**1. Introduction**

The optimization of additively manufactured (AM) porous structures for biomedical applications aims at increasing fatigue life, enhancing mass transport properties for tissue regeneration, decreasing the occurrence of infections, minimizing powder release from the structures, and minimizing stress shielding. Stress shielding is caused by differences between Young's moduli of the bone and the implant, and can be prevented by adjusting

**Citation:** 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

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Academic Editor: Francesco Iacoviello

Received: 9 July 2021 Accepted: 20 August 2021 Published: 29 August 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Young's modulus of the implant through manipulating its structure (porosity) and material [1]. The designed porosity in regular-geometry lattice systems primarily depends on the type of unit cell. Usually, beam-based or sheet-based cell elements are used. AM porous structures based on the beam-like elements are intensively studied [2] and are most commonly used for porous scaffolds design.

Triply Periodic Minimal Surfaces (TPMS) have recently gained interest as the new approach to the design of the sheet-based porous scaffolds for tissue engineering. TPMS attracts attention due to zero-mean curvature at every point that is admittedly a grea<sup>t</sup> advantage since it improves the structure load-bearing capacity simultaneously assisting bone cell ingrowth [3]. The well-known TPMS are Schwarz Gyroid (G), Schwarz Primitive (P), and Schwarz Diamond (D) [4].

There are different approaches of using TPMS geometries for designing porous structures. First approach utilizes beam-based TPMS, strut-based [4], network-based or skeletal structure designs [5,6]. They are used to overcome stress concentrators in the sharp turns of the metal that are typical for unit cells with straight beam-like struts and a polyhedral core. Porous structures using straight beams can experience severe stress concentrations under loading, especially in regions where beams are merging, or bending at acute angles. Severe overloading and increased fatigue-related failure in the stress-concentration zones can lead to a complete collapse of the corresponding structural elements [7]. Beam-based TPMS are designed to have smooth struts and smoother connections between horizontal and vertical elements as compared to conventional beam-based structures. Most of the beam-based TPMS were manufactured using struts with circular cross-section. Beam-based TPMS structures were manufactured by the stereolithography rapid prototyping [8,9], selective laser sintering (SLS) [10] and laser powder bed fusion (L-PBF) [11]. Beam-based TPMS structures were also manufactured by Electron Beam Melting (EBM) by Yánez et al. [12,13] and Ataee et al. [14].

A second approach to designing TMPS structures is by using sheet-based [4] or sheetlike [15] elements. Such structures are also referred to as list structures or matrix phase lattices [5]. They comprise a wall of solid material bounded by two unconnected void regions. The continuity of the sheet-based TPMS is supposed to provide higher strength and damage-tolerance through effective obstruction of crack propagation [16]. Crack propagation in continuous sheet-based porous structures requires more energy as compared to common strut-based ones. Sheet-based gyroid structures also have higher Young's modulus, peak stress, and toughness in comparison with beam-based gyroid structures. For example, Al-Ketan et al. [6] demonstrated that sheet-TPMS structures have superior mechanical properties in terms of Young's modulus in comparison with conventional strut-based and skeletal-TPMS porous structures. Among such TPMS structures, gyroid structures attract the attention of many scientists. Kapfer et al. [17] demonstrated that the sheet-based gyroid structures have higher stiffness than the beam-based ones with the same porosity and manufactured from the same material. Aremu et al. [18] noted that gyroid lattices, unlike several other lattice types, possess axisymmetric stiffness making them desirable candidates for applications where the exact nature and direction of the loads are not fully known or if such loads are subject to large variations. Sheet-based structures have been manufactured by selective laser sintering (SLS) [6,15], L-PBF [5,19] but so far not by EBM. It is well-known that EBM structures have lower resulting porosity [18] and lower residual stress as compared to similar L-PBF- and SLS-manufactured structures because of the preheating during manufacturing that acts as a stress relief heat treatment [20,21]. Internal defects of the EBM-manufactured objects affect their fatigue life [22]. To evaluate manufacturing quality and porosity, the size and the form of the defects process monitoring approaches for is investigated [23]. Moreover, manufacturing parameters' optimization leads to porosity reduction [24]. One way to optimize manufacturing parameters is EBM process simulation that helps to predict physical properties of AM [25,26]. To evaluate the behavior of the Ti-6Al-4V implant in human body, friction and wear performance of

the wrought and EBM-manufactured Ti-6Al-4V in simulated body fluid solution were studied [27].

