Compute the true stress and the logarithmic strain using the data given below and plot the results on log$-$log paper.

Then, find the plastic strength coefficient ${}_0$ and the strain$-$strengthening exponent m $.$ The yield strength and the

ultimate strength after the specimen has had $20$ percent cold work. The original diameter of the test specimen is

$0\mathrm{.}504$ in $.$ and the original length, $L_o=2\mathrm{.}0in.$ The following data was obtained for the elastic and plastic states.

For the elastic state

For the plastic state

What are the yield and the ultimate tensile strengths following $20\%$ cold working? Assume the tensile strength prior to cold working is

$85\mathrm{.}6$ kpsi $.$

The yield and the ultimate tensile strengths are

$S_y^{\text{'}}=,k$

$S_u^{\text{'}}=,k$