Relationships among manufacturing parameters, apparent density, ultimate tensile strength, and post-machining surface roughness of FFF 316L stainless steel parts

1 Introduction

Additive manufacturing (AM) enables layer-by-layer fabrication of complex geometries and is widely applied to 316L stainless steel because of its excellent corrosion resistance, ductility, and suitability for complex engineering applications. However, AM-processed 316L often exhibits process-induced anisotropy, residual porosity, and relatively high surface roughness compared with conventionally manufactured counterparts. These characteristics significantly influence machinability, mechanical performance, and functional surface integrity. Consequently, the final quality of additively manufactured metallic components is strongly affected by the combined effects of processing parameters, microstructural characteristics, and post-processing operations.

Recent studies have emphasized the importance of simultaneously considering density, mechanical properties, and surface quality rather than evaluating these characteristics independently. For instance, Deng et al. (2020) proposed a multi-objective optimization strategy that simultaneously considered density and surface roughness and demonstrated that laser power and scanning speed were the dominant process variables affecting overall quality. Similarly, Ni et al. (2024) reported that build orientation and deposition direction strongly influence the mechanical response and anisotropy of additively manufactured stainless steel, reinforcing the importance of directional effects on material performance.

Build orientation is recognized as one of the most influential processing parameters in fused filament fabrication (FFF), affecting tensile strength (Quarto et al., 2021), shrinkage (Kurose et al., 2020), interlayer bonding, and surface quality. Agrawal and Thoma (2022) further showed that localized porosity distribution, rather than average density alone, has been reported to influence surface defects and machining response in additively manufactured 316L stainless steel, suggesting that bulk density measurements may not fully capture the heterogeneity responsible for surface generation mechanisms.

FFF-produced 316L stainless steel generally exhibits higher porosity and stronger anisotropy than powder-bed-based processes (Spiller et al., 2022). Printing parameters, including layer thickness, raster angle, and build orientation, significantly affect sintered density, microstructure, and mechanical performance (Hassan et al., 2021). Previous studies have also demonstrated that process optimization can improve green density and surface roughness (O'Connor et al., 2024), while sintering conditions strongly influence densification, pore evolution, and microstructural development (Boschetto et al., 2022).

Raza et al. (2024) demonstrated that high density and enhanced mechanical performance in FFF-fabricated 316L stainless steel can be achieved through careful optimization of debinding and sintering parameters, whereas Cerlincă et al. (2024) showed that ironing and process parameter optimization substantially improve dimensional accuracy and surface quality.

Several additional investigations have focused on different aspects of FFF-fabricated 316L stainless steel. Some proposed simplified fabrication routes (Sadaf et al., 2021), whereas others demonstrated that sintering schedules significantly affect pore morphology and microstructure (Wagner et al., 2022). Practical studies have confirmed the capability of FFF technology to produce functional 316L components with controlled geometry, microstructure, and mechanical performance (Zaitceva et al., 2024).

The anisotropic mechanical behavior of FFF 316L stainless steel has also been quantitatively characterized using digital image correlation (DIC), demonstrating that deformation and strain localization strongly depend on build orientation and interlayer bonding quality (Pellegrini et al., 2022). Caminero et al. (2021) further showed that build orientation is a dominant factor influencing tensile strength, stiffness, and dimensional accuracy, whereas Jiang and Ning (2021) demonstrated that pore morphology, grain structure, and interlayer defects significantly affect fatigue resistance.

In polymer-based FFF systems, similar conclusions have recently been reported. Greco et al. (2025) demonstrated that build orientation simultaneously influences tensile properties, dimensional accuracy, and surface roughness, revealing strong interactions among mechanical performance and surface quality. More recently, Russo et al. (2026) employed surrogate-based optimization to identify build orientations that simultaneously maximize tensile strength while minimizing geometrical deviations and surface roughness, further confirming that build orientation is a dominant manufacturing variable governing overall part quality. Although these studies considered polymeric materials, they collectively highlight the critical role of manufacturing parameters in controlling both mechanical behavior and surface characteristics.

In hybrid manufacturing, where additive fabrication is followed by subtractive finishing processes such as micro milling, the relationship between mechanical properties and surface roughness becomes considerably more complex. Previous statistical analyses have shown that correlations between surface roughness and mechanical properties are often direction dependent (Dinc et al., 2025) and may also be affected by process-induced residual stresses generated during machining operations (Fergani et al., 2014; Martignoni et al., 2024).