Studying EBM TPMS sheet structures is of grea<sup>t</sup> interest for biomedical applications as the manufacturing of implants with porous elements is one of the core applications of EBM technology. Sheet-based TPMS can be produced by EBM using different manufacturing parameter sets commonly known as Themes. "Melt" Themes originally designed for manufacturing solid structural elements require a 3D model with predetermined material thickness. The "Wafer" Theme originally designed for manufacturing different support structures uses zero-thickness 3D models [28]. Taking into consideration the complexity of TPMS, the Wafer Theme may become a new key to controlling specimen's porosity and preventing the stress shielding effect. The differences between the gyroid samples manufactured using Melt and Wafer Themes are the subject of this work.

Our initial assumption was that specimens based on 200 μm thick model manufactured using Melt Theme and specimens based on zero-thickness model manufactured using Wafer Theme would have identical sheet thickness and identical mechanical properties. This assumption was based on the fact that the beam spot diameter set in the ARCAM A2 machine is commonly 200 μm [28].

In this work, we investigate the mechanical properties of the TPMS porous specimens based on model with 200 μm thickness manufactured by EBM using the Melt Theme and specimens with an equivalent design but produced by EBM using the Wafer Theme, zero-thickness model. Samples were manufactured using the standard Themes provided by ARCAM EBM for Ti-6Al-4V alloy.

We address the relationship between structural performance and manufacturing modality, keeping porosity constant. The novelty of the research lies in combination of design methods of TPMS and EBM-manufacturing modalities. The aim of the current investigation was to evaluate the worthiness of Wafer Theme in comparison with the Melt Theme for TPMS structures' fabrication from the mechanical point of view.

### **2. Materials and Methods**

### *2.1. TPMS File Preparation*

Wolfram Mathematica (version 12) [29] was used to visualize the gyroids using the following equation:

$$
\sin(kx)\cos(ky) + \sin(ky)\cos(kz) + \sin(kz)\cos(kx) = 0\tag{1}
$$

The limits of the surface were chosen from −5/2 π to 5/2 π in all directions. So, the designed structure consists of three unit cells along each coordinate direction (X, Y, Z), resulting in a total size of 15 mm × 15 mm × 15 mm. The coefficient *k* controls the unit cell size. For this research *k* = 1 was chosen. Two different sets of the 3D models were implemented. The models of the first set with zero-thickness were exported from Mathematica as STL files with the default density of the polygon mesh, Figure 1a.

The second set of models was produced from the first one by assigning a thickness of 200 μm to all surfaces, Figure 1c and also was exported from Mathematica as STL files with the same conditions. Since the surface of gyroid consists of semicircular surfaces, the exported 3D models had a large number of vertices (more than 106), 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.

**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.

For the tensile samples, two opposite 4 cm long tapering blocks were added to the gyroid structures of both types, Figure 1e,g. The total length of these specimens was 95 mm. The process of error correction was repeated in FreeCAD [31]. This software was used for STL to STEP file conversion (necessary for the FE analyses). The obtained STL files were used for designing all specimen models and for processing in the ARCAM Build Assembler—for EBM—manufacturing.

### *2.2. Finite Element Analysis*

The aim of FE simulations was to qualitatively analyze the deformation process and the stress distribution. The models with thicknesses of 0.25 and 0.4 mm were imported to ANSYS Workbench (ANSYS, Canonsburg, PA, USA). The values of thicknesses were taken based on the experimental results (see Section 3.2). A tetrahedral mesh model was implemented. This method was convenient since the initial models obtained in Wolfram Mathematica consisted of triangle polygons. The total number of nodes and elements for the model with the thickness of 0.25 mm were 910,727 and 489,256, respectively. Using the physical properties of Ti-6Al-4V, the modeled specimen had an estimated mass of 1.53 g and a porosity of 85%. The total number of nodes and elements for the model with the thickness of 0.4 mm were 1,070,675 and 610,874, respectively. Using the physical properties of Ti-6Al-4V, the modeled specimen had an estimated mass of 3.18 g and a porosity of 75%. The von Mises failure criterion was chosen, and a yield strength of 970 MPa for Ti-6Al-4V was selected [32]. Boundary conditions were applied as follows: frictionless support was applied to the bottom face and 1 mm displacement was applied to the top. Only the elastic regime was simulated for both tension and compression tests.
