Commercially available Ti-6Al-4V (Grade 5) powder was used to 3D-print the metallic substrates by LPBF (see Section 2.2.1). Its chemical composition (virgin) consisted of the following: 6.13 wt.% Al, 3.90 wt.% V, 0.16 wt.% O, 0.0281 wt.% N, 0.01 wt.% C, 0.07 wt.% Fe, 1.1 ppm Ar, 21 ppm H and balance of Ti (Meier et al., 2022a; Meier et al., 2022b). Particle size distribution and sphericity were measured in accordance with ISO 13322-2 by Dynamic Image Analysis carried out with a Retsch CAMSIZER XT optical particle analyzer (Germany). Particle size distribution were measured as follows: D10 = 18.8 µm; D50 = 33.6 µm; D90 = 48.7 µm. Sphericity: W/H = 0.89; bh13 = 0.94.

For the manufacturing of each specimen, two different thermoplastic materials were used: one for the coating layer only and another for the subsequent layers. The coating layer material consisted of Polyamide 6/66, supplied in a filament form (ø 2.85 mm) by Ultimaker (Netherlands). Glass transition temperature (T_g), melting onset (T_onset) and melting peak (T_m) were measured by (Belei et al., 2022a) at 50°C, 167°C and 190°C, respectively. Melt mass flow rate (MFR) of 6.2 g/10 min was measured by the supplier based on ISO 1133, at 250°C and with a load of 1.2 kg (Ultimaker Nylon TDS, 2023).

As for the subsequent layers, a commercial-grade polyamide reinforced with short carbon fibers was used, also in filament form (ø 2.85 mm), being supplied by BASF (Netherlands). Fiber volume fraction was 6.5% ± 0.2%, while fiber length and diameter 136.2 ± 83.0 μm and 5.6 ± 1.0 μm, respectively. T_g, T_onset, and T_m were measured by (Belei et al., 2022a) at 67°C, 203°C and 237°C, respectively. MFR at 275°C and 5 kg was measured by the supplier based on ISO 1133, registering a value of 51.9 g/10 min (Ultrafuse^® PAHT CF15, 2023).

Ti-6Al-4V plates (see dimensions in Figures 2A) were 3D-printed by Laser Powder Bed Fusion using an EOS 280 printer (Germany) equipped with a 400 W laser (wavelength of 1,064 nm). Process parameters were kept constant, with a laser power of 280 W, a scan speed of 1,200 mm/s, a hatching distance of 140 µm and a layer thickness of 30 µm. The inclination angle θ in relation to the platform was varied between 40° and 90° in multiples of ten, for a total of six different θ values. No support structures were used. After the process, the 3D-printed substrates were stress relieved for 2 h at 650°C (heating and cooling rates of 30 K/min and 5 K/min, respectively). Parameters for both the process and the stress relieving were obtained based on (Meier et al., 2022a).

The 3D-printing of the polymer part on the metallic substrate (AddJoining) was carried out in an Ultimaker S5 FFF printer (Netherlands). Before proceeding with the AddJoining stage, the substrates were cleaned with an ultrasonic bath for 15 min using water, then rinsed with acetone.

The substrates were then fixed to the print bed using a sample holder originally designed to produce single-lap joints (Belei et al., 2022a), with the schematics presented in Figure 3. The DS of the substrate was positioned facing upwards, being therefore the surface on which the polymer was deposited. Masking tapes (3M Scotch Tape, United States) were applied on both substrate extremities to increase its stability during the polymer deposition.

The polymer part 3D-printed on the metallic substrate consisted of a 25 × 5 × 4 mm block, positioned on the center of the substrate as showed in Figure 2B. This block was printed in two stages. First, one layer of the unreinforced polyamide 6/66 was deposited directly onto the metallic substrate (coating layer). In this stage, process parameters (printing speed v and layer height h, see Table 1), as well as the substrate inclination angle θ (Figure 2A) were varied based on a 3^k full-factorial design of experiments; however, since θ had six levels (instead of three levels, which as the case for the other two factors), the experimental matrix tallied 54 unique conditions. Three replicas per condition were produced.

Next, following the deposition of the coating layer, subsequent layers of the PA-CF block (“composite part”) were printed with the reinforced polyamide, using constant process parameters for every condition (Table 1). Those parameters were obtained based on a previous optimization study (Belei et al., 2022b).

Finally, for some pre-determined conditions (v = 5, 35 and 65 mm/s; h = 0.4 mm; θ = 90^°), the temperature at the metal-polymer interface during the coating layer deposition was recorded using a type K thermocouple inserted from underneath the substrate through a hole drilled on it (Figure 3C). The acquisition rate was 300 Hz. Specimens used during temperature measurements were not mechanically tested afterwards.

