Calculating the Modulus of Elasticity from a Stress-Strain Curve

[kasse]

I've got a computer plot showing relations between stress and strain for steel. But how can I find the modulus of elasticity (E) from the graph? Isn't it so that E=(stress/strain)? The thing is that I get very different answers when I compute E in this way for various points on the graph.

 

[AlephZero]

See http://www.uoregon.edu/~struct/courseware/461/461_lectures/461_lecture24/461_lecture24.html

The simple relation "E = stress/strain" only applies to the linear first part of the curve, i.e. the straight line through the origin on the plots.

If you load a structure so the stress and strain are larger than the linear part of the curve, the material deforms plastically and when you remove the load it will not return to its original length.

 

[Rope]

Strictly speaking, Young's modulus of elasticity is tan(alpha), where alpha is the slope of the tangent line to the stress-strain curve at origin. If you define a function E_t=sigma/eps along the curve, you get the "tangent modulus, which as you noted, becomes function of total strain.