1 Introduction

Besides excellent mechanical properties, silicon nitride (Si3N4) also has exceptional thermal properties that make it suitable for demanding industrial and medical applications comprising ball and roller bearings, heating tubes, turbocharger rotors, spark igniters, and orthopedic implants [1,2,3,4]. However, Si3N4, as an advanced ceramic, is difficult to cut material due to its elevated strength, hardness, corrosion resistance, and fracture toughness. Grinding with diamond tools is the primary machining process of Si3N4 and other hard and brittle materials. However, efficient grinding of these materials is countered by high cutting forces and temperature, tool wear, and generally reduced workpiece quality due to the brittle material removal regime [5]. Accordingly, despite the superior material properties of advanced ceramics, the use of these materials in the industry is mainly limited by the high machining costs and the mentioned technical constraints. According to the definition of precise machining, the dimensional and geometrical accuracy should be at least two orders of magnitude below the characteristic length of the component [6]. Meeting this requirement in the grinding and micro-grinding of hard materials leads to the challenge of restricting the dimensional accuracy and the size of thermally and mechanically influenced surface zones well below the limit values required by conventional grinding.

The brittle material removal regime, as the dominant material removal mechanism in abrasive machining of hard and brittle materials, differs significantly from the well-known ductile removal regime. The brittle material removal generally causes breakouts and micro-cracks formation on the workpiece surface [5, 7]. The laser structuring on the brittle material would enhance the material removal rate and grinding efficiency by propagating the lateral cracks [8]. The induced micro-cracks on the workpiece surface and in the subsurface of the workpiece cause significant strength reduction and substantial loss of tolerable stresses of the workpiece [5, 9,10,11]. Hence, in the case of Si3N4 and other hard and brittle materials, the surface integrity of the ground workpiece plays a crucial role in the performance, wear, and fatigue life of the workpiece [5].

It is shown that the quality loss of brittle workpieces such as advanced ceramics caused by induced subsurface damages through the brittle grinding regime could be overcome by material removal in a dominant ductile mode. The ductile grinding mode generates chips via plastic deformation rather than fracture [12]. The threshold between the ductile and brittle material removal regimes and hence the threshold for the lateral cracks’ initiation into the workpiece due to the grits’ penetration is defined by the critical chip thickness of the brittle material [13, 14]. It is necessary to keep the uncut chip thickness continuously below the critical chip thickness of the brittle material in order to cut the material in ductile mode. Hence, to reduce the subsurface damages, the advanced ceramics are generally ground with a very low material removal rate, causing a low uncut chip thickness (low depth of cuts and/or feed speeds).

On the other hand, low uncut chip thicknesses exponentially increase the required grinding energy (specific grinding energy) due to the size effect [5]. Although, the high hardness of advanced ceramics also causes high specific grinding energies due to the required energy for penetrating the workpiece and cutting the materials by grits [15].

Non-conventional and hybrid machining processes are developed to reduce the cutting forces and temperature and increase the achievable material removal rate in advanced ceramics machining [5, 16]. Laser structuring of the workpiece surface combined with the grinding process is one of the recently developed non-conventional and hybrid machining processes for increasing the machining efficiency of hard-to-cut materials [17]. Long-pulse laser irradiation causes more pile-up, cracks, and thermal damage than ultrashort-pulse laser [18, 19]. In other words, ultrashort-pulse lasers such as pico- and femtosecond lasers can be employed for machining difficult-to-cut materials with superior accuracy and controllability, where the ablation mechanism of the workpiece material is mainly sublimation (cold ablation) [20]. Hence, the workpiece surface can be ablated by ultrashort-pulse lasers without significant thermal damage or with minimal and controllable subsurface damage [8]. Accordingly, laser-assisted grinding, where patterned microstructures are generated on the workpiece surface by an ultrashort-pulse laser prior to the grinding process, can significantly decrease the specific cutting energy of the cutting process along with the structural damage and increase the machinability, removal rates, and tool life [8, 17, 21,22,23]. Hence, in view of the challenges mentioned above in precise machining, using ultrashort-pulse laser grinding as a hybrid machining process can be a promising solution [8, 24, 25].