The pre-determined conditions mentioned earlier were selected as such in order to enable a direct comparison with the temperature measurements reported by (Belei et al., 2022a). By that time, the authors kept h constant at 0.4 mm since this was the value that resulted in the highest joint strength (via single-lap shear tests). Additionally, the inclination angle θ (variable absent in (Belei et al., 2022a)) was kept at 90° for the present study, since this was the value resulting in the closest surface roughness (see Section 3.1) in comparison to (Belei et al., 2022a).

In this work, the effectiveness of a parameter combination on the joint strength was evaluated using an energy approach based on the work from Birro et al. (2021). This approach consisted in the following steps: (i) the total resilience of the substrate-block system up to the detachment (W _total ) is calculated based on the integral of the Force x Displacement curve, (ii) the resilience expected for the substrate without the block (W _metal ) is calculated and then (iii) subtracted from W _total . The result is the resilience of the composite block (including the coating layer), which is represented by W _composite . The sequence is summarized by Figure 4. With this approach, it is possible to mitigate the influence of possible differences in substrate stiffness across different parameter combinations, which would affect a direct comparison using only F _c .

For step (i), the area below the Force x Displacement curve for substrate-block hybrid joints was approximated by subdividing it into individual rectangles up to the displacement at F _c , see Figure 4A. The area from rectangles below 10 N were discarded. The total area (W _total ) was equal to the sum of the areas of each rectangle. The width of the rectangles was equal to one displacement step, or 8.3 × 10⁻⁵ mm.

For step (ii), an approach similar to step (i) was implemented, this time using Force x Displacement curves from standalone, substrate-only specimens. Three different curves for each θ value where averaged, point by point, resulting in six individual curves. Then, for each hybrid joint condition, the area below the substrate-only curve (W _metal ) was calculated up to F _c (Figure 4B), with the corresponding substrate-only curve being selected depending on θ. Similar to step (i), the area from rectangles below 10 N were discarded. Finally, for step (iii) W _metal was subtracted from W _total to obtain a W _composite (Figure 4C).

The Decision Tree Regression (DTR) algorithm generates, based on the input data set, a single decision tree which will predict a specific outcome dependent on various input parameters. In this case, generating a model means training a model with a certain training data set. Depending on the desired response, python builds a regression or classification decision tree following the, slightly changed, CART-algorithm (Classification And Regression Tree). With this algorithm, only binary trees can be built, meaning that at each node there are only two possible ways to go.

An ensemble is an approach that combines multiple algorithms into a single predictive model able to decrease bias and variance, and increase predictive ability. A single decision tree will rarely generalize well to data it was not trained on, as is the case described herein, due to the fact that “pure” decision trees display low bias and high variance. To overcome this, several decision trees can be combined to obtain accurate predictions, since averaging the result of many trees will reduce variance while maintain bias.

This work brings together not only application of ''pure'' DTR, but also a comparison with ensemble methods based on Decision Tree theory (Breiman et al., 1984), from which the best model was selected and scrutinized for the purposes of AddJoining performance optimization. Table 2 summarizes relevant statistical indicators obtained for the generated ensemble models. Even though each ensemble’s hyperparameters were optimized, a considerable amount of overfitting was observed for Random Forest, Extra Trees, Bagging and AdaBoost. Nonetheless, for all the aforementioned, MSE was reduced in comparison with DTR, which indicates the ensemble approach was effective in curtail bias. Contrastingly, Gradient Boosting Regression (GBR) exhibits very satisfactory R 2 and MSE values, that alludes to adequate bias-variance trade-off. This evidence will be made clear when validating the model in Sub-Section 3.2.2. for unseen, randomly selected data points (parameter combinations).

Since GBR proved to be the most reliable model, for the sake of completion, a more in-depth review over the mathematical details of this algorithm is provided in the upcoming sub-section.

The Machine Learning (ML) endeavors realized herein, where performed using python programming language, with proper use of the relevant API’s (e.g., sklearn, numpy, pandas, etc.). To train a model that can adequately fit the data, but also generalizes well for “unseen” observations, a suitable train/test split must be specified. For this problem, due to the low amount of data available, a sensitivity analysis was conducted, from which a train/test split of 75% and 25% was considered, respectively, and partitioned in 6-fold-cross-validation. Additionally, the hyperparameters of each algorithm were tuned, using automated using “GridSearchCV” technique. This method creates a grid of hyperparameters of interest and their considered values, subsequently fitting models to every single combination of these parameters (Raschka and Mirjalili, 2019). An optimized set of parameters, regarding specific criterion (e.g., the lowest MSE or the highest R 2 ), was displayed and evaluated.

