An integrated approach for the modelling of silicon carbide components laser milling process

The investigated material was a sintered silicon carbide (SiC) in the form of bars, 25×5×5 mm³ in dimension, supplied by TKC-Technische Keramik GmbH. SiC is technical ceramic characterised by exceptional hardness, high strength, low density (compared to steel), high elastic modulus, high thermal shock resistance, chemical inertness, high thermal conductivity (compared to other ceramic materials) and low thermal expansion. Thanks to its properties, SiC has found extensive application in aerospace and automotive components (brake discs, bearings or as oil additive), electronics component (for the production of LEDs, diode and semiconductor), hydraulic valve bodies and seal rings, missile parts, munitions, pistons, watch components, orthopaedic equipment and, of course, as abrasive (carborundum).

In Table 1, the chemical composition and the main properties of the SiC ceramic are reported as declared by the producer, while in Fig. 1, images of the specimen and its surface are reported.

Figure 2 shows a schematic of laser milling processes (LMP). As aforementioned, in this technique, the laser beam is adopted to remove the material layer by layer. First, the contour of the geometric pattern is defined in CAD environment; then, the inner area delimited by the contour is machined from side to side by hatching: the laser beam moves line after line up to completely cover the area to be machined. The distance between the lines is called hatching distance (Hd). Since the machined layer is thin, the process is repeated several times, up to the required depth. The number of times the area is hatched is called repetitions (R).

The experimental tests were performed adopting a laser system (LASIT Fly30 fiber) equipped with a Q-switched pulsed Ytterbium fiber laser (IPG, model: YLP-RA30-1-50-20-20) working at the fundamental wavelength λ=1064 nm. The system is equipped with a galvanometric scanning head, a “flat field lens” 160 mm in length, a suction system and a monitoring camera and it is controlled via a personal computer. The latter allows the geometric patterns generation (contour and hatching distance) and setting of the process parameters: average power (Pa), scan speed (Ss) pulse frequency (f) and repetitions (R). Since the laser source works at a fixed pulse duration (D=50 ns), the pulse energy (Ep) and the pulse power (Pp) can be calculated by way of the well-known equations [50, 51]:

Moreover, knowing the beam footprint or the beam diameter (ds) and the hatching distance (Hd), it is possible to calculate the overlapping factor along the directions parallel (Of %) and orthogonal (Ho %) to the laser beam travel, that represents the superposition between two consecutive pulses (pulse overlapping) and between two consecutive lines (hatching overlap), respectively:

This kind of laser source was chosen for the good absorption of SiC at its wavelength, the possibility to release high pulse power (up to 20 kW) and the higher conversion efficiency (about 25%) as well as its flexibility, which makes it suitable to perform different operations, like marking, texturing, micromachining and surface treatments on several materials, such as metals [20, 43, 52, 53], composite materials [29, 54] and, of course, ceramics [13, 19, 55]. In Table 2, the detailed characteristics of the laser system are reported, while in Fig. 3 the laser equipment and an example of SiC milled specimen are reported.

In order to study the process behaviours, a systematic approach to planning design of experiments (DOE) was adopted. This approach involves different tasks: problem definition; a collection of information about the process by way of bibliographic analysis and relevant background; control factors (i.e. the process parameters) and their level definition, response variables (measured quantities) identification, experimental planning, tests execution and data analysis [56‐58]. As aforementioned, laser machining involved different mechanisms: melting and vaporisation [19, 20], thermal degradation [21‐23], and mechanical effect (the molten material pull-out due to the vaporisation-induced recoil force [19, 26, 27]). The presence of each mechanism depends on the laser characteristics (wavelength, spot diameter, pulse length, average power and pulse frequency), the investigated material as well as the adopted process parameters (scan speed, hatching distance, pulse frequency, repetition,…).

The selection of the control factors and their values is a critical issue in experiment planning. Based on relevant bibliography [11, 14, 15, 30, 32‐34, 48], previous studies [13, 19, 29, 59, 60] and preliminary tests, a 3³×2² full factorial plane was developed according to the design of experiment (DOE) [56, 57, 61]. It was chosen to fix the average power at the maximum level (30W) and to change the scan speed, the pulse frequency and the number of repetitions on 3 levels. The hatching distance and the scanning strategy (Strategy) were selected on 2 levels (the scanning strategy represents the hatching mode). Table 3 summarises the factors and their levels adopted for the experimentation.

