# Stiffness of Anatomically Shaped Lattice Scaffolds Made by Direct Metal Laser Sintering of Ti-6Al-4V Powder: A Comparison of Two Different Design Variants

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{0.2}) decreased 12 times across the porosity range of 50% to 80% (ranging from 138 to 11 MPa). Mondal et al. [19] produced different scaffold designs with approximately 65% porosity. The scaffolds’ modulus of elasticity closely matched the ones of the human bone.

## 2. Materials and Methods

#### 2.1. ASLS Design

^{3}). For ASLS×60°, porosity was calculated to be 82.7% (as the volume of the scaffold was 38 mm

^{3}), and for ASLS×90°, porosity was 87.8% (as the volume of the scaffold was 26.72 mm

^{3}). Figure 4 shows that the apparent difference in porosity may seem more substantial than the calculated 5.1% (87.8–82.7%). However, it is essential to consider that the porosity calculation was based on the volume of bone the scaffold was intended to replace (220 mm

^{3}). This volume significantly exceeded the actual volumes of the scaffolds, which were 38 mm

^{3}for ASLS×60° and 26.72 mm

^{3}for ASLS×90°. Directly comparing the volumes of the two scaffolds revealed a more nuanced perspective. If the volume of ASLS×90° was used as a reference, ASLS×60° took up 42% more volume than ASLS×90°.

#### 2.2. Manufacturing and Testing the ASLS

^{2}. ASLS×90° was easier to calculate, since half of the struts were collinear to the compression axis, so only one cross section could have been used. Because of this, the area of the cross section was A_90° = 1.52 mm

^{2}. Figure 7a shows a characteristic plane that was used to create and calculate the cross section of ASLS×90°, and Figure 7b shows a series of planes that were used to build and calculate a series of corresponding cross sections of ASLS×60°.

## 3. Results and Discussion

- ${\mathrm{F}}_{\mathrm{A}\mathrm{S}\mathrm{L}\mathrm{S}\times 90\xb0}$ is the pressure force acting upon ASLS×90°;
- ${\mathrm{F}}_{\mathrm{A}\mathrm{S}\mathrm{L}\mathrm{S}\times 60\xb0}$ is the pressure force acting upon ASLS×60°;
- ${\mathrm{A}}_{\mathrm{n}\_\mathrm{a}\mathrm{v}\mathrm{g}\_\mathrm{A}\mathrm{S}\mathrm{L}\mathrm{S}\times 90\xb0}$ is the average (approximatively taken) area of the ASLS×90° structure cross section, which is normal to the direction of the compression force (Figure 7a);
- ${\mathrm{A}}_{\mathrm{n}\_\mathrm{a}\mathrm{v}\mathrm{g}\_\mathrm{A}\mathrm{S}\mathrm{L}\mathrm{S}\times 60\xb0}$ is the average (approximatively taken) area of the ASLS×60° structure cross section, which is normal to the direction of the compression force (Figure 7c).

^{2}, whereas for ASLS×60°, it was 172.85 N/mm

^{2}.

- ${\mathrm{F}}_{\mathrm{f}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e}\_\mathrm{A}\mathrm{S}\mathrm{L}\mathrm{S}\times 90\xb0}$ is the force which causes the fracturing of the first strut of ASLS×90°;
- ${\mathrm{F}}_{\mathrm{f}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e}\_\mathrm{A}\mathrm{S}\mathrm{L}\mathrm{S}\times 60\xb0}$ is the force which causes the fracturing of the first strut of ASLS×60°;
- ${\mathsf{\sigma}}_{{\mathrm{n}\mathrm{U}\mathrm{C}\mathrm{S}}_{\mathrm{a}\mathrm{p}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{x}\_\mathrm{A}\mathrm{S}\mathrm{L}\mathrm{S}\times 90\xb0}}$ is the ultimate compression strength of the ASLS×90° structure;
- ${\mathsf{\sigma}}_{{\mathrm{n}\mathrm{U}\mathrm{C}\mathrm{S}}_{\mathrm{a}\mathrm{p}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{x}\_\mathrm{A}\mathrm{S}\mathrm{L}\mathrm{S}\times 60\xb0}}$ is the ultimate compression strength of the ASLS×60° structure.