Two types of Force x Displacement curves could be identified. The criterion to differentiate both types was whether the derivative of the Force with respect to the Displacement ever assumed negative values; if so, that would represent a relatively sharp loss in stiffness as a result of the detachment of the polymer block. On the other hand, if that derivative never assumed negative values, that would mean that the loss in stiffness was smoother, being therefore harder to infer, from the curve, the moment at which the polymer block detached from the substrate. For the following discussion, the former case will be termed “sharp curve” and the latter “smooth curve”. A visual representation of those two types of curves can be seen in Figure 7.

The emergence of either type of curve, however, did not seem to be due to any special circumstance or combination of parameter. Table 3 summarizes the average values from parameters and responses for each curve type. Other than a slight tendency of having sharp curves on conditions with lower v, sharp curves also tended to appear in conditions with higher θ, that is, when the surface roughness was lower (see Figure 5A). In terms of responses (F _c and W _composite ), no noticeable differences could be observed with respect to the average results. In either case, there was a high standard deviation on both responses, showing that a given curve could be sharp or smooth within a wide range of outcomes, i.e., both stronger and weaker joints could yield either type of curve. Furthermore, the frequency of occurrence from both curve types is virtually equal.

Those results suggest that the occurrence of a given curve type is mostly random. Other authors also suggested that a stepwise stiffness reduction might be a consequence of defects present at the interface, resulting in a more gradual crack propagation at the metal-polymer interface (Birro et al., 2021; Belei et al., 2022a). In the present case, the interface is highly irregular, containing not only defects such as entrapped air bubbles (as covered in Section 3.2.3), but also protuberances of irregular shapes and sizes (see Figure 6). Those may have affected the shape of the curve unpredictably.

However, it is also important to point out that the substrate thickness may have also played a role on this matter. A stepwise crack propagation on a thinner substrate would most likely reveal a curve with a distinct peak (F _c ) followed by a gradual descent with several smaller peaks until the curve reached the substrate baseline. This was evidenced by (Belei et al., 2022a), which used rolled Ti-6Al-4V substrates with a thickness of 0.5 mm. On the other hand, since the substrates used on the present study were substantially thicker (2 mm), the substrate baseline was higher; thus, the visual features expected from a stepwise propagation curve were blended with the substrate baseline itself, resulting in a single smooth curve. Nevertheless, the use of thicker substrates in this case was justified, since they required a higher force to deform plastically. This ensured that the three-point testing of hybrid joints would be carried out entirely on the elastic domain, meaning that any deviation from the expected linear-elastic behavior could only stem from the presence of the PA-CF block, and not from any plastic strain on the substrate itself.

Lastly, it is important to emphasize that, despite the high scatter observed in the average responses across all conditions, the results of the statistical analysis revealed that process parameters did have a significant influence on both F _c and W _composite , see Table 4. By performing Analysis of Variance (ANOVA) using an α of 0.05, both θ and v were found to have a statistically significant effect, as indicated by their very low p-values and F above F-crit both with respect to F _c and W _composite . These findings suggest that despite the variability in the data, there are clear associations between the response variable and these parameters, which will be further discussed in the upcoming sections.

Valuable information can be drawn from the GBR model concerning the influence of parameters in the bending performance of AddJoined components. In terms of performance, the model achieved a coefficient of determination (R ²) of 0.997 and 0.860 for the training and test sets, respectively, as already described in Table 2. Figure 8A provides visual intuition to those statistical indicators, highlighting the adequacy of GBR, as predicted W _composite values matched the actual experimental values. This hold true for both training and tests sets. Moreover, a validation set, consisting of five experiments each with distinct parameter sets, was used for the post hoc evaluation of the GBR model, revealing a satisfactory predicting ability.

In terms of feature importance (Figure 8B), the printing speed v was considered the most influent parameter on the response W _composite , followed by the inclination angle θ and layer height h, respectively. This corroborates the results from the ANOVA presented earlier, but were the opposite of what has been observed in (Belei et al., 2022a). In that study, using F _c as a response, h was considered statistically significant while v was not. However, even in that case, a tendency indicating the average F _c being inversely proportional to v could be noticed. Moreover, according to the present findings, such a tendency appeared to be boosted by the substrate roughness, which in turn was dependent on θ. This can be concluded by comparing the resulting contour plots for different θ values, see Figure 9. As θ decreased, the response (W _composite ) progressively increased towards the left-hand side of the plot, i.e., low v values. Moreover, it is also possible to see an increase towards low h values, although less prominently. Ultimately, this culminated in the global peak at θ = 40°, v = 5 mm/s and h = 0.10 mm (lower left-hand corner), where W _composite surpassed 200 J. Further discussion on this topic is addressed on Section 3.2.3.

