Optimization of FDM manufacturing parameters for the compressive behavior of cubic lattice cores: an experimental approach by Taguchi method

Lattice structures are regularly employed in different industries ranging from biomedical to automobile and aircraft due to their excellent mechanical properties, outstanding load carrying and energy absorption capabilities, and better strength-to-weight ratio compared to traditional structures. On the other hand, fused deposition modeling (FDM) is a cost-effective method of additive manufacturing (AM) vastly used for plastic materials which are biocompatible, biodegradable, and environment-friendly in nature. The main aim of this study is to investigate the effect of FDM printing parameters, namely, layer height, nozzle temperatures, printing speeds, and bed temperatures, on a simple cubic lattice structure printed from PLA filament. The design of the experiment is conducted through L16 orthogonal array. After conducting compression tests, four significant outcomes, namely, modulus of elasticity, compressive strength, fracture strain, and modulus of toughness, are calculated from the stress–strain curves. Furthermore, an ANOVA (analysis of variance) test is carried out to find out the influence of each parameter. The analysis revealed that layer height is the most crucial parameter for modulus of elasticity and compressive strength. Secondly, the study also demonstrates the signal-to-noise ratio (S/N) analysis of each parameter and suggests the best manufacturing parameters, such as the layer height, printing temperature, printing speed, and bed temperature as 0.1 mm, 210 °C, 30 mm/s, and 60 °C, respectively, for the highest compressive strength. An SEM (scanning electron microscopy) analysis is carried out to examine the defects of the optimized lattice structure and found that the optimized structure has fewer defects in comparison to the non-optimized lattice core. Finally, based on these optimized parameters, a bone scaffold model is proposed for future biomedical applications.