Previous studies, including our recent work (Dinc et al., 2025), have primarily focused on evaluating the relationships between manufacturing parameters—including layer thickness, raster angle, build orientation, and workpiece orientation—and post-machining surface roughness using statistical correlation and regression-based modeling. While these investigations successfully identified the dominant manufacturing variables, they provided limited insight into whether apparent density and ultimate tensile strength (UTS) exhibit independent statistical associations with post-machining surface roughness after accounting for the effects of the controlled manufacturing parameters and the anisotropic microstructures inherent to FFF-fabricated materials.

The objective of this study is to investigate the relationships among manufacturing parameters, apparent density, ultimate tensile strength (UTS), and post-machining surface roughness of FFF-fabricated 316L stainless steel following micro milling. Unlike previous studies that primarily emphasized process parameter optimization or predictive statistical modeling (Dinc et al., 2025; Greco et al., 2025; Russo et al., 2026), this work evaluates whether apparent density and UTS exhibit statistically significant associations with post-machining surface roughness after accounting for layer thickness, raster angle, build orientation, and workpiece orientation. Surface roughness was evaluated in three measurement directions (0°, 90°, and 180°) to assess potential directional characteristics of the machined surfaces.

The novelty of this work lies in evaluating whether apparent density and UTS exhibit statistically significant independent associations with post-machining surface roughness after accounting for the principal additive manufacturing and machining variables. The study further demonstrates that the controlled manufacturing parameters, particularly workpiece orientation, are the dominant factors associated with post-machining surface quality, whereas apparent density and UTS do not exhibit statistically significant independent associations after adjustment for the manufacturing variables. These findings complement previous process-parameter-focused studies and contribute to a more comprehensive statistical understanding of hybrid additive–subtractive manufacturing of FFF-fabricated 316L stainless steel.

2 Materials and methods

This section describes the materials, specimen fabrication, post-processing, and experimental procedures used to investigate the relationships among manufacturing parameters, apparent density, ultimate tensile strength (UTS), and post-machining surface roughness of 316L stainless steel specimens produced by fused filament fabrication (FFF). The experimental methodology integrates additive manufacturing, thermal post-processing, apparent density measurements, mechanical characterization, micro milling, surface roughness evaluation, and statistical analysis to investigate the relationships between the manufacturing variables, apparent density, UTS, and post-machining surface roughness.

The overall experimental workflow consisted of the following sequential steps:

• 3D printing (FFF fabrication)
• Thermal debinding and sintering
• Apparent density measurement (Archimedes method)
• Tensile testing (ASTM E8)
• Micro milling of the fractured tensile specimens
• Surface roughness measurements
• Statistical analysis

2.1 Specimen fabrication

The specimens were manufactured using a MakerBot Method X fused filament fabrication (FFF) system (Figure 1). Three-dimensional specimen geometries were first created using computer-aided design (CAD) software and exported as STL files for slicing and printing. The feedstock material consisted of BASF Ultrafuse 316L composite filament with a diameter of 1.75 mm, containing approximately 80 wt% 316L stainless steel powder and 20 wt% polymeric binder.

Prior to printing, the build plate was thoroughly cleaned and coated with Magigoo Pro Metal build-plate adhesive to improve first-layer adhesion and dimensional stability. Although the MakerBot Method X is equipped with dual extruders, only the metal-filament extruder was used throughout this study.

Tensile specimens were designed and fabricated in accordance with ASTM E8. The specimens had nominal gauge-section dimensions of 12.5 mm in width and 6 mm in thickness and were printed in two build orientations: horizontal (flat) and vertical (on-edge), as illustrated in Figures 2, 3.

Printing parameters were selected based on the material manufacturer’s recommendations and previous studies on metal FFF. The nozzle temperature was maintained at 245 °C, the build chamber temperature at 85 °C, and a 100% linear infill pattern was used for all specimens. Two layer thicknesses (0.10 mm and 0.20 mm) and three raster angles (0°, 30°, and 45°) were investigated to evaluate their relationships with apparent density, ultimate tensile strength, and post-machining surface roughness.

A total of 36 independently manufactured specimens were produced, corresponding to three independent specimens for each of the twelve fabrication conditions defined by the combinations of two layer thicknesses, three raster angles, and two build orientations. Following fabrication, all specimens underwent thermal debinding and sintering. Apparent density measurements and tensile testing were subsequently performed on each specimen. After tensile testing, the fractured specimens were micro milled and surface roughness measurements were conducted prior to the statistical analyses.

