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Study on the unstable crack propagation mechanism in turning machinable ceramics based on the energy conversion principle and the fracture mechanics theory

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Abstract

Through machinable ceramic turning tests, the crack propagation at the machined surface and subsurface is explored, and the mechanism of unstable propagation is studied. The arrangement of the grains affects the direction of crack propagation, and the instability deflection angle (IDA) has a positive correlation with the instability deflection length (IDL). Crack propagation occurs in four stages: initial crack formation stage, metastable propagation stage, unstable propagation stage, and upward propagation stage. Based on the energy conversion principle and the fracture mechanics theory, a binary model of unstable crack propagation is developed. The IDA and IDL are quantified together with their positive correlation and accuracy. The experimental validation results reveal that the theoretical values of the IDA and IDL approach the experimental values, indicating that the model is accurate and may be utilized as a theoretical basis for forecasting the unstable crack propagation behavior in brittle material cutting.

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Data availability

All data generated or analyzed during this study are included in this published article.

Code availability

Not applicable.

Abbreviations

a p :

Cutting depth (mm)

b D :

Cutting layer width (μm)

c :

Instability deflection length (μm)

c M :

Total length of the crack at the initial crack formation stage and metastable propagation stage (μm)

E :

Elastic modulus (GPa)

F :

Tensile force when the stress at the crack tip reaches the breaking strength (N)

F c :

Main cutting force (N)

F c 1 :

Component force of the cutting movement direction on the rake face (N)

F f :

Axial thrust force (N)

F n :

Elastic reaction force on the flank face (N)

F p :

Radial thrust force (N)

F p 1 :

Component force perpendicular to the work plane on the rake face (N)

F rake :

The vector sum of Fs and fF (N)

F s :

Shear force (N)

f :

Feed rate (mm/rev)

f B :

Frictional force on the flank face (N)

f F :

Frictional force on the rake face (N)

H :

Hardness (GPa)

h c :

Crack propagation depth (μm)

h D :

Thickness of cutting layer (μm)

h s :

Elastic recovery height (μm)

K I :

Stress-intensity factor of mode I (MPa·m1/2)

K IC :

Fracture toughness (MPa·m1/2)

k 1 :

Constant fitted to the measured value

k 2 :

Constant

k 3 :

Constant

L c :

Transverse displacement of the crack propagation before instability (μm)

L s :

Elastic recovery length (μm)

r β :

Rounded cutting edge radius (μm)

r ε :

Corner radius (μm)

S :

Crack surface area (μm2)

U c :

Brittle fracture energy for the formation of powdery tiny chips (J)

U E :

Strain energy during the unstable crack propagation (J)

U K :

Kinetic energy during unstable crack propagation (J)

U S :

Surface energy of crack propagation (J)

u e :

Strain-energy density (J/μm3)

V :

Volume of the removed material (μm3)

V e :

Deformation volume under the triaxial stress state (μm3)

v c :

Cutting speed (m/min)

v fF :

Chip speed (m/min)

v lim :

Terminal velocity of crack propagation (m/min)

W :

The energy input from the tool during the unstable crack propagation (J)

W c :

The work done by the main cutting force (J)

W fB :

Frictional work between the workpiece and the tool flank face (J)

W fF :

Frictional work between the workpiece and the tool rake face (J)

α :

Specimen geometry edge correction factor

α 0 :

Clearance angle (°)

β :

Frictional angle (°)

γ :

Surface energy per unit area (J/m2)

γ 0 :

Tool rake angle (°)

δ :

Initial crack angle (°)

θ :

Instability deflection angle (°)

κ r :

Cutting edge angle (°)

λ s :

Cutting-edge inclination angle (°)

μ :

Coefficient of friction

υ :

Poisson’s ratio

ρ :

Density (g/cm3)

σ c :

Breaking strength (MPa)

σ s :

Elastic recovery stress on the freshly machined surface (MPa)

σ yy :

Tensile stress perpendicular to the crack propagation direction (MPa)

σ 1 :

Triaxial stress corresponding to the component force Fc1 (MPa)

σ 2 :

Triaxial stress corresponding to the component force Fp1 (MPa)

σ 3 :

Triaxial stress corresponding to the component force Ff (MPa)

φ :

Shear angle (°)

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Funding

This work was supported by the National Natural Science Foundation of China (grant number 51975113).

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, Liaoning, China

    **g Jia, Lianjie Ma, Wenhao Du, Yang Sun & Chunyu Dai

  2. School of Aeronautics, Inner Mongolia University of Technology, Hohhot, 010051, Inner Mongolia, China

    **g Jia

  3. School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao, 066004, Hebei, China

    Lianjie Ma, Yanqing Tan & Yunguang Zhou

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  1. **g Jia
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Contributions

**g Jia: conceptualization, methodology, software, experiment, writing—original draft, writing—review and editing. Lianjie Ma: supervision, writing—review and editing, funding acquisition, resources. Wenhao Du: software, investigation. Yang Sun: validation. Chunyu Dai: investigation. Yanqing Tan: supervision. Yunguang Zhou: supervision, experiment.

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Correspondence to Lianjie Ma.

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Jia, J., Ma, L., Du, W. et al. Study on the unstable crack propagation mechanism in turning machinable ceramics based on the energy conversion principle and the fracture mechanics theory. Int J Adv Manuf Technol 127, 4591–4606 (2023). https://doi.org/10.1007/s00170-023-11817-z

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