# Adjustable Elasticity of Anatomically Shaped Lattice Bone Scaffold Built by Electron Beam Melting Ti6Al4V Powder

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- Reinforcing the liquid material of the bone graft, which, similar to its own provisional bone tissue, should transform during the recovery process into mature and healthy bone tissue and connect with the surrounding bone.
- Forming the volume of the bone graft into the desired anatomical shape of the future bone tissue, corresponding to the anatomy of the missing bone part.
- Enabling the targeted elastic deformation of the volume of the bone graft is crucial for the design of an ASLS. In fact, the elasticity of the ASLS needs to adapt to the loading that the patient’s bone will undergo during recovery. The appropriate elastic deformation, or strain, of the ASLS and the bone graft within is of utmost importance for accelerating the process of ossification (bone formation) or transformation of provisional bone tissue into mature bone tissue. Therefore, one of the goals of designing the ASLS is to ensure the desired strain, i.e., the targeted elastic deformation of the ASLS for the most common loading scenario during recovery, through suitable design and construction.

## 2. Materials and Methods

- the scaffold was compressed up to a certain force, once this force was achieved it was maintained for 2 s,
- next, the scaffold was unloaded down to a force smaller than that of the previous step (not zero, to keep the scaffold in contact with the fixtures), once this force was achieved, it was maintained for 2 s.

^{2}) to calculate approximate normal stress. Based on this and the starting 10 mm scaffold height (length), it was possible to create an approximation of the stress-strain graph.

^{3}, while the volume of the scaffold itself (all the struts) is 38 mm

^{3}. Thus, even though for this kind of lattice structure, such ASLS, porosity is not an adequate feature as it is for porous structures (foam-like structures), for the sake of comparison, the porosity of this ASLS can be calculated as a ratio of these two volumes (38/220), thus, it is 82.7%.

## 3. Results

#### 3.1. Experiment 1-Determining the Whole Range of Compression, up to 35% Deformation of Initial Length of ASLS (dx = 3.5 mm, Xo = 10 mm)

#### 3.2. Experiment 2–Exploring the Quasi-Elastic Properties of the ASLS for the First Compression Stage

^{2}. It is important to note that this is an approximate calculation used as an orientation value. The principal deformation of the ASLS is primarily caused by torsion in the joints of the scaffold’s struts, and strut fracture results from the high shear stresses induced by this torsion. For an ASLS that rigidifies by applying the initial compression stage limit force of 37 N (without crossing the yield point), a portion of the stress-strain diagram calculated this way can be used to determine the modulus of elasticity (Figure 12). The calculated value of the modulus of elasticity for a series of ASLSs ranges from 1450 to 1850 N/mm

^{2}.

#### 3.3. Experiment 3-Exploring the Quasi-Elastic Properties of the ASLS throughout the Entire Range of Compression, Including the Second and Third Compression Stages

_{_after_initial_stiffening}(ε) = 1842·ε, which appears as 68.25% stiffer than in the initial compression stage (σ

_{_initial}=1095 N/mm

^{2}·1.6825), E ≈ 1842 N/mm

^{2}.

^{2}. σ

_{_after_150N_stiffening}(ε) = 6278·ε, indicating an increase of approximately 260.55% compared to the second compression stage (1842 N/mm

^{2}·2.6055).

^{2}.

