Question

stress-strain graph derivation​

Answer 1

HERE IS YOUR ANSWER ☆

Refer to the image also.

From the origin O to the point called proportional limit, the stress-strain curve is a straight line. This linear relation between elongation and the axial force causing was first noticed by Sir Robert Hooke in 1678 and is called Hooke's Law that within the proportional limit, the stress is directly proportional to strain or

 

σ∝εσ∝ε   or   σ=kεσ=kε

 

The constant of proportionality k is called the Modulus of Elasticity E or Young's Modulus and is equal to the slope of the stress-strain diagram from O to P. Then

 

σ=Eε

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