Lee and Shaffer’s relationship between and is derived on the assumption that:

A. The material being cut behaves like an ideal plastic which does not strain harden.

B. The shear plane represents a direction of maximum shear stresses in the material cut.

Any point in the material to be cut is initial unstressed when it is some distance away from the tool tip.

As the tip of the tool approaches the stress builds up till it reaches a value high energy to cause plastic deformation.

The material is then converted into chip and proceeds up the tool face. The stress in the chip gradually falls off to zero.

Assuming a possible slip line field to represent these conditions of plastic deformation Lee and Shaffer gave the following equation for shear angle.

$\emptyset=\frac{\pi}{4}+\gamma-\beta---A$

This value $\emptyset$ of (in equation A), however was found to be not correct for all values of $\gamma$ and $\beta$ was modified by Lee and Shaffer to include the effect of a built up edge to be made of two straight lines and a circular are with a subtended angle $\theta$ as shown in figure. It was shown that the plastic flow relationship should take the form.

$\emptyset=\frac{\pi}{4}+\gamma+\theta-\beta$