Experimental and statistical investigation on flexural properties of FDM fabricated PLA specimens applying response surface methodology

Additive manufacturing (AM) is a modern technology currently adopted by manufacturing industries to benefit from its low-cost applications, versatility and fabrication of complex parts. Fused deposition modeling (FDM) is distinguished among the different AM technologies due to its fast, yet accurate operations. However the properties of fabricated components are strongly depended by FDM-related parameter settings. This work examines the effect of FDM-related parameters namely flow rate, printing speed and printing temperature on the response of flexural strength. Experiments according to L9 orthogonal array and a custom response surface experimental design were performed to obtain the results necessary for further examination and analysis corresponding to parameter effects on flexural strength and statistical outputs. Experiments were designed as per the ASTM D790 standard whilst failure modes of experimental samples were observed for correlating the independent printing parameters with the response of flexural strength. The full quadratic regression model generated for predicting results concerning flexural strength was found adequate for explaining the variation of FDM-related parameters on flexural strength response.


Introduction
Additive manufacturing (AM) technologies are widely applied to modern part design and production processes owing to their advantages and low cost compared to other manufacturing operations.A common method to additively manufacture parts and products is Fused Deposition Modeling (FDM) or simply 3D-printing.In this method the material is deposited in the form of heated filament on a platform while the component is built in a "layer-by-layer" fashion [1].The conditions under which the additively manufactured components are employed, suggest static and dynamic loads that these parts are subjected; therefore their mechanical properties should be carefully examined [2,3].Another important aspect is the suitable selection of process parameters with respect to objectives involving mechanical strength, fatigue, wears, tension-compression, etc. [4][5][6].In [4] an extensive review concerning the effect of important process parameters of fused deposition modeling are discussed.Emphasis is given to the fatigue performance of polymeric specimens fabricated using FDM.The authors mention that even though each individual parameter exhibits positive or negative effect by altering loading types or material changes, it is rather hard to draw a general conclusion for each one of them.In [7] the authors studied the effect of printing speed, filling ratio as well as raster angle on mechanical properties of PLA+ parts produced by FDM.Moreover, mathematical models were created so as to predict PLA+ material's properties having examined the samples used in their experiments.The authors in [8] examined the effect of FDM process-related geometrical parameters on part strength for open-source desktop 3D printers using PLA as the main filament material.Their research involved several nozzle diameters and a range of layer heights from minimum to maximum physical limits of the 3D printer type.This work focuses on an experimental study concerning the influence of three FDM-related parameters on flexural strength, FS (MPa) of PLA fabricated samples designed according to ASTM D790 standard.The FDM-related parameters where flow rate; printing speed and printing temperature.Experiments were established with reference to L9 orthogonal array whereas a continuous experimental domain was determined by implementing a customized response surface design with same lower and upper FDM parameter bounds.

Experimental
Three independent FDM process-related parameters were studied for their influence on flexural strength (MPa) of PLA-made samples with standard geometry (ASTM D790).The parameters are flow rate, FL (%); printing speed, PS (mm/sec) and nozzle temperature, NT ( o C).Flow rate controls the magnitude of filament to be extruded.Flow rate is predetermined to 1.0 or 100% (maximum flow rate) according to the slicer's module.The second FDMrelated parameter (printing speed) controls the linear speed of the extruder and the third (nozzle temperature) controls the filament's temperature to be extruded by the extruder's nozzle.The values for 3D-printing parameters were selected according to the work material and the manufacturer's general recommended aspects concerning the experimental resources; 3D printer and corresponding software environment.The parameters and levels for designing the experiment are given in Table 1.In printing of the entire specimen the vertical (90 o ) building orientation with respect to ISO 52900:2021 standard was followed.Given the three FDM-related parameters and their levels, an L9 orthogonal array was adopted to establish the sequence of experimental tryouts.To study the results for flexural strength in a continuous experimental domain in terms of the independent variables, a custom response surface design was applied maintaining the same boundaries for low and high parameter levels.With reference to the response surface design, non-linear effects of process parameters can be examined whilst flexural strength is predicted by generating a reliable second-order full quadratic model correlating inputs and outputs (FDM parameters and response of flexural strength respectively).As a first step a CAD model of the standard ASTM D790 flexural test sample was prepared in CATIA® V5R18 and then imported to Repetier Host® for FDM process setup and slicing.Experimental samples were then fabricated in a Craftbot® Plus Pro 3D-printer.Flexural experiments were conducted under a controllable environment (room temperature 23±2 o C; relative humidity 50±5%) as ISO R291:1977 suggests.To reduce printer bed positioning error, each of the PLA samples was fabricated in the middle of the printer's working envelope.The bed's temperature was set to 65 o C. Next step dealt with dimensional accuracy of printed specimens.Finally the samples were sequentially tested for their flexural properties (3-point bending) in an Instron® 4482 dual-column universal testing machine accompanied with Bluehill® 2 data acquisition software.Experimental tests were performed by maintaining cross-head speed equal to 5 mm/min to ensure stability in material deformation prior to total failure.Cross-head motion is interrupted when observing severe fracture or reaching to total failure.The experimental outputs of flexure stress-strain as well as flexure load-extension were recorded and gathered using Bluehill® 2. The experimental se-tup is depicted in Fig. 1a, whilst Fig. 1b shows an indicative experimental output obtained by the 1 st run.The forces, under which the experimental samples were subjected to, indicate the phase where recoverable-viscoelastic deformation is exceeded, thus; resulting to plastic deformation.During the 3-point bending experiments, different failure modes were observed in experimental samples since these were built by determining different FDM-related process parameter settings.In the study, we examined the specimens with the maximum and minimum flexure stress values obtained during the bending tests.Optical microscopy in bright mode was employed to examine the fractured surfaces of specimen 1 and specimen 9, representing the specimens with the highest and lowest flexure stress values, respectively.Fig. 2 depicts micrographs of the outer layers of these specimens, specifically focusing on the layers subjected to tension and compression during the 3-point bending test.The examination of fractured surfaces using optical microscopy provides valuable insight into the failure modes of the interlayer bonds.The fractured surface of specimen 1 exhibited rougher surfaces, indicating robust layer bonding and a clear indication of strong interlayer bonds.Conversely, the fractured surface of Specimen 9 displayed smoother surfaces, suggesting weaker interlayer bonds due to the specific parameters used in its printing.These microscopy results are consistent with the findings from the mechanical bending tests, establishing a correlation between the observed fracture characteristics and the flexure stress values.The rougher fractured surface of 1 st specimen suggests improved interlayer adhesion, which likely contributed to its higher flexure stress value.Conversely, the smoother fractured surface of 9 th specimen implies compromised interlayer bonding, aligning with its lower flexure stress value.

