain curves for the gyroid samples manufactured in (

**a**) MT; (

**b**) WT. (Note the different y-axis scales). Energy absorption per unit volume versus strain curves for lattice samples of (

**c**) MT; (

**d**) WT. (Note the different y-axis scales).

**Figure 7.**Steps of mechanical deformation during compression: (

**a**) WT; (

**b**) MT. Red arrows indicate places where the structure lost integrity during compression. The encircled layers keep integrity even at the 50% strain.

**Figure 9.**Simulations of the stress distribution during uniaxial tension (elastic region) of the gyroids with different thicknesses.

**Figure 10.**Assumption on the through-holes’ appearance: (

**a**) CT in vertical cross-sectional view; (

**b**) Scheme of manufacturing process in vertical cross-sectional view.

Specimen Parameters | Melt Theme | Wafer Theme |
---|---|---|

Mass m, g | 3.4 ± 0.1 | 2.3 ± 0.2 |

Volume V, cm^{3} | 3.4 ± 0.1 | 3.2 ± 0.1 |

Density ρ, g/cm^{3} | 1.07 ± 0.13 | 0.74 ± 0.15 |

ρ/ρ_{0 (ρ0 = 4.43 g/cm3)} | 0.24 ± 0.3 | 0.17 ± 0.2 |

Porosity p, % | 76 ± 3 | 86 ± 5 |

**Table 2.**Summary of the results of the quantitative image analysis of XCT data. (Measurement errors cannot be estimated; the error intervals represent the variance of all the measured values).

Reconstructed Specimen Parameters | Melt Theme | Wafer Theme |
---|---|---|

Mean wall thickness, mm | 0.38 ± 0.07 | 0.25 ± 0.06 |

Max. wall thickness, mm | 0.56 | 0.44 |

Defect volume ratio, % (Micro-pores to bulk volume) | 0.4 | 0.3 |

Parameters | Compression | Tension | ||
---|---|---|---|---|

MT | WT | MT | WT | |

Porosity, % | 76 | 85 | 76 | 85 |

Quasi-elastic gradient E_{qe}, GPa | 1.5 ± 0.1 | 1.5 ± 0.1 | 1.2 ± 0.1 | 1.2 ± 0.2 |

Compressive offset stress/Yield strength σ_{y}, MPa | 65 ± 1 | 30 ± 5 | 37 ± 5 | 5 ± 0.6 |

Yield strain, % | 4.6 | 2.3 | 3.5 | 0.7 |

First maximum compressive strength/σ_{e}, MPa | 88 ± 2 | 40 ± 3 | ||

UTS, MPa | 76 ± 0.3 | 24 ± 0.6 | ||

Plateau stress σ_{p}_{l 20–40}, MPa | 49 ± 2 | 15 ± 3 | – | – |

Energy absorption W_{50}, MJ/m^{3} | 29 ± 0 | 11 ± 2 | – | – |

Specific energy absorption ψ (50%), J/g | 27 ± 0 | 27 ± 1 | – | – |

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**MDPI and ACS Style**

Khrapov, D.; Kozadayeva, M.; Manabaev, K.; Panin, A.; Sjöström, W.; Koptyug, A.; Mishurova, T.; Evsevleev, S.; Meinel, D.; Bruno, G.;
et al. Different Approaches for Manufacturing Ti-6Al-4V Alloy with Triply Periodic Minimal Surface Sheet-Based Structures by Electron Beam Melting. *Materials* **2021**, *14*, 4912.
https://doi.org/10.3390/ma14174912

**AMA Style**

Khrapov D, Kozadayeva M, Manabaev K, Panin A, Sjöström W, Koptyug A, Mishurova T, Evsevleev S, Meinel D, Bruno G,
et al. Different Approaches for Manufacturing Ti-6Al-4V Alloy with Triply Periodic Minimal Surface Sheet-Based Structures by Electron Beam Melting. *Materials*. 2021; 14(17):4912.
https://doi.org/10.3390/ma14174912

**Chicago/Turabian Style**

Khrapov, Dmitriy, Maria Kozadayeva, Kayrat Manabaev, Alexey Panin, William Sjöström, Andrey Koptyug, Tatiana Mishurova, Sergei Evsevleev, Dietmar Meinel, Giovanni Bruno,
and et al. 2021. "Different Approaches for Manufacturing Ti-6Al-4V Alloy with Triply Periodic Minimal Surface Sheet-Based Structures by Electron Beam Melting" *Materials* 14, no. 17: 4912.
https://doi.org/10.3390/ma14174912