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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.

1 Answer

5 votes

Answer:

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

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