Introduction
The fused deposition model (FDM) three-dimensional (3D) printing technique is considered an emerging technology in additive manufacturing (AM) due to their higher accuracy in printing, lower cost in manufacturing, feasibility to print, ability to fabricate complex geometries, and environmental friendliness [1][2][3].With these positive effects, FDM 3D printing has been employed in aerospace, automobile, and biomedical applications [4].The filaments or extrusion materials used in FDM are made of plastic.Generally, plastics are produced from chemical-based products such as petroleum, which may cause serious issue to human health.Moreover, most plastics are non-biodegradable [5].Thus, the demand to design and fabricate biodegradable, recyclable, and sustainable filament is crucial.Polylactic acid (PLA) is suitable for the prospect of sustainability, which is mainly made from starch and collected from natural resources (sugar, potatoes, wheat, corn, etc.) [6].Moreover, PLA exhibits better mechanical properties, biocompatibility, and low immunogenicity and is thus suitable for multiple applications, including biomedical [7], bone scaffolding [8], tissue engineering [9], additive manufacturing or 3D printing [10], sustainable packaging [11], textile [12], structural [13], automotive [14], tissue engineering [15], drug delivery [15], and technical items [16].However, there are some drawbacks in PLA filament, such as poor elongation at break, lower toughness, less water absorption capability, and poor melting strength [6].Also, the use of 3D-printed PLA materials in load-bearing structures is still limited [17].
FDM process parameters such as layer thickness, extrusion temperature, infill density, printing speed, raster angle, and infill pattern significantly influence the mechanical properties of fabricated parts [18][19][20].Among all these FDM processing parameters, layer height is a crucial parameter that can remarkably contribute to mechanical properties.Moreover, this study also found that different combinations of printing parameters with layer height may provide disparity in outcomes which requires further analysis [21].Although most of the researchers disregarded bed temperature, some of the analysis suggests that it has a moderate effect on mechanical properties.A previous study reported that when the bed temperature increases, the shrinkage rate increases by around 7.14% for thin samples.However, for the thick FDM printed part, the shrinkage percentage remained constant with increasing bed temperature [22].Moreover, an experimental study revealed that when the bed temperature increased, the tensile strength and flexural strength increased linearly [23].Besides these considerations (layer height, nozzle temperatures, and bed temperatures), several studies suggest that printing speed is a vital manufacturing parameter for FDM printed parts.In terms of compressive behavior, it is found that when the speed is increased, the compressive strength and modulus of elasticity is decrease by around 34.3% and 14.6%, respectively [24].A similar observation is also found in another literature when the maximum printing speed resulted in lower tensile and compressive strength outcomes [25].
Lattice is a category of cellular structure where the solid and void sections are designed and fabricated to absorb kinetic energy based on different application requirements [26].Besides, they can be tailored to achieve specific mechanical properties suitable to manufacture lightweight structure, thus reducing fuel consumption on the aerospace and automotive industries [27].Furthermore, due to their multidisciplinary applications, these lattice cores have also gained notable interest among researchers and in biomedical industries (for example, bone scaffold) [28,29].AM methods such as fused deposition modeling (FDM), selective laser melting (SLM), selective laser sintering (SLS), and manufacturing materials such as metallic alloys, ceramic, and polylactic acid (PLA) are regularly adopted by current industries to fabricate different lattice structures [30].However, considering high fabrication cost, complexity in design, and fabrication time, some AM methods such as selective laser melting (SLM), selective laser sintering (SLS), and the manufacturing materials such as metallic alloys, ceramics, etc. are becoming challenging options for clinical applications compared to FDM printing method and PLA filament [30].Besides, undesired porosity is often evident in the aforementioned AM techniques [30,31].In the long run, these drawbacks can affect cell attachment and migration improvement [32,33].However, PLA filament is one of the well-known biocompatible and biodegradable materials which has been approved by the US Food and drug administration for different biomedical and clinical applications [34].A recent review study suggests that apart from the biodegradation and biocompatibility characteristics, PLA in bone tissue engineering can provide almost identical elastic modulus to human bone, satisfactory chemical, and physical properties and also have a decent degradation rate.Therefore, PLA-printed scaffolds are getting significant attention and are vastly used in long and short-term bio implantations in bone tissue engineering [35].To achieve a satisfactory degradation rate, less defective parameters have a crucial role.A recent study found that better printing parameters can significantly improve cell growth into the lattice scaffold [36].Furthermore, a similar observation such as the relationship in cell numbers increment/decrement with manufacturing parameters in PLA printed scaffold can be found in the literature [37].Therefore, reducing manufacturing defects and enhancing the mechanical properties of PLA lattice structures are crucial for better biomedical applications.A comparative study based on the type of lattice structures (shell, truss, plate) and materials (PLA, ABS) demonstrated that different architectures of lattice cores and materials can exhibit different characteristics.The outcome of the investigation suggests that trussbased lattice performs moderate mechanical characteristics [38].However, in terms of lattice materials, it is found that compared to ABS, PLA exhibits better stiffness and strength [38,39].More recently, FDM printed lattice structures have been investigated experimentally and using the finite element method (FEM) to estimate the mechanical properties [40,41].However, for FEM analysis, the main limitation for predicting mechanical properties is that FEM cannot consider variable parameters in one simulation even though it has no additional cost and requires less analysis time [41].A comparative study constructed on FDM printed PLA lattice structure revealed that when the nozzle temperatures and printing speed is increased, the tensile strength and elastic modulus is increased significantly.Even though the increment trends of FDM printed part and lattice structures are almost similar, the main differences appeared in the increment percentage (in lattice tensile strength is increased by 3.42%, while for FDM printed simple part, 20%) [17,18].
Generally, in normal FDM printed parts, it is often evident that the highest infill density provokes maximum impact on the mechanical properties [42].However, a comparative study based on experiments on cellular lattice structures between two infill densities (70% and 100%) revealed that small fractions of infill in lattice structures perform better mechanical strength and strength-to-mass ratio [43].In addition, with the increment of material volume, the bending strength of the structure rises steadily [44].
From the above literature, it is apparent that a significant amount of research has been conducted to investigate the mechanical properties (such as tensile, compressive, and bending) of FDM printed PLA parts considering layer height, nozzle temperature, printing speed, bed temperature, infill density, etc.However, very limited research is considered the above factors on the lattice structures [17,38,39,43,44], and no study is found for optimizing the printing parameters for best mechanical outcomes for PLA lattice design.Thus, the main objective of this study is to investigate the effectiveness of various printing parameters on a PLA-based cubic lattice structure and to optimize the printing parameters for the best mechanical properties outcomes.Finally, the microstructural performances of lattice structures are studied through scanning electron micrograph (SEM) to investigate and compare the defect of the optimized structure and the non-optimized structure.

