3.1. Finite Element (FE) Modeling of the Microlens Cavity Lapping Process
It is known that two-body or three-body wear are two typical contact wear mechanisms [
12]. In the lapping process, the abrasive particle is pressed by both the WC lapping tool and the SSiC surface and may be embedded inside the lapping tool, leading to scratches and grooves on the SSiC surface, similar to the micro grinding process [
13]. However, with a longer machining duration, the two-body wear mode is weakened by the wear of the abrasive particle itself and it gradually transfers to the three-body wear mode, of which the small abrasive particles impact the surface, leading to surface cracks, fracture pits, and discrete breakouts [
14]. In this study, the utilization of a WC lapping tool head results in a larger exposed diamond abrasive particle surface and allows for a more aggressive material removal and faster lapping, compared to using a softer lapping tool. Therefore, the material removal is more effective.
The self-defined constitutive model is employed to characterize the behavior of the material, thereby encompassing the determination of the mold properties. The material’s yield and failure criteria are established using the Drucker–Prager criterion that considers various factors such as hydrostatic pressure, work hardening, strain rate, and thermal softening [
15]. This criterion is expressed as:
where
is the working hardening function,
is the strain rate function, and
is the thermal softening function.
When
, the working hardening function can be defined as:
Among which, is the initial yield stress, is the plastic strain, is the reference plastic strain, is the strain value at fracture, and is the strain hardening coefficient.
When
, the thermal softening function is defined as:
When
, the thermal softening function is defined as:
Since the rotational speed in the lapping process is low and the abrasive particles are randomly distributed on the workpiece, the influence of temperature on the processing is not considered.
When
, the strain rate is defined as:
While
, the strain rate is defined as:
where
is the strain rate,
is the reference plastic strain rate,
is the critical strain rate for the transition between high and low strain rates,
is the low strain rate sensitivity coefficient, and
is the high strain rate sensitivity coefficient.
Based on the above theory, the interactions between the spherical WC lapping tool diamond abrasive slurry and the workpiece were conducted. An FE model of a single abrasive diamond cutting process was developed for this study using Advantedge FEM. It is assumed that the abrasive particle is a rigid body because of its high hardness. The abrasive wear is ignored. The unit is defined as a solid six node equilateral triangle that is meshed using continuous adaptive mesh generation. The tool is also represented by a rigid body and its behavior is described using linear elastic law. The initial grid of the tool and workpiece is shown in
Figure 4. A fine and dense grid is set on the surface of the workpiece, with a minimum grid size of 5 nm in order to analyze the processed surface. The friction between the abrasive particles and the workpiece is set to comply with Coulomb’s friction law. The simulation model of the single abrasive micro-cutting process is illustrated in
Figure 5.
The analysis reveals the presence of distinct deformation zones and the occurrence of continuous chip formation during the machining process. Notably, as the abrasive particles plow into the SSiC surface, plastic deformation occurs, causing the material to flow and undergo plastic deformation. This plastic deformation plays a crucial role in smoothing the surface and refining the surface finish. Based on the single abrasive diamond micro-cutting finite element (FE) model, it becomes evident that the material removal of the abrasive grain embedded in the workpiece surface is primarily governed by plastic rheology. The material undergoes plastic deformation and plastic flow, resulting in the removal and accumulation of material accompanied by the formation of bumps and ploughing trails. Comparatively, plastic working offers advantages over brittle fracture as it contributes to the attainment of a smoother surface. The findings highlight the importance of understanding the material removal mechanism during the lapping process using multiple abrasives to obtain a smoother surface finish and enhance the overall quality of the SSiC microlens molds.
3.2. Surface Morphology and Elemental Composition Characterization
SEM (Hitachi SU5000, Hitachi, Ltd., Tokyo, Japan) was used to observe the microscopic surface morphology of the SSiC workpiece. The SEM image of the pristine SSiC is shown in
Figure 6. Although the surface is very rough, no large pores or cracks can be observed. Energy dispersive X-ray spectroscopy (EDX) was performed to measure the surface elemental composition. The surface is mainly composed of carbon (C) (40.54%, atomic percentage) and silicon (Si) (59.55%, atomic percentage).
Three microlens cavities were machined consecutively using the same lapping tool without any replacement parts. The experimental parameters remained consistent throughout the process including the usage of W20 abrasive slurry and a bottom delay of 100 s. The surface morphology of each cavity is presented in
Figure 7,
Figure 8 and
Figure 9, respectively. These figures show the resulting surface characteristics achieved.
