# Modeling and Experiment of the Critical Depth of Cut at the Ductile–Brittle Transition for a 4H-SiC Single Crystal

^{*}

## Abstract

**:**

## 1. Introduction

_{c}is the fracture toughness. This formula was amended by later scholars; for example, Gaobo’s study on the critical depth of cut of 6H-silicon carbide indicated that the experimental results were not in line with the calculation of Formula (1) and the amended constant α [24].

## 2. Modeling

#### 2.1. Modeling of the Indenter Structure

_{1}is the distance from Section 1 to the nose vertex, d

_{2}is the distance from Section 2 to the nose vertex, r

_{0}is the radius of Section 1, r is the circular arc radius of the intersection between the sphere and the triangular pyramid, and l is the length of the intersection between the section which is normally aligned to the centerline and the edge plane in the transition part.

#### 2.2. Modeling of the Critical Depth of Cut

_{1}is the average contact pressure between the indenter and workpiece, A

_{1}is the projected area of the contact surface between the indenter and part (${A}_{1}=3\sqrt{3}{(d+{d}^{*})}^{2}{\mathrm{tan}}^{2}\theta $), and μ is the frictional and adhesive coefficient.

_{dn}

_{1}is the normal force component caused by the elastic restoring force, F

_{dn}

_{2}is the normal force component caused by the frictional and adhesive forces, F

_{dn}

_{3}is the normal force component caused by the chip formation force, F

_{dt}

_{1}is the tangential force component caused by the elastic restoring force, F

_{dt}

_{2}is the tangential force component caused by the frictional and adhesive force, and F

_{dt}

_{3}is the tangential force component caused by the chip formation force.

_{2}is the cutting deformation contact stress, S

_{1}is the projected area given by the shaded area in Figure 2, and S

_{2}is the contact area between the region of ductile deformation, which is the area from the unmachined surface to the machined surface.

_{1}and S

_{2}, respectively, are

_{e}is the part elastic recovery depth and is equal to the height difference between the scratching and residual depths. Note that the elastic recovery depth is not constant and increases linearly as the scratching depth increases [20].

_{1}is obtained from Equation (15).

_{1c}is the critical average contact pressure.

## 3. Experimental Setup

## 4. Results, Analysis, and Discussion

#### 4.1. Determination of the Indenter Nose Radius

_{max}is the maximum load. For standard fused quartz, the hardness is 9.5 GPa. For the Berkovich indenter used in this study, α = 77.3°, β = 57.64°, θ = 65.27°, and γ = 60°. Table 2 shows the indenter height and projected area for a variety of maximum loads. Using least squares, the projected area was related to the indenter height by ${A}_{p}=25.58\times {\left(123.8+d\right)}^{2}$, as shown in Figure 4. The indenter nose radius was calculated as R = 4952 nm via Equation (8).

#### 4.2. Analytic Surface Morphology

#### 4.3. Comparison of the Critical Depth of Cut between Simulation and Experiments

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Dimension parameters and geometric shape of the Berkovich indenter: (

**a**) model diagram, (

**b**) top view, (

**c**) side view, and (

**d**) 3-D solid model.

Test Parameters | Unit | Values |
---|---|---|

Pre-scan/post-scan load | mN | 0.1 |

Loading range | mN | 0.1–80 |

Scratch length | μm | 250 |

Scratch velocity | μm/s | 4 |

Load (mN) | Indenter Height (nm) | Contact Area (nm^{2}) |
---|---|---|

20 | 164.5 | 2.2053 × 10^{6} |

40 | 274.2 | 4.2905 × 10^{6} |

60 | 379.6 | 6.4158 × 10^{6} |

80 | 460.1 | 8.3211 × 10^{6} |

100 | 522.9 | 1.0426 × 10^{7} |

120 | 578.6 | 1.3032 × 10^{7} |

140 | 625.4 | 1.4037 × 10^{7} |

160 | 676.5 | 1.5642 × 10^{7} |

180 | 750.4 | 1.8247 × 10^{7} |

Test Number | Critical Depth of Cut (nm) |
---|---|

1 | 92 |

2 | 93 |

3 | 90 |

Average value | 91.7 |

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**MDPI and ACS Style**

Chai, P.; Li, S.; Li, Y.
Modeling and Experiment of the Critical Depth of Cut at the Ductile–Brittle Transition for a 4H-SiC Single Crystal. *Micromachines* **2019**, *10*, 382.
https://doi.org/10.3390/mi10060382

**AMA Style**

Chai P, Li S, Li Y.
Modeling and Experiment of the Critical Depth of Cut at the Ductile–Brittle Transition for a 4H-SiC Single Crystal. *Micromachines*. 2019; 10(6):382.
https://doi.org/10.3390/mi10060382

**Chicago/Turabian Style**

Chai, Peng, Shujuan Li, and Yan Li.
2019. "Modeling and Experiment of the Critical Depth of Cut at the Ductile–Brittle Transition for a 4H-SiC Single Crystal" *Micromachines* 10, no. 6: 382.
https://doi.org/10.3390/mi10060382