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Research Papers

Effect of Thermal Softening on Anisotropy and Ductile Mode Cutting of Sapphire Using Micro-Laser Assisted Machining PUBLIC ACCESS

[+] Author and Article Information
Hossein Mohammadi

Mechanical and Aerospace Engineering,
Western Michigan University,
4601 Campus Dr.,
F-232 Floyd Hall
Kalamazoo, MI 49008
e-mail: hossein.mohammadi@wmich.edu

John A. Patten

Industrial and Entrepreneurial Engineering
and Engineering Management,
Western Michigan University,
E-205 Floyd Hall, Mail Stop 5336,
Kalamazoo, MI 49008
e-mail: john.patten@wmich.edu

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MICRO- AND NANO-MANUFACTURING. Manuscript received October 4, 2016; final manuscript received November 26, 2016; published online January 10, 2017. Editor: Jian Cao.

J. Micro Nano-Manuf 5(1), 011007 (Jan 10, 2017) (7 pages) Paper No: JMNM-16-1060; doi: 10.1115/1.4035397 History: Received October 04, 2016; Revised November 26, 2016

Ceramics and semiconductors have many applications in optics, micro-electro-mechanical systems, and electronic industries due to their desirable properties. In most of these applications, these materials should have a smooth surface without any surface and subsurface damages. Avoiding these damages yet achieving high material removal rate in the machining of them is very challenging as they are extremely hard and brittle. Materials such as single crystal silicon and sapphire have a crystal orientation or anisotropy effect. Because of this characteristic, their mechanical properties vary significantly by orientation that makes their machining even more difficult. In previous works, it has been shown that it is possible to machine brittle materials in ductile mode. In the present study, scratch tests were accomplished on the monocrystal sapphire in four different perpendicular directions. A laser is transmitted to a diamond cutting tool to heat and soften the material to either enhance the ductility, resulting in a deeper cut, or reducing brittleness leading to decreased fracture damage. Results such as depth of cut and also nature of cut (ductile or brittle) for different directions, laser powers, and cutting loads are compared. Also, influence of thermal softening on ductile response and its correlation to the anisotropy properties of sapphire is investigated. The effect of thermal softening on cuts is studied by analyzing the image of cuts and verifying the depth of cuts which were made by using varying thrust load and laser power. Macroscopic plastic deformation (chips and surface) occurring under high contract pressures and high temperatures is presented.

Monocrystal sapphire has many applications in optics and electronic industries such as blue LED, infrared detectors, substrates for semiconductors, and superconductors as it has high strength, good electric insulation, and low dielectric loss [1,2]. It is a very inert material to the majority of wet chemicals and dry etching and has many limitations for laser ablation due to the thermal effects of laser processing [3]. Different methods such as grinding [4], superfinishing [5], laser machining [6], and plasma [7] are the techniques for processing the sapphire, although mechanical finishing methods can cause surface and subsurface damages to the sapphire [8].

Sapphire is extremely hard and in the Mohs scale, in which diamond hardness is ten, sapphire hardness is nine. Therefore, there is a high demand for a method for efficiently machining it with no surface and subsurface damage and without the drawbacks of the current techniques. Sapphire shows a high anisotropic behavior; therefore, the effect of its crystal orientation on the machining is also another challenge for this material [911]. Machining sapphire in ductile mode has been reported by a few researchers. Liang et al. [1] investigated brittle to ductile transition during an ultrasonic assisted grinding process by performing scratch tests on the sapphire. They validated that this technique can be used for machining of sapphire in ductile mode. In another study by Smith et al. [12], stress change during the grinding of sapphire optics was measured by aid of the Twyman effect. They found out that the maximum stress is occurring during the brittle to ductile transition.

Tool wear is still an obstacle in the turning process and researchers are trying to decrease or at least model the tool wear to be able to predict it [13,14]. Although, for brittle materials, grinding and polishing are very common methods to achieve smooth surfaces [15], enhancing the machinability of these materials is on high demand [16].

Microlaser assisted machining (μ-LAM) is a method to thermally soften the workpiece material exactly at the tip of a diamond cutting tool, as shown schematically in Fig. 1 [1720]. In μ-LAM, a transparent diamond (to infrared laser) is used as a cutting tool and a laser is focused through it to the tip of the tool. This hybrid process, which is a combination of thermal softening and mechanical cutting, can increase the material removal rate (MRR) and since material is softer, because of laser heating, can decrease the tool wear. μ-LAM was effectively used in our research group for machining different semiconductors and ceramics such as silicon, spinel, and silicon carbide [1720].

