Page 84 - MSAM-1-3

Materials Science in Additive Manufacturing Increasing density and strength in binder jetting

3.3. Statistical analysis 40 µm density was found to be 5.11% and 6.77% larger

Statistical analysis was performed on density values and than the 20 and 30 µm groups, respectively. The 30 + 10
UFS to determine any statistical differences between and 40 + 10 µm bimodal groups displayed a much higher
groups. Both sintered density (n = 4) and UFS (n = 5) density than any of the unimodal groups with average
relative densities of 71.83% and 71.57%. In addition, the
results were compared based on powder size groups (six 30 + 10 and 40 + 10 µm bimodal groups showed a 20.18%
groups). A Ryan-Joiner test (similar to Shapiro–Wilk) and 19.74% increase in sintered density when compared
was performed (α = 0.05) in Minitab to verify for normal to the highest density group of 10 µm unimodal powders.
distribution before Bartlett’s test for equal variance.
One-way analysis of variance (ANOVA; α = 0.05) was The Ryan-Joiner test showed that the sintered density
performed, along with a Tukey multiple comparison test data presented were not normally distributed. Because of
to compare group means. If the normality test failed, a this, a Kruskal–Wallis (α = 0.05) non-parametric test was
Kruskal–Wallis non-parametric test was run in Python to performed, showing P < 0.05. This value indicated that
evaluate the statistical difference in median values between due to the statistical difference between median values of
groups. A Dunn’s test, with a Bonferroni correction, was each group, particle size distribution does have a statistical
applied to identify the statistically different groups and to impact on the sintered density results obtained through this
reduce family-wise error rate and Type I errors. study. A Dunn’s test with Bonferroni correction found that
the 30 µm group was the only group that was statistically
3.4. ReaxFF MD simulations lower than both bimodal groups, as shown in Figure 6.

ReaxFF MD simulations are a force field-based atomistic Additional density measurements were calculated using
modeling method. The smooth bond order transition for XCT data. Although minor differences can be observed in
bond breaking and formation enables ReaxFF to model the obtained XCT densities when compared to physical
the solid/liquid and solid/solid chemical reactions in the measurements (8.2%), the trends are consistent with each
binder jetting additive manufacturing process. In a previous other. For instance, the highest density was still achieved
work by the authors, the solid-liquid interactions between in bimodal groups at 74.82% and 76.99% followed by the
Cr-oxide in SS particles and binder solutions were modeled unimodal 10 µm at 66.80%, as shown in Figure 7.
with a system that contains Cr-oxide nanoparticles,
diethylene glycol, and water molecules . The simulation 4.2. Three-point bending
[25]
results provided a molecular level explanation of the UFS results (n = 5 bars) from each group, obtained from
strengthening mechanism from print to the sintering the 3-point bending test, are shown in Figure 8. A clear
stages. In another study by the authors, two sizes of decreasing trend in UFS with an increase in particle size
particles were prepared to model the bimodal particle size among the unimodal group can be observed, which agrees
distribution . The particles have a Fe-Cr O core-shell with the results found with the sintered density in Section
[26]
3
2
structure. The ReaxFF MD simulations were carried out 4.1. However, unlike the density trend reported previously,
at room temperature, 120°C, and 1120°C to compare the which saw a slight increase in 40 µm density compared to
bimodal and unimodal particle size distribution regarding the 20 µm and 30 µm, a continuous decrease in UFS from
the chemical and physical evolution at the print, curing, 10 µm to 40 µm was observed in this study.
and sintering stages, respectively. Rupture strengths were
computed after the system reaches equilibrium at each
temperature. More details regarding the simulations can
be found in this paper . In this work, we compared the
[34]
rupture strengths of sintered products computed with the
ReaxFF potential from Gao et al. with experimental
[34]
measured by the 3-point flexural test.
4. Results

4.1. Sintered density
Sintered density (n = 4 cylinders measured with calipers)
corresponding to each of the six particle size distribution
groups is shown in Figure 6. A visible trend within the
unimodal groups is observed, showing a decrease in Figure 6. Sintered density values across unimodal and bimodal particle
density as the particle sizes increase up to 40 µm. The size groups. *P = 0.01 – 0.05.

Volume 1 Issue 3 (2022) 6 https://doi.org/10.18063/msam.v1i3.20