Statistical analysis and regression model generation
The series of experiments are given in Table 2 along with the results obtained for flexural strength (MPa) per experiment.From the 9 experiments, no. 7, 8 and 9 exhibited the highest flexural strength, i.e., 56.4,63.9 and 67.6 (MPa) respectively.This observation indicates that 100% flow rate should be the dominant parameter value when it comes to flexural properties as expected, whilst the rest two parameters yield variations based on their interactions.A flow rate equal to 100% with nozzle temperature set to 230 o C and printing speed set to 60mm/s should be close to the most advantageous parameter levels in terms of PLA material printing.Experimental data analysis was conducted using MINITAB® 17 software.As a response representation model, the full-quadratic mathematical expression (Eq.1) was implemented.
The above mathematical expression involves the linear terms (process-related variables as independent control parameters), the quadratic terms of independent control parameters and their two-way interactions whose number depends on the number of independent variables in the experiment.With "Y" the response of flexural strength (MPa) is represented whereas the number of independent variables is depicted as x i (i th variable).The model's adequacy in terms of response prediction is validated by either F or p-values.Increased F values should normally correspond to reduced p-values and vice-versa.Low p-values (p<0.05)found in analysis of variance (ANOVA) suggest that their corresponding variables hold significant influence on the response under question.As far lack of fit is concerned it should be insignificant enough for the model to well-fit the experimental results, therefore large p-

Conclusions and future perspectives
Major scope of this work was to investigate the effect of the FDM-related parameters namely flow rate, nozzle temperature and printing speed on flexural strength of PLA 3D-printed samples.Series of experiments were performed by establishing a custom response surface experimental design with 9 tryouts according to an L9 orthogonal array.This approach enabled the investigation of complex behaviour concerning the independent variables of FDM process on flexural strength.Statistics and regression outputs justified the prediction model's capability of representing variability in terms of the FDM process parameters examined and exploiting the experimental domain for further analysis.The FDM-related parameters were examined as pairs of two parameters with the aid of contour plots.Experimental indications and statistical results have shown that different advantageous bounds for selecting the values of nozzle temperature and printing speed can be tracked, provided that flow rate is set to its maximum setting (i.e., 100% or 1).Linear terms of the quadratic model generated seem to have a dominant influence on the response of flexural strength.Printing speed holds dominant effect on thermal energy absorbed by neighbouring deposited layers.Printing speed ought to be determined to middle and high levels for avoiding thermal deformations of FDM-build parts which might further degrade flexural strength.As a near-future research, FDM materials and variables other than those studied in this work are to be experimentally investigated with the concept of delivering robust predictive entities (either regression models or neural networks) towards the broader goal of optimizing different criteria by implementing intelligent algorithms.Furthermore different filament materials will be provided to examine their properties by establishing multi-level experiments, creating regression models and formulating optimization problems dealing with wear, strength, surface topography and other crucial performance indicators important to real world applications and industrial projects.

Table 1 .
FDM-related parameters and experimental levels.

Table 2 .
Order of experiments and corresponding results for flexural strength (MPa).