Understanding Stress-Strain Curves and Force-Extension

[Lyszko]

So a stress-strain curve: σ on the x-axis and ε on the y axis.
σ = F / A and ε = ΔL / L
of course, L is a constant, and A is a constant if the material can be assumed to not-deform.
Can a stress-strain curve therefore be thought of as a force-extension curve?
i.e. essentially F on the x-axis and ΔL on the y axis?
That would make it a lot easier to predict properties from.

 

[Dale]

If you make the assumption of no deformation then your strain is 0 by definition.

 

[Lyszko]

If you make the assumption of no deformation then your strain is 0 by definition.

For simple purposes, how about if you assume that you increase the force but don't change the area? This happens when the material elastically deforms under Hooke's Law after all.

 

[Dale]

Then the material density would change. I am not sure if that would cause any problems.

 

[Philip Wood]

For small strains (say up to 1%), a stress-strain graph is, to all intents and purposes, a rescaled force-extension graph. But for large strains, for example when a metal goes past its elastic limit and deforms plasticly, there is a noticeable difference. For a metal in this region, the force-extension graph rises to a maximum and goes down before the metal breaks. This is because the wire has become thinner (not necessarily uniformly along its length) thereby increasing the stress, so a smaller force is required to produce the same stress as if it had its initial area. If you plot true stress against strain, the graph doesn't go down before the metal breaks. [In fact it goes up, but that's for non-trivial reasons - what's going on inside the metal.] These graphs are not usually plotted, though. Even graphs which are labelled stress-strain usually plot Force/original area for stress.

 

[Dale]

This may be helpful
http://www.engineeringarchives.com/les_mom_truestresstruestrainengstressengstrain.html

 

[SteamKing]

So a stress-strain curve: σ on the x-axis and ε on the y axis.
σ = F / A and ε = ΔL / L
of course, L is a constant, and A is a constant if the material can be assumed to not-deform.
Can a stress-strain curve therefore be thought of as a force-extension curve?
i.e. essentially F on the x-axis and ΔL on the y axis?
That would make it a lot easier to predict properties from.

A regular stress-strain curve has stress values along the y-axis and strain values along the x-axis.

 

[Chestermiller]

So a stress-strain curve: σ on the x-axis and ε on the y axis.
σ = F / A and ε = ΔL / L
of course, L is a constant, and A is a constant if the material can be assumed to not-deform.
Can a stress-strain curve therefore be thought of as a force-extension curve?
i.e. essentially F on the x-axis and ΔL on the y axis?
That would make it a lot easier to predict properties from.

Force vs ΔL is not a fundamental physical property of the material. If you change the length or the cross sectional area of the sample, the curve moves. On the other hand, stress vs strain is a fundamental physical property of the material. If you change the length or the cross sectional area, the curve does not move.

Chet