(1) It is one of the essential ploblems to consider how the shear plane is determined in orthogonal machining.
In this report the process to determine a shear plane is explained by means of plastic dynamics.
The shear plane of orthogonal machining is treated as a plain strain problem, and the angle θ
f between the direction of principal stress and the rake surface of a tool is calculated mathematically from the normal stress and the shear stress on the rake surface of a tool.
The primary shear angle φ
1 is expressed as follows :
φ
1=45°-θ
f+α
(2) On the other hand, Mohr's stress circle and the diagram of a shear plane are shown for the orthogonal machining of lead.
From Mohr's circle of lead the following relation is obtained experimentally.
p/
k=1.72.0
p : mean stress-
p=1/3(σ
x+σ
y+σ
z)
k : shear yield stress of chip.
Lee-Shaffer assumes that one of the principal stress in the plastic zone of chip is zero.
i.e. σ
x=-
p+
k=0 ∴
p/
k=1
This assumption is not sufficient for the practical cutting process, and is considered as one of the reasons why Lee-Shaffer's formula of a shear angle shows the different value from the experimental shear angle.
(3) The stress-strain curves of material are seemed to be useful to investigate the relation between the sum of shear strains γ
t and the total mean value of shear stresses τ
t which are explained in Report 3.
Loizou and Sims have performed high speed compression tests for lead by using the cam plastometer under the conditions of various strains, strain rates and temperature.
From those results the following experimental fomula can be obtained, assuming that the temperature is constant at room temperature.
σ
ij=3.8·ε
i0.23·ε
j0.033σ
ij : compression stress for ε
i and ε
j (kg/mm
2)
ε
i : compression strain
ε
j : compression strain rate.
(4) The cutting tests of lead are performed at the room temperature and very slow cutting speed 50mm4, 000mm/min.
The mean temperature rises so little in those cutting tests that the effect of temperature on the shear yield stress of chip is negligible. According as the increase of rake angles ranging from 20° to 40°, γ
t decreases but τ
t increases a little.
The increase of τ
t is presumed that the strain rate increases according to the increase of rake angles, and hardend the chip.
As the results of calculation by the experimental formula of σ
ij, the mean strain rate γ
t showed the order of 10
210
4 sec
-1.
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