Given a 100 mm long square bar of fully annealed Copper with

Given a 100 mm long square bar of fully annealed Copper with a width and height of 9mm and yield strength of 160Mpa; while remaining square, improve the yield strength by 90% with cold working. A. What is the final width and height of the Copper bar. B. What is the ductility?

Solution

final yield strength required = 160 + 0.9 * 160   = 304 MPa

From the yield strength vs percent cold work provided at 304 MPa we get 35% CW for copper

Therefore    0.35     = (initial Area - final area) / initial area

                 0.35 = (81 - final area) / 81

                 final area of cross section = 52.65 mm^2

maintaining square cross section we have width = height   = 7.256 mm

From the ductility vs percent cold work provided at 35% CW for copper

we get approx. 7 %EL ductility