Young module of sapphire decreases in elevated temperatures [21,22]. Therefore, it is expected that using this mechanical-thermal technique can help to enhance the machining of sapphire. In the current experimental research, μ-LAM is utilized to carry out the scratch tests on a sapphire C-plane wafer in different directions. Scratches with different loads and laser powers are performed in [1¯1¯ 20], [1 1¯ 00], [11 2¯ 0], and [1¯ 100] directions of a C-plane monocrystal sapphire. The depth as well as the nature of cuts, ductile or brittle, for each test, is examined and compared. The monocrystal sapphire sample used in this study was a C-plane polished wafer with a flat, which is representing the A-plane. Figure 2 shows the schematic of the sample and the directions in which scratch tests were performed. Table 1 presents the properties of the monocrystal sapphire sample used in this study.

In order to perform the scratch tests, as shown in Fig. 3, the μ-LAM setup was mounted on a tribometer which can be programmed for cutting speeds as low as 1 μm/s. The utilized laser was a 1070 nm wavelength continuous wave fiber laser with a power range of 10–100 W. A diamond with nose radius of 1 mm and negative rake angle of −45 deg and relief angle of 5 deg was used as a cutting tool. The negative rake angle provides a compressive stress during the process, which is necessary to avoid any fracture in the machining of brittle materials. The laser beam is then directed through the diamond to the tip of the tool and the cutting zone.

Experimental parameters such as length, speed of cuts, loads, and laser powers and also their values are listed in the Table 2. The actual laser output after going through the diamond was less than what was adjusted due to scattering, reflection, and absorption. For each laser power level, the actual output was measured and presented in Table 2. As the actual laser output and adjusted laser power were not showing the same gradients, the output power is addressed in this paper. Two series of tests were performed in this study, first with the constant loads and second with the increasing load to find the depth that the ductile to brittle transition (DBT) occurs. In the first series, the thrust load was constant for each test and for each laser power level, three different loads, 100, 200, and 300 milliNewtons (mN), were used. In the second series, the increasing load of 50–500 mN (except for [1 1¯ 00] direction to 700 mN) was utilized. A white light interferometer was used to measure the depth of cuts and the average of measurements is reported for each cut. Figure 4 shows the technique used to measure the depth of cuts. Any instability that usually took place at the beginning and at the end of the cut was excluded. Two modes of load and position control are available for the tribometer, and in this work, load control mode was used to carry out the tests.

Constant Loads
[1¯1¯20] Direction.

The first series of scratch tests were carried out in the [1¯1¯ 20] direction of the sapphire sample. At first, three different thrust loads, 100, 200, and 300 mN, with no aid of laser were performed. Then the same cuts with 1.6, 6.75, 11.8, and 16.8 W laser powers were performed in the same direction. As Fig. 5 shows for 200 mN and 300 mN, depth is significantly increased with 16.8 W; however, this is mainly due to fracture, or in other words, brittle mode cut. Figure 6 shows the cutting nature, ductile or brittle mode, of the 200 mN scratches with 11.8 and 16.8 W laser powers after cleaning the sample. A three-dimensional (3D) profile of each cut, which helps to visualize it, shows the depth of ductile cut and the pits caused by the fracture. Even though the laser can enhance the ductility of the material, a very high laser power can cause more fracture probably due to thermal stresses (Fig. 6(b)). That is the main reason that laser power is needed to be optimized for each machining condition and material. Based on previous works [1720,23], it is expected that the temperature at the cutting zone be in the range of 300–1000 °C. The ability of the material to reach to this temperature depends on the laser power and materials absorption. As expected by increasing the thrust load, depth of cut also increases. Although depth increases slightly by applying 1.6 W laser power, by increasing the power to 6.75 W and then to 11.8 W, a deeper cut was not achieved. The significant increase was observed for 16.8 W laser power, which is mainly due to fracture enhancement because of the thermal stresses induced by the laser.

[11¯00] Direction.

For the second direction, [1 1¯ 00], increasing laser power decreased the brittleness of the material and therefore decreased the depth of cuts. Comparing the depth achieved in this direction in Fig. 7 to [1¯1¯ 20] direction as shown in Fig. 5 indicates that for the no laser case, depth of the cut is almost doubled. The other obvious difference of the results of [1 1¯ 00] direction is that by increasing the load, a deeper cut was achieved while for [1¯1¯ 20] direction, increasing the load did not change the depth significantly, except for when 16.8 W laser power was used and the cut was in brittle mode.