2.2 Debinding, sintering, and experimental design

Following fabrication, the green specimens were thermally debound and sintered by DSH Technologies, LLC using a controlled nitrogen–argon furnace cycle. The thermal schedule consisted of heating to 450 °C at 4 °C/min under 300 Torr nitrogen, followed by a 180 min hold at the same temperature. The furnace was then heated to 600 °C at 4 °C/min under 300 Torr nitrogen with a 180 min hold, followed by heating to 1,050 °C at 5 °C/min under 300 Torr nitrogen with a 45 min hold. Subsequently, the furnace was heated to 1,380 °C at 5 °C/min under 600 Torr nitrogen and held for 180 min. Finally, the specimens were cooled to 700 °C under 600 Torr nitrogen and then to 75 °C under 650 Torr argon.

Table 1 summarizes the fabrication variables, post-processing conditions, specimen replication, and measurement protocol used throughout the experimental program. A balanced full-factorial experimental design comprising 36 independently manufactured specimens was employed to investigate the relationships among the manufacturing parameters, apparent density, ultimate tensile strength (UTS), and post-machining surface roughness. The experimental factors included two layer thicknesses (0.10 and 0.20 mm), three raster angles (0°, 30°, and 45°), and two build orientations (horizontal and vertical), resulting in 12 unique fabrication conditions. Three independently manufactured specimens were produced for each fabrication condition, yielding a total of 36 specimens. These fabrication replicates were treated as independent observations throughout the statistical analyses and were not averaged.

TABLE 1. Experimental design and measurement protocol.

Following density measurements, tensile testing was performed on each specimen in accordance with ASTM E8. The tensile stress calculations were based on the original ASTM E8 gauge-section dimensions (12.5 mm × 6 mm). After tensile testing, each fractured specimen was assigned one workpiece orientation (AngleCut = 0°, 30°, or 45°) for the subsequent micro milling operation. Surface roughness measurements were then performed on the micro milled surfaces. Because micro milling was conducted after tensile testing, the machining operation did not affect the measured UTS. Using the same specimens enabled direct specimen-level comparison between apparent density, UTS, and post-machining roughness while eliminating specimen-to-specimen manufacturing variability. The potential influence of prior tensile loading is acknowledged as a limitation.

2.3 Density and mechanical characterization

After sintering, the apparent density of each specimen was determined using the Archimedes principle with a Torbal AGCN220 analytical balance (220 g × 0.0001 g) equipped with a Torbal Density Kit. The dry mass (m d) and immersed mass (m w) of each specimen were measured after direct immersion in water without sealing or wax coating. The apparent density was calculated using the Archimedes relation given in Equation 1:where,

ρ a = ρ w t m d m d − m w (1)

ρ a: Apparent density of the part.

ρ w t: Water density at the measurement temperature

m d: Dry mass of the part

m w: Wet mass of the part

Ultimate tensile strength (UTS) was determined in accordance with ASTM E8 using an ADMET universal testing machine (Model 1032FGR-50K-B) with a maximum load capacity of 222 kN (50 klbf). Tensile testing was performed on the sintered specimens prior to the micro milling operation. The tensile stress calculations were based on the original ASTM E8 gauge-section dimensions (12.5 mm × 6 mm).

2.4 Micro milling and surface roughness measurements

Following tensile testing, the fractured specimens were subjected to micro milling under identical machining conditions. Micro milling was performed only on the top (XY) surface of each specimen, regardless of build orientation, thereby ensuring identical machining conditions while allowing differences arising from the printed microstructure to be evaluated. Since the micro milling operation was conducted after tensile testing, it did not influence the measured ultimate tensile strength.

A 1.6 mm (0.063 in.) diameter end mill was used for all machining operations. The spindle speed, feed rate, and depth of cut were maintained at 2000 rpm, 152.4 mm/min, and 0.20 mm, respectively. A new 1.6 mm diameter end mill was used for each specimen to eliminate the potential influence of progressive tool wear on the measured surface roughness. All machining parameters were maintained constant throughout the study. To investigate the relationship between workpiece orientation during machining and post-machining surface roughness, the workpiece orientation (AngleCut) was set to 0°, 30°, and 45° relative to the machine X-axis. For each workpiece orientation, micro milling was performed along three machining directions (0°, 90°, and 180°), as illustrated in Figure 4.