The single diamond grit scratching test is an approach that replicates the kinematic and dynamic of the grinding process and is widely employed to investigate the material removal mechanism of hard and brittle materials [26,27,28,29,30,31,32,33]. Researchers also employed single grit scratching to predict the grinding forces, calculate, and model the specific grinding energy of hard and brittle materials [34,35,36,37,38,39]. Therefore, understanding the single grit scratching on the material workpiece is vital to model the overall grinding process by integrating the numerous actions performed by single grit. Single diamond grit is generally mounted on the periphery of a rotating wheel body and scratches against the workpiece surface, which is fixed on the machine table. Single tracks or grooves are scratched with various depths of cuts.

Structuring workpiece surfaces by an ultrashort-pulse laser prior to the grinding process affects the specific grinding energy and may alter the critical chip thickness of the material and hence the dominant material removal mechanism. These effects are partially due to controllable induced damages into the subsurface of the structured workpieces. However, the impacts of this surface structuring technique on the material removal mechanism of advanced ceramics such as Si3N4 are not yet thoroughly investigated. In this paper, single diamond grit scratching has been performed to examine the material removal mechanisms of laser-structured Si3N4 fundamentally. The scratching forces and the morphologies of scratch grooves have been measured and analyzed. The effects of cutting speed and undeformed chip thickness on pile-up area, area and width of the grooves, depth ratio, normal and tangential forces, and specific scratching energy have been explored on non-structured and laser-structured surfaces.

2 Experimental setup and procedures

Figure 1 illustrates the experimental setup, including the workpiece, a piezo multi-component dynamometer (Kistler type 9256C), and a single diamond grit with a defined geometry. The tip radius (R) and angle of single grit (\(\alpha\)) are 215 µm and 120°, respectively. This single grit was brazed to a rod mounted on the perimeter of a disk. The distance between the grit’s tip and the disk’s center was 84 mm. It means that the rotation diameter (ds) is 168 mm. The experiments were carried out on a 5-axis grinding center Haas Multigrind® CA.

Fig. 1
figure 1

(a) Experimental setup. (b) Magnified view of the experimental setup. (c) Magnified view of single diamond grit and related fixture. (d) Single diamond grit with a defined geometry (tip radius (R) of 215 µm and tip angle (\(\alpha\)) of 120°)

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Gas pressure-sintered silicon nitride (GPSSN) was selected as the workpiece material. The thermomechanical properties of the workpiece material are mentioned in Table 1. Block samples with dimensions of 30 × 20 × 10 mm were ground and polished, and the surface roughness (Ra) of about 0.13 µm was induced on the surface of the specimens. Before the single grit scratching, the workpiece surface was structured with two different laser percentages, 25% and 50%, by a CNC-laser machine (GF Femto Flexipulse Laser P 400 U). The workpiece was irradiated with a femtosecond Yb:YAG laser with a wavelength of 1030 nm, a beam diameter (dB) of 40 µm, a pulse duration of 250 fs, a pulse frequency of 400 kHz, a focal length of 70 mm, an average power of 40 W, and a scanning speed of 2 m/s. The laser structuring pitches were 100 µm and 50 µm for 25% and 50% (Fig. 2) laser structuring, respectively. Moreover, the wall thicknesses between the microstructures were 75 µm and 25 µm for 25% and 50% laser structuring (Fig. 3). The laser-structured depth is about 20 µm for both laser-structured samples.

Table 1 Thermomechanical properties of GPS Si3N4 [39]
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Fig. 2
figure 2

Polished samples. (a) Non-structured sample. (b) 50% laser-structured sample (laser parameters: vL = 2 m/s, PL = 40 W, tpulse = 250 fs)

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Fig. 3
figure 3

Schematic laser-structured surfaces at (a) 25% and (b) 50% laser structuring

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The single grit scratching tests were carried out at different depths of cuts (hcu max) within three cutting speeds (vc) 4, 8, and 10 m/s, and a constant feed rate (vf) of 5 m/min. The tests were carried out in the dry condition and up-grinding mode, where the grit traveled up the workpiece in the opposite direction of the table movement. Also, the direction of scratching tests for the laser-structured samples was perpendicular to the structured surface. The 3D topology and characteristics of scratch grooves, including the groove’s depth, width, and length, the pile-up, and the material removed volume, have been measured by a confocal microscope (Nanofocus Mobile µsurf) and analyzed by µsoft analysis premium 7.2 and MATLAB software. The 3D views of the single grit scratch on non-structured and laser-structured samples are shown in Fig. 4. Area of grooves and pile-up were obtained using MATLAB code by finding the most profound section in the grit path in the images analyzed by the µsoft analysis software from the confocal microscopy. As the actual and theoretical scratch depths might be different owing to the elastic deformations of the machining setup and environmentally induced uncertainties, the measurement of the scratch path length on the captured 3D images, as shown in Fig. 4, is used to evaluate the actual depth of cut values corresponding to the individual cutting path lengths.