Ductile and plastically deformed chips in Fig. 8 are good evidence of a ductile mode cut occurring in this direction. Although both cuts in Fig. 8 look ductile, a close look at the cut with 11.8 W in Fig. 8(a) indicates that in some points very small pits and fractures caused the depth to be higher than the cut with 16.8 W. Further evidence for this is the shape of the chips, which for the pure ductile cut, Fig. 8(b), is continuous while for Fig. 8(a), it is broken in half (see Fig. 8(a)). However, further investigation is needed to validate this claim. The lines perpendicular to cutting direction are tool nose marks on the surface as the tribometer in load control mode is trying to keep the programmed load constant during the process.

[112¯0] Direction.

Depth of cuts of the direction [11 2¯ 0] for 100 and 200 mN loads show a decreasing trend by increasing the laser power, as depicted in Fig. 9 (except for the 200 mN and 6.75 W condition). On the other hand, for 300 mN thrust load, the depth first decreased from no laser to 1.6 W and then increased for 6.75 W and beyond. With 1.6 W laser power, the nature of cut changed from brittle—or partially brittle—to ductile and by increasing the laser power, thermal stresses changed it back to brittle mode cut. The 3D profile of the cut illustrated in Fig. 10 clearly shows this transition. The cut is brittle for no laser, shown in Fig. 10(a), and a smooth cut was not achieved. However, by using 1.6 W laser, a ductile mode cut was obtained, as shown in Fig. 10(b). As it is mentioned before, the beginning and the end of a cut are usually unstable and that is why the end of the scratch is not smooth. Using the 6.75 W laser power caused fracture, as it can be seen in Fig. 10(c), and even though it is deeper than no laser case, it is not a smooth cut and is full of pits and voids. Figure 11 shows an example of effect of the thrust load on the nature of cut for the same level of laser power. By increasing the thrust force from 200 to 300 mN, even when the 11.8 W laser was used, the cutting regime changed from ductile to brittle.

[1¯100] Direction

The deepest cuts were achieved in the last direction, [1¯ 100], as shown in Fig. 12, while laser power has no considerable effect on the results. Increasing the thrust loads from 100, to 200, and then 300 mN significantly changed the results, which is a sign of fracture that occurred due to higher thrust loads. Ductile mode cut in brittle materials occurs when the chip thickness is less than a critical size. By increasing the load and exceeding this critical thickness, the mode of the cut changes from ductile to brittle. Figure 13, as an example, shows the brittle mode cut of the scratch for the tests with 300 mN by using 1.6 and 6.75 W laser powers. However, it seems less fracture occurred using the higher laser power (6.75 W), which is due to the decrease of brittleness and therefore less tendency of brittle mode cut of the material in an elevated temperature.

Anisotropy Effect.

Comparing the depth of cuts for different directions in one graph can help to understand the anisotropy behavior of the monocrystal sapphire during the machining. In Fig. 14, the results achieved for different directions with no aid of lasers are illustrated. The shallowest cuts were achieved for the [1¯1¯ 20] direction and the deepest were achieved for the [1¯ 100] direction, although the nature of cuts in the latter case was brittle. [1 1¯ 00] and [11 2¯ 0] directions behave almost the same for 100 and 200 mN, and for 300 mN, a 32% deeper cut was achieved for the [11 2¯ 0] direction. For other laser power levels such as 1.6, 6.75, and 11.8 W, although different depth of cuts were achieved, they showed the same trend as the cuts were made with no laser case. For the highest laser power used in this study, 16.8 W, the results were different. As depicted in Fig. 15, for the [1¯1¯ 20] and [1¯ 100] directions with the 200 and 300 mN, as well as for 300 mN for [11 2¯ 0] direction, the deepest cuts were achieved in the brittle mode cut. A pure ductile cut was achieved in the [1 1¯ 00] direction, and for 100 and 200 mN thrust loads for [11 2¯ 0] direction.

Increasing Load
Ductile Mode Machining.

