Question

Engineering stress, strain vs true stress, strain.

Answer 1

Answer with Explanation:

Stress is defined as the force acting per unit area on a material.

Mathematically

$\sigma =\frac{dF}{dA}$

where

$\sigma$  is the stress ,$dF$ is an infinitesimal force that acts on an infinitesimal area $dA$

When a body is under stress it's dimensions change and this change in dimensions is known as strain.

Mathematically

$\epsilon =\frac{\Delta x}{X}$

where

$\epsilon=$ strain in the object

$\Delta x =$ is the change in any dimension of the body

Now in the above relation of stress, the area involved  also changes when the body is loaded as the load produces strain which changes the dimensions of the body.

Now while calculating the stress if we use the original area of the cross section of the body prior to loading the stress that we calculate is the engineering stress and the strain associated with it is the engineering strain.

On the other hand if we use the true cross section of the body when it is loaded  the stress that we calculate is the true stress and the strain associated with it is the true strain.

Mathematically they are related as

$\epsilon _{true}=ln(1+\epsilon _{engineering})}$

Thus the true stress is found to be larger than engineering stress.