Fabrication and design
The material used in this research is a commercial PLA filament with a diameter of 1.75 mm.The material was purchased from Creality (Shenzhen, P.R. China).

Sample generation
Compared to other lattice structures such as body-centered cubic and face-centered cubic, simple cubic lattice structure provides better mechanical performance [45].Therefore, this research considers a simple cubic lattice structure.Firstly, a CAD model is designed in a commercial CAD software with a dimension of 36.0 mm × 36.0 mm × 30.21 mm to conduct the compression test (according to ASTM D695) [46] and evaluate the mechanical properties.

Design of experiments
The design of the experiment (DOE) has been performed through Minitab 19.For Taguchi selection, 4 level design has been opted, considering four significant printing parameters such as layer height, printing temperatures, printing speed, and bed temperatures.The levels were chosen based on the manufacturer's instruction and existing literature.Finally, the L 16 orthogonal array has been employed to design the DOE.DOE is presented in detail in Table 1.
To fabricate the design on the FDM 3D printing machine, the model has been introduced with an available slicer software named Creality Slicer.After combining all the input parameters from the DOE into the slicing software, the software provides a predicted production time with a G-code.Later on, the obtained G-code was inserted into the FDM printing machine using a memory card.During fabrication, some crucial factors, such as the dimension of the lattice structure and strut diameter, have been scrutinized.In addition, PLA filament can be significantly affected by moisture content and humidity [47,48]; therefore, this study considers some precautions, such as using a polyethylene bag to put the sample after fabrication and checking the dimension measurements against CAD modeling for printing accuracy, as shown in Fig. 1b.However, other parameters, like the infill density of 100%, shell thickness of 1.2 mm, flow rate of 100%, and the nozzle size of 0.4 mm, are kept constant during printing.

Experimental setup
The compression test has been conducted (according to ASTM-D695) on a SENS universal testing machine (model CMT-6000) with a compression speed of 2 mm/min and a 10 KN load cell.An earlier study found that different compression speeds can remarkably influence mechanical properties [39].
To achieve better outcomes, this study considered 2 mm/min speed, which has been obtained from other literatures of PLA materials [17,49,50].Likewise, to get accurate results, five samples are tested of each consideration (from DOE).The preload between platens and samples is 0-5N for all tests.The accuracy of this universal testing machine is ± 0.5%.On the other hand, SEM test has been conducted on a JSM7800F (origin-Japan) machine.First, the sample is cut with scissors, and a specific size is taken from different regions of the sample.After that, the sample was attached to the sample plate by using conductive glue.Before conducting the test, all samples were dried and sputtered with gold in a sputtering machine.Each sample sputtered 4 times (a total of 120 s).It is important to note that the conductive glue and spraying gold are used to increase the conductivity of the sample surface.The thickness of the coating was approximately 2-3 nm.Later on, the sample plate was placed in the sample chamber.Finally, SEM photos of different samples have been collected at 5.0 kV and secondary electron mode with different magnifications.