It should be noted that AngleCut (workpiece orientation during machining), raster angle (printing parameter), and machining direction are distinct experimental variables representing different aspects of the manufacturing and post-processing procedure.

Surface roughness was evaluated using the arithmetic mean roughness parameter (Ra) with a Mitutoyo Surftest Portable Surface Roughness Tester in accordance with ISO 4287:1997. Measurements were performed on the micro milled surfaces after machining.

Because the machined surfaces exhibited a directional surface lay, roughness was measured along the corresponding profilometer traverse directions (0°, 90°, and 180°), producing the responses Ra0, Ra90, and Ra180, respectively. Accordingly, Ra0, Ra90, and Ra180 denote the arithmetic mean surface roughness (Ra) measured along profilometer traverse directions of 0°, 90°, and 180°, respectively. MeanRa was calculated as the arithmetic mean of the three directional measurements, whereas MaxRa represents the maximum value among Ra0, Ra90, and Ra180 for each specimen. Measuring roughness in multiple directions enabled the directional characteristics of the machined surface texture to be evaluated while reducing potential measurement bias associated with a single traverse direction. In addition to the directional measurements, MeanRa and MaxRa were calculated to provide representative specimen-level surface roughness metrics.

All roughness measurements were performed using the same instrument and measurement procedure to ensure consistency throughout the experimental program.

Although the machining operation removed the visible staircase features produced during FFF, it did not eliminate the underlying microstructural heterogeneity created during printing and sintering. Variations in interlayer bonding, residual porosity, and local material consolidation may have remained after machining and may have influenced tool–material interactions and the resulting surface roughness. However, these microstructural features were not directly characterized in the present study and are therefore discussed only as possible explanations rather than experimentally verified mechanisms.

Micro milling was performed on fractured specimen portions at locations outside the visible necking and fracture regions, as illustrated in Figure 5. Material within the gauge section may have undergone uniform plastic deformation, strain hardening, and residual-stress development before fracture localization. Differences in the geometry and clamping stiffness of the fractured portions may also have affected machining stability. Therefore, the measured roughness cannot be attributed exclusively to the original printing and sintering conditions, and the nonsignificant UTS–roughness relationship should be interpreted cautiously.

A limitation of this study is the use of previously tensile-tested specimens for micro milling. Although visibly necked regions were avoided, prior plastic deformation at the machining locations was not quantified.

2.5 Statistical analysis

Descriptive statistics, Pearson correlation analysis, simple and adjusted multiple linear regression, and Type III analysis of variance (ANOVA) were used to evaluate the relationships among the manufacturing parameters, apparent density, ultimate tensile strength (UTS), and post-machining surface roughness.

The statistical analyses were based on measurements obtained from 36 independently manufactured specimens, representing 12 combinations of layer thickness, raster angle, and build orientation, with three independent fabrication replicates for each manufacturing condition. The fabrication replicates were treated as independent observations and were not averaged. Each specimen was machined at a single workpiece orientation (AngleCut = 0°, 30°, or 45°). Surface roughness was measured in three profilometer traverse directions (0°, 90°, and 180°), yielding the directional responses Ra0, Ra90, and Ra180. These responses were analyzed individually, and the derived specimen-level roughness metrics MeanRa and MaxRa were also evaluated.

Descriptive statistics included the number of observations (N), missing values, mean, standard deviation, minimum, and maximum for all measured variables. Pearson correlation coefficients were calculated to quantify the linear associations among apparent density, UTS, and the surface roughness parameters. Correlation strength was interpreted using the absolute value of the Pearson correlation coefficient, and statistical significance was assessed at a significance level of α = 0.05.

Separate simple linear regression models were first developed to evaluate the individual relationships between apparent density or UTS and the principal roughness responses (MeanRa and MaxRa). Subsequently, adjusted multiple linear regression models were developed for each roughness response (Ra0, Ra90, Ra180, MeanRa, and MaxRa). The explanatory variables included layer thickness, raster angle, build orientation, workpiece orientation (AngleCut), apparent density, and UTS. The manufacturing parameters (layer thickness, raster angle, build orientation, and AngleCut) were treated as categorical variables, whereas apparent density and UTS were treated as continuous covariates. The statistical significance of the regression models and individual predictors was evaluated using Type III ANOVA. Model performance was assessed using the coefficient of determination (R ²), adjusted coefficient of determination (adjusted R ²), F-statistics, and corresponding p-values.

