Figure 2 shows length, width, and depth averages which were calculated for each analysis group. The difference from nominal (length = 22 mm, width = 9 mm, depth = 8 mm) was quantified and compared across groups. Results were averaged for all test groups within each printer group (n = 40). All Laser 1 measurements varied from the nominal by less than 0.2 mm and results show averages greater than the nominal value for length, width, and depth dimensions (Fig. 2A(i)). The EBM measurements varied between 0.4 mm-0.7 mm from the nominal value and showed average lengths below the nominal dimension while the width and depths were greater than the nominal values.

Fig. 2
figure 2

External coupon dimensions were quantified relative to the nominal by subtracting the nominal design values for length (22 mm), width (9 mm) and depth (8 mm) from the caliper measurements. A The average nominal values of all groups combined (n = 40) (i), the comparison between the frame and no frame groups (n = 20) (ii), and the post-HIP comparison between the frame and no frame groups (n = 10) (iii) are shown. Legend labels with “frame” refer to samples containing a frame. B External dimensions were also compared between the solid portion and the lattice portion of each sample

The Laser 1 and EBM printing methods each contain two groups, one with an external frame and one without an external frame. Length, width, and depth averages were calculated for each test group and quantified relative to the respective nominal dimension. As shown in Fig. 2A.ii, most experimental groups differed from the nominal; the minimum average difference was the framed Laser 1 length measurement at 35 μm over the total 22 mm length while the maximum average difference occurred in the unframed EBM depth at 669 μm over the total 8 mm depth. In addition, there is a statistical difference (p < 0.05, Tukey’s HSD) between framed and unframed groups in all three external dimensions for the Laser 1 samples. For the EBM samples, there was only a statistical difference (p < 0.05, Tukey’s HSD) between the framed and unframed coupons for the width dimension. Both the length (p = 0.066, ANOVA) and the depth (p = 0.454, ANOVA) measurements did not show statistical differences between framed and unframed groups. The EBM width was approximately 0.41 mm greater than nominal and the depth was approximately 0.67 mm greater than the nominal for both groups. Similar to the Laser 1 groups, the EBM groups all differed from the nominal and did not show any preferences between framed and unframed groups.

To evaluate the influence of the HIP process on dimensional variability of 3D Printed lattice coupons, half of all samples were post-processed using a HIP method (Fig. 2A(iii)). All length, width, and depth measurements were obtained and plotted as stated previously. Trends in the data appeared consistent with the as-printed samples with the largest variations occurring in the Laser 1 length samples where the difference between the as-printed and post-HIP means was 150 μm. The width and depth change were less than 30 μm. The HIP process had a statistically significant (p < 0.05, Tukey’s HSD) effect on most of the external dimension measurements for Laser 1 samples. In samples with a frame, only the depth measurement did not show a statistically significant difference between the as-printed and HIP states (p = 0.241, Tukey’s HSD). For Laser 1 samples without a frame, all external dimensions showed a statistically significant difference post-HIP (p < 0.05, Tukey’s HSD). The EBM samples had a difference of approximately 10 μm in length, 63 μm in width, and 76 μm in depth between as-printed and HIP states. Statistical analysis showed that the EBM samples had a statistically significant difference after the HIP process for the width and depth measurements for both the framed and unframed groups (p < 0.05, Tukey’s HSD).

To isolate the solid portion from the influence of the lattice structure dimensional deviations, the first measurement of the width and depth was analyzed separately from the remaining measurements for each sample. It was found that there is a difference between the average first measurements and the remaining measurements for the width and depth dimensions for both Laser 1 and EBM groups (Fig. 2B). The Laser 1 measurements for width and depth showed a very small difference between the averages with all averages for solid and lattice below 0.1 mm. However, the EBM groups had the largest average dimensional difference between the solid and lattice components. For the width dimension, the solid was less than 0.05 mm above the nominal value while the lattice portion had greater than 0.5 mm average difference above the nominal. In the depth dimension, the solid portion was farther from the nominal than the other solid groups, but the lattice portion was approximately 0.75 mm greater than the nominal.

Images were taken of the top and the side of each sample (Fig. 1) using a HiRox Microscope and the lattice regions were evaluated for pore area using ImageJ. Data was quantified relative to the respective designed pore area for each group by subtracting the nominal designed pore area from the experimental value (Fig. 3A). Trends in the data show the pores tend to be smaller than the designed geometry, and EBM test groups show large variability in pore size for both the top face and the side face of the lattice coupons.

Fig. 3
figure 3

The pore area (A) was measured using optical imaging and ImageJ, and the strut diameter (B) was measured using micro-computed tomography

Three samples of each group were evaluated using a microCT system. Strut thickness values were quantified relative to the designed strut thickness for the corresponding group (Fig. 3B). Results indicate the average strut diameter was smaller than the nominal design, however, the variability was relatively consistent between all groups.

