Yes, both you can use because till the yield point or elastic limit the engineering stress-strain curve or true stress-strain curve is almost similar i.e. there is almost no variation. It varies after yield point i.e. where the plastic deformation occurs. So, slope of engineering stress-strain curve or true stress-strain curve i.e.  the Young's modulus is same i.e. almost no variation at all.  So you use any one of them.

Yes, both you can use because till the yield point or elastic limit the engineering stress-strain curve or true stress-strain curve is almost similar i.e. there is almost no variation. It varies after yield point i.e. where the plastic deformation occurs. So, slope of engineering stress-strain curve or true stress-strain curve i.e.  the Young's modulus is same i.e. almost no variation at all.  So you use any one of them.

Hi Chen,

it depends on the strain value. For small strains, say less than 5%, there is little difference between engineering and true stress. So, you may identify all the properties like Young's modulus, yield point, tensile stress etc directly. Some materials exhibit large strains within the elastic range. In this case you have to use appropriate stress and strain measures to identify elastic properties.

Hi Chen

The slope of the initial linear part of the curve is the Young's modulus. Just calculate that slope, then take a straight line of that slope from the x-axis at 0.002 or 0.2% and the intersection point you find with the stress-strain curve is the yield strength.

Use either engineering or true stress-strain curve.

Regards

As Konstantin indicates, the answer depends on the material which you are testing. The Young's modulus is a constant in a linear fit to the uniaxial stress-strain curve. Therefore, you need to fit a stress-strain curve which uses the same stress and strain as in your constitutive equations. Here you could e.g. write Hooke's law with engineering quatities or alternatively the de-Saint-Kirchhoff material law with true stress and Green-Lagrange strain.

But I guess that you use standard structural materials. In this case the strains are typically so small so that there will hardly be any difference.

In metals where the compressive strain  is more than  5%, there is a difference. The elastic modulus can be evaluated from the slope of the load deflection plot. But as true stress and engineering stress would be different  ( due to bulging and barelling  that causes the cross section to be more the true stress would be lower of the two) the corresponding strains would be different to maintain an elastic modulus that is derived from stiffness. True yielding begins earlier and engineering yielding , later in the testing. So true yield stress is lower than the engineering yield stress provided strains are large in compression. In tension, it would the other way.

The stress-strain curve cannot represent a material law, if bulging and barreling occur in unconfined plastic compression. There is a strong effect of geometry and friction. The stress is not uniaxial and the deformation is not homogeneous. The situation in tension is also complex because necking is related to voids (inhomogenoeus material). Therefore, simple material constants become questionable. And all these problems cannot be solved by the choice of the definition of stress and strain.

If I want to find the tangent modulus, which curve should I use. Engineering or true S-S curve?

The question has been answered quite clearly. For many materials it makes no difference which stress and strain is used. This can be checked with some simple calculations for isotropic material: at the elastic limit Rp0.2=E*eps so that the maximum elastic strain is eps=Rp0.2/E. For steel this is in the order of 0.001.

Then calculate the ratio deformed cross-section/deformed cross-section = 1/(1-nu*eps)^2 which is in the oder of 1.0006 for steel. For me this is simply 1.

Now you can repeat the analysis with your expected material data to see if there is any reason to consider the question a problem in your case.

Hello Chen Liu ,

The theory says upto Elastic limit, true stress-strain and engineering stress-strain curve are APPROXIMATELY same.

In the formula:

true strain=Ln(1+engg strain);

since in the expansion of log we are neglecting the higher order terms of engg strain, in case of lower strain that typically yields the same value of slope(Young modulus.)

But precisely in my compression test the E(true stress-strain)=1530MPa and E(engg stress-strain)= 1606.3MPa.