# A Nanomechanical Analysis of Deformation Characteristics of 6H-SiC Using an Indenter and Abrasives in Different Fixed Methods

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## Abstract

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## 1. Introduction

## 2. Experimental

#### 2.1. Materials

#### 2.2. Nanoindentation Experiment

#### 2.3. Fixed Abrasive Machining

#### 2.4. Free Abrasive Machining

#### 2.5. Semi-fixed Abrasive Machining

## 3. Results and Discussion

#### 3.1. Results and Theoretical Analysis of this Nanoindentation Experiment

_{c}and H represent fracture toughness (generally, K

_{c}is 1.9 Mpa m1/2 for single crystal SiC [25]) and hardness of materials. The theoretical critical loads for the brittle fractures of the C and Si faces of single crystal SiC are defined below respectively.

#### 3.2. The Results of Grinding with Fixed Abrasives and Materials Removal Analysis

_{c}stand for the elastic module, hardness, and fracture roughness of materials, respectively, so by substituting the experimental results above into Equation (8), the authors found that the critical grit cutting depth for C and Si faces of single crystal 6H-SiC were 5.3 nm and 6.1 nm, respectively.

_{v}(when the diamond density was 3.25 $\mathrm{g}/{\mathrm{cm}}^{3}$, ${F}_{v}=0.25\mathrm{C}$) and ${r}_{m}$ indicate the concentration of grinding materials of diamond grinding wheels, the volume fraction of the layers of material in the grinding wheels, and the radius at any point on the surface of the workpieces, respectively. According to the study by Shang [27], the maximum thickness of undeformed substrate ${h}_{\mathrm{max}}$ was:

_{m}was 25.4 mm). Moreover, the value of concentration C in Equation (9) can be obtained through simple geometric relationships, as shown in the following equation [28]:

_{d}, and f represent the equivalent spherical diameter of diamond particles, the volume fraction of diamonds in the grinding wheel, and the fraction of diamond particles that actively cut when grinding, respectively. The grinding wheel used in the present study had a density of 100, or in other words, the volume fraction v

_{d}was 0.25. To obtain the value of C, it was assumed that only one-half of the diamond particles on the wheel surface was actively engaged in cutting [28], or the value of f was equal to 0.5.

#### 3.3. The Lapping Results of Free Abrasives and Analysis of Material Removal

_{w}indicate the hardness of the workpieces and the average pressure on single abrasive, then [31],

#### 3.4. The Cluster MR Finishing Results of Semi-fixed Abrasives and Analysis of Material Removal

_{F}of the MR micro grinding heads on the workpieces was a complex parameter which included hydrodynamic pressures, and pressures produced by the MR effects and liquid buoyancy. Moreover, the pressures produced by MR effects consisted of magnetizing and magnetostrictive pressures, and since MR fluids are non-compressible, the magnetostrictive pressures in the magnetic fields induced by changes in volume were approximately zero, the expression for polishing pressures is

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Symbol | Nomenclature |

f_{s} | Spindle feed(µm/s) |

n_{w} | The rotational speed of workpiece (rpm) |

n_{s} | The rotational speed of grinding wheel (rpm) |

H | Hardness (Gpa) |

E | Elasticity modulus (Gpa) |

K_{c} | The fracture toughness (Mpa m^{1/2}) |

$\rho $ | The radius of curvature of grinding grains on the materials (mm) |

F_{0} | The contact load (mN) |

F_{C} | The contact load of C face (mN) |

F_{Si} | The contact load of Si face (mN) |

P* | The critical load for brittle materials changing from plastic deformation to brittle fracture (mN) |

P*_{C} | The critical load for C face changing from plastic deformation to brittle fracture (mN) |

φ | The proportion of magnetic particles in the MR fluids |

h_{max} | The maximum thickness of undeformed substrate (nm) |

d_{c} | The critical grit cutting depth (nm) |

R | The radius of the grinding wheels (mm) |

L_{w} | The circumference of layers of grinding material of the cupped grinding wheels (mm) |

C | The concentration of grinding materials of diamond grinding wheels |

K_{β} | The coefficient relating to the shape of the grinding grains |

d_{w} | The radius of grinding grain (μm) |

r_{m} | The radius at any point on the surface of the workpieces |

v_{d} | The volume fraction of diamonds in the grinding wheel |

h_{wp} | The space between the workpieces and the lapping plates (mm) |

F_{in} | The abrasive forces at the entrance of the polishing belts (μN) |

S | The workpiece area (mm^{2}) |

P_{F} | The polishing pressures (kPa) |

P_{m} | The pressure produced by MR effects of the MR fluids (kPa) |

P_{d} | The hydrodynamic pressure (kPa) |

P_{g} | The buoyancy of MR fluids (kPa) |

μ_{0} | The magnetic inductivity of a vacuum |

μ | The magnetic inductivity of magnetic particles |

η | The initial viscosity of the MR fluids (Pa.s) |

v | Speed of polishing disk (m/s) |

F_{v} | The volume fraction of the layers of material in the grinding wheels (g⁄cm^{3}) |

P*_{Si} | The critical load for Si face changing from plastic deformation to brittle fracture (mN) |

K_{b} | The distribution coefficient of abrasives between the workpieces and lapping plates |

H_{m} | The strength of the external magnetic fields (Gs) |

h_{0} | The distance from the polishing plates to the surfaces of workpieces (mm) |

t | The thickness of workpieces (mm) |

Δ | The machining gap (mm) |

W | The tooth width of layers of grinding material of the cupped grinding wheels (mm) |

