Answer
$σ_{T} = 66,421.74 psi$
Work Step by Step
Given:
refer to given table for a brass alloy
Required:
true stress to produce true strain of 0.21
Solution:
Using Equation 6.19 for the two given conditions, two equations with unknowns are expressed:
$log( 60,000 psi) = log K + n log (0.15)$
$log( 70,000 psi) = log K + n log (0.25)$
Solving for n, we find:
$n = \frac{log (60,000 psi) - log (70,000 psi)}{log (0.15)- log (0.25)} = 0.302 $
Solving for K using the first first expression:
$log K = log (60000 psi) - (0.302) log (0.15) = 5.027$
$K = 10^{5.027} = 106,414.30 psi$
Solving for $σ_{T}$ when $ε_{T} = 0.21$:
$σ_{T} = K (ε_{T})^{n} =(106,414.30 psi)(0.21)^{0.302} = 66,421.74 psi $
