unit 1 metal cutting and chip formation - IGNOU

Theory of Metal Cutting
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the shear angle (φ) which included an additional angle θ, which depends on the size of
the built up edge,
π
φ = + ( α − β)
+ θ
4
In 1952, Shaw, Cook and Finnie extended the Lee and Schaffer theory by further
analytical and experimental investigations, and arrived at the following relationship :
π
φ = + ( α −β ) + η ′
4
While deriving the above relation, they assumed that the shear plane is not a plane of
maximum shear. Here, η′ is established by the analytical method and it is not constant. η′
is the angle between the shear plane and the direction of the maximum shear stress. To
determine the value and sign of the η′, it is necessary to draw the Mohr’s circle diagram.
Figure 1.14 : Shear Plane Model of Lee and Shaffer
Based on the experimental study of the mechanics of chip formation and the flow of
grains in the material during cutting, Palmer and Oxley observed that the deformation
does not take place along a plane, rather it takes place in a narrow wedge shaped zone.
But for analytical simplicity, it was considered as a parallel sided shear zone
(Figure 1.15).
Figure 1.15 : Shear Zone Model by Oxley
A further contribution towards the solution of this problem was made by R Hill in 1954,
who analyzed the state of stress at the shear zone, using a new principle “On the limits set
by plastic yielding to the intensity of singularities of stress”. But in 1959, Eggleston,
Herzog and Thomsen tried to show by their test results that none of the three Eqs. (by
Ernst and Merchant, Lee and Shaffer, and Hill) was correct which implies that metal in
the shear zone under the existing conditions of stress, high rates of strain and elevated
temperature does not behave as ideal plastic solid. Since no single criterion is applicable
to the shear angle relationship in metal cutting, and since a satisfactory theory has not
been advanced at present to explain the experimental observations adequately, the
challenge exists for a closer solution to the problem of angle relationship. This problem is
so tedious because the complexity is created by the simultaneous presence of so many
variables at a time, for example :
(i) plastic deformation,
(ii) work hardening,