_{ASLS}), which is defined as the ratio of the force and the corresponding deflection (deformation) of the structure, ASLS×60° demonstrated a superior stiffness compared to ASLS×90° in the third stage of deformation (see Figure 16a,b).

- ${\mathrm{K}}_{\mathrm{A}\mathrm{S}\mathrm{L}\mathrm{S}\times 90\xb0}$ is the stiffness of the ASLS×90°;
- ${\mathrm{K}}_{\mathrm{A}\mathrm{S}\mathrm{L}\mathrm{S}\times 60\xb0}$ is the stiffness of the ASLS×60°.

^{2}(Figure 17a), and for ASLS×60° it was 3325 N/mm

^{2}(Figure 17b). This underscores the significance of optimal strut orientation in ASLSs for achieving targeted rigidity (compressibility) of the structure in the required direction. Importantly, this result highlights that, even with the utilization of less material in manufacturing, the careful selection of strut orientation can lead to stiffer structures. Just for reference, when observing the elasticity coefficient of the same ASLS×60° model manufactured with EBM technology [28], when a force of around 500 N was applied (which is comparable to the force presented here for models made from DMLS), the elasticity coefficient was 9738 N/mm

^{2}.

- 1.
- The value of the elasticity coefficient of the ASLS structure (as an object, and not a material) is much lower (from 20 to 40 times lower) than the modulus of elasticity of the test specimen produced by the same process (DMLS) from the same material (Ti64 powder). This can be explained by the fact that in the case of the test specimen (Figure 20a), the neck of the specimen is 5 mm in diameter, i.e., the area of the specimen cross section (19.635 mm
^{2}) is much greater (156 times) than the area of an ASLS strut (~0.126 mm^{2}) (Figure 20b). A vast number of Ti-alloy powder particles in every cross-sectional layer and between the layers are joined. This causes the inner structure of the test specimen (D = 5 mm), which is made of Ti-alloy powder from DMLS, to appear much more homogenous than the inner structure of the ASLS struts (D ≅ 0.4 mm), that is, it appears very similar to the specimen made of the same Ti alloy, but conventionally, due to being cut from the rolled plate of the same Ti alloy.

- 2.
- The value of the elasticity coefficient (Ec) of the ASLS lattice structure depends to a significant extent on two angles: (1) the angle at which the struts cross (α), and the angle (γ) that is between the load direction and the axis of the struts in the outer layer of the ASLS (Figure 4). Additionally, one can observe that the mutual ratio of the elasticity coefficient of the ASLS×90° and ASLS×60° structures differs depending on which stage of quasi-reversible deformation the elasticity coefficient is being sampled in. In the stage of quasi-reversible deformation, which is characterized by a higher degree of deformation (compression) of the scaffold (150 ≤ F ≤ 400), the ratio of the elasticity coefficient of these structures is smaller (Equations (7) and (8)):$${\left(\frac{{\mathrm{E}\mathrm{c}}_{\mathrm{A}\mathrm{S}\mathrm{L}\mathrm{S}\times 90\xb0}}{{\mathrm{E}\mathrm{c}}_{\mathrm{A}\mathrm{S}\mathrm{L}\mathrm{S}\times 60\xb0}}\right)}_{0\le \mathrm{F}\le 30\mathrm{N}}=\frac{2708\frac{\mathrm{N}}{{\mathrm{m}\mathrm{m}}^{2}}}{921\frac{\mathrm{N}}{{\mathrm{m}\mathrm{m}}^{2}}}=2.94$$$${\left(\frac{{\mathrm{E}\mathrm{c}}_{\mathrm{A}\mathrm{S}\mathrm{L}\mathrm{S}\times 90\xb0}}{{\mathrm{E}\mathrm{c}}_{\mathrm{A}\mathrm{S}\mathrm{L}\mathrm{S}\times 60\xb0}}\right)}_{150\le \mathrm{F}\le 400\mathrm{N}}=\frac{4486\frac{\mathrm{N}}{{\mathrm{m}\mathrm{m}}^{2}}}{3325\frac{\mathrm{N}}{{\mathrm{m}\mathrm{m}}^{2}}}=1.35$$