Model assumptions were evaluated using residual-versus-fitted plots, normal probability (Q–Q) plots, leverage values, and Cook’s distance to assess linearity, normality, homoscedasticity, and the presence of influential observations.

Occasional missing roughness measurements resulting from experimental limitations were retained as missing values (NaN) and excluded using complete-case analysis. Apparent density and UTS measurements were available for all 36 specimens. No data imputation was performed.

3 Results and discussion

This section presents the descriptive statistics, Pearson correlation analysis, Type III ANOVA, regression analysis, and regression diagnostics used to investigate the relationships among manufacturing parameters, apparent density, ultimate tensile strength, and post-machining surface roughness.

3.1 Descriptive statistics

The descriptive statistics of the experimental dataset are summarized in Table 2. A total of 36 specimens were fabricated and characterized. Complete apparent density and ultimate tensile strength (UTS) measurements were obtained for all specimens, whereas four specimens contained incomplete surface roughness measurements. Consequently, the roughness analyses and the derived metrics (MeanRa, MaxRa, and RangeRa) were based on the remaining 32 complete observations.

TABLE 2. Descriptive statistics of apparent density, ultimate tensile strength, and post-machining surface roughness.

As shown in Table 2, the apparent density exhibited relatively low variability, with a mean of 7.368 g/cm³ and a standard deviation of 0.154 g/cm³, indicating good repeatability of the FFF fabrication and sintering process. The average UTS was 388.3 MPa with a standard deviation of 61.5 MPa, demonstrating greater variability in mechanical properties than in density.

The post-machining surface roughness measurements exhibited substantially greater variability than either density or UTS. Mean roughness values ranged from 0.683 μm (Ra180) to 0.909 μm (Ra90), while the average maximum roughness (MaxRa) reached 1.074 μm. The relatively large standard deviations of the roughness parameters suggest that post-machining surface quality may be more strongly influenced by manufacturing and machining conditions than by the measured material properties. This observation is investigated further in the subsequent statistical analyses.

The comparatively high variability of the roughness responses indicates that surface generation was sensitive to localized tool–material interactions. However, this variability alone does not establish that the original manufacturing parameters were dominant. As discussed in the following sections, AngleCut was the only investigated factor that exhibited a consistent statistically significant association with most roughness responses.

3.2 Pearson correlation analysis

The Pearson correlation structure among apparent density, ultimate tensile strength (UTS), and the post-machining surface roughness parameters is illustrated in Figure 6, while the correlations specifically relating density and UTS to the roughness responses are summarized in Table 3.

TABLE 3. Pearson correlation coefficients between apparent density, UTS, and post-machining surface roughness.

Pearson correlation coefficients were calculated using the 32 specimens with complete surface roughness measurements. None of the reported correlations were statistically significant at the 0.05 significance level.

As shown in Figure 6, the strongest positive correlations occurred among the roughness parameters themselves. MeanRa exhibited a very strong positive correlation with MaxRa (r = 0.957). Strong positive correlations were also observed between Ra90 and MaxRa (r = 0.925), Ra90 and MeanRa (r = 0.903), Ra0 and MeanRa (r = 0.891), and Ra0 and MaxRa (r = 0.850). These strong associations were expected because MeanRa and MaxRa were calculated from the same directional roughness measurements (Ra0, Ra90, and Ra180) obtained from each specimen.

In contrast, apparent density exhibited only negligible to weak correlations with the post-machining roughness parameters, with correlation coefficients ranging from −0.118 to 0.059, as shown in Table 3. The strongest association involving density was observed for Ra180 (r = −0.118), although this relationship remained weak and statistically non-significant. Similarly, UTS showed negligible to weak correlations with the roughness responses, with correlation coefficients ranging from −0.074 to 0.116. The largest association involving UTS was observed for Ra90 (r = 0.116). None of the correlations between density or UTS and the roughness parameters were statistically significant (p > 0.05).

Apparent density varied over a relatively narrow range and represents an average property of the complete specimen. It does not distinguish pore size, morphology, orientation, connectivity, or proximity to the machined surface. Specimens with similar apparent densities may therefore present substantially different local conditions to a 1.6 mm micro milling tool. This distinction agrees with previous observations that localized porosity distributions can provide more relevant information about surface-defect formation than average density alone (Agrawal and Thoma, 2022).

