Q uestion on stress and strain?

Question

A bar of 8mm and length 40mm is subjected to a tensile load of 45 KN and the length changes to 60mm.calculate the engineering stress, true stress, engineering strain and true strain.

Answer 1

E = stress/strain

Stress = Force/Area

Strain = delta L / Length

So, for 8mm square bar, area = 64mm^2.

Engineering stress = 45kN/64mm^2.

Engineering strain = (60mm-40mm)/40mm = 50%

True stress requires the area after strain. Assuming homogeneous strain, and Poisson's of 0.5 (elastomer), then the volume of the solid remains the same. For other poisson's ratio's, such as 0.3 for steel, the volume changes. Vol before = 8*8*40. Volume after = x * x * 60. Setting equal, area (x*x) = 42 2/3. Then, stress = 45kN/(42 2/3 mm^2).

True strain = ln (60mm/40mm) = 0.4