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goldm066
2008-07-10, 16:59
I am an engineering student working on modeling a hyper-elastic tube in ABAQUS 6.7. The goal of the research is to increase the axial compliance of the tube by patterning holes in it. I have been matching simple physical stress/strain tests with ABAQUS simulations, by converting the the 'true' stress (abaqus results) into the engineering stress (benchmark testing). This was no problem for the solid tube, (assuming constant volume, incompressibility) the experimental, and and simulated stress/strain curves matched right up. (I entered uni-axial stress strain data to about 60% strain, and fit the material to an Ogden energy potential of order n=3 ).

The calculations of "true area" get more complicated as the hole patterns are modeled. I was curious of there was a way in the ABAQUS simulation to have it output the thickness/cross section area of the tube to get an exact area that the software is using to calculate true stress, so I could easily convert to engineering stress to verify the benchmark tests of more complicated patterns.

I noticed ABAQUS has a 'Profile' feature, but I do not really understand its purpose. I input the initial profile of the tube, and stretch it to 60% strain I could not figure out how to make it display the profile at each step in the static analysis. If anyone knows how to do this, or another easy way to convert the true stress given by ABAQUS into engineering stress for a simple straight tube (w/ cut outs on the walls) it would be much appreciated, as I have no prior FEM experience.

Thanks A Lot,
David

Jorgen
2008-07-10, 19:14
I am not quite sure I follow your description. When you say "true area" are you referring to the cross sectional area created by a virtual cut perpendicular to tha axis of the tube?

In the case of a tube with holes isn't the stress going to be different at different locations (i.e. inhomogeneous), and the best you can do is to determining some type of average stress?

- Jorgen

goldm066
2008-07-10, 20:24
Hello Jorgen,

Yes, I am referring to the cross sectional area that is perpendicular to the axis through the tube, not necessarily just where the cuts are, but throughout the length of the tube. My thought was I could get an average thickness/cross-sectional area of the tube (while in strain), and use that data to convert the true stress into engineering stress for the whole tube.

Looking at another post, I see that this would be what I want:

(Lo/L)*(True Stress) = Engineering Stress

I suppose my new question would be: Is the above formula is valid for the tube with holes in the sides???

Below are descriptions of the Physical Tensile Test and ABAQUS Procedures:

In the physical tensile test, I place dowels in the very ends of the tubes (to avoid excessive deformation) and then clamp the dowels with hose clamps. One of the hose clamps is fixed, while the other one is hooked up to a load cell. The load cell is a on a lathe-stage which moves by a computer controlled stepper motor. The software is set up to record the force on the load cell, and displacement of the stage at every 0.1 mm. For this scenario (at least for a solid tube w/ no holes) the entire tube is in a constant state of stress/strain (ie. Homogeneous) except very near the end that is clamped, correct?

What I did was only analyze the end nodes of the tube in ABAQUS, (the end which would be connected to the load cell in the above experiment). The nodes are located on the end face perpendicular to the central axis through the tube. I plotted the Maximum Principle Stress Vs. Maximum Principle Strain from the ABAQUS simulation (enforcing encastre boundary on the fixed end, and displacing the other end to the same strain in the lab). I converted to engineering stress using the constant volume approximation, and I was able to get a very good match with the physical test data (see JPEG).

Is the procedure described correct (for a solid tube w/ no holes)?
For the tube w/ cutouts, is there an easy way to average out all of the nodes to get total average stress and strain? Won't the nodes on the end (described earlier) have a stress corresponding to the physical tensile test, as they are basically what is pulling on the load cell?

I repeated the same procedure with a hole drilled through the middle of the tube, and again the tensile test in the lab matched up with the ABAQUS simulation. In order to convert to engineering stress in this situation, I took the surface area of the sides of the tube, and subtracted the area of the hole (the hole went ALL the way through the tube) and multiplied by the thickness of the tube to get the volume. I then held the product of thickness and surface area constant (incompressibility), modifying the thickness as the surface area increases with increasing strain and recalculating the cross-sectional area. It also seemed to match up fairly well (see JPEG). (Thickness=> referring to the thickness of the sheet if you slit and unrolled the tube; Cross-Sectional Area meaning PI/4(Dout^2-Din^2)).

Thanks A Lot,
David