Page 208 - IJB-9-4

International Journal of Bioprinting b-Ti21S TPMS FGPs produced by laser powder bed fusion

Figure 14. Comparison between 2D and 3D characterizations in the case of (a) TPMS-FGPS 2.5 and (b) TPMS-FGPS 4.0.
manufactured thickness values were used to calculate A more accurate analysis was obtained, considering the
the homogenized properties for each cell dimension and as-manufactured ligament thickness (E hom ).
real
density level using the software nTopology (nTopology
Inc., USA). Since the design of the TPMS unit cell size To define the overall elastic modulus of both TPMS-
was done by means of the implicit Equation V, the FGPSs, the stiffness values reported in Table 8 were input
calculation of the real level constant “t” by means of the as- into Equation III, and the obtained numerical values are
manufactured ligament thickness is necessary. Equations summarized in Table 9 along with the experimental E cyclic .
XIII and XIV, obtained by CAD data, were used to The theoretical values obtained by means of the
calculate the corresponding level constant “t” in the case homogenization method and Equation III lead to a
of as-manufactured ligament thickness of TPMS-FGPS 2.5 discrepancy from the experimental values of around 10% and
and TPMS-FGPS 4.0, respectively. −8% considering the as-designed and the as-manufactured
t = -0.7572 + 0.1842l + 0.4998l - 0.1365l ligament thickness of TPMS-FGPS 2.5. Good correlation
3
2
2.5
t
t
t
Adj R = 0.99982X XIII in both conditions, namely using CAD and as-printed
2
values, was resulted owing to the small geometric deviation
t = -1.1454 - 0.8071l + 1.0483l - 0.1723l
3
2
4.0 t t t from as-manufactured sample and CAD shown through
Adj R = 0.99995 XIV 3D metrological characterization. In addition, a result
2
The results are summarized in Table 7. Lower level close to the experimental values was obtained, highlighting
constants were achieved in the case of as-manufactured the promising ability of the homogenization simulation to
samples due to the undersizing effect caused by the 3D reduce the number of experimental trials and consequently
printing process. Finite element analysis was performed the time consumption to evaluate the elastic modulus of
to compute the homogenized material properties [64,65] . a designed and printed cellular structure. Different results
Table 8 shows the elastic modulus obtained by the were observed in the case of TPMS-FGPS 4 where a large
homogenization in the case of as-designed (E hom ) and as- significant undersizing (−61% and −79%) was obtained,
nom
hom
manufactured (E real ) samples. Elastic modulus values of considering both the as-designed and as-manufactured
the different relative density levels in the case of 2.5 mm ligament thickness with respect to the experimental results.
and 4.0 mm unit cell size are obtained as demonstrated by The homogenization method relies on the hypothesis of
the Gibson–Ashby equation, i.e., Equation I. Therefore, an infinite cell repetition in space. In the TPMS 4.0, the
no influence of the unit cell size was detected for the same specimen has a limited number of unit cells: 3 × 3 unit cells
relative density level. In other words, the elastic modulus on the normal area with respect to the load, meaning along
of a porous structure is affected by the type of cellular x and y directions. This deeply influences the degree of
structure, the bulk material, and the relative density. As accuracy the homogenized model is able to achieve, since
shown in Equation I, an increased relative density leads to the effect given by the edge effect is non-negligible [64,69,70] .
an increased elastic modulus. In order to highlight the importance of the number of unit
Volume 9 Issue 4 (2023) 200 https://doi.org/10.18063/ijb.729