In detail, the average power was fixed at the maximum value to assure a high material removal rate. The scan speed and the pulse frequency were selected based on preliminary tests. During these tests, it was noted that too high scanning speed or pulse frequency (that corresponds to low pulse energies or pulse power according to Eqs. (1–2)) does not allow machining, while too low scan speed (<500 mm/s) allows the formation of a greater amount of molten material, and this material solidifies on the machined surface producing the protrusion of the same from the surface and the presence of micro-fracture; this is consistent with that reported in [19].

The hatching distance controls the lateral superposition (hatching overlap) between two parallel scansions. Too large value does not assure a sufficient overlapping, especially when small surfaces were machined, while too narrow Hd may involve local over-heating, micro-fractures formation and debris accumulation. Thus, to assure an adequate hatching overlap, Hd was selected as a fraction of the declared beam spot at the focusing point (about ¼ and ½ of the declared beam spot diameter, see also Fig. 2). It is worth noting that, while the overlapping percentage varies in the range 60–90% (Eq. (3), for Ss=1000 and f=30 kHz and Ss=500 and f=60 kHz, respectively), the hatching overlap varies between 25 and 50% (Eq. (4), for Hd=60 and Hd=40, respectively). The difference in overlapping may result in texture formation on the surface (due to the formation of burr rows at groove sides), with a consequent increase in roughness. Therefore, in order to reduce this phenomenon, it was decided to adopt a pattern made of horizontal lines placed along with four different directions 0°, 90° and ±45° (CROSS strategy) or two single directions: 0° and 90° (NET strategy), as reported in Fig. 4, where each angle is carried out during a single repetition. The number of repetitions was selected to consider the need to use a multiple of four (due to the CROSS strategy that requires a minimum of four repetitions) and to obtain a depth to be measured with a low error and in any case less than the depth of field of the laser system (about ±0.5 mm respect the focussing point) to avoid excessive defocusing. To reduce the effect of any noise factor, the order of trials was fully randomised. No test replication was performed; in other words, one test for each control factor combination(treatment) was performed. This choice may introduce a limitation in the determination of higher-order interactions (as a matter of fact, no high order interaction can be checked), as well as in terms of model robustness. In addition, the replications adoption is not useful for ANNs modelling since it introduces errors during the trial phase and prevents the fitting [46, 62]. However, also considering the number of tests carried out (108 tests or treatments), this choice is an acceptable compromise in terms of the resolution of the statistical model and the number of tests to perform.

To quantify the process behaviour, the following response variables were selected: machined depth, material removal rate (MRR), calculated as the machined volume/process time, and the surface roughness parameters. The depth was measured by way of digital microscopy (Hirox, mod. KH-8700) as the average value of three profiles, 10 mm in length, acquired over the whole cavity. The surface roughness was measured by way of a 3D surface profiling system (Taylor Hobson, mod. Talysurf CLI 2000) equipped with an inductive gauge 2 μm radius diamond stylus. For each specimen, 4 profiles, 4 mm in length, were acquired directly in the cavity, adopting an axis resolution of 0.5 μm, a lateral resolution of 0.5 μm and a vertical resolution of 40 nm. Before the measuring, in order to avoid debris retention, each specimen was cleaned with acetone in an ultrasonic bath for 5 min.

Surface analysis software (TalyMap Universal, release 3.1) was adopted to measure the roughness parameters Ra (arithmetic mean deviation of the assessed profile), Rz (maximum height of the profile), Rt (total height of the profile), and RSm (mean spacing of profile elements), according to UNI EN ISO 4287:2009 standard [63]. For each treatment, the average value of the four profiles was adopted as roughness parameters. Once the depth was measured by digital microscopy, the material removal rate (MRR) was calculated as the ratio between the machined volume/treatment time by way of the equations:

where t_i is the machining time and L the size of the square pocket side (5 mm).

In addition, electronic microscopy (ZEISS mod. LeoSUPRA 35) was adopted to study the surface morphology.

