Failure Due to Stress or Strain?

  • #1

Main Question or Discussion Point

Currently I am studying the mechanical properties of artery tissue, and was tasked with determining if the tissue fails due to shear stress or shear strain. I have always worked under the assumption that they go hand in hand with each other, but the nature of this question obviously suggests this isn’t necessarily the case.

After some research, I've found some sources (link below) suggesting that in anisotropic materials, materials where the mechanical properties are differ based on direction of loading/displacement, simple conversions between the stress and strain no longer hold true.

I’m most likely going to run experiments using both strain and stress as the independent variable and seeing which reaches failure first, but I’m having trouble finding any theoretical proof that this would be a valid conclusion. I was thinking that necking is an indicator for failure due to strain, but I couldn’t think of an observable property that would indicate failure due to stress. Additionally, since I’m doing direct shear tests I don’t think necking will be observable anyway.

Anybody have any ideas or a direction to point me?

http://www.failurecriteria.com/isitstressorstra.html
 

Answers and Replies

  • #2
5,439
7
Hello and welcome Killingtim

An interesting problem to investigate.

Some thoughts.

1) Time is a very important variable with materials such as those you are dealing with, as the material response to load takes time to develop. Creep in some materials is one aspect of this.

2) The nature of the load plays a large part in the failure of materials, or even if they fail at all. Loads can be uniaxial, biaxial or triaxial or bending or whatever.

3) Temperature and moisture content are liekly to also be important variables with your material.

Much work has been done on a material that has many similarities, namely bread dough.
there is a whole chapter on this in the excellent Cambridge University book

Elasticity, Plasticity and the Structure of Matter
by Houwink and DeDecker

with many references.

Another book, (a New Scientist Popular Science book) has published data and discussion about the stress strain curves for blood vessels (after Shadwick)

Cats Paws and Catapaults
by
Steven Vogel

go well
 
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  • #3
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I wonder if what the 'tasker' is concerned with is whether you can predict failure based on just stress or just strain. For example maybe it fails with a particular strain state, but the stress required to cause that strain can vary based on all sorts of paramaters like time history, moisture content, etc.

Even then it seems doubtful that the answer could be so simple for such a material.
 
  • #4
69
1
Currently I am studying the mechanical properties of artery tissue, and was tasked with determining if the tissue fails due to shear stress or shear strain. I have always worked under the assumption that they go hand in hand with each other, but the nature of this question obviously suggests this isn’t necessarily the case.

After some research, I've found some sources (link below) suggesting that in anisotropic materials, materials where the mechanical properties are differ based on direction of loading/displacement, simple conversions between the stress and strain no longer hold true.

I’m most likely going to run experiments using both strain and stress as the independent variable and seeing which reaches failure first, but I’m having trouble finding any theoretical proof that this would be a valid conclusion. I was thinking that necking is an indicator for failure due to strain, but I couldn’t think of an observable property that would indicate failure due to stress. Additionally, since I’m doing direct shear tests I don’t think necking will be observable anyway.

Anybody have any ideas or a direction to point me?

http://www.failurecriteria.com/isitