Question

 A steel wire of 2 mm diameter is to be drawn from a wire of 5 mm diameter. The value of true strain developed is _______ (up to three decimal places).

Answer 1

Concept:

True strain (ϵ_T) = \(\ln\left(\frac{A_o}{A_i}\right)=\ln\left(\frac{l_i}{l_o}\right)\)

ϵT = \(\ln\left ( \frac{d_o}{d_i} \right )^2=2\ln\left ( \frac{d_o}{d_i} \right )\) 

Calculation:

Given:

d_o = 5 mm, d_i = 2 mm

Then, 

ϵT = \(2\ln\left ( \frac{d_o}{d_i} \right )=2\ln\left ( \frac{5}{2} \right )=1.832\)