F_{w} | The average pressure on single abrasive (mN) |

S_{A} | The actual contact area between a single abrasive and the workpieces (mm^{2}) |

p | The lapping pressure (kPa) |

d_{g} | The equivalent spherical diameter of diamond particles |

f | The fraction of diamond particles that actively cut when grinding |

d_{max} | The maximum diameter of abrasives (mm) |

F_{out} | The abrasive forces at the exit of the polishing belts (μN) |

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**Figure 4.**Test results of Single crystal 6H-SiC substrates under small loads (

**a**) Load and depth curve in small loads of C face and (

**b**) Load and depth curve in small loads of Si face.

**Figure 5.**Test results of Single crystal 6H-SiC substrates under large loads (

**a**) Load and depth curve in large loads of C face and (

**b**) Load and depth curve in large loads of Si face.

**Figure 7.**Morphology of Single crystal 6H-SiC substrates ground with different grades of grit (

**a**) No.1 (Ra 0.303 μm), (

**b**) No.2 (Ra 0.029 μm), (

**c**) No.3 (Ra 0.015 μm) and (

**d**) No.4 (Ra 0.002 μm).

**Figure 9.**Morphology of single crystal 6H-SiC substrates after lapping. (

**a**) After lapping by W14 diamond. (

**b**) After lapping by W1.5 diamond.

**Figure 10.**Contact state diagram of the abrasives, workpiece, and lapping plate. (

**a**) Ideal contact state. (

**b**) Actual contact state.

**Figure 11.**Scanning electron microscope (SEM) morphology of Single crystal 6H-SiC wafer polishing belt. (

**a**) Schematic diagram of polishing, (

**b**) schematic diagram of the polishing belt, (

**c**) SEM morphology of entrance and (

**d**) SEM morphology of exit.

Process No. | Grinding Wheel Type (Abrasive Grain Size) | Feed Rate f_{s} (µm/s) | $\mathbf{Workpiece}\text{}\mathbf{Speed}\text{}{\mathit{n}}_{\mathit{w}}\text{}\left(\mathbf{rpm}\right)$ | $\mathbf{Wheel}\text{}\mathbf{Speed}\text{}{\mathit{n}}_{\mathit{s}}\left(\text{}\mathbf{rpm}\right)$ |
---|---|---|---|---|

No.1 | 325# (45µm) | 5 | 151 | 1800 |

No.2 | 325# (45µm) | 0.1 | 151 | 1800 |

No.3 | 325# (45µm) | 0.1 | 151 | 3200 |

No.4 | 8000# (1.6µm) | 0.1 | 151 | 3200 |

**Table 2.**Hardness and elastic modulus of Single crystal 6H-SiC substrates by quasi-static indentation.

Loads | 1 mN | 2 mN | 5 mN | 10 mN | 20 mN | 50 mN | 100 mN | 200 mN | 300 mN | 500 mN | |
---|---|---|---|---|---|---|---|---|---|---|---|

Hardness/ Elasticity Modulus | |||||||||||

Hardness of C face (Gpa) | 47.867 | 55.418 | 55.825 | 52.596 | 50.514 | 46.745 | 43.741 | 41.435 | 39.861 | 38.596 | |

Elasticity modulus of C face (Gpa) | 538.075 | 581.841 | 627.822 | 618.019 | 612.893 | 596.833 | 576.843 | 567.615 | 562.4 | 563.019 | |

Hardness of Si face (Gpa) | 48.211 | 46.381 | 50.788 | 48.446 | 45.693 | 42.392 | 39.651 | 37.315 | 36.311 | 36.246 | |

Elasticity modulus of Si face (Gpa) | 533.033 | 554.146 | 614.533 | 601.814 | 589.13 | 570.998 | 548.221 | 535.773 | 525.946 | 524.839 |

Parameter | Value |
---|---|

Thickness of workpiece t (mm) | 0.3 |

Machining gap $\Delta $ (mm) | 0.8 |

Abrasive diameter ${d}_{w}$ (μm) | 2.8 |

The initial viscosity of the MR fluid $\eta $ (Pa·s) | 0.5 |

The magnetoconductivity of magnetic particles $\mu $ | 2000 |

Vacuum permeability ${\mu}_{0}$ | 1 |

Magnetic field intensity H_{m} (Gs) | 2000 |

Speed of polishing disk v (m/s) | 1.27 |

The proportion of magnetic particles in the MR fluid $\phi $ | 0.33 |

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## Share and Cite

**MDPI and ACS Style**

Pan, J.; Yan, Q.; Li, W.; Zhang, X.
A Nanomechanical Analysis of Deformation Characteristics of 6H-SiC Using an Indenter and Abrasives in Different Fixed Methods. *Micromachines* **2019**, *10*, 332.
https://doi.org/10.3390/mi10050332

**AMA Style**

Pan J, Yan Q, Li W, Zhang X.
A Nanomechanical Analysis of Deformation Characteristics of 6H-SiC Using an Indenter and Abrasives in Different Fixed Methods. *Micromachines*. 2019; 10(5):332.
https://doi.org/10.3390/mi10050332

**Chicago/Turabian Style**

Pan, Jisheng, Qiusheng Yan, Weihua Li, and Xiaowei Zhang.
2019. "A Nanomechanical Analysis of Deformation Characteristics of 6H-SiC Using an Indenter and Abrasives in Different Fixed Methods" *Micromachines* 10, no. 5: 332.
https://doi.org/10.3390/mi10050332