## 4. Conclusions

^{2}) and elasticity coefficient (4866 N/mm

^{2}) in comparison to ASLS×60°, which exhibited a maximal compression strength and elasticity coefficient of 172.85 N/mm

^{2}and 3325 N/mm

^{2}, respectively. This finding is particularly intriguing considering that the volume of ASLS×90° was 42% smaller (if the volume of ASLS×90° is used as a reference) than that of ASLS×60° (26.72 mm

^{3}and 38 mm

^{3}, respectively). Just for reference, the porosity of the ASLS×90° model was 87.8%, and 82.7% for ASLS×60° (when calculated with the volume of the part of the bone which the ASLS models would replace, which was 220 mm

^{3}).

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Position of the missing piece of traumatized rabbit tibia and its ASLS, with a magnified view. The ASLS should keep the bone graft in its cage.

**Figure 3.**ASLS model where outer struts are colored green, cross struts blue, and inner struts yellow. (

**a**) Front view of the ASLS model; (

**b**) back view of the ASLS model.

**Figure 4.**Models and samples of ASLSs with different strut orientations: (

**a**) model of ASLS×60°; (

**b**) model of ASLS×90°; (

**c**) sample of ASLS×60° after completion of the compression test; (

**d**) sample of ASLS×90° after completion of the compression test (the permanent deformation of the scaffold is obvious).

**Figure 5.**Dimensions of the missing piece of bone: (

**a**) lateral view of the traumatized rabbit tibia; (

**b**) isometric view showing the width of the missing piece of bone.

**Figure 6.**Compression testing setup: (

**a**) Shimadzu Table-top AGS-X 10 kN universal testing machine; (

**b**) testing setup; (

**c**) specialized custom-made tool (compression plates) with seating mechanism; (

**d**) ASLS×90° during compression test.

**Figure 7.**The cross section of the ASLS: (

**a**) ASLS×90°; (

**b**) series of cross sections of ASLS×60° (grey lines represent planes from which the cross sections were made); (

**c**) one ASLS×60° cross section.

**Figure 9.**Characteristic zones and stages of compression of the scaffolds: (

**a**) ASLS×90°; (

**b**) ASLS×60°.

**Figure 10.**Series of compressions and decompressions administered to the ASLS×90° model on the universal testing machine.

**Figure 11.**Series of compressions and decompressions done to the ASLS×60° model on the universal testing machine.

**Figure 12.**Comparison of the reactive force and stroke in the given compression stages for two ASLS models (ASLS×90° and ASLS×60°): (

**a**) percentage of the reactive force in the given stage of compression, considering the maximal reactive force; (

**b**) percentage of the stroke in the given stage of compression, considering the total stroke.

**Figure 13.**Diagrams of both force and cumulative work versus displacement in the first zone of deformation for two ASLS models: (

**a**) ASLS×90°; (

**b**) ASLS×60°.

**Figure 14.**Diagrams of comparison of work invested for compression of ASLS and energy dissipated after its decompression for every compression–decompression cycle for two ASLS models: (

**a**) ASLS×90°; (

**b**) ASLS×60°.

**Figure 15.**Dissipated energy trends versus relative deformation of ASLS during compression–decompression cycles for two ASLS models.

