In a typical metal cutting operation, using a cutting tool

In a typical metal cutting operation, using a cutting tool a positive rake α = 10°, it is as observed that the shear angle was 20°. The friction angle is

α = 10°, φ = 20°
Ernest & Merchants' theory 2φ + β – α = 90°
2 × 20 + β – 10 = 90°
40 + β – 10 = 90°
β = 60°