
62 Fundamentals of Machining Processes
tan( )
f
ϕ
+
−
cot()
1
k
f
Merchant called the value of cot
−1
k the machining constant.
3.3.8 Theory of Lee and Shaffer
Lee and Shaffer derived another relationship for φ based on the following
assumptions:
1. The machined material is ideal plastic, which does not strain harden.
2. The shear plane represents a direction of maximum shear stress.
As shown in Figure 3.15, the slip line eld A–B–C is plastically rigid and
subjected to a uniform state of stress. Accordingly, it is seen that the angle
ABD = η′. Therefore,
and
Therefore,
f
C
D
45°
45°–β
f
A
γ
t
c
B
β
f
t
FIGURE 3.15
Lee and S ...