Fig. 4
figure 4

Single grit scratches. (a) Non-structured surface. (b) 25% laser-structured surface. (c) 50% laser-structured surface

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3 Results and discussion

3.1 Area of groove and pile-up

The effects of the maximum depth of cut (hcu max) on the groove and pile-up areas and the width of scratches in the deepest section for three cutting speed levels (4, 8, and 10 m/s) are shown in Fig. 5 for non-structured surfaces. As shown in Figs. 5 and 6, the groove and pile-up area and the groove width rise with scratch depth (hcu max) independent of the utilized cutting speed. Hence, rising the material removal rate causes higher groove areas. Generally, in brittle materials such as Si3N4, the pile-up area around the scratched groove is caused by the lateral microcracks in the subsurface region of the groove [26, 41]. The number and length of the lateral microcracks increased with the undeformed chip thickness, increasing the acting stress on the workpiece surface.

Fig. 5
figure 5

Effects of the cutting speed (vc) on the area of groove and pile-up at the feed rate of 5 m/min for different values of maximum depth of cut, hcu max

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Fig. 6
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Effects of the cutting speed on the groove width at the deepest sections (hcu max) of various grooves

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Figures 7 and 8, which correspond to the deepest section of the scratches, show that the remaining pile-up area and the width of the groove are, respectively, reduced and increased by increasing the cutting speed. The reduction of the remaining pile-up area lies in the fact that the supporting area for the pile-up formation was diminished owing to the expansion of the groove width in direct correspondence with the cutting speed. The impact force of the diamond grit on the workpiece surface rises with the cutting speed, increasing the microcrack growth in axial and lateral directions [26]. The initiation and propagation of microcracks cause more chipping along the width of the scratch (Fig. 9) and may even lead to material removal beneath the actual grit path. Although more pile-up area could be expected by increasing the lateral microcracks, the supporting surface of the pile-up was removed by the chipping of the groove walls, causing an increase in the groove width (Fig. 6). The deviant point in Figs. 5 and 6 for the process condition of feed speed, vf = 5 m/min, cutting speed, vc = 10 m/s, and maximum depth of cut, hcu max = 13 µm is an indication of the occurrence of significant chipping or fragmentation which cause a remarkable increase in the area and width of the groove and a notable reduction in the pile-up area. Accordingly, Figs. 7(c) and 8(c) illustrate the increment of groove cross-sectional area at the highest cutting speed of vc = 10 m/s. Furthermore, the deviant point in Fig. 5 for the process condition of feed speed, vf = 5 m/min, cutting speed, vc = 4 m/s, and maximum depth of cut, hcu max = 13 µm verifies the considerable increase of micro-crack occurrence, which leads to noticeably larger pile-up areas. In other words, when the dominant material removal mechanism is brittle, the length and number of microcracks will be raised. Consequently, structural damage will increase even in the subsurface of hard and brittle workpiece material.

Fig. 7
figure 7

Area of groove and pile-up at the deepest section of the scratches (hcu max = 13 µm) induced at various cutting speeds on non-structured surface. (a) vc = 4 m/s. (b) vc = 8 m/s. (c) vc = 10 m/

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Fig. 8
figure 8

Section view at the deepest section of the scratches (hcu max = 13 µm) induced at various cutting speeds on non-structured surface. (a) vc = 4 m/s. (b) vc = 8 m/s. (c) vc = 10 m/s

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Fig. 9
figure 9

Effect of laser structure and wall thickness on crack propagation and chipping along the width of scratch. (a) Non-structured surface. (b) 25% laser-structured surface. (c) 50% laser-structured surface

