Page 461 - IJB-9-4

International Journal of Bioprinting β-Ti21S auxetic FGPs produced by laser powder bed fusion

software, and the mean and the standard deviation were auxetic FGPS elastic modules were calculated by Equation
calculated. The pore size was measured by means of the III and compared with the experimental data.
diameter of the inscribed circumference, while µ-CT scan
was used for 3D metrological characterization by using a 3. Results and discussion
voxel size of 25 µm for each sample. The Nanotom S system 3.1. 2D metrological characterization: SEM analysis
with X-ray voltage between 100 and 130 kV and current
80 – 90 mA was used. Image analysis was performed using On the lateral surface of the two auxetic FGPSs, the
ORS-Dragonfly software and wall thickness analysis on three relative densities were evaluated by quantitative
the entire volume to define the thickness of the strut and image analysis on SEM micrographs. Differently, the top
the pore size at each relative density level. To consider the surface was characterized only for the lower density level.
frequency of the different measurements and the non- The micrographs in Figures 3 and 4 show the details
normal distribution of the values, median and median of the different relative density levels on the lateral and
absolute deviation (MAD) were used to define the pore top surfaces of the auxetic FGPSs with θ = 15° and 25°,
size and strut thickness rather than the mean and standard respectively. Considering Figure 4, the loss of auxetic
deviation. When the distribution leads to a normal profile, geometry of the high relative density level in case of auxetic
the mean and median become equal. Since standard FGPS with θ = 25° is evident in the printed sample as well
deviation is excessively affected by the outlier values and as in the CAD. The strut thickness and pore size of the
not by the frequency, MAD seems to be a better scatter as-built samples for both auxetic structures are compared
indicator. In addition, overlapping of µ-CT to computer- with the CAD values and summarized in Table 3.
aided design (CAD) images was performed thanks to Inside brackets, the percentage deviation with respect
the align function and generation of a contour mesh in to the CAD values is reported. An anisotropy in terms
Dragonfly ORS software. of pore size and strut thickness in the lower density
Standard metallographic preparation was carried out regions (0.34 for θ = 15° and 0.40 in case of θ = 25°) of
to characterize the microstructure. Kroll’s reagent (1 mL the as-manufactured samples is highlighted thanks to
of HF, 30 mL of HNO , and 85 mL of distilled water) was the investigation of the lateral and top side. Considering
3
used to highlight the microstructure according to ASTM the strut thickness, the anisotropy is due to the printing
E407-07 . Three specimens for each auxetic geometry process. Instead, decreasing the printing angle from 90°
[46]
were quasi-static compression tested at room temperature to 0° strongly affected the strut morphology by decreasing
[54]
(20 ± 3°C) according to ISO 13314:2011 using a servo- the strut quality . Higher surface irregularities and
[47]
hydraulic Instron testing machine with a crosshead speed scattered surface texture is evident on the upper and
of 1 mm/min and a LVDT transducer to remove the under skin of the strut parallel to the x-axis (top view in
machine compliance. Five loading-unloading compression Figures 3 and 4). Differently, the deviation in pore size
ramps were imparted between 20% and 70% of the yield is due to the 2D characterization where the pore size is
stress on one sample in order to obtain the cyclic stabilized evaluated considering the inscribed circumference on the
Young’s modulus . The elastic modulus of the different different 2D views. Since the auxetic cell is not cubic, the
[48]
layers was determined by means of Gibson-Ashby equation pores size is different considering the top or the lateral side
(Equation I) and using numerical homogenization of the cell. This deviation is not present in CAD since it was
method. This method replaces the single unit cell with an evaluated by means of a 3D image analysis where the pore
equivalent bulk elastic material model and with equivalent and the strut size are equal to the diameter of the inscribed
mechanical response of the lattice [49-52] . The auxetic unit cell sphere at each position. This analysis gives the median and
could be further simplified by considering the geometrical MAD values of the pores, and the struts refers to the entire
symmetry as done by Yang et al. A mesh size equal to volume of the relative density level. To correctly correlate
[53]
0.1× strut radius and the mechanical properties of Ti-21S the CAD with the printed sample, top and lateral values
bulk material evaluated by Pellizzari et al. were used in case of lower relative density were put together leading
[18]
in the homogenization analysis, and the stiffness matrix to a lower deviation from the CAD value. The percentage
of an orthotropic linear elastic material was defined. variations from CAD for both structures are plotted in
Subsequently, compliance matrix obtained by the inverse of Figure 5.
the stiffness matrix was defined, and the elastic modulus in Auxetic FGPS with θ = 15° shows a maximum oversizing
the loading direction was calculated. The homogenization of 13% in the pore size and a maximum undersizing of 8%
method was conducted on unit cell with designed in the strut thickness. The same result is observed in the
(E hom nom. ) and printed (E hom real. ) strut thickness at auxetic FGPS with θ = 25° exhibiting a maximum strut
all different levels of relative density. The corresponding thickness undersizing of 13%. Different behavior is evident

Volume 9 Issue 4 (2023) 453 https://doi.org/10.18063/ijb.728