Question

A 100-mm-long strip of metal is stretched in two steps, first to 200 mm and then to 400 mm. Show that the total true strain is the sum of the true strains in each step; in other words, the true strains are additive. Show that, in the case of engineering strains, the strains cannot be added to obtain the total strain.

Answer 1

Kindly check the explanation section.

Step-by-step explanation:

Determine the strain in units in both steps.

For step one, strain = [ final length - Initial length]/ initial length = 200 - 100/ 100 = 1 unit.

For step two, the strain = final length - Initial length]/ initial length = 400 - 200/ 200 = 1 unit.

Total strain for the two steps = 1 unit + 1 unit = 2 units.

Estimation using single step is given below;

400 - 100/ 400 = 0.75.

It can be shown from above that the Engineering strength is Addictive.

The next thing to do is to determine the true strength. This is how it can be proved that the strength is Addictive or not.

b1 + b2 = (200 - 100/100) + (400-200/ 200)

b1 + b2 = 1 + 1 = 2.

b(total) = 400 - 100/100 = v2 - v1/v1.