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The area of groove and pile-up at the deepest sections of scratches induced at the process parameter of feed speed, vf = 5 m/min, cutting speed, vc = 8 m/s, and maximum depth of cut, hcu max = 13 µm on the non-structured and laser-structured samples are illustrated in Fig. 10. The groove area was increased from 424 µm2 in the case of non-structured surface to 2397 µm2 (465%) and 801 µm2 (89%) for 25% and 50% laser structuring, respectively. The laser structuring of the workpiece caused intermittent cutting, which resulted in a series of impacts during the scratching procedure. With a significant increase in the groove area, the interrupted cutting could promote the initiation and propagation of lateral and axial microcracks [42, 43] (Fig. 11). A higher percentage of laser structuring leads to an increase in the effects of intermittent impacts. However, an excessive wall thickness reduction due to a greater extent of surface structuring could set a barrier to the growth of lateral cracks. Accordingly, the amount of structural damage decreases with the percentage of the laser-structured surface, limiting the rise in groove area and decreasing the groove width (Fig. 10 and Fig. 12).

Fig. 10
figure 10

Area of groove and pile-up at deepest section of the scratches at the cutting speed of 8 m/s (hcu max = 13 µm). (a) Non-structured surface. (b) 25% laser-structured surface. (c) 50% laser-structured surface

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Fig. 11
figure 11

Effects of the workpiece laser structuring on the area of groove and pile-up at the cutting speed of 8 m/s and the feed rate of 5 m/min

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Fig. 12
figure 12

Effects of the workpiece laser structuring on the groove width at the deepest sections

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The effect of wall thickness on crack propagation has been shown in Fig. 9. While the wall thickness is large enough (Fig. 9b), the lateral crack propagation is more efficient, and consequently, the structural damage and the chip formation efficiency increase.

The pile-up area decreased wherever the impact force increased, whether this impact force was due to an increase in the cutting speed (Fig. 7) or due to the intermittent cutting by laser structuring (Figs. 10 and 11). As shown in Fig. 9, the chipping will occur during the scratching so that the number and volume of these fragmentations directly increase by increasing the percentage of laser structure (increasing the number of intermittent occurrences) and increasing the wall thickness of the laser structures. Furthermore, successive elastic deformation and recovery of the diamond grit increase due to more intermittent occurrences, and consequently, the actual depth of cut rises; therefore, more structural damage will happen. In the case of intermittent cutting on the laser-structured surfaces, more evidence of brittle fracture can be observed in the form of lateral and radial cracks, which contribute to the material chipping and fragmentation. As shown in Fig. 9, along each scratch path, the length of cracks or the sizes of the fragmentations are not directly related to the depth of cut; besides the nonregular nature of the brittle removal mechanism, this deviation would be due to the inhomogeneity, structural defects, and anisotropy of the hard and brittle workpiece material.

3.2 Single grit path

The theoretical path of single diamond grit, scratching the workpiece surface, could be calculated according to the below equation:

$${h}_{\mathrm{cu max}}=R-R\mathrm{cos}\theta$$
(1)
$$\theta ={\mathrm{sin}}^{-1}\left(\frac{L}{2R}\right)$$
(2)

where R, θ, and L are the distance from the single grit to the center of the rotating disk, half path angle, and projected path length, respectively (Fig. 13).

Fig. 13
figure 13

Schematic of a single grit path

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The generated paths by the single diamond grit scratching experiments on non-structured and 25% and 50% laser-structured surfaces at hcu max = 13 µm, vc = 8 m/s, and vf = 5 m/min are shown in Fig. 14. The theoretical path of the single diamond grit on the workpiece surface is plotted by fitting a circle to three points of the path, including the first point and endpoint of the path, which is measured by a confocal microscope and the theoretical hcu max. As shown in Fig. 14, for non-structured surfaces, the experimental real grit path lies significantly above the theoretical path. Only in the case of laser-structured surfaces, the experimental and the theoretical paths approach each other. The path followed by the diamond grit on laser-structured surfaces is even deeper than the theoretical path. The larger grit penetration depth on laser-structured surfaces could be due to the earlier onset of the brittle material removal regime, where the initiation and propagation of micro cracks and, consequently, macro cracks will be more and cause more structural damage. Accordingly, the depth ratio is defined in Eq. 3 and plotted in Fig. 15 to evaluate the differences between scratches produced on non-structured and laser-structured surfaces.

