A copper wire of original diameter. 80 m exhibits a maximum tensile load / strength at an engineering stress = 248.2 mpa. its ductility is measured as 75 reduction of area. Determine the true strain at failure.

True Strain at failure = 1.386

Explanation:

For the question, ductility is given in reduction In the area to be 0.75

Let the initial Cross sectional Area of wire be Ao

And the final cross sectional Area of wire of cross sectional Area of wire at fracture be A

(Ao - A) / Ao = ductility = 0.75

Ao - A = 0.75Ao

A = Ao - 0.75Ao

A = 0.25 Ao

True Strain = In (Lf/Lo)

To obtain the ratio of the lengths of wire,

The volume of the wire stays constant, that is, Vo = Vf; Vo = Ao * Lo and Vf = A * Lf

AoLo = ALf

Lf/Lo = Ao/A

In (Lf/Lo) = In (Ao/A) = In (Ao/0.25Ao) = In 4 = 1.386

True Strain = 1.386