As shown in Fig. 4, there are visible structural differences in the lattice coupon between the two printing methods when the same design file was printed. It is important to note that there were challenges in analyzing pore area in the EBM samples when using the non-destructive visual assessments shown in Fig. 3A.

Fig. 4
figure 4

SEM Images of the same coupon design printed with the Laser 1 and EBM systems

Additional samples were created to evaluate the effect of relative density on dimensional variability. Samples were designed with varying relative densities (15%, 25%, 35%, 45%) and manufactured on a separate laser system (Laser 2) than the Laser 1 samples discussed previously. However, similar measurement techniques were applied to these samples. External length, width, and depth measurements were obtained for each relative density and quantified relative to the respective nominal dimension: length = 22 mm, width = 9 mm, depth = 8 mm (Fig. 5A(i)) by subtracting the nominal. There was a statistically significant difference in the length dimensions when the different relative densities were compared (p < 0.05, ANOVA). However, post-hoc analysis of as-printed samples only showed a statistical difference between the 15% and 35% length dimensions (p = 0.03, Tukey’s HSD).

Fig. 5
figure 5

The effect of relative density on coupon dimensions was also examined. External dimensions were measured and subtracted from the nominal values for length (22 mm), width (9 mm) and depth (8 mm). A The average nominal values of all as-printed groups (n = 10) (i) and the average nominal values of the post-HIP groups (n = 5) (ii) are shown. B External dimensions were also compared between the solid portion of the sample and the lattice portion. C The pore area was measured using optical imaging and ImageJ, and (D) the strut diameter was measured using micro-computed tomography

To evaluate the influence of the HIP process on dimensional variability, length, width, and depth measurements were again obtained (Fig. 5A(ii)). There was a statistically significant difference for all three dimensions as a function of relative density. For the length dimension, the 15% and 25% RD samples did not show a statistically significant difference in the Tukey’s HSD analysis (p = 0.053, Tukey’s HSD), while all other length comparisons were statistically significant (p < 0.05, Tukey’s HSD). When comparing the width dimension, there was not a statistically significant difference between the 15% and 25%, 15% and 35%, and the 25% and 35% groups (p > 0.05, Tukey’s HSD). For the depth measurements, there was not a statistically significant difference between the 25% and 35% and the 35% and 45% groups (p > 0.05, Tukey’s HSD).

Trends for these samples mimicked those of the as-printed samples. When comparing the HIP dimensions to the as-printed state, there were no statistically significant differences found (p > 0.05, ANOVA). However, the length measurements appeared to cluster more closely to the nominal in the HIP state (< 0.2 mm) than the as-printed state (< 0.4 mm).

Similar to the printing method groups shown previously, data was compiled into two additional groups: the first measurement from each sample and the remaining measurements for each sample to represent the solid portion and the lattice portion of the sample, respectively. Width and depth measurements were obtained, and it appeared that there is a visible difference between the solid and lattice measurements for width and depth measurements for all relative densities (Fig. 5B) with the solids closer to nominal, the width larger than nominal, and the depth smaller than nominal.

The top and the side of each sample were imaged, and ImageJ was used to evaluate pore size. Data was quantified compared to the designed pore area for each group (Fig. 5C). Trends in the data show that the pores tend to be larger than the designed geometry, but the variability in pore size for both the top face and the side face of the lattice coupons did not appear to vary between relative density groups.

Three samples of each group were evaluated using a microCT system to quantify the average strut thickness values of each sample. Strut thickness values were normalized to the designed strut thickness for the corresponding group (Fig. 5D). Results indicate that the average strut diameter was smaller than the nominal designs for each relative density. However, the dimensional variability appeared to be consistent across groups whether the samples were as-printed or post-HIP.

As shown in Fig. 6, there are visible structural differences in the lattice coupon with varying relative densities. Despite these visible differences, there is little effect in the measured lattice parameters (Fig. 5) relative to the nominal and compared for differences in variability across all relative density groups.

Fig. 6
figure 6

SEM Images of the varying relative densities (RD) printed with the Laser 2 system

As stated previously, this analysis began with non-destructive testing to evaluate assessment methods that maintained the structural integrity of each sample. However, due to the conflicting results shown in Figs. 2 and 3, a different and destructive test method (ASTM F1854-15 “Standard Test Method for Stereological Evaluation of Porous Coatings on Medical Implants”) was also used. Cylindrical lattice coupons were evaluated using the microCT method and subsequently the ASTM F1854 method allowing the strut thickness measurements to be compared for the same samples.

A frequency graph of the difference between the ASTM F1854-15 values and the microCT values are shown in Fig. 7. It was found that the ASTM F1854-15 method gave consistently higher strut diameter values. The average difference between the two methods is 62.9 μm with a maximum difference of 138.4 μm.

Fig. 7
figure 7

A frequency graph of the additional lattice samples that were used to compare measured strut diameter for the microCT (μCT) method to the ASTM F1854-15 standard. MicroCT results were subtracted from ASTM F1854-15 standard, differences were classified into 25 μm bins

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