UTS is likewise a global mechanical property determined from the response of the entire tensile gauge section. It does not directly measure local hardness, interlayer separation resistance, pore-edge strength, or the tendency for material smearing and pullout at the machining location. Moreover, micro milling was conducted after tensile failure. Even though visibly necked and fracture-affected areas were avoided, material within the gauge section may have experienced uniform plastic deformation, strain hardening, residual-stress development, dimensional change, or alteration of the pore structure before fracture localization. The local condition encountered during machining may consequently have differed from the original condition represented by the measured UTS. This experimental sequence may have weakened or obscured a potential relationship between the original tensile response and subsequent machining behavior.

Clamping portions of fractured specimens may also have produced differences in workpiece stiffness and dynamic stability depending on the remaining specimen geometry and unsupported length. Such differences could contribute to roughness variability through vibration or changes in tool engagement. Therefore, the nonsignificant regression results should be interpreted as showing that apparent density and UTS did not provide statistically distinguishable independent predictive information within the adopted experimental conditions. They should not be interpreted as evidence that local porosity, strength, or deformation history has no physical relationship with surface generation.

The correlation heatmap further illustrates two distinct groups of variables. The roughness parameters form a highly correlated cluster, whereas apparent density and UTS remain largely independent of the post-machining roughness responses. Therefore, within the investigated experimental conditions, variations in apparent density and tensile strength were not accompanied by corresponding changes in post-machining surface finish. These findings indicate that the observed roughness variability is more closely associated with the investigated manufacturing and machining conditions than with the measured material properties. This interpretation is examined further through the subsequent ANOVA and adjusted regression analyses.

3.3 Main-effects ANOVA

The Type III ANOVA results are summarized in Table 4, while representative main-effect plots and boxplots are presented in Figure 7.

TABLE 4. Summary of type III ANOVA results for the effects of manufacturing parameters on post-machining surface roughness.

The moderate partial η² values (0.19–0.29) indicate that workpiece orientation had not only statistical significance but also a practically meaningful effect on post-machining surface roughness.

Bold values indicate statistically significant effects at α = 0.05.

Among the four investigated manufacturing variables, workpiece orientation (AngleCut) consistently exhibited the strongest influence on post-machining surface roughness. As summarized in Table 4, AngleCut was statistically significant for Ra0 (p = 0.014), Ra90 (p = 0.035), MeanRa (p = 0.008), and MaxRa (p = 0.015), with partial η² values ranging from approximately 0.24–0.32, indicating moderate practical effect sizes.

The representative main-effect plots (Figures 7a,b) clearly demonstrate that changes in workpiece orientation produced the largest variation in MeanRa and MaxRa. Similarly, the corresponding boxplots (Figures 7c,d) show distinct separation among the AngleCut levels, further confirming its dominant influence on post-machining surface roughness.

Conversely, layer thickness, raster angle, and build orientation did not significantly affect most roughness responses (p > 0.05). Layer thickness approached statistical significance only for MaxRa (p = 0.076), whereas raster angle and build orientation exhibited consistently small effects across all response variables.

Although none of the investigated factors reached statistical significance for Ra180, workpiece orientation again produced the largest F-statistic among the four manufacturing variables, suggesting that its influence depends on the roughness measurement direction.

The significant effect of workpiece orientation (AngleCut) can be attributed to the interaction between tool-induced shear and the direction-dependent microstructure of FFF-fabricated 316L stainless steel. Filament tracks, interlayer interfaces, and residual pores associated with the deposition pattern may remain after debinding and sintering (Agrawal and Thoma, 2022; Hassan et al., 2021; Boschetto et al., 2022). Rotating the workpiece changes the orientation of the cutting path relative to these features, thereby modifying the local shear conditions and tool–material interaction during micro milling. When the cutting path intersects filament interfaces and residual pores obliquely or transversely, local cutting resistance and material support may fluctuate, increasing the likelihood of pore-edge fracture, material pull-out, interfacial separation, smearing, and irregular chip formation. In contrast, cutting more nearly parallel to consolidated filament tracks may provide more continuous material support, more stable chip formation, and improved surface generation. These physically plausible mechanisms are consistent with previous studies reporting anisotropic interlayer bonding, residual porosity, and direction-dependent machining behavior in extrusion-based 316L stainless steel (Agrawal and Thoma, 2022; Hassan et al., 2021; Boschetto et al., 2022; Dinc et al., 2025). However, because cutting forces, chip morphology, post-machining microscopy, and subsurface microstructural characterization were not performed in the present study, these mechanisms should be regarded as literature-supported interpretations rather than experimentally verified causes.