In turning of brittle materials, to achieve a smooth surface, machining should be in ductile mode. In diamond turning as shown in Fig. 16(a), chip thickness varies along the nose of the cutting tool, starting from theoretically zero at the tool tip. If the depth of the cut and feed rate are bigger than a certain amount, critical chip thickness, tc, in which the mode of the cut changes from ductile to brittle, will be somewhere in middle of the chip cross section. Damage depth, yc, should not extend beyond the cut surface plane in order to avoid a brittle mode cut and a damaged surface left behind [24]. Since cutting passes overlapping each other, to have a surface machined in ductile mode, feed rate, f, should be small enough to remove the brittle fractures from the previous pass by succeeding passes [25]. This feed rate, which is usually small, is a limitation for the machining of the brittle materials as it increases the machining time. Longer machining time increases the length of tool cutting track and leads to higher tool wear. Critical chip thickness for various materials is different as well as for different directions of materials with anisotropy effect. However, by enhancing the ductile response of a material and pushing the boundaries, higher critical chip thickness can be achieved and therefore higher feed rate can be used as shown in Fig. 16(b) schematically. In the μ-LAM process, ductility of the nominally brittle materials is enhanced due to laser heating and thermal softening [18,19].

Sapphire is known to generate dislocations and exhibit microscopic plastic deformation at elevated temperatures, 400–700 °C and 1.5 GPa pressure [26], which emphasizes the “very low dislocation density.” Compared to the present work, where macroscopic plastic deformation (chips and surface) occurs under much higher contract pressures, >15 GPa, with higher temperatures. The underlying resultant plastic deformation mechanisms are presumable different, but no unifying explanation currently exists to explain the latter macroscopic results (the authors suggest a high pressure phase transformation may be the origin, but have no personal confirming evidence).

Ductile to Brittle Transition Tests.

Ductile response of different brittle materials with various properties is not same. Their response to the laser heating is also different as they have diverse optical properties. In the constant loads section, the achieved depths were reported, no matter of the nature of the cuts, ductile or brittle. However, it would be more beneficial to see the effect of the laser on increasing or decreasing the ductility of the material. The DBT tests with different laser power levels were performed on different directions. For this purpose, based on the initial tests, the load increased from 50 to 500 mN (for [1 1¯ 00] direction 50 to 700 mN was used) and different laser powers, similar to the constant load section tests, were used. Experiments were repeated to increase the reliability of the results. Then by using an interferometer and cross section of the cuts, the deepest point right before the cutting mode transition from ductile to brittle (or the last point of the ductile part) of each cut was measured as shown in Fig. 17.

[1¯1¯20] Direction.

For direction [1¯1¯ 20] as depicted in Fig. 18, the test with no laser resulted in a 103 nm DBT depth. Using the 1.6 W laser power barely increased the depth by 2% and for the laser powers of 6.75 and 11.8 W, the depth increased by 17.5% and 24.3% (compared to the no laser depth), respectively. The laser power of 16.8 W resulted in a decrease of DBT depth by 25%, which means the excessive laser power caused fracture, possibly due to thermal stresses. These results are compatible with the results of the constant load test and Fig. 5.

[11¯00] Direction.

Preliminary tests in the direction [1 1¯ 00] showed that the cut does not reach the DBT if increasing load range of 50–500 mN is used and all cuts would be in ductile mode. Therefore, since DBT should be achieved to be able to measure the depth associated with it, load range of 50–700 mN was used. The laser increased the DBT depth for this direction significantly. While the DBT depth for the cut with no laser was 63 nm, using a 1.6 W laser power increased it to 83 nm (∼ +32%). Increasing the laser power caused a linear depth increase as is shown in Fig. 19. This linear DBT depth increasing behavior is similar to the ductility enhancement in Fig. 7 for this direction. Unlike the [1¯1¯ 20] direction, no premature fracture occurred when16.8 W laser power was used in the [1 1¯ 00] direction.

[112¯0] Direction.

For the direction [11 2¯ 0], DBT depth of 79 nm with no laser obtained and 1.6 W laser power increased depth by ∼ 23% as shown in Fig. 20. The depth increased by 76% and 128% (compared to no laser depth) by using 6.75 and 11.8 W laser powers, respectively. The same behavior of the first direction, [1¯1¯ 20], was observed for this direction, [11 2¯ 0], and DBT depth dropped for the 16.8 W case, although a depth slightly bigger than the no laser cut was achieved.

[1¯100] Direction.

