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

longitudinal engineering strain = 624.16

true strain is 6.44

Explanation:

given data

diameter d1 = 0.5 mm

diameter d2 = 25 mm

to find out

longitudinal engineering and true strains

solution

we know both the volume is same

so

volume 1 = volume 2

A*L (1) = A*L (2)

(π/4 * d1²) * L (1) = (π/4 * d2²) * L (2)

(π/4 * 0.5²) * L (1) = (π/4 * 25²) * L (2)

0.1963 * L (1) = 122.71 * L (2)

L (1) / L (2) = 122.71 / 0.1963 = 625.16

and we know longitudinal engineering strain is

longitudinal engineering strain = L (1) / L (2) - 1

longitudinal engineering strain = 625.16 - 1

longitudinal engineering strain = 624.16

and

true strain is

true strain = ln (L (1) / L (2))

true strain = ln (625.16)

true strain is 6.44