The nonsignificant AngleCut effect on Ra180 indicates that the observed roughness also depends on profilometer traverse direction. Measurements taken along or across the machining lay sample different groove, feed-mark, and pullout geometries; therefore, the measured directional roughness reflects both surface formation and measurement orientation.

Layer thickness, raster angle, and build orientation showed weaker effects partly because all specimens were machined on the top XY surface using identical cutting conditions. The 0.20 mm depth of cut removed the original bead contours and staircase features. Although these printing parameters may still influence internal interfaces, porosity, and consolidation, their effects may have been smaller than the local variability associated with pores, prior tensile deformation, and tool-path orientation. The marginal relationship between layer thickness and MaxRa may indicate an effect on isolated peaks or pullout valleys without a consistent change in average roughness.

Overall, the ANOVA results indicate that machining orientation after fabrication exerted a substantially greater influence on post-machining surface roughness than the original FFF processing parameters.

3.4 Regression analysis

The results of the simple and adjusted regression analyses are summarized in Tables 5, 6, respectively, while representative regression plots are presented in Figure 8. The simple linear regression models confirmed the absence of statistically significant linear relationships between apparent density or ultimate tensile strength (UTS) and the principal surface roughness responses (MeanRa and MaxRa). All models exhibited negligible coefficients of determination (R ² ≤ 0.001) and non-significant p-values (p > 0.05), indicating that neither apparent density nor UTS alone provided meaningful predictive capability for post-machining surface roughness.

TABLE 5. Summary of simple linear regression analyses between apparent density, UTS, and principal surface roughness responses.

Simple linear regression was performed using the 32 specimens with complete roughness measurements. None of the models demonstrated a statistically significant relationship between the predictor and response variables (p > 0.05).

TABLE 6. Summary of adjusted multiple regression models for post-machining surface roughness.

Adjusted multiple regression models simultaneously incorporated the manufacturing parameters together with apparent density and UTS. The models explained up to 45% of the observed variation in the surface roughness responses. Workpiece orientation (AngleCut) was the only consistently significant predictor, whereas apparent density and UTS, were not statistically significant independent predictors.

To account for potential confounding effects, adjusted multiple regression models were developed by simultaneously including the manufacturing parameters (layer thickness, raster angle, build orientation, and workpiece orientation) together with apparent density and UTS. As summarized in Table 6, these models explained approximately 18%–45% of the observed variation in surface roughness (adjusted R² = 0.18–0.45). However, none of the overall regression models reached statistical significance at the 95% confidence level, although the MeanRa model exhibited the greatest explanatory capability and approached statistical significance (adjusted R ² ≈ 0.45; p ≈ 0.06).

The representative regression plots (Figure 8) illustrate the weak linear relationships between apparent density, UTS, and the principal surface roughness responses, with considerable scatter and nearly horizontal regression lines. Furthermore, neither apparent density nor UTS was identified as a statistically significant independent predictor of post-machining surface roughness after accounting for the manufacturing variables. These findings are consistent with the Pearson correlation and Type III ANOVA results, which collectively indicate that workpiece orientation (AngleCut) is the dominant factor influencing post-machining surface finish under the investigated manufacturing conditions.

From a process-planning perspective, the results indicate that the orientation in which an FFF-fabricated 316L component is presented to the micro milling tool may be important for controlling post-machining surface finish. When fixture design and part geometry permit, the cutting direction should be selected with consideration of the underlying deposition structure and the required surface-texture direction. Nevertheless, the present results do not identify a universally optimal orientation because the response may depend on local pore morphology, tool-path direction, and roughness-measurement direction. Confirmation through cutting-force measurements, surface and subsurface microscopy, local hardness testing, and matched undeformed specimens would be required before establishing general machining recommendations.