For the last direction, [1¯ 100], as illustrated in Fig. 21, DBT depth of 93 nm for the nonlaser cut was achieved. Using 1.6 W laser power increased the DBT depth by 44% that is the highest depth increase for this laser power level among all directions. The DBT depth increase for 6.75 and 11.8 W laser power was almost similar, +102% and +103%. Similar to [1¯1¯ 20] and [11 2¯ 0] directions, using 16.8 W laser power does not follow the same trend as the lower laser powers and a drop occurred; however, DBT depth is still higher than the no laser case for this direction too.

This paper was the first attempt to study the anisotropy effect and ductile mode cutting of the monocrystal C-plane sapphire by using the μ-LAM technique. Results showed that for [1¯1¯ 20] direction using and increasing laser power slightly increased the depth of cut. However, an excessive laser power may cause more fracture (probably due to thermal stresses), which is usually an unwanted result where a smooth surface is the goal (the opposite may be true if a high material removal rate is desired). The DBT tests for this direction showed that the laser heating increased the ductile depth, compared to no laser case, about 24%. For [1 1¯ 00] direction, the laser was obviously increasing the ductility and quality of the resultant surfaces and ductile chips were achieved. The DBT depth increased 144% by using 16.8 W laser power for this direction. Increasing the thrust load in [11 2¯ 0] direction can cause a brittle mode cut; however, for low thrust loads, increasing the laser power enhanced the ductility of the cut. Also, using 11.8 W laser power increased the DBT depth by 128%. Even though the deepest cuts were achieved in the [1¯ 100] direction in constant load experiments, analyzing the images showed that it was mainly due to the fracture that occurred during the cutting operation. In addition, it was observed that increasing both laser and thrust load caused more fracture. For a pure ductile cut, the laser power of 11.8 W increased the DBT depth by 103% for the [1¯ 100] direction. No noticeable tool wear was observed under microscope (400×) as the total tool cutting track was minimal. The underlying resultant plastic deformation mechanisms reported in the literature in microscopic scale and in this work in macroscopic scale are presumably different, but more investigation is needed to verify it.

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References

Liang, Z. , Wang, X. , Wu, Y. , Xie, L. , Jiao, L. , and Zhao, W. , 2013, “ Experimental Study on Brittle–Ductile Transition in Elliptical Ultrasonic Assisted Grinding (EUAG) of Monocrystal Sapphire Using Single Diamond Abrasive Grain,” Int. J. Mach. Tools Manuf., 71, pp. 41–51. [CrossRef]
Wang, Q. , Liang, Z. , Wang, X. , Zhao, W. , Wu, Y. , and Zhou, T. , 2015, “ Fractal Analysis of Surface Topography in Ground Monocrystal Sapphire,” Appl. Surf. Sci., 327, pp. 182–189. [CrossRef]
Qi, L. , Nishii, K. , Yasui, M. , Aoki, H. , and Namba, Y. , 2010, “ Femtosecond Laser Ablation of Sapphire on Different Crystallographic Facet Planes by Single and Multiple Laser Pulses Irradiation,” Opt. Lasers Eng., 48(10), pp. 1000–1007. [CrossRef]
Feng, W. , Lu, W. , Zhou, H. , Yang, B. , and Zuo, D. , 2016, “ Surface Characterization of Diamond Film Tool Grinding on The Monocrystal Sapphire Under Different Liquid Environments,” Appl. Surf. Sci., 387, pp. 784–789. [CrossRef]
Furushiro, N. , Yamaguchi, T. , Hirooka, D. , Matsumori, N. , and Tanada, K. , 2016, “ Multistage Superfinishing of Sapphire With Vitrified Bonded Diamond Super Abrasive Stones,” 31st Annual Meeting of American Society for Precision Engineering, Portland, OR, Vol. 1, pp. 478–482.
Schütz, V. , Young, K. , Matsumura, T. , Hanany, S. , Koch, J. , Suttmann, O. , Overmeyer, L. , and Wen, Q. , 2016, “ Laser Processing of Sub-Wavelength Structures on Sapphire and Alumina for Millimeter Wavelength Broadband Anti-Reflection Coatings,” J. Laser Micro Nanoeng., 11(2), pp. 204–209. [CrossRef]
Bastawros, A. F. , Chandra, A. , and Poosarla, P. A. , 2015, “ Atmospheric Pressure Plasma Enabled Polishing of Single Crystal Sapphire,” CIRP Ann. Manuf. Technol., 64(1), pp. 515–518. [CrossRef]
Xu, Y. , Lu, J. , and Xu, X. , 2016, “ Study on Planarization Machining of Sapphire Wafer With Soft-Hard Mixed Abrasive Through Mechanical Chemical Polishing,” Appl. Surf. Sci., 389, pp. 713–720. [CrossRef]
Cheng, J. , Wu, J. , Gong, Y. D. , Wen, X. L. , and Wen, Q. , 2017, “ Grinding Forces in Micro Slot-Grinding (MSG) of Single Crystal Sapphire,” Int. J. Mach. Tools Manuf., 112, pp. 7–20. [CrossRef]
Voloshin, A. V. , Dolzhenkova, E. F. , and Litvinov, L. A. , 2015, “ Anisotropy of Deformation and Fracture Processes in Sapphire Surface,” J. Superhard Mater., 37(5), pp. 341–345. [CrossRef]
Vodenitcharova, T. , Zhang, L. C. , Zarudi, I. , Yin, Y. , Domyo, H. , Ho, T. , and Sato, M. , 2007, “ The Effect of Anisotropy on The Deformation and Fracture of Sapphire Wafers Subjected to Thermal Shocks,” J. Mater. Process. Technol., 194(1), pp. 52–62. [CrossRef]
Smith, M. B. , Schmid, K. A. , Schmid, F. , Khattak, C. P. , and Lambropoulos, J. C. , 1997, “ Controlling Stress in Sapphire Optics,” Proc. SPIE, 3134, pp. 284–292.
Niaki, F. A. , Ulutan, D. , and Mears, L. , 2016, “ Parameter Inference Under Uncertainty in End-Milling γ′-Strengthened Difficult-to-Machine Alloy,” ASME J. Manuf. Sci. Eng., 138(6), p. 061014. [CrossRef]
Niaki, F. A. , Ulutan, D. , and Mears, L. , 2015, “ Stochastic Tool Wear Assessment in Milling Difficult to Machine Alloys,” Int. J. Mech. Manuf. Syst., 8(3–4), pp. 134–159.
Guo, B. , Zhao, Q. , and Fang, X. , 2014, “ Precision Grinding of Optical Glass With Laser Micro-Structured Coarse-Grained Diamond Wheels,” J. Mater. Process. Technol., 214(5), pp. 1045–1051. [CrossRef]
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Figures