## 4. Discussion

## 5. Conclusions

- Lattice scaffolds, produced using the EBM additive manufacturing process with Ti6Al4V powder and intended for bone tissue recovery, exhibit the characteristic of plastic deformation even at low forces.
- Prior to the stresses in the struts of the EBM-built lattice scaffold reaching a value that causes structural cracking, compression induces three distinctive stages of elastic-plastic deformation. The most intriguing phenomenon accompanying each of these deformation phases is the high degree of reversibility of the scaffold deformation after relaxation, although the force-elongation relationship shows significant nonlinearity. After the initial exposure of the scaffold to the upper limit of the load characteristic for each of these three phases of compression, the scaffold becomes stiffer compared to the state before that initial load, and each subsequent cycle of loading and relaxation in each range (characteristic for that phase) allows the scaffold to behave quasi-elastic (deformations are almost completely reversible). This feature is recognized as very useful for the situation where the stiffness of the lattice scaffold needs to be adjusted to the load generated by a specific patient during recovery, thus adjusting the deformation of the bone graft inside the scaffold in order to maximize the rate of the ossification process.
- The stiffness of ASLSs already manufactured using EBM with Ti6Al4V can be changed (improved) by applying an appropriate compression (stiffening) load to it, thus achieving the target elasticity of the scaffold structure.
- The research established a functional relationship between the compression (stiffening) force and the alteration in the elastic modulus of ASLS. Given that ASLS is a unique form of a lattice scaffold, the technique for measurement and data processing capable of determining this functional relationship, as showcased in the paper, holds a broader universal significance.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Anatomically shaped lattice Ti6Al4V scaffold specifically designed to address large trauma in the proximal diaphysis of a rabbit’s tibia fabricated by EBM.

**Figure 3.**Experimental setup: (

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

**b**) some of the specimens to be tested.

**Figure 4.**The scaffold cross-sections were obtained through the analysis of the CAD model of ASLS. (

**a**) ASLS with a series of planes making a set of 20 cross-sections in the direction of compression, (

**b**) a cross-section whose area (3.63949 mm

^{2}) is almost equal to the average value (3.61 mm

^{2}).

**Figure 6.**Three compression stages within the first zone of compression characterized by specific dF(x)/dx.

**Figure 8.**A closer look at the first two stages of compression, with the first stage defined between 1 and 37 N, and the second stage between 37 and 40 N.

**Figure 9.**The third stage of compression extends from 2% to 10% of the total relative deformation of the ASLS, resulting in a reactive force range of 40 N to 1300 N.

**Figure 10.**Compression–decompression cycles: stroke and reactive force of ASLS versus time during a series of measurements.

**Figure 11.**The diagram of compression force in function of the deformation F(x) for the first compression stroke and a series of decompression and compression strokes afterward. Arrows, which are directed upwards indicate compressive strokes, while the ones which are directed downwards, indicate relaxation strokes.

**Figure 12.**The diagram of the approximately calculated normal stress (σ) in function of strain (ε) for the first stage, i.e., after stiffening the ASLS. E ≈ 1479 N/mm

^{2}, σ

_{_after_initial_stiffening}(ε) = 1479·ε.

**Figure 13.**The diagram of the force F(x) for the case of series of compression/decompression (relaxation) strokes with corresponding small increase of the limit force. Black arrows, which are directed upwards, indicate compressive strokes, while the red ones, which are directed downwards, indicate relaxation strokes.

**Figure 14.**The diagram of changing the compression force and stroke versus time, in accordance with the experiment plan.

**Figure 15.**F(x) diagram with focus on complete fourth and beginning of the fifth compression-relaxation cycle. Black arrows, which are directed upwards, indicate compressive strokes, while the red ones, which are directed downwards, indicate relaxation strokes.

**Figure 16.**F(x) diagram with focus on complete fifth and beginning of the sixth compression-relaxation cycle. Black arrows, which are directed upwards, indicate compressive strokes, while the red ones, which are directed downwards, indicate relaxation strokes.

**Figure 17.**F(x) diagram with focus on the final, sixth compression-relaxation cycle. Black arrows, which are directed upwards, indicate compressive strokes, while the red ones, which are directed downwards, indicate relaxation strokes.

**Figure 18.**Diagram of reactive force of two ASLSs under compression load, focusing on deformation that exceeds 10% of the initial height (length) of the scaffold.

**Figure 19.**Two moments during the compressive deformation that exceeds 10% of the initial height of the scaffold.

**Figure 20.**ASLS struts made through EBM in their real shape. (

**a**) A magnified view of the scaffold strut, (

**b**) error-bar diagram of the struts’ thickness (diameter) based on 25 measurements (5 measurements of 5 struts of non-deformed ASLSs). The designed diameter is 0.4 mm.

**Figure 21.**The magnified (max. 1600×) view of fractured ASLS Struts: (

**a**,

**b**) views of the cross-section (colored by the red felt pen) of the fractured strut, (

**c**) the magnified view of the strut’s cross-section where it has been sheared off. The boundary of the cross-section is highlighted by an orange polyline.