Experimental results and discussions
After conducting the compression test (based on DOE), the obtained results (load and displacement) are plotted in Fig. 2a, and a comparison of the structures' mechanical performance from the initial stage to ultimate failure is highlighted, similar to the literature [51].From the load vs. displacement curve, stress and strain for each DOE are calculated and presented in Fig. 2b.This load-displacement and stress-strain curves are generated from an average of 5 samples (close to the average result plotted on the curve).The stress-strain curve from Fig. 2b shows that all DOEs have provided a similar trend as expected from the lattice structure.For example, the fracture strain in all DOEs ranges from 0.53 to 0.60.Likewise, the stress-strain curve exhibits a similar trend in all DOE.
Experimental phenomena observed during the test are presented in Fig. 3 which also demonstrates the layer wise collapse of the lattice structure.The serrate shapes in the load-displacement curve Fig. 2a indicate the initial buckling in Fig. 3b.Then collapsed in the 1st, 2nd, and 3rd layers can be seen in Fig. 3c, d, and e.Finally, the ultimate failure is shown in Fig. 3f.Similar results are also observed in the literature for lattice structure [39].This study also suggests the possible reason for this discontinuous graph during the compression test.
The mechanical properties are calculated from the stress strain curve for all DOE, and the outcomes are enlisted in Table 2.In general, higher outcomes in modulus of elasticity and compressive strength reflect the better stiffness of the material.Interestingly, this study indicates that the modulus of elasticity and compressive strength has a direct correlation.For example, while the modulus of elasticity increases, the compressive strength is increased at the same DOE.Similarly, decreasing the modulus of elasticity at any particular DOE, compressive strength also reduced, which indicates a co-relationship between these two outcomes.For this research, the maximum modulus of elasticity and compressive strength is found at DOE (E-3) for 0.1 mm layer height, 205 °C, 50 mm/s printing speed, and 60 °C bed temperature.

Comparison with responses
As discussed earlier, the modulus of elasticity has a correlation with compressive strength, which is also apparent from Fig. 4. As the modulus of elasticity increases, the compressive strength also increases.

ANOVA analysis
ANOVA analysis has been generated to investigate the percentage of contribution (PC) to each parameter of the responses.In this research, the confidence level of ANOVA analysis was set to 95%.As a result, any parameter providing P values less than or equal to 0.05 (α-alpha value) will be considered a significant parameter in this study.Significant parameters for this analysis (those with P values less than or equal to 0.05) are marked with (*).ANOVA analysis with PC of each parameter for elasticity, compressive strength, fracture strain, and toughness modulus is described in Table 3.
Table 3 shows that the layer height is the most influential parameter for modulus of elasticity with P values less than 0.05 and PC 86.748%.However, other parameters such as printing temperature, printing speed, and bed temperature provided insignificant P values with PC 2.883%, 0.2416%, and 0.05%, respectively.In the case of compressive strength, layer height is also the most crucial parameter with P values less than 0.05 and PC 75.34%.The other parameters have no significant role in compressive strength.Moreover, the PC for printing temperature, printing speed, and bed temperature is 2.96%, 3.66%, and 1.64%, respectively.Although, in other responses (modulus of elasticity and compressive strength), the layer height showed a satisfactory PC and P values (in Table 3), there is no significant parameter in the range of 0.05 (α-alpha value) in terms of fracture strain (%).Moreover, the most important parameters according to PC for fracture strain (%) are followed by printing speed 5.689%, printing temperature 4.3248%, layer height 0.09%, and bed temperature 0.06%.
Interestingly, three parameters provide satisfactory P values with less than 0.05 for modulus of toughness.The significant parameters are followed by printing temperature with PC 26.79%, printing speed with PC 25.045%, and layer height with PC 15.468%.However, bed temperature showed a negligible contribution to the modulus of toughness with PC 1.6634%.