The ANOVA assumes that the observations are normally and independently distributed with the same variance for each treatment or factor level. Before the analysis, the ANOVA assumptions were successfully checked by way of the analysis of residuals, according to what was reported in [56]. However, for the sake of brevity, this analysis was not reported here. In Table 4, the results of ANOVA are summarised for all the response variables in terms of p-value and the F-value. The analysis was carried out adopting a 95% confidence level (α = 0.05). Thus, a control factor is statistically significant (i.e. its variation affects the response variable) if the p-value is less than 0.05. While the presence of an interaction (p-value<0.05) indicates that the effect of a control factor on the response variables depends on the level (value) of the other control factor. The F-value indicates the weight of the effect; the greater the F-value, the greater the variation of the response variables at control factors change. The table also provides the error estimators: R-sq [%], R-sq (adj) [%] and Error [%]. The R-Sq [%] (R-square or R²) describes the amount of variation in the observed response that is explained by the control factors; R-sq (adj) [%] is a modified R-Sq [%] that has been adjusted for the number of terms in the analysis, while the Error [%] is complementary to 100 of R-sq [%].

From Table 4, almost all the control factors are statistically significant for the different response variables, except that Hd and Strategy for Rz, Hd for Rt and f for RSm parameter. In addition, several interactions are present, too. The F-values indicate that the most influencing factors are, by order of importance, R and Ss for the Depth, Hd and Strategy for the MRR, and f and Ss for Ra, Rz and Rt. For the RSm parameter, there are several significant factors and an interaction with very similar weight (F-values): Ss, R, Hd, Strategy and the interaction Hd×Strategy.

It is worth noting that, in all the cases where one or more control factors are not significant, there is at least one strong interaction (with high F-value). As shown below, this indicates the presence of anti-synergic interactions that can mask the presence of a main effect.

Once the significance of the control factors and their interaction has been verified by ANOVA table, to study their effect on the response variables, the main effect plots and the interaction plots were carried out. However, for the sake of briefness, only the factors and interactions with greater weight (high F-value) are discussed in the following section.

The possibility to effectively machine very brittle materials, as the SiC, without degradation or fracture production depends on the interaction mechanisms (cold ablation, vaporisation, melting, mechanical effect, cracking…) that determine the quantity of molten material produced and how heat is accumulated in the machining area during the process itself.

For the adopted sources (see Table 2), the power density (Pd>1.99*10^¹² W/m²) is high enough to produce, during the laser pulse action, the material melting and vaporisation, as reported in [10, 19]. The vaporised material forms hot plasma from the leading edge of the pulse and the plasma is sustained during the rest of the pulse. Therefore, a significant part of the removal mechanisms is due to the vaporisation-induced recoil force (so-called recoil pressure [26]). According to the described mechanisms, the molten material is partially ejected from the surface by the gas vapour and plasma pressure and only a limited part of the material is deposited on the surface or in the neighbour. The latter quickly dissipates in the surface of the material leading to the formation of a recast zone (recast layer). Moreover, although SiC melts at about 1900°C, in presence of oxygen at above 1100° C, SiC decomposition is obtained according to the following reaction [68]:

The SiC decomposition contributes to the gas formation and molten material expulsion, as confirmed by the presence of white porous deposit (formed by incoherent SiO₂) on the edge pocket (see Fig. 6), small filaments on the surfaces (Fig. 7) and light brown and inconsistent particles (made of SiO₂ + C traces) found far away to the sample after the machined process.

However, the contribution of each removal mechanism (melting, vaporisation, degradation, recoil pressure) and then the overall mechanism depends on the process parameters. In details, low pulse frequency corresponds to high pulse energy and pulse power (see Table 3); thus, the plasma formation and the mechanical effect are favoured: this allows to obtain a smooth and regular surface characterised by a texture formed during the last scansion, a very limited number of droplets and some voids due to the droplets or SiC particles detachment, as visible in Fig. 8, where surfaces obtained at Ss=500 mm/s, f=30 kHz and R=60 are reported. Conversely, at high frequency, the reduction of the pulse energies and the increase of the pulse overlapping results in a reduction of the mechanical effect and, at the same time, an increase of the local overheating. Consequently, the molten material increases and the surface results characterised by a large number of droplets. As can be inferred by the analysis of Fig. 9, where images of the surface obtained at 1000 mm/s, 60 kHz and 20 repetitions are reported. From the analysis of the various surfaces, it was possible to note that the increase in the number of droplets seems to be linked neither to the cutting speed nor to the number of repetitions. Conversely, the adoption of a larger hatching distance results in the formation of droplets that are larger in size as visible comparing the image on the right and left side of Fig. 9. However, excluding the presence of the pores, no evident damages (fractures) are visible on the surface also when magnification of 2000× is adopted (for instance in Fig. 7). This is due in part to the selection of the value to be adopted in the experimentation during the pre-tests and in part to the fact that, also in the actual worst conditions, the molten materials form only a thin recast layer or droplets; consequently, the contraction due to the phase transition is not such as to produce fractures.

