## Q. 8.1

Cold Working a Copper Plate
A 1-cm-thick copper plate is cold-reduced to 0.50 cm and later further reduced to 0.16 cm. Determine the total percent cold work and the tensile strength of the 0.16 cm plate. (See Figures 8-6 and 8-7.)  ## Verified Solution

Note that because the width of the plate does not change during rolling, the cold work can be expressed as the percent reduction in the thickness t.
Our definition of cold work is the percentage change between the original and final cross-sectional areas; it makes no difference how many intermediate steps are involved. Thus, the total cold work is

% CW = $[\frac{t_{0} – t_{f}}{t_{0}}] × 100 = [\frac{1 \ cm \ – \ 0.16 \ cm}{1 \ cm}] × 100 = 84$%

and, from Figure 8-6, the tensile strength is about 85,000 psi.
We can predict the properties of a metal or an alloy if we know the amount of cold work during processing. We can then decide whether the component has adequate strength at critical locations.
When we wish to select a material for a component that requires certain minimum mechanical properties, we can design the deformation process. We first determine the necessary percent cold work and then, using the final dimensions we desire, calculate the original dimensions from the cold work equation.