Question

A paper clip is made of wire 0.5 mm in diameter. If the original material from which the wire is made is a rod 25 mm in diameter, calculate the longitudinal engineering and true strains that the wire has undergone during processing.

Answer 1

Engineering strain =2499

True strain = 7.82

Step-by-step explanation:

Given that

Initial diameter D= 25 mm

Final diameter = 0.5 mm

As we know that ,the volume of material will remain constant

`A_iL_i=A_fL_f`

`(\pi )/(4)D^2L_i=(\pi )/(4)d^2L_f`

So now by putting the values

`(\pi )/(4)* 25^2L_i=(\pi )/(4)* 0.5^2L_f`

`(L_f)/(L_i)=2500`

We know that

`Engineering\ strain=(L_f-L_i)/(L_i)`

`Engineering\ strain\ e=(2500L_i-L_i)/(L_i)`

e=2499

We also know that

`True\ strain=\ln\left ( 1+e \right )`

`True\ strain=\ln\left ( 1+2499 \right )`

True strain = 7.82