Parameter optimizations
In order to estimate and optimize the better responses for printing parameters, the obtained outcomes are further analyzed through signal-to-noise ratio (S/N).For the current calculation, it is determined for all responses, larger is better.Higher values of modulus of elasticity and compressive strength reflect better material stiffness.Likewise, higher fracture strain values and toughness modulus induce large deflection rates and maximum energy absorption capacity in the material.The equation for the S/N ratio (considering larger is better) is presented below: Here, y ij is the mean of the response values and n is the number of responses.The predicted and optimal responses are listed in Table 4 (larger responses are marked with a * symbol).
According to the S/N ratio analysis in Table 4, the modulus of elasticity can be best achieved when the combination is 0.1 mm layer height, 205 °C printing temperature, 40 mm/s printing speed, and 60 °C bed temperature.After combining these parameters, 3D printed samples (five) are again made, and compression tests are performed to compare the results further.In this study, the best outcomes from DOE, software prediction (SP), and experimental results (S/N predicted parameter-based experimental results) are compared in Table 5.Interestingly, there is a negligible difference (0.49%) between the S/N prediction and the S/N predicted parameter-based experimental result.However,  this study also compares experimental results (based on S/N combination) with the best outcomes (for modulus of elasticity) from DOE, and the difference is also insignificant (2.38%).This means that the prediction of the modulus of elasticity has provided satisfactory outcomes.Likewise, S/N predictions for compressive strength yield the best results at 0.1 mm layer height, 210 °C printing temperature, 30 mm/s printing speed, and 60 °C bed temperature.Similar predicted parameters (compared to the modulus of elasticity) are also observed for layer height and bed temperature.After considering these parameters and performing the experiment, the results reveal that the difference between the software calculation and the experimental result is 6.74%.However, the difference between the DOE (E-3) and software-predicted results is about 1.5%, which is significantly smaller.
Regarding fracture strain (%), S/N ratio analysis predicts the best combination at 0.25 mm layer height, 200 °C printing temperature, and 50 °C bed temperature.However, the software provides two estimates for printing speed such as 40 mm/s and 60 mm/s.Later, based on these two combinations, the compression test is carried out.Overall, these two combinations provide an expected result similar to the software prediction with negligible differences (5.08% and 3.63%) for print speeds of 40 and 60 mm/s, respectively.As illustrated in Table 4, the best-optimized parameters of S/N analysis for modulus of toughness are 0.20 mm layer height, printing temperature 210 °C, printing speed 60 mm/s, and bed temperature 60 °C.After calculating the modulus of toughness based on these parameters, it is evident in Table 5 that the experimental results have significantly decreased by 21.15% compared to the software's predicted results.However, if we compare this experimental result (based on the S/N predicted parameter) with the DOE (E-4) result in Table 5, the difference is negligible (6.04%) and in satisfactory condition.

Stress-strain curve analysis
The stress-strain curves based on the optimized parameters for each response are plotted in Fig. 6.In the optimized stress-strain graph, E represents the modulus of elasticity, CS for compressive strength, MT for the modulus of toughness, and FS for fracture strain percentage.Moreover, FS-40 and FS-60 describe the fracture strain when the printing speed is 40 mm/s and 60 mm/s, respectively.

