L 11.1 Stress and Strain in the Chip

A Chip is supposed to experience both the stress and strain during metal machining because it is produced as a result of plastic deformation of the metal. For calculating their values, the conditions at the cutting plane are considered. In Fig. 11.1, you will notice that two mutually perpendicular forces Fs and Fn act on the shear plane. The average stresses on the shear plane area are:


Fig. 11.1 Forces acting in Orthogonal Cutting (Merchant's Circle Diagram).


where                                    Fs = Shea r force in kgs ;

and                                        Fn = Normal force in kgs

and                                        As = Area of the shear plane


We Know,


By substituting the values of Fs and As in equation (1), we get



We also know,


By substituting this value of Fn and that of As in equation (2), we get,


Now, let the shear strain = γ

Considering no loss of work during shearing:

Work done in shearing a unit volume of the metal = Shear stress x Shear strain


But we know that


By substituting the value of τs the above equation, we get


We Know,


So,