Elastoplastic Stress - Strain Conversion

[backdude]

Hi Everybody,

I am doing some experimental work on hole cold expansion and have measured the strains around a cold expanded hole. I have full field principal strains around the cold expanded hole and would like to convert these strains to stresses.

I am looking for a clear analytical (i.e I don't want to put the data into Abaqus, Nastran etc.) algorithm or method to convert the plastic strains to stresses.

I have having a hard time finding clear information on how to do this so any advice, tips etc would be helpful.

Thanks in advance,
Dave

 

[rb1957]

i recognise that this is a very difficult problem to investigate.

this may sound like a trivial response, but if you have strain data, can't you apply the material stress/strain curve to obtain the the stress for a given strain ?

i expect you're dealing with tri-axial strains, but i would have thought that the standard (linear) approaches for these would solve your problem.

 

[backdude]

Thanks for your answer.

Just to clarify the crux of my problem is coming up with the principal strains. I have no problem getting the effective strain and calculating the effective stress, but doing the stress separation is what I'm having trouble with.

Thanks in advance.
Dave

 

[rb1957]

that's mohr's circle ... like principal stress. like stresses to determine principal strains, you'll need axial strains (two or three directions) and shear strains (in one, two, or three planes).

i'm not familar with the term "stress separation" ... is this something like shear stress ?

 

[backdude]

Mohr's circle will work fine for elastic stress strain conversion.

For plasticity you need to use incremental plastic strain theory or some other methodology.


So basically to recap:

- I have measured elastic-plastic strains experimentally
- In the elastic region stress strain conversion is no problem and I can calculate max/min principal stresses

Problem: In the plastic region, I can calculate effective strain and thus effective stress. What I would like to be able to do is calculate principal strains in the plastic regime.

Thanks for your time.
Dave

 

[40818]

The link below takes you to a site where you can purchase papers etc.
$32 will get you the paper that has the following abstract.

"In reducing strain-rosette data, it is not always possible to tell by inspection whether permanent strains are present. If permanent strains are present, the reduction of the principal strains to principle stresses, assuming perfectly elastic conditions, can be much in error. This paper gives equations for the principal stresses which can be used when purely elastic or elastic-plus-plastic strains are present. Comparisons of theoretical and experimental results are given in order to check the validity of the theory.
Paper was presented at 1962 SESA Spring Meeting held in Dallas, Tex., on May 16–18."

http://www.springerlink.com/content/t67206253t401473/

 

[backdude]

Thanks 40818

I have already ordered the paper and will post again after I have reviewed it.

Regards
Dave

 

[Compositepro]

You may want to search under the term "autofrettage". It sounds like that is the name for your process.

 

[smyth13]

From your posts it appears that you have your 3 principal strains (i.e. E1, E2, E3).

For the elastic region, as you mentioned, you have calculated the principal stresses using Hooke's Law or Mohr's circle, etc.

For the nonlinear region you must assume some type of relationship between the stress and the strain. For example, if the material is steel (sorry I can't remember if you mentioned the material) you could use a relationship such as the Ramberg and Osgood equation:

As an example, the uniaxial equation is as follows:

strain = stress/E + (stress/k)^(1/n)
k, n are strain hardening constants