The high relative importance of v was most likely a product of the temperature evolution at the metal-polymer interface, which was a function of v itself (see Figure 10). As reported by (Belei et al., 2022a), the speed at which the coating layer is printed affects the temperature of the substrate both ahead and after the deposition. Slower prints cause a greater heat build-up effect (also reported by (Belei et al., 2022b), which in turn can (i) decrease the viscosity of the deposited polymer (Bechtel et al., 2020; Brostow et al., 2020; Calafel et al., 2020), allowing for a greater penetration into surface cavities and (ii) improve the wettability by providing enough energy to trigger a Cassie-Wenzel state transition (Ishino et al., 2004; Bormashenko, 2015; Su et al., 2016; Wang et al., 2016), which will be further discussed in Section 3.2.3. In either case, a stronger bond between metal and polymer would be achieved.

Based on Figure 10, it can be observed that at v = 5 mm/s, the temperature of the measured region was already above T_onset for around 15 s before the deposition, staying above that level for an extra 30 s interval afterwards. This comes in stark contrast with faster prints, where the temperature is raised above T_onset almost instantaneously before the deposition and then falling off much sooner. Although this was also observed by (Belei et al., 2022a), the present findings showed temperature peaks up to 30°C higher in comparison, most likely as a result of the difference in the width of the coating layer (14 mm and 5 mm, respectively). This is in accordance with (Belei et al., 2022b), which discussed that the shorter are the successive nozzle paths, the more prominent the heat build-up effect will be. Ultimately, these conclusions suggest that, for the AddJoining approach on larger models, it is advisable to subdivide the coating layer in several narrow strips as a means to locally increase temperature and consequently adhesion. This strategy may substitute a further increase in T_bed, which is less energy efficient and also potentially harmful to the substrate (Moreira, 2020; Belei et al., 2022a).

During the AddJoining process, polymer from the coating layer was able to infiltrate irregularities present on the as-printed LPBF surfaces. This occurred regardless of roughness (i.e., θ), meaning that even cavities present on the roughest DS surfaces could potentially be infiltrated by the unreinforced polymer. However, Figure 11 shows that not every cavity could be fully infiltrated, since some of those contained air pockets that were subsequently entrapped by the coating layer. This phenomenon has been also observed with sandblasted surfaces with much lower surface roughness (Belei et al., 2022a). This was most likely a result of the polymer freezing while the metal-polymer interface was still at a transitional state between Cassie–Baxter (wetting prevented by entrapped air, metastable) and Wenzel (full wetting, stable) regimes, as mentioned earlier. Nevertheless, despite the occasional presence of air pockets at the interface, the joint strength could be considered satisfactory depending on the parameter combination, as discussed in Section 3.2.2.

Under peeling, the intricate contact between substrate and coating layer led to a number of different fracture micromechanisms at the joint interface. Those affected both polymer and metal. For one, particles embedded in the coating layer deformed plastically and eventually failed, detaching themselves from the metallic substrate while remaining embedded in the polymer. An evidence for this can be seen in Figure 12, where a region previously occupied by a particle (or a group thereof) presented dimples; these features are a result of micro void coalescence, being normally observed on LPBF Ti-6Al-4V parts that experienced ductile fracture under tensile stress (Hooreweder and Sas, 2012; Cao et al., 2017; Gorsse et al., 2017). The extent of the individual dimpled regions depended on the prior contact area with the metallic substrate, with a diameter ranging from a few to tens of micrometers (Figures 12A, B, respectively). A similar observation was made by Englert et al. (2022), although in a milimetric scale; in their study, surface structures (i.e., pins) designed to enhance metal-polymer anchoring partially fractured as a result of shear stresses.

Based on those observations, it can be reasonably assumed that the presence of partially-molten particles on as-printed L-PBF substrates contributed positively to the metal-polymer joint strength, as the breakage of those particles provided the joint with an additional energy dissipation mechanism (Kim et al., 2010; Libanori et al., 2016). Evidence of particles ripped off from the metallic substrate was found regardless of θ (see Figures 13A, B), being therefore a general tendency of the AddJoining process on as-printed LPBF substrates. The difference between θ values, however, was the amount of particles on the detached polymer after testing. Figures 13C, D show a comparison between detached coating layers from 90° to 40° substrates, respectively, whereby a much greater amount of detached particles could be observed on 40°. Such a difference can be attributed to the increasing presence of partially-molten particles on the DS as the inclination angle θ decreases, as discussed in Section 3.1. It also explains the increase in W _composite as θ decreases, as detected by the aforementioned prediction model (see Figure 9).