**Figure 22.**E(F)–Diagram that expresses the relation between the increase of modulus of elasticity and applied compression (stiffening) force.

Parameters | ARCAM A1 (EBM) |
---|---|

Energy source | 50–3000 W (electron beam) |

Min. Beam size | 200 µm |

Environment | Vacuum |

Layer thickness | 70 µm |

Print speed | 4 mm/h |

Scan speed | 1500 mm/s |

Technologies | Aluminium (Al) | Vanadium (V) | Iron (Fe) | Oxygen (O) | Nitrogen (N) | Carbon (C) | Hydrogen (H) | Titanium (Ti) |
---|---|---|---|---|---|---|---|---|

EBM Arcam A1 Ti-6Al-4V | 5.5–6.5% | 3.5–4.5% | <0.30% | <0.20% | <0.05% | <0.08% | <0.015% | Balance |

Mechanical Properties | Arcam Titanium Ti6Al4V (Grade 5) Powder |
---|---|

Ultimate Tensile Strength, | 951 MPa |

Yield Strength, Rp_{0.2} | 1020 MPa |

Fatigue Strength @ 600 MPa | >10,000,000 cycles |

Elongation at Break | 14% |

Modulus of Elasticity | 120 GPa |

Rockwell Hardness | 33 HRC |

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

Model | Table-top AGS-X 10 kN |

Weight | 85 kg |

Power | 1.2 kW |

Max load/capacity | 10 kN |

Dimensions | W 653 mm × D 520 mm × H 1603 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 |

# | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Speed (mm/min) | F (N) | F (N) | F (N) | F (N) | F (N) | F (N) | F (N) | F (N) | F (N) | F (N) | F (N) | F (N) | |

1 | 1 | 37 ↓^{1} | 5 ↑^{2} | 42 ↓ | 800 ↓ | 42 ↑ | 1300 ↓ | 42 ↑ | |||||

2 | 1 | 37 ↓ | 5 ↑ | 42 ↓ | 5 ↑ | 55 ↓ | 5 ↑ | 150 ↓ | 55 ↑ | 500 ↓ | 150 ↑ | 1300 ↓ | 5 ↑ |

3 | 0.25 | 37 ↓ | 5 ↑ | 42 ↓ | 5 ↑ | 55 ↓ | 5 ↑ | 150 ↓ | 55 ↑ | 500 ↓ | 150 ↑ | 1300 ↓ | 5 ↑ |

^{1}The sign ↓ represents compression (loading) stroke.

^{2}The sign ↑ represents relaxation (unloading) stroke.

**Table 6.**Correlation between ASLS deformation under the corresponding compression force and calculated modulus of elasticity of ASLS structure.

dx (mm) | F (N) | E (N/mm^{2}) |
---|---|---|

0.115 | 10 | 1095 ^{1} |

0.185 | 37 | 1842 |

0.41 | 150 | 6278 |

0.6 | 500 | 9738 |

0.955 | 1300 | 14010 |

^{1}Calculation based on F(x) of initial compression stroke, i.e., before stiffening.

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**MDPI and ACS Style**

Stojković, J.R.; Stojković, M.; Turudija, R.; Aranđelović, J.; Marinkovic, D.
Adjustable Elasticity of Anatomically Shaped Lattice Bone Scaffold Built by Electron Beam Melting Ti6Al4V Powder. *Metals* **2023**, *13*, 1522.
https://doi.org/10.3390/met13091522

**AMA Style**

Stojković JR, Stojković M, Turudija R, Aranđelović J, Marinkovic D.
Adjustable Elasticity of Anatomically Shaped Lattice Bone Scaffold Built by Electron Beam Melting Ti6Al4V Powder. *Metals*. 2023; 13(9):1522.
https://doi.org/10.3390/met13091522

**Chicago/Turabian Style**

Stojković, Jelena R., Miloš Stojković, Rajko Turudija, Jovan Aranđelović, and Dragan Marinkovic.
2023. "Adjustable Elasticity of Anatomically Shaped Lattice Bone Scaffold Built by Electron Beam Melting Ti6Al4V Powder" *Metals* 13, no. 9: 1522.
https://doi.org/10.3390/met13091522