A cylindrical specimen of coldworked copper has a ductility

A cylindrical specimen of cold-worked copper has a ductility (%EL) of 25%. The following figure shows the change in ductility (%EL) with percent cold work for copper. If the specimen\'s cold-worked radius is 7.5 mm, what was its radius before deformation?

Solution

Elongation is 25%

Radius of cold work is R_c = 7.5mm

Radius before deformation i.e., original radius R_o need to calculated

% Elongation = 100 *(R_o - R_c) / R_o

25 = 100*(R_o - 7.5) / R_o

0.25*R_o = R_o -7.5

From this we will get the value of R_o is 10mm

So, the Radius before deformation is 10mm