Fig. 14
figure 14

Experimental and theoretical grit paths (a) on the non-structured surface, (b) on 25% laser-structured surface, and (c) on 50% laser-structured surface

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Fig. 15
figure 15

Effects of the laser structuring on the depth ratio at different hcu max

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$$\mathrm{Depth}\;\mathrm{Ratio}=\frac{h_{\mathrm{cumaxTheo}}-h_{\mathrm{cumaxExp}}}{h_{\mathrm{cumaxTheo}}}$$
(3)

As depicted in Fig. 15, in non-structured surfaces, the depth ratio decreases while the depth of cut increases, which is due to the fact that the contribution of elastic deformation is smaller, and the propagation of radial cracks is more pronounced in larger cutting depth values. Furthermore, the reduction of depth ratio is more significant at lower cutting speeds, resulting from less elastic deformation and sufficient cutting time. In other words, while the depth of cut increases, the effects of elastic backlash, spring back, unbalancing of disk carrying the single grit, out of flatness, and also the roughness value of workpiece will be more negligible in microscale and consequently, the experimental grit path converges more to the theoretical path.

The depth ratio was much lower for laser-structured surfaces compared to non-structured surfaces. This reduction may be due to the intermittent cutting, which decreases the effect of spring back, elastic deformation, and cutting forces (compare Fig. 19). The material weakening owing to the laser-structuring also contributes to the decrement of cutting forces and elastic deformation of the diamond grit and the workpiece. Additionally, the single diamond grit follows the theoretical path during each laser structure period (since there is no contact between the grit and the workpiece surface in this period). Accordingly, the subsequent engagement of the diamond grit with the workpiece occurs at a depth corresponding to the theoretical path. Moreover, the impact forces due to this intermittent cutting can initiate and propagate microcracks on the walls of the structures, leading to a weakening of the material in such a way that, in some cases, the depth ratio changes to minus values. Negative depth ratio values indicate that the actual material removal is extended beyond the limit defined by the theoretical grit path. This negative ratio could be due to the domino effect of crack propagation and secondary chipping that amplify the effect of intermittent phenomena in laser structure surfaces. However, the depth ratio increased with the depth of cut in the case of laser-structured samples. As presented in Fig. 16, the increase in depth ratio at higher depths of cuts is due to the geometrical characteristic of laser structures, which makes it impossible to generate perfectly vertical structure walls. Therefore, the structure thickness increases, and the effect of laser structuring on the material removal decreases. Furthermore, the concentration of laser-induced damage in the vicinity of the laser structures and their contribution to the chip removal reduce (Fig. 16) at higher depths of cut.

Fig. 16
figure 16

Induced cracks around the structures by the laser material removal

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3.3 Lateral crack propagation

While the single diamond grit scratches the workpiece surface, the stress in the front end of the grit is mainly compressive, and the stress in the plastic removal zone is tensile. The lateral cracks propagate along the direction of the maximum stress gradient, which is in the oblique front of the grit [26, 44]. Accordingly, Figs. 17 and 18 confirm that on both non-structured and laser-structured surfaces, the lateral cracks were generated oblique to the groove direction, and the number and the length of these cracks increased with the depth of cut. On the laser-structured surfaces, the generated lateral cracks mainly cause chipping and fragmentation, which could be due to the lack of bulk material to absorb the crack propagation energy and support the weakened wall.

Fig. 17
figure 17

Lateral crack propagation by single grit scratching on non-structured surfaces at different hcu max, the cutting speed of 8 m/s, and the feed rate of 5 m/min

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Fig. 18
figure 18

Lateral crack propagation by single grit scratching on 25% laser-structured surfaces at different hcu max, the cutting speed of 8 m/s, and the feed rate of 5 m/min

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3.4 Normal and tangential forces

The effect of cutting speed on normal and tangential forces of single grit scratching tests on non-structured surfaces at different hcu max is presented in Fig. 19. Both normal and tangential cutting forces decreased by increasing the cutting speed, resulting from higher kinetic energies of the diamond grit and impact forces that are more likely to generate and propagate microcracks. An increase in the scratch depth or undeformed chip thickness caused higher material removal rates, raising the induced cutting forces.

Fig. 19
figure 19

Effects of cutting speed on the normal (left) and tangential (right) cutting forces at different hcu max

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The influence of laser structuring on normal and tangential cutting forces at vc = 8 m/s, vf = 5 m/min, and different hcu max are plotted in Fig. 20. Both normal and tangential forces significantly are reduced compared with the scratching of non-structured surfaces, as observed in previous researches [8, 17]. The main reasons may be related to the reduced workpiece volume, microcracks, controllable subsurface damages generated during laser structuring, and the increased impact forces due to the intermittent cutting. The reduction in cutting forces for laser-structured surfaces could be observed at all examined undeformed chip thicknesses.

