Influence of Impact Angle on Nanometric Abrasive Cutting of Single‑Crystal Copper: A Molecular Dynamics Study

Background

Ultra‑precision machining underpins modern microelectronics, micromechanics, and optical component manufacturing, demanding nanometer‑scale dimensional accuracy and pristine surface finish. Among the finishing techniques, abrasive flow polishing (AFP) stands out for its ability to eliminate sub‑surface damage while maintaining geometric tolerances. AFP involves ultrafine abrasive particles dispersed in a fluid that impinge on the workpiece surface, removing material through repeated micro‑cutting events. While extensive experimental work has explored macro‑scale parameters—fluid rheology, abrasive concentration, and process parameters—microscale investigations remain sparse, especially concerning the atomic‑level mechanics of impact angle and force generation.

MD simulations offer a powerful, atomistic lens to interrogate these phenomena. Prior studies have used MD to examine nanoscale cutting of copper, silicon, and other materials, revealing insights into dislocation dynamics, phase transformations, and energy dissipation. Building on this foundation, we model the interaction between SiC abrasives and single‑crystal copper, focusing on how the impact angle modulates cutting force, energy transfer, and defect evolution.

Methods/Experimental

We constructed a realistic SiC abrasive model (radius 15 Å, 1406 atoms: 681 C + 725 Si) and a single‑crystal copper slab containing 159,020 atoms. The simulation box was equilibrated over 10,000 relaxation steps (Δt = 0.001 ps) before initiating cutting. Two SiC particles impinged on the copper surface at angles ranging from 0° to 45°, each with a velocity of 80 m/s. The total simulation comprised 100,000 cutting steps, allowing us to capture the evolution of stress, temperature, and dislocation density throughout the process.

Interatomic potentials were selected to reflect the distinct material interactions: Morse for Cu–SiC contacts, Embedded Atom Method (EAM) for Cu–Cu interactions, and Tersoff for SiC–SiC bonding. This combination has been validated in prior nanomachining studies and ensures accurate representation of elastic, plastic, and fracture behavior.

Figure 1. Sketch of the abrasive cutting scenario illustrating the impact angle relative to the copper surface.

Results and Discussion

Cutting Mechanics and Force Analysis

The SiC grains remove material by disrupting the copper lattice, generating shear stresses that manifest as cutting forces. Figure 6 demonstrates that cutting force magnitude grows with both depth and impact angle, especially along the [010] and [001] crystallographic directions. At small angles (≤ 15°), forces remain modest and relatively stable, whereas larger angles induce higher stresses and more pronounced fluctuations, indicative of increased lattice distortion and defect nucleation.

Figure 6. Cutting force as a function of simulation step for different impact angles: (a) [100], (b) [010], (c) [001] directions.

Energy Transfer During Cutting

Energy analysis reveals that kinetic energy rises steadily as the abrasive contacts the copper, peaking when the particle fully penetrates the lattice. Potential energy increases with angle up to ~20°, after which it plateaus, reflecting the onset of dislocation and phase transition events. The total energy remains relatively constant across angles because kinetic and potential components compensate each other.

Figure 7. Kinetic energy evolution for varying impact angles.

Figure 8. Potential energy variation with impact angle.

Figure 9. Total energy profile for all tested angles.

Atomic Displacement and Dislocation Evolution

Atomic displacement maps (Figure 10) illustrate that higher impact angles produce deeper penetration and more extensive lattice disorder. The transition from face‑centered cubic (FCC) to hexagonal close‑packed (HCP) and eventual amorphous structures is evident, especially for angles ≥ 25°. Dislocation density, identified via bond‑angle analysis (Figure 11), rises sharply with angle, indicating that large impact angles exacerbate plastic deformation and defect accumulation.

Figure 10. Atomic displacement fields for impact angles 0°–45°.

Figure 11. Dislocation line maps for impact angles 0°–45°.

Friction Coefficient Assessment

Calculated friction coefficients (ratio of tangential to normal force) remain largely invariant across all impact angles (Figure 13). This suggests that surface adhesion and atomic interlocking dominate friction behavior, rather than the macroscopic cutting geometry.

Figure 13. Friction coefficient trends for varying impact angles.

Conclusions

MD simulations confirm that impact angle is a decisive factor in AFP nanometric cutting. Angles between 0° and 15° generate modest cutting forces, limited dislocation activity, and superior surface integrity. Larger angles amplify lattice damage, increasing defect density and compromising material performance. The friction coefficient is insensitive to angle, underscoring the dominance of atomic adhesion over geometric factors. Accordingly, maintaining a small impact angle is recommended to optimize surface quality and minimize internal defects during abrasive flow polishing of single‑crystal copper.