Concept:
The relationship between true stress and strain is governed by the equation
σ = σ0 ϵη
At UTS, ϵ = n
ϵ = True strain \(= \ln \left( {\frac{{{L_f}}}{{{L_i}}}} \right)\)
Where (Lf) is the final length; (Li) is the initial length.
Calculation:
Here σ = 1020 ε0.4
So ϵ = 0.4 at (UTS)
\(\Rightarrow 0.4 = \ln \left( {\frac{{{L_f}}}{{{L_i}}}} \right) \Rightarrow \frac{{{L_f}}}{{{L_i}}} = {e^{0.4}}\)
\(\Rightarrow \frac{{{L_f}}}{{{L_i}}} = 1.491\)
As volume remains constant throughout
(AiLi = Af Lf) Given Ai = 100 mm2
⇒ 100 Li = Af Lf
\(\Rightarrow {A_f} = 100 \times \frac{{{L_i}}}{{{L_f}}} \Rightarrow {A_f} = \frac{{100}}{{1.49}}\)
A
f = 67.03 mm
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