Figure 7 shows the surface morphology of the lapping surface (abrasive slurry: W20, bottom delay: 100 s). It clearly shows that the microlens cavity is full of lapping trails. When the lapping tool is swept on the workpiece surface, the diamond abrasive particle applies a lapping force on SSiC, and as the tool moves across the SSiC surface, it ploughs and shears the surface, causing material to be removed in small chips. As shown in
Figure 7b,f, small pits appear after lapping and the local pits can become enlarged, as in
Figure 7c. This might be due to the micropores formed during the sintering process. Another possible reason is due to the material removal of small chips. In addition, the lapping trails are shown with different brightness and are not uniform with different diameters. When lapping SSiC with diamond abrasive particles, the hard diamond abrasive particles create a cutting action against the SSiC surface and remove the material through a combination of micro-cutting and micro-fracturing mechanisms. The diamond abrasive particles can also generate new sharp cutting edges through fracturing during the lapping process, which helps to maintain a consistent material removal rate. It is also noteworthy that at the center location of the cavity, as shown in
Figure 7e, there is little material removal in this area. The reason for this phenomenon is that the relative local speed is zero, meaning that the diamond abrasive cannot take part in the lapping machining.
As shown in
Figure 8, one more microlens cavity has been machined using the same experimental parameters, without any tool replacements. The surface morphology of the entire cavity and the locally enlarged area is shown. Similar to the first cavity, the surface is full of lapping trails along with micropores on the surface after lapping. It is noteworthy that more micropores appeared and a discrete breakout occurred during the lapping process, meaning that the brittle removal of SiC was dominant in the material removal of this cavity, as shown in
Figure 8b and enlarged in
Figure 8c. Meanwhile, there are many pits along the lapping trails. The diamond abrasive particles are firstly pressed tightly against the workpiece surface. The elastic deformation is released suddenly when the abrasive particle is in contact with a pit edge. Then, the abrasive particle continues to move forward and crush the surface. Brittle cracks are also formed, as shown enlarged in
Figure 8e,f.
Another microlens cavity has been machined using the same tool, as shown in
Figure 9. The lapping trails can be observed to be much shallower, compared with
Figure 7 and
Figure 8. This might be due to the wear of the lapping tool head itself. As the tool becomes worn, there are some changes in the shape and size of the tool, which can affect the material removal rate and the resulting surface finish. The changes in the tool geometry can alter the distribution of pressure and the path of the tool over the SSiC surface. This can lead to uneven material removal and surface finish, as well as increased surface roughness and waviness. In addition, it may lead to the formation of burrs or defects on the SSiC surface that can negatively impact the final product quality, causing the formation of scratch marks on the SSiC surface. The brittle cracks, micropores, and pits can still be clearly seen on the lapping surface, as shown enlarged in
Figure 9c.
It has also been observed that there are local dark areas on the lapping surface, as shown in
Figure 10a,b. The EDX spectra indicate that the carbon content can be increased to 70.54% (atomic percentage) after lapping, compared to the normal trail area 23.49%. One possible reason may be due to the formation of a hardened layer on the workpiece surface. During the SSiC lapping process, the local high temperature generated by the friction between the diamond abrasive particles and SSiC can cause the carbon atoms in the material to diffuse towards the surface. This can lead to the formation of a hardened layer on the workpiece surface that may contain higher levels of carbon element than the bulk of the material. Another possible reason is that SSiC lapping can create micro-cracks and other defects in the material surface. These defects can cause carbon to be trapped and concentrated in the surface layer, leading to an apparent increase in the carbon content.
3.3. Surface Topography Characterization
The surface topography of the machined microlens cavity (abrasive slurry: W7, bottom delay: 100 s) was measured using 3D laser confocal scanning microscopy, as shown in
Figure 9. The results correspond well to the surface morphology change. It can be observed that micropores and discrete breakouts happened on the lapping surface. Fracture pits can be observed as well. Apart from these characteristics, plastic flow bumps and ploughing trails are shown with height variation. Since SSiC is a hard and brittle material, it is prone to cracking and fracturing under mechanical stress. During lapping, the lapping tool or diamond abrasive particles apply a great local pressure to SSiC that creates stresses that exceed the material’s fracture toughness. As a result, the material undergoes brittle fracture and small chips are removed from the surface. It was also found that the surface topography, including the size and distribution of chips, depends on the lapping parameters, as shown in
Figure 11.
