Concept:
True strain \({\epsilon _T}\; = \;ln\left( {\frac{{original\;area}}{{instantaneous\;area}}} \right) = \;ln\left( {\frac{{original\;thickness}}{{instantaneous\;thickness}}} \right)\), when length is not changing.
Flow stress σf = KϵTn, where K is yield strength in MPa and n is strain hardening component.
Calculation:
True strain ϵT \(= ln\frac{{100}}{{95}} = 0.05129\)
σ = 500 × (0.05129)0.1 ⇒ 371.5147523 = 371.5147523 MPa
Upto elastic limits using hooks law
\(\sigma = E\epsilon = E.\frac{{{\rm{\Delta }}l}}{l}\)
\(371.514 \times {10^6} = 200 \times {10^9} \times \left( {\frac{{{\rm{\Delta }}l}}{{100}}} \right)\)
⇒ Δl = 0.18575 mm = considering this for elastic recovery
∴ This will be added to 95 mm
⇒
Final dimension = 95.18575 mm