In Fig. 10, the main effect plots for the different response variables are reported. In the figure, the continuous lines indicate the significant factors, vice versa the dashed ones.

From Fig. 10a, the depth decreases at the increasing of scan speed, hatching distance and pulse frequency, while it increases at the increasing of the repetitions and passing from CROSS to NET strategy. In addition, the interaction Hd×Strategy shows an F-value higher than the frequency f.

The effects of Ss, R and Hd are expected, since the latter determine the total energy released per unit area (Es). This can be calculated through the following:

where t_i is the machining time and S is the machined area (L²). Obviously, the higher the Es (lower Hd and Ss), the higher the depth, as also confirmed by Fig. 11, where the depth is reported against Es as a function of the strategy. This is consistent to previous studies performed on different materials [19, 59, 60].

It is worth noting that the effects of f and the Strategy are not justified by the Es dependence (Eq. (9)). However, they can be related to the pulse power and the temperature reached by the materials during the machining itself, respectively. More in detail, the lower the frequency, the higher the pulse energy and the pulse power (Eqs. (1) and (2)). Consequently, at low frequencies, also the plasma developed during the ablation is more intense; this results in a greater contribution of the mechanical effect. However, compared to the other control factors, the effect of frequency is quite limited, as confirmed by the low F-value. On the other hand, for a small machined area, the Strategy influences the local temperature, since the time required to reposition the laser on the same point changes at the Strategy changing (the time doubles passing from NET to CROSS). Clearly, a higher temperature of the substrate allows a higher material removal, since the energy required for material machining is reduced. This effect is confirmed in the Hd×Strategy interaction (Fig. 12a), where it can be observed that when adopting the narrow step (which allows the material local heating) and the NET strategy, the reached depth increases. The previous behaviours are confirmed by the MRR diagrams: as a matter of fact, the MRR increases passing from CROSS to NET strategy (Fig. 10b). The effect of Hd on MRR is explained considering that, despite low Hd promotes local heating, it results in a longer process time. Since the MRR is obtained as a ratio between the removed volume and the time, the effect of the latter prevails over the heating effect.

The roughness parameter Ra varies in the range 0.6–3.3 μm, and that, considering the adopted laser source (a nanosecond pulse duration), is a good result. Ra decreases at the Ss increase or at the f and R increase (Fig. 10c), while it seems insensitive to both Hd and Strategy. The increase of Ss has two effects: a decrease of both the pulse overlaps and the local temperature. Therefore, the single laser pulse produces a less deep crater with a wide distance between the previous and the following crater, resulting in a smoother surface. Conversely, as aforementioned, the increase of the frequency results in overheating phenomena, the mechanical effect is reduced and droplets are produced; therefore, the roughness increases. The roughness increase due to the repetitions increases is a consequence of the surface re-working; consequently, the surface roughness can only worsen, and this is consistent with the literature analysis [13, 19, 60]. About the effect of Hd and strategy, it is worth noting that their effects are hidden by the presence of an anti-synergic interaction as visible by the interaction plots (Fig. 12b). As expected, the roughness parameters Rz and Rt follow the Ra behaviours, with the difference that the first is weakly influenced by the Strategy while the second is weakly influenced by both Hd and Strategy (Fig. 10d and Fig. 10e). it is reasonable to assume that this is a consequence of the droplets’ size increase occurring under these conditions. However, the F-values of Hd and Strategy, when compared with those of Ss, f and R, are one or more order lower (Table 4).