**Figure 16.**A part of the F(x) diagrams that are focused on the third stage of deformation (50 N ≤ F ≤ 500 N) can be used for determination of the ASLS stiffness in this stage of deformation: (

**a**) F(x) for ASLS×90° (0.27 < dx < 0.75 mm) and (

**b**) F(x) for ASLS×60° (0.34 < dx < 0.75 mm).

**Figure 17.**Approximated stress–strain diagrams for both ASLS models, with linear trendlines in the quasi-linear part of the diagrams taken from the third stage (150 N ≤ F ≤ 400 N) indicating elasticity coefficients of ASLSs: (

**a**) ASLS×90°; (

**b**) ASLS×60°.

**Figure 18.**Parts of the F(x) diagrams that are focused on the first zone of deformation (0 N ≤ F ≤ 28 N) can be used for determination of ASLS stiffness in this zone of deformation: (

**a**) F(x) for ASLS×90° (dx < 0.18 mm) and (

**b**) F(x) for ASLS×60° (dx < 0.16 mm).

**Figure 19.**Approximated stress–strain diagrams for both ASLS models, with linear trendlines in the quasi-linear parts of the diagrams taken from the first stage of deformation (0 N ≤ F ≤ 28 N), i.e., elasticity coefficient of the ASLSs: (

**a**) ASLS×90°; (

**b**) ASLS×60°.

**Figure 20.**CAD models of standard specimen and ASLS strut for comparison. (

**a**) CAD model of the standard Ti64 specimen shape fabricated by DMLS that is used for testing the mechanical properties of parts made by DMLS; (

**b**) approximative CAD model of ASLS strut fabricated through DMLS.

Basic Data | Value |
---|---|

Dimensions (w × d × h) | 2200 mm × 1070 mm × 2290 mm |

Weight | 1250 kg |

Mains supply | 400 V |

Max power consumption * | 5.5 kW |

Wavelength of the laser | 1060–110 nm |

Diameter of laser beam at building area | 100–500 µm |

Positioning speed | 40–500 mm/s |

Platform heating module operating temperature | 40–100 °C |

Thinnest possible layer thickness | 20 µm |

Chemical Composition |
---|

Aluminum (Al) 5.5–6.75% |

Vanadium (V) 3.5–4.5% |

Iron (Fe) < 0.3% |

Oxygen (O) < 20% |

Nitrogen (N) < 0.05% |

Carbon (C) < 0.08% |

Hydrogen (H) <0.015% |

**Table 3.**Mechanical properties of the parts from Ti64_Speed 1.0 manufactured on the EOSINT M 280–400 W-type machine.

Mechanical Properties | Value |
---|---|

Ultimate Tensile Strength | 1240 Mpa |

Yield Strength, Rp0.2 | 1120 Mpa |

Elongation at Break | 10% |

Modulus of Elasticity * | 110 Gpa |

Vickers Hardness | 320 HV5 |

Brand | Shimadzu |
---|---|

Model | Table-top AGS-X 10 kN |

Weight | 85 kg |

Power | 1.2 kW |

Max load/capacity | 10 kN |

Dimensions | W653 × D520 × H1603 mm |

Crosshead speed range | 0.001 to 1000 mm/min |

Crosshead speed accuracy | 0.1% |

Crosshead—table distance (tensile stroke) | 1200 mm (760 mm, MWG) |

Data capture rate | 1000 Hz max |

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**MDPI and ACS Style**

Turudija, R.; Stojković, M.; Stojković, J.R.; Aranđelović, J.; Marinković, D.
Stiffness of Anatomically Shaped Lattice Scaffolds Made by Direct Metal Laser Sintering of Ti-6Al-4V Powder: A Comparison of Two Different Design Variants. *Metals* **2024**, *14*, 219.
https://doi.org/10.3390/met14020219

**AMA Style**

Turudija R, Stojković M, Stojković JR, Aranđelović J, Marinković D.
Stiffness of Anatomically Shaped Lattice Scaffolds Made by Direct Metal Laser Sintering of Ti-6Al-4V Powder: A Comparison of Two Different Design Variants. *Metals*. 2024; 14(2):219.
https://doi.org/10.3390/met14020219

**Chicago/Turabian Style**

Turudija, Rajko, Miloš Stojković, Jelena R. Stojković, Jovan Aranđelović, and Dragan Marinković.
2024. "Stiffness of Anatomically Shaped Lattice Scaffolds Made by Direct Metal Laser Sintering of Ti-6Al-4V Powder: A Comparison of Two Different Design Variants" *Metals* 14, no. 2: 219.
https://doi.org/10.3390/met14020219