3.5 Regression diagnostics

Regression diagnostic analyses were performed to assess the validity of the fitted multiple linear regression models. Representative diagnostic plots for the adjusted multiple regression model of MeanRa are presented in Figure 9. Residual-versus-fitted plots, normal probability (Q–Q) plots, Cook’s distance, leverage statistics, and standardized residual analyses were examined to evaluate the assumptions of linear regression. The diagnostic results indicated no substantial violations of the assumptions of linear regression, including linearity, homoscedasticity, normality of residuals, and the absence of influential observations. All Cook’s distance and leverage values remained below commonly accepted thresholds, indicating that no individual observation exerted undue influence on the fitted model.

No systematic residual patterns or influential data points were identified that would materially affect the fitted models. Consequently, the weak relationships observed between apparent density, UTS, and post-machining surface roughness are considered intrinsic to the experimental dataset rather than artifacts arising from violations of regression assumptions, influential observations, or model inadequacy. These findings provide additional confidence that the conclusions drawn from the Pearson correlation, Type III ANOVA, and regression analyses are statistically reliable.

4 Conclusion

This study investigated the relationships among apparent density, ultimate tensile strength (UTS), manufacturing parameters, and the post-machining surface roughness of fused filament fabrication (FFF) 316L stainless steel following micro milling. Pearson correlation analysis revealed only negligible to weak relationships between the measured material properties and the evaluated surface roughness parameters. Likewise, both simple and adjusted multiple regression analyses demonstrated that neither apparent density nor UTS was a statistically significant independent predictor of Ra0, Ra90, Ra180, MeanRa, or MaxRa after accounting for the manufacturing parameters.

Among the investigated manufacturing variables, workpiece orientation (AngleCut) consistently emerged as the dominant factor affecting post-machining surface roughness, exhibiting statistically significant effects on Ra0, Ra90, MeanRa, and MaxRa. In contrast, layer thickness, raster angle, and build orientation did not significantly influence the measured roughness responses, although layer thickness exhibited a marginal effect on MaxRa. Collectively, these findings indicate that machining orientation and manufacturing conditions exert a substantially greater influence on the final surface finish than the measured bulk material properties represented by apparent density and tensile strength.

Regression diagnostic analyses confirmed that the fitted models satisfied the underlying assumptions of linear regression, including linearity, homoscedasticity, normality of residuals, and the absence of influential observations. These results provide additional confidence that the observed weak relationships between apparent density, UTS, and post-machining surface roughness reflect the characteristics of the experimental dataset rather than artifacts arising from model inadequacy.

Within the investigated conditions, workpiece orientation during micro milling (AngleCut) showed the most consistent statistically significant association with surface roughness. Layer thickness, raster angle, and build orientation generally did not exhibit statistically significant independent associations with the roughness responses. The findings support a directional effect of workpiece orientation under the tested conditions but do not demonstrate that manufacturing and machining conditions generally dominate surface roughness.

Overall, the findings suggest that apparent density and UTS alone are insufficient predictors of post-machining surface quality in FFF-fabricated 316L stainless steel. Instead, manufacturing and machining parameters—particularly workpiece orientation during micro milling—should be considered primary factors when optimizing surface finish in hybrid additive–subtractive manufacturing processes.

Although the revised statistical analyses utilized the complete balanced dataset of 36 independently manufactured specimens, the overall sample size remains relatively modest for a manufacturing process such as metal fused filament fabrication, which inherently exhibits specimen-to-specimen variability. Consequently, the statistical findings should be interpreted within the scope of the present experimental dataset. Future studies employing larger experimental datasets and additional manufacturing conditions would further improve statistical power and the generalizability of the reported relationships.

Future work should investigate additional microstructural characteristics, including pore morphology, porosity distribution, interlayer bonding quality, grain orientation, residual stresses, and microhardness, together with expanded experimental datasets and a wider range of machining conditions. Incorporating these variables into predictive statistical and machine learning models may further improve the understanding and prediction of surface integrity in hybrid additive–subtractive manufacturing of metallic components.

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Footnotes

Edited by: Mantra Prasad Satpathy, KIIT University, India

Reviewed by: Jesús Hernández Saz, Sevilla University, Spain

Mario Brandon Russo, Università della Campania Luigi Vanvitelli, Italy

Footnotes

AM, Additive Manufacturing; UTS, Ultimate Tensile Strength; FFF, Fused Filament Fabrication; FDM, Fused Deposition Modeling; DIC, Digital Image Correlation; ANOVA, Analysis of Variance; ρ a , Apparent density of the part; ρ w t , Water density at the measurement temperature; m d , Dry mass of the part; m w , Wet mass of the part.