SEM analysis
The microstructure of the lattice structures has significant contributions to the mechanical properties.Therefore, SEM analysis has been conducted in this research to find out possible reasons and to clarify the dissimilarities between the responses.In addition, to reduce the defects and enhance the mechanical properties, SEM analysis also plays a crucial role [17].Hence, SEM analysis is carried out on the responses of modulus of elasticity, compressive strength, and modulus of toughness and compared between DOE maximum and minimum outcomes with optimized responses.However, this work did not consider the fracture strain (%) for the SEM analysis because fracture strain (%) does not change remarkably with printing parameters (ranging from 53 to 60%). Figure 7a-d represents the DOE (E-3), which exhibits the maximum outcomes, and Fig. 7e-h represents the DOE (E-14), which shows the minimum results in modulus of elasticity and compressive strength, respectively.In SEM Fig. 7a-d, DOE (E-3) with low layer height (0.10 mm), medium printing temperature (205 °C), printing speed (50 mm/s), and bed temperature (60 °C) shows low manufacturing defects such as small gaps between two adjacent layers and fewer holes.However, it is visible in DOE (E-14) that there are major manufacturing defects such as unmelted filaments, improper extruded material on the surface, many holes, and especially excessive gaps between layers, which might be responsible for giving minimum outcomes in modulus of elasticity and compressive strength.This is particularly true for most of the AM fabricated parts.For example, as the number of holes increased in the AM-manufactured parts, the parts experienced the earliest catastrophic failure [52,53].Moreover, a possible explanation would be (for  As shown in Fig. 8a-d, the optimized responses provide fewer manufacturing defects (fewer voids, holes, and gaps between two layers) than DOE (E-3).Although the software estimates (S/N analysis) similar parameters to obtain better results than DOE (E-3) in modulus of elasticity, for example, layer height (0.1 mm), printing temperature (205 °C), and bed temperature (60 °C), the only exception is found at printing speed (50 mm/s and 40 mm/s for DOE (E-3) and optimized modulus of elasticity, respectively).SEM analysis indicates that the lowest printing speed (40 mm/s) can provide better results with fewer manufacturing defects for the modulus of elasticity than the highest printing speed (50 mm/s).In terms of compressive strength, SEM analysis shows similar characteristics in optimized response and DOE (E-3).Interestingly, similar parameters have been found in layer height and bed temperature.However, the exceptions are printing temperature (205 °C for DOE (E-3) and 210 °C for the optimized response, respectively) and printing speed (50 mm/s for DOE (E-3) and 30 mm/s for the optimized response, respectively).The main reason for this better outcome in compressive strength would be the maximum printing temperature (210 °C) and low printing speed (30 mm/s), which provide fewer manufacturing defects (holes, voids and layer gaps) and better extrusion.Similar observations (in results) were found and demonstrated in this literature for 3D-printed parts of PLA and PTEG materials [19].
Furthermore, a comparison is also performed by SEM analysis between DOE (E-1) (minimum modulus of toughness), DOE (E-4) (maximum modulus of toughness), and optimized responses for modulus of toughness in Fig. 9.Although the optimized responses in modulus of elasticity and compressive strength give satisfactory and expected behavior (less manufacturing defects such as voids, holes, and gaps) compared to DOE, an exceptional phenomenon is observed for modulus of toughness.For example, DOE (E-4) performs better than the optimized response.The small layer height (0.1 mm) on the DOE (E-4) is the main factor that makes this difference with the optimized response (layer height, 0.2 mm).However, if we compare DOE (E-1) and DOE (E-4), the logical explanation would be lower printing temperature (195 °C) and bed temperature (50 °C) cause many defects such as excessive gaps, unmelted filaments, and a lot of holes, which prevent the structure from carrying excessive loads.As a result, the lattice structure collapses earlier and provides less energy absorption capacity in DOE (E-1).

Literature comparison
This study further validates and explores optimized responses with available literature responses.Table 6 is added below to compare the improvement and reduction percentage of the authors' optimized results with other lattice structures, filament types, unit cells, and dimensions (overall structure).As illustrated in Table 6, the authors' optimized parameters, such as layer height (LH), printing temperature (PT), printing speed (PS), and bed temperature (BT), exhibit better results (in most cases) than other studies.In terms of compressive strength, the authors' optimized results show a decrease of about 19.75% (PLA) and 109.765%(TPU-thermoplastic polyurethane) compared to this study [54].Although the printing parameters, dimensions, and unit cell are quite similar to the authors' optimized parameters, the compressive strength reduction percentage is still very high compared to this study [54].A significant explanation would be that the compressive strength increases significantly in this study due to the different types of lattice structures and filaments.Similarly, the compressive strength is drastically increased in this work compared to the authors' results (56.39% and 98.26% for ABS (acrylonitrile butadiene styrene) and PC (polycarbonate), respectively) [50].However, our simple cubic lattice structure has performed better against this work [55].Although other considerations, including lattice dimension, unit cell number, and filament type, are quite similar to this research, the compressive strength (of the author) improves remarkably (about 125.65% for hexagonal shape and square shape 51.0%, respectively) due to the lattice structure and the authors' better manufacturing parameters.Interestingly, compared to the composite (PLA/ KBF) (PLA and basalt blend) and PLA/PCL (PLA and polycaprolactone), the compressive strength obtained as a higher percentage in our consideration is about 60.71% and 73.75%, respectively.On the other hand, for the modulus of elasticity, the authors' obtained better outcomes (about 30% to 76%) than other literature [50,55,56].Among these studies, although the lattice structure, filament type, dimension, and unit cell are different, the authors' optimized outcomes are comparatively better for the modulus of elasticity.Moreover, a relationship between the modulus of elasticity and compressive strength is highlighted (with the increase or decrease of modulus of elasticity, compressive strength will increase or decrease), which is also observed in the literature [55,56].Overall, different lattice types, dimensions, filament types, and unit cells can significantly affect the mechanical performance of lattice structures.