The 3D surface topography of the microlens cavities machined using W7 and W20 abrasives is depicted in
Figure 12a–f, respectively. These figures illustrate the surface characteristics of the microlens cavities under different abrasive sizes. Throughout the machining process, a constant lapping bottom delay time of 100 s was employed. Importantly, the microlens cavities were machined consecutively without replacing the lapping tool. Based on the surface topography, it is evident that the wear of the lapping tool head can significantly impact the material removal mechanism and resulting surface topography. As demonstrated, despite utilizing the same parameters for microlens cavity machining in (a–c), there is a noticeable distinction between the initially machined surfaces and the later ones. The initial surfaces exhibit non-uniform material removal and a rougher finish when compared to the subsequent surfaces. This observation holds true for microlens cavities that were machined using larger abrasive particles as well, as shown in (d–f).
This phenomenon can be attributed to the surface quality of the WC lapping tool head that directly impacts the distribution of diamond abrasive particles and their interaction with the SSiC surface during the lapping process. When the lapping tool head has a rough or uneven surface, it can lead to an uneven distribution of abrasive particles. Consequently, the material removal rate becomes non-uniform, and the resulting surface finish appears rougher. Conversely, a smooth and uniform surface will allow the abrasive particles to be more evenly distributed and produce a more uniform material removal rate and a smoother surface finish. The wear of the lapping tool after machining three cavities using W7 and W20 abrasives are shown in
Figure 13a,b, respectively. As the tool wears, the tool’s geometry changes and the sharpness is reduced, compared with the initial sharpness, as shown in
Figure 2c. The desirable lapping process cannot be achieved either. In addition, it is found that the material removal mechanism and surface topography are affected by the abrasive particle size. The material removal volume is apparently higher when using W20 diamond abrasive slurry. The surface topography is shown to have deeper lapping trails as well. While the microlens cavity is machined using the W7 diamond abrasive size results in a lower material removal rate. In contrast,
Figure 12a–c exhibit an increased presence of fracture pits, micropores, and discrete breakout features.
These characteristics are more pronounced when smaller abrasive particles are employed during the machining process. Specifically, the smaller particles tend to create shallower and narrower scratches on the surface. Conversely, when larger abrasive particles are utilized, the resulting scratches are deeper and wider, leading to a rougher surface texture. Therefore, it can be concluded that larger diamond particles remove material mainly through a ploughing mechanism, where the particles push and displace the material. However, smaller diamond abrasive particles will remove material through a cutting mechanism, where the particles break and remove material. This corresponds to the surface topography and morphology observation.
Based on the above-mentioned results, the material removal mechanism of SSiC during the lapping process with a spherical WC lapping tool and diamond abrasive slurry is primarily brittle removal. SSiC is a hard and brittle material, meaning that it is prone to cracking and fracturing under mechanical stress. The material is removed through a combination of ploughing, shearing, micro-cutting, and micro-fracturing mechanisms, resulting from the formation and propagation of cracks and fractures in the SSiC material. During the lapping process, the spherical tungsten carbide lapping tool or diamond abrasive particles apply a high local pressure to the SSiC surface that creates stresses that exceed the material’s fracture toughness. As a result, the material undergoes brittle fracture and small chips are removed from the surface. The size and distribution of the chips depend on the properties of the SSiC material, lapping parameters, and the characteristics of the lapping tool or abrasive particles.
It was found that WC lapping tool wear and the diamond abrasive particle size can affect the material removal mechanism when lapping SSiC using a spherical WC lapping tool and diamond abrasive slurry. WC lapping tool wear can cause changes in the shape and size that can affect the material removal rate and the resulting surface finish. The size of the diamond abrasive slurry will affect the depth and texture of the scratches left on the surface. Larger abrasive particles will create deeper and wider scratches, while smaller particles will create shallower and narrower scratches. It is important to note that larger abrasive particles displace the material during lapping and create a ploughing effect. Moreover, smaller abrasive particles are less likely to cause deep scratches because they cut the material rather than displace it. Therefore, a combination of larger and smaller abrasive particles may be used to optimize both the material removal rate, material removal mechanism, and surface finish. Thus, a combination of diamond slurry with different sizes for lapping SSiC have been tried in order to improve the results. In this study, we chose W7 and W20. The microlens cavity was firstly machined using small abrasive particles (W7) that can help remove any surface defects or scratches left by the previous steps. Followed by the larger abrasive particles (W20) in order to remove the bulk material at a faster rate. The surface topography is shown in
Figure 14. Despite the fact that there are a few materials around the center area, the figure clearly shows that the material removal is uniform. The micropores, discrete breakout, and fracture pits are removed. The ploughing trails are shown with high uniformity.
However, the success of step lapping depends on various factors such as the abrasive particle size and distribution, the lapping pressure, the lapping speed, and the diamond slurry concentration. Optimization of the parameters is essential to achieve the desired surface finish and material removal rate in our future study.