The true, true stress-strain curve?

In summary, the engineering stress-strain curve and the true stress-strain curve of a steel specimen start to differ after the yield point, with the true curve tilting slightly more upward in the elastic region. This deviation is likely too small to be noticed, and there is also some effect from Poisson's ratio and finite deformation. In a tensile test, the engineering curve is below the true curve, while the opposite occurs in a compressive test.
  • #1
Gunde
3
0
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)
 
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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #5


I can confirm that the true stress-strain curve does indeed differ from the engineering stress-strain curve, especially after the yield point. This is because the engineering stress-strain curve is calculated using the original dimensions of the specimen, while the true stress-strain curve takes into account the actual dimensions of the specimen as it deforms under strain.

You are correct in your thinking that the true curve should tilt more upward in the elastic region, as the specimen becomes thinner as it deforms. However, this deviation may be small and not easily noticeable, especially if the material has a high yield strength. In addition, the difference between the two curves may also depend on the testing method and conditions.

Overall, it is important to consider both the engineering and true stress-strain curves in materials testing and analysis, as they provide different insights on the behavior of a material under stress. Thank you for your question and keep up the critical thinking!
 

1. What is the true, true stress-strain curve?

The true, true stress-strain curve is a graphical representation of the relationship between the stress applied to a material and the resulting strain. It takes into account the actual cross-sectional area of the material, rather than assuming it remains constant throughout the testing process.

2. How is the true, true stress-strain curve different from the engineering stress-strain curve?

The engineering stress-strain curve assumes that the cross-sectional area of the material remains constant, which may not be the case in real-life situations. The true, true stress-strain curve takes into account the decrease in cross-sectional area as the material is subjected to increasing stress, providing a more accurate representation of the material's behavior.

3. What is the significance of the true, true stress-strain curve in material testing?

The true, true stress-strain curve allows for a more accurate assessment of a material's properties, including its strength, ductility, and toughness. This information is crucial for engineers and scientists in designing and selecting materials for various applications.

4. How is the true, true stress-strain curve determined?

The true, true stress-strain curve is determined by conducting a tensile test on a material, where a sample is subjected to increasing amounts of stress until it reaches its breaking point. The resulting data is then plotted on a graph to create the curve.

5. Can the true, true stress-strain curve be applied to all materials?

The true, true stress-strain curve can be applied to most materials, including metals, polymers, and ceramics. However, it may not be suitable for highly elastic materials, such as rubber, as their behavior is better represented by other stress-strain curves.

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