Application
This study designs a lattice scaffold and prints with optimized parameters of layer height 0.1 mm, printing temperature (210 °C), printing speed (40 mm/s), and bed temperature (60 °C) to remove the manufacturing defects.Moreover, an SEM analysis is conducted on the 3D printed scaffold (application), where minimal manufacturing defects have been observed.The printed scaffold and SEM analysis have been presented in Fig. 10.Since PLA is non-toxic, biodegradable, and biocompatible (with better body fluid interaction), this proposed design and optimized parameters can be used for future investigation in biomedical applications such as in rapid prototyping, educational purpose, bone regeneration, and bone replacement, especially in fracture zones.

Conclusions
PLA filament is a widely adopted FDM printing material in biomedical and clinical applications.In this study, a set of experiments have been conducted to determine the influences of manufacturing parameters on the compressive  behavior of a PLA lattice cubic structure.The results revealed that manufacturing parameters could significantly influence mechanical properties.Aside from this, a correlation has been developed among considered outcomes.
Additionally, this study also generates different statistical simulations and SEM analyses to improve the mechanical properties with fewer manufacturing defects.The experimental results of this research are summarized below; • The maximum modulus of elasticity and compressive strength is obtained with a combination of 0.1 mm layer height, 205 °C printing temperature, 50 mm/s printing speed, and 60 °C bed temperature.• The highest fracture strain percentage (60.06%) is found for 0.1 mm layer height, 200 °C printing temperature, 40 mm/s printing speed, and 55 °C bed temperature.However, the highest outcome of modulus of toughness (1104.53kJ/m 3 ) is obtained for 0.1 mm layer height, 210 °C printing temperature, 60 mm/s printing speed, and 65 °C bed temperature.• ANOVA analysis reveals that layer height is the most crucial parameter with a significant effect on modulus of elasticity and compressive strength with percentage contributions of 86.75% and 75.34%, respectively.Additionally, for fracture strain percentage and modulus of toughness, printing speed and printing temperature are the most influential parameters, with contribution percentages of 5.69% and 26.79%, respectively.
• Predicted responses from S/N analysis and experimental responses (based on S/N predicted parameters) provide minimal differences, such as for modulus of elasticity only 0.49%, compressive strength 6.74%, and fracture strain 3.63%.However, the percentage difference in modulus of toughness is slightly high, around 21.15%.• SEM investigations reveal that experimental results (based on S/N predicted parameters) show fewer manufacturing defects in modulus of elasticity and compressive strength, while compared to DOE maximum outcomes.This means the experimental results found on S/N predicted parameters are better than the DOE results.However, for the modulus of toughness in the S/N predicted parameters, different manufacturing defects are observed in contrast to the DOE tests.This study only investigated the compressive behavior of a simple cubic lattice structure; however, a future study would be generated by considering different biological environments, such as in vitro and vivo analysis of the proposed applications.

Fig. 8
Fig. 8 SEM micrographs of the 3D printed lattice surface, a-d optimized modulus of elasticity, e-h optimized compress strength at different magnification and resolution scales

Fig. 9
Fig. 9 SEM micrographs of the 3D printed lattice surface, a-d minimum modulus of toughness DOE (E-1) and DOE (E-4), e-h maximum modulus of toughness, i-l optimized modulus of toughness at different magnification and resolution scales • A comparison has been performed with other lattice structures and filaments.Comparative studies reveal that present simple PLA lattice structure shows better mechanical properties than other lattice structures and filaments (such as ABS and PLA composites).

Fig. 10 a
Fig. 10 a-c 3D printed PLA scaffold from normal lattice cube structure with hole and without hole, designed scaffold in ABAQUS d without hole and f with hole, e and g SEM analysis on the 3D printed scaffold

Table 2
Detailed experimental outcomes based on DOE

Table 5
Comparison in DOE,

Table 6
Comparison of the outcomes of the present work with the existing literature