Cauchy stress/strain conversion

[Roham]

Hi all,

I am confused about a very basic concept in ABAQUS, I'm sure you folks can help me. As we all know ABAQUS uses cauchy(true) stress/strains in the calculations. What we basically obtain from experimental tests (for example uniaxial tension) is in the form of nominal stress/strain curves. As long as we have small strain/deformations we are all set and it doesn't matter. Once we get into large strain/deformation business we have to convert the material curves to true stress/strain curves before plugging the numbers into the material models in ABAQUS. I went through the ABAQUS documentation to see what it suggests. Surprisingly ABAQUS is introducuing very basic equations to convert these numbers for finite deformations (section 10.2.3 of "getting started with ABAQUS"):

epsilon_true=ln(1+epslion_nom)

sigma_true=sigma_nom*(1+epslion_nom)

from what I know these two simple equations assume that the material is incompressible and basically if isotropic poisson's ration is equal to 0.5!!! then how do I convert my curves to true stress/strain curves when I have other values for poisson's ratio and when my material is not incompressible? at the same time with assuming 0.5 for poisson's ratio in FEM it will run into convergence problems if I'm not wrong. I'm just confused now and can't think clearly about it. Any comments is really appreciated.

Thanks,

Roham.

PS: I can't match my viscoplastic model in ABAQUS with my experimental relaxation results; I thought maybe it has something to do with this issue that I'm not converting my curves in a correct way.

[hhspiny]

plasticity normally assumes that 1. plastic strain dominates 2. no volumetric deformation associated with plastic deformation. thus, it is safe to use the conversion. similarly, for hyperelastic materials, incompressible is a valid assumption. if the incompressibility is not a valid assumption, then the above conversion should not be used. However, the strain conversion is by defintion, is always valid.

[Roham]

Thanks. I agree that strain conversion is always valid. But I need to convert stress too to get the true stress/strain curves. What about the poisson's ratio of 0.5 issue when material is not incompressible. How do I convert it when I have 0.4 poisson's ratio? that equation for stress just holds for poisson's ratio of 0.5 because it is derived from incompressibility assumption. My material is not hyperelastic, I'm working on polymer ionomers, semi-crystalline materials that show visco-plastic behavior.

[Dave_Holmes]

As you no doubt know, true stress is simply a function of applied force (measured in tensile test) and instantaneous cross sectional area of the test specimen. Short of actually measuring this during a test, if you know Poisson's ratio and the instantaneous uniaxial elongation then you should be able to calculate the instantaneous lateral strains and thus the corresponding cross sectional area. Using this with the measured force will then give you true stress.

With polymeric materials using elongation can be problematic in as much as local deformation can vary over the length of a test specimen. Also, be wary of using constant Poisson's ratio in as much as this can change in some circumstances. Aside from these cautions, you should be OK using this type of methodology.

David

[Roham]

Thanks David. I actually decided to measure poisson's ratio while it changes in the uniaxial test and changed the equations to incorporate variable poisson's ratio. I guess that will work. The only thing is that I am measuring in-situ displacements in x and y directions with a video extensometer, since my specimen is a very thin membrane (1 mil thickness) it's not easy to measure displacements in z direction. I have to assume Poisson's ration is the same in 2 directions.

Roham.