## Q. 8.2

Design of a Cold Working Process
Design a manufacturing process to produce a 0.1-cm-thick copper plate having at least 65,000 psi tensile strength, 60,000 psi yield strength, and 5% elongation.

## Verified Solution

From Figure 8-6, we need at least 35% cold work to produce a tensile strength of 65,000 psi and 40% cold work to produce a yield strength of 60,000 psi, but we need less than 45% cold work to meet the 5% elongation requirement. Therefore, any cold work between 40% and 45% gives the required mechanical properties.
To produce the plate, a cold-rolling process would be appropriate. The
original thickness of the copper plate prior to rolling can be calculated from Equation 8-5,
Percent reduction in thickness = $[\frac{t_{0} \ – \ t_{f}}{t_{0}}] × 100$   (8-5)
assuming that the width of the plate does not change. Because there is a range of allowable cold work—between 40% and 45%—there is a range of initial plate thicknesses:

% $CW_{min}=40=[\frac{t_{min} \ – \ 0.1 \ cm}{t_{min}}] × 100, \ \ \therefore t_{min}=0.167 \ cm$

% $CW_{max}=45=[\frac{t_{max} \ – \ 0.1 \ cm}{t_{max}}] × 100,­ \ \ \therefore t_{max}=0.182 \ cm$

To produce the 0.1-cm copper plate, we begin with a 0.167 to 0.182-cm copper plate in the softest possible condition, then cold roll the plate to a 40% to 45% reduction in thickness to achieve the 0.1 cm thickness.