Fig. 20
figure 20

Effects of the workpiece laser structuring on normal (left) and tangential (right) cutting forces at different hcu max

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3.5 Specific cutting energy

Specific cutting energy, ec, indicates the material removal efficiency and is defined as the energy required to remove a unit volume of material. This parameter in the single grit test is calculated as follows:

$${e}_{c}=\frac{\left({{v}_{c}+v}_{f}\right){\int }_{0}^{T}{F}_{t}dt}{{V}_{w}}$$
(4)

where vc, vf, Ft, Vw, and T are cutting speed, feed rate, tangential force, removed material volume, and scratching test time, respectively. The plus sign in the numerator of Eq. 4 means that single grit and workpiece velocities are in opposite directions (up-grinding). In this equation, Vw is calculated by analyzing the 3D confocal images of the grooves and their post-processing in MATLAB software. The area below the tangential force curve of single grit tests (\({\int }_{0}^{T}{F}_{t}dt\)) is also calculated by evaluating the measurement data obtained by the Kistler dynamometer using MATLAB software.

The effects of cutting speed and feed rate on the specific energy of laser-structured and non-structured samples are shown in Fig. 21. In the case of non-structured surfaces, the specific energy had its highest value at low material removal volumes. Hence, most of the energy was spent on sliding and plowing instead of cutting the workpiece material, which is in accordance with the well-investigated size effect in machining. However, the specific energy tended to a constant value when the material removal volume increased, demonstrating the dominance of the cutting portion. In other words, the sliding and plowing portions in specific grinding energy will be decreased by increasing the undeformed chip thickness or material removal volume.

Fig. 21
figure 21

Effects of the workpiece laser structuring on the specific scratching energy

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Interestingly, the specific energy almost did not vary at different removed material volumes for laser-structured surfaces. Although, this constant value was lower than the lowest specific energy measured for scratching on non-structured surfaces. It appears that the sliding and plowing forces are negligible compared to the cutting forces in the case of scratching laser-structured surfaces because the specific energy is constant, and consequently, the portion of cutting is dominant. In other words, the microcracks on the walls of the structures and subsurface structural damage caused by the laser material removal [8, 17], and also the intermittent phenomena due to laser structuring and increased impact forces caused a significant reduction of specific energy at different material removal volumes.

Although cutting speed has a proportional relationship with the specific energy, it also increases the impact force of the grit, which leads to the initiation and propagation of more microcracks, and the weakening of the material. Correspondingly, the cutting forces will be reduced. The interaction of these two opposite effects finally leads to a reduction in the specific energy in sintered silicon nitride material (Fig. 21).

4 Conclusions

The effects of ultrashort-pulse laser structuring on single diamond grit scratching of gas pressure sintered silicon nitride (GPSSN) material considering surface and subsurface damages have been experimentally investigated. The following results are concluded:

  • On non-structured surfaces, the pile-up area rises along with the undeformed chip thickness. At the same time, the cutting speed has a reverse relation with the pile-up area. Furthermore, the area and width of the groove directly increase with the undeformed chip thickness.

  • On laser-structured surfaces, the groove’s area and width increase with increasing the undeformed chip thickness. These increment trends have an optimum value in laser-structured surfaces.

  • The wall thickness of laser-structured surfaces significantly affects the grooves’ area and width compared to the percentage of laser structuring.

  • On non-structured surfaces, the depth ratio reduces with increasing the undeformed chip thickness. In contrast, the depth ratio converges to zero or even minus values for laser-structured surfaces.

  • Both on non-structured and laser-structured surfaces, the lateral cracks onset and propagate in the oblique front of the grit.

  • On non-structured surfaces, increasing cutting speed reduces normal and tangential scratching forces.

  • Laser structuring surfaces cause a significant reduction in normal and tangential scratching forces.

  • The specific cutting energy for laser-structured surfaces was nearly constant at different material removed volumes. In contrast, the specific energy showed an exponentially decreasing trend with removed material volume in the unstructured surfaces.

  • The extension of the obtained results regarding single diamond grit to model the micro-grinding process constitutes the future of the present investigation.