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In an ideal orthogonal cutting experiment (see figure), the cutting speed V is 1 m/s, the rake angle of the tool α = 5°, and the shear angle, φ, is known to be 45°. Applying the ideal orthogonal cutting model, consider two shear planes PQ and RS close to each other. As they approach the thin shear zone (shown as a thick line in the figure), plane RS gets sheared with respect to PQ (point R1 shears to R2, and S1 shears to S2). Assuming that the perpendicular distance between PQ and RS is δ = 25 μm, what is the value of shear strain rate (in s⁻¹) that the material undergoes at the shear zone?

1. 1.84 × 10⁴
2. 5.20 × 10⁴
3. 0.71 × 10⁴
4. 1.30 × 10⁴

Correct answer: 5.20 × 10⁴

Solution

The shear strain rate is calculated using the formula that relates the cutting speed, the shear angle, and the distance between shear planes. Given the parameters, the calculation yields a shear strain rate of 5.20 × 10⁴ s⁻¹, which reflects the high rate of deformation in the thin shear zone during the cutting process.

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