Simulation of the ductile machining mode of silicon
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-05-13 |
| Journal | The International Journal of Advanced Manufacturing Technology |
| Authors | Hagen Klippel, Stefan SĂŒssmaier, Matthias Röthlin, Mohamadreza Afrasiabi, Uygar Pala |
| Institutions | ETH Zurich, Federal Office of Meteorology and Climatology MeteoSwiss |
| Citations | 11 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive Summaryâ- Core Objective: Developed a GPU-accelerated Smoothed Particle Hydrodynamics (SPH) numerical model to simulate single-grain cutting of silicon, focusing on the transition between ductile and brittle material removal modes relevant to Diamond Wire Sawing (DWS).
- Model Limitations: The Johnson-Cook (JC) flow stress model, using parameters derived from literature, showed limited validity in accurately predicting process forces and residual depths near the ductile-to-brittle transition zone.
- Force Prediction Discrepancy: Simulated cutting forces (Fc) were acceptably close to experimental values, but normal forces (FN) were consistently over-estimated, suggesting the model needs extensions (e.g., fracture criteria) to account for low-energy brittle fracture.
- Phase Transformation Evidence: Simulations predicted extremely high local hydrostatic pressures (up to 60 GPa) at larger cut depths (1000 nm and 1500 nm), supporting the assumption that high-pressure phase transformations occur in the silicon workpiece.
- Ductile Regime Extension: Experimental scratch tests using a real, non-idealized diamond grain geometry demonstrated predominantly ductile material removal at residual depths (hres) up to 1.48 ”m, significantly exceeding the typically cited critical depth (hcu,crit ~ 60 nm).
- Future Model Improvement: Accurate prediction of the ductile-to-brittle transition requires incorporating anisotropic material behavior, phase transformation effects, and a robust fracture criterion into the constitutive model.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Workpiece Material | Monocrystalline Silicon | - | (100) direction assumed isotropic in simulation. |
| Numerical Method | SPH (Smoothed Particle Hydrodynamics) | - | GPU-accelerated (NVIDIA Quadro GP100). |
| Cutting Speed (vc) | 10 | m/s | Experimental and simulation parameter. |
| Simulated Cut Depths (hcu) | 200, 500, 1000, 1500 | nm | Range investigated in simulations. |
| Lowest Experimental Residual Depth (Ductile) | 0.55 | ”m | Scratch #1 (Ductile mode). |
| Highest Experimental Residual Depth (Ductile) | 1.48 | ”m | Scratch #6 (Ductile mode). |
| Max Simulated Hydrostatic Pressure | >60 | GPa | Observed at hcu = 1500 nm, suggesting phase change. |
| Max Simulated Equivalent Stress (von Mises) | 10-11 | GPa | Observed at hcu = 500 nm to 1500 nm. |
| Max Simulated Temperature (Tmax) | 1700 | K | Observed at hcu = 1000 nm and 1500 nm (near melting point). |
| Silicon Youngâs Modulus (E) | 129.09e9 - 0.01413e9 T exp(-709/T) | Pa | Temperature dependent model used. |
| Silicon Thermal Conductivity (λ) | -32.98 ln(T + 273K) + 251.62 | W/mK | Temperature dependent model used. |
| Friction Coefficient (”) | 0.3 | - | Coulomb friction assumed. |
| Taylor-Quinney Coefficient (ηTP) | 0.9 | - | Fraction of plastic work converted to heat. |
Key Methodologies
Section titled âKey Methodologiesâ- Grain Geometry Measurement: A single diamond grain from a commercial wire was isolated. Its 3D geometry was captured using an Alicona optical microscope, generating a point cloud, which was converted into a 3D tetrahedron mesh (4426 elements) for use as the rigid cutting tool in simulations.
- Experimental Scratch Setup: Scratch tests were performed on a polished silicon wafer using a Fehlmann Picomax Versa 825 5-axis milling machine. The wafer was rotated by the spindle, while the stationary diamond grain was mounted on a Kistler 9256C three-component force dynamometer.
- Kinematics and Speed: The cutting speed (vc) was fixed at 10 m/s. The tool path was spiral, achieved by simultaneous vertical and horizontal feed, resulting in an increasing depth of cut over 20 spindle rotations.
- Data Acquisition: Process forces (Fc and FN) were measured by the dynamometer (sampling rate 211.64 kS/s). Flash temperatures were monitored using a two-color fiber optic pyrometer.
- Residual Depth Determination: The residual scratch depth (hres) was determined optically by analyzing the median profile height of the scratch topography relative to the unscratched surface.
- Numerical Modeling (SPH): Simulations were executed using the GPU-accelerated SPH code
mfree_iwf. The silicon workpiece was modeled using the Johnson-Cook flow stress model, incorporating temperature-dependent material properties. - Thermal and Frictional Modeling: Heat conduction was included using the Particle Strength Exchange (PSE) approximation. Coulomb friction (”=0.3) was applied, and 90% of plastic work was assumed to convert to heat (Taylor-Quinney coefficient ηTP=0.9).
Commercial Applications
Section titled âCommercial Applicationsâ- Solar Wafer Production: Directly supports the optimization of Diamond Wire Sawing (DWS) processes for silicon ingots. Improved understanding of the ductile-to-brittle transition allows manufacturers to select optimal cutting parameters (feed rate, wire speed) to minimize subsurface damage and reduce subsequent etching costs.
- Ultra-Precision Machining: Relevant to the micro-machining and grinding of other hard, brittle electronic and optical materials (e.g., SiC, GaAs, sapphire) where surface integrity is paramount for device performance.
- Tool Design and Engineering: The methodology, which uses real, non-idealized grain geometries, provides a pathway for tool manufacturers to optimize the shape and distribution of diamond grains on cutting wires and grinding wheels to maximize ductile material removal.
- Constitutive Model Development: The experimental and simulation data serve as a benchmark for developing advanced constitutive models that accurately capture complex phenomena in silicon cutting, including high-pressure phase transformations and anisotropic fracture mechanics.