Why don't true and engineering stress-strain curves diverge in the elastic region?

[Gunde]

If you look at a engineering stress-strain curve compared to the true* stress-strain curve of a steel for example, they start to differ somewhere after the yield point. Before the yield point they seem to be the same.
If you look at the specimen in the in the elastic region, as it deforms elastic it also becomes a bit thinner. I’m thinking that the true stress-strain curve should differ from the engineering curve, also in the elastic region. But it don’t seem that whey. The true curve should tilt a bit more upward as the specimen gets under strain, still in the elastic region.
Is this deviation to small to be noticed or am whey off in my thinking here?
Thanks!
*(calculated for the actual diameter of the specimen when it deforms under strain)

 

[FredGarvin]

There is not really necking that is happening below UTS . There is undoubtedly some poisson's effect, but the necking is really considered to be happening after UTS. That allows us to use engineering stress and strain (S, e) to determine true stress (σ, ε) through the relations σ = S(e+1) and
ε = ln(e+1). Again, the constraint is that it is below the UTS. I would think that the initial change in cross sectional area is so small that it really isn't going to have any real effect in the elastic region.

 

[PerennialII]

I'll echo Fred's statement + when in some cases have included finite deformation effects also when evaluating yield strength the differences have been approximately < 5%, typically < 0.5-2% (note that quite a bit of this arises from how you define your yield strength in the first place), so nothing too influential.

 

[stewe]

why is the engineering stress- strain curve below the true stress- strain curve in a tensile test and the opposite occurs in a compressive test.