A closer look at the embedded particles reveals not only the opposite fracture surfaces in relation to the ones presented in Figure 12, but also the situation of those particles with respect to the surrounding polymer as of the moment of their fracture. While fully enveloped particles expectedly broke off from the substrate (Figure 14A), particles that were only partially surrounded by polymer also presented signs of breakage (Figure 14B). This suggests that in spite of the occasional presence of air entrapment preventing a full embedding, those particles still contributed somehow to the overall joint strength. However, the fractured areas in those cases were found to be relatively small in comparison to the fully enveloped particles. This means that the presence of a neighboring air pocket most likely avoided particle breakage in situations where there was a larger contact area between partially-molten particle and substrate, hindering the effectiveness of the micromechanical interlocking.

In most cases, however, the fracture of metallic particles did not occur; instead, the coating layer itself failed (see Figure 15), resulting in cavities and occasionally lacerations from ductile drawing (Greenhalgh, 2009). Cavities in the detached coating layer were a direct consequence of particles being pulled out from it (comparable to what is normally observed on fiber pullout in fiber-reinforced composites (Belei et al., 2022b). Similar cavities have been also reported in a previous study reproducing similar circumstances (Schmidt and Chen, 2022). Around such cavities, a damage zone comprised of plastically-deformed polymer was present (Figure 15-2), which has been identified elsewhere as well (Seo et al., 2021). The presence of those features is another indication that the interface failed under peeling loading. In this scenario, the presence of lacerations (see Figure 15-3) would also be expected, as previously observed for the AddJoining approach using sandblasted Ti-6Al-4V substrates (Belei et al., 2022a).

While lacerations resulting from ductile drawing were somewhat discernable on the detached coating layer (as seen in Figure 15-3), they could be better observed as a part of polymer leftovers found on the metallic substrate after testing, see Figure 16. However, polymer residue on the substrate was not present on all conditions, being instead limited to specimens with low h values. In those cases, polymer residue was found surrounded by partially-molten particles, which previously constituted deep, intricate cavities where molten polymer could penetrate during AddJoining. The exact same tendency was also observed on rolled, sandblasted substrates (Belei et al., 2022a), where low h values also led to polymer residue on the metallic substrate. In the referred study, it was suggested that the coating layer—acting as a ductile interphase between metal and composite—was able to store energy via plastic deformation as the test progressed. Thus, decreasing h reduced the amount of ductile interphase material and consequently the amount of storable energy as well. Eventually, this resulted in two different outcomes: (i) at low enough h values (h = 0.10 mm), the coating layer torn apart before the onset of metal-polymer delamination; or (ii) for higher h values (h = 0.25 mm and above), detaching the polymer from the metal required less energy than tearing the coating layer, which led to the former occurring before the latter.

A fundamental difference between the present study and (Belei et al., 2022a) is, however, the surface roughness of the respective substrates. The sandblasted pre-treatment on rolled substrates (the strategy utilized in the referred study) resulted in a considerably lower areal surface roughness (S_a = 1.4 µm), therefore providing the deposited polymer with less anchoring sites. The referred study suggested that the outcome (ii) (i.e., coating layer detachment without failure) could cease to occur by increasing the metal-polymer interfacial strength, which in turn could be done, for example, by increasing the substrate roughness. However, according to the present findings, substrate roughness did not seem to matter: under peeling stresses, thinner coating layers were more prone to failure than thicker ones, regardless of the substrate roughness.

In terms of the “global” hybrid joint strength, however, a conclusion on this subject is not as straightforward. On the one hand, the previous study with sandblasted substrates (Belei et al., 2022a) suggested that h was indeed a statistically-significant parameter, with a positive effect on the response (in that case F _c ). On the other hand, the present findings show that the influence of h had a negative effect on the response (W _composite ), although only observable at low v and θ values. However, the apparent contradiction may stem from a multitude of factors, being a direct comparison difficult due the different experimental approaches. For one, the referred study only evaluated the effect of h using a constant printing speed of v = 35 mm/s and at a surface roughness level that could not be achieved by any θ value. There may exist an interaction of higher order between h, v and θ, perhaps only identifiable beyond the hereby evaluated ranges, which could potentially explain the observed contradiction.