About the RSm, it varies in the range 0.03–0.13 mm, and these values suggest that the RSm may depend on the presence of burrs and drops of recast material produced at the edges of the laser path, the material structure, since the latter is obtained by powder sintering, as well as the direction of the laser beam along the last surface scansion, as visible in Fig. 8 and Fig. 9. From Fig. 10f, the effect of Ss and R is similar to those described for the other roughness parameters.

The effect of Hd and Strategy is more complicated to describe, since their interaction is significant (from Table 4, p-value=0.000) and the F-value of the interaction is of the same order as that the single parameter ones (from Table 4, F-value=15.21, 15.89 and 14.33 for Hd, Strategy and their interaction, respectively). Generally speaking, an increase in Hd involves an increase in the distance between the channels produced by the laser during the single travel (see Fig. 2). This is true for the CROSS strategy, as inferred by Fig. 12c where the interaction plot Hd-Strategy is reported for the RSm. Conversely, for the NET strategy, a change in the Hd does not affect the RSm (as it was confirmed by the ANOVA test performed on only the NET data).

About the Strategy, it is worth noting that for the CROSS strategy, the last beam travel is placed along the 45° and the roughness was acquired along the 0° direction, then the distance between two parallel lines is higher than the hatching distance (0.057 μm and 0.085 μm for the Hd=0.4 μm and Hd=0.6 μm, respectively); for the NET strategy, the roughness was acquired along with one of the scanning directions; in both cases (CROSS and NET), the RSm average values are highest than the Hd. Consequently, the RSm is not only a function of the distance of the grooves formed during the laser machining (i.n. Hd), but it also depends on the mode in which the droplets and the burr are produced on the surface. Adopting the CROSS strategy, the distance between the groove edge is higher, and each surface scansion partially removes the surface topography produced in the previous scansion; consequently, the surface is smoother and more regular, and the droplets have no preferential organisation; thus, the measurement is more sensitive to actual Hd. Conversely, the surface produced adopting the NET is the superposition of more travel in the same direction, resulting in a different organisation of droplets and ribs, as visible comparing the surfaces reported in Fig. 9. Consequently, for the NET strategy, the effect of the change in Hd is partially hidden by the presence of the debris.

Due to the complexity of the phenomena occurring during laser milling operation, the response surface methodology (RSM) was adopted to model the process. As aforementioned, RSM provides a regression model (second-degree polynomial) able to describe the relationship between control factors and the response variables. Generally speaking, the model requires a number of points not necessarily larger, so it allows obtaining a model with a limited number of tests, provided the experimental plan is properly designed for the analysis (for instance, the quadratic terms, necessary to model the curvature presence, are available only for control factors with at least three levels). On the other hand, since the commercial software uses predefined laws (here a second-degree polynomial), it is not sure these are the best appropriate equations to model the physical phenomenon.

Before the model construction, the analysis of the statistical significance of the model term was carried out for each response variable. Table 5 summarises the results together with the errors performed in the estimation. As for the ANOVA table, this test assesses the significance of the control factors in the model and provides an estimation of their weights in the model (the F-value). From Table 5, the significant terms are almost the same of the ANOVA (Table 4); thus, the model is sufficiently sensitive in identifying the significant factors and interactions. The table also provides the error estimators: Error [%], R-sq [%]; R-sq (adj) [%], and R-sq (model) [%]. The first three terms have the same meaning described for the ANOVA table; the last one indicates a measure of how well the model predicts the response for new observations. However, the analysis of the errors performed by the models shows a good correlation for the Depth, Ra and Rz (high R-sq.s); a correlation just enough for the Rt parameters (good R-sq.s) and a low correlation for the MRR and RSm parameters (low R-sq.s). In Table 6, the regression equation in uncoded units for the different response variables, separate for the two strategies, is reported. In Fig. 13, the model data, calculated by means of the equations of Table 6, are reported against the experimental one. In the figure, the dotted line at 45° represents the reference line: model response=experimental data; Error [%] = 0. Figure 13 clearly shows that the RSM model is able to follow the general trend of all the control factors, since in any case the points align along the reference line. Depth, Rz and Rt show a better fitting since their points are closer to the reference line. The Ra parameter has a singular behaviour: the trend follows the reference line; the points are enough closed; however, the model overestimates the experimental values (there is an upward shift). Conversely, both MRR and RSM present some points far from the reference line (i.e. show a certain data dispersion).