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

Answer:

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