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Fig. 1

Schematic of the μ-LAM technique

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Fig. 2

Monocrystal sapphire C-plane wafer and test directions

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Fig. 3

μ-LAM experimental setup

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Fig. 4

Technique used to measure depth of cut

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Fig. 5

Depth of cut of [1¯1¯20] direction

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Fig. 6

Microscopic image and 3D profile of cutting nature of [1¯1¯20] direction with 200 mN: (a) 11.8 W and (b) 16.8 W

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Fig. 7

Depth of cut of [11¯00] direction

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Fig. 8

Cutting nature of [11¯00] direction with 300 mN and laser power of: (a) 11.8 W and (b) 16.8 W

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Fig. 10

Three-dimensional profile of 300 mN load cut: (a) No laser, (b) 1.6 W, and (c) 6.75 W laser powers, [112¯0] direction

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Fig. 11

Cutting nature of [112¯0] direction with 11.8 W laser power and: (a) 200 mN and (b) 300 mN load

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Fig. 9

Depth of cut of [112¯0] direction

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Fig. 12

Depth of cut for [1¯100] direction

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Fig. 13

Cutting nature of [1¯100] direction with 300 mN: (a) 1.6 W and (b) 6.75 W with fractured chips

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Fig. 14

Depth of cuts for no laser for different directions

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Fig. 15

Depth of cuts for 16.8 W for different directions

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Fig. 16

Diamond turning of brittle materials: (a) cross section of the chip during the process and (b) laser heating is enhancing the ductile response

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Fig. 17

(a) DBT depth measurement of cross section of a cut and (b) 3D profile of a DBT test

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Fig. 18

DBT depth of cut of [1¯1¯20] direction

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Fig. 19

DBT depth of cut of [11¯00] direction

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Fig. 20

DBT depth of cut of [112¯0] direction

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Fig. 21

DBT depth of cut of [1¯100] direction

Tables

Table Grahic Jump Location
Table 1 Properties of the monocrystal sapphire*
Table Footer Note*Note: Marketech Intl, Inc.
Table Grahic Jump Location
Table 2 Experimental parameters and their value

Errata

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