A paper clip is made of wire 0.75 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

True strain = 3.7704

Explanation:

Strain is the measure an object that is stretched or deformed. This occurs when a force is applied to an object. Strain deals mostly with the change in length of the object. Strain = Δ L / L = Change in Length over the original Length:

Volume Constancy:

ΔL/L0=A0/ΔA = (D0 / ΔD) = (25mm/0.75mm) ^2

ΔL/L0=44.4

Engineering strain:

Engineering strain = ΔL-L0/L0=ΔL/L0-1

Engineering strain = 44.4-1=43.4

True strain, ε=In (ΔL/L0) = In (43.4) = 3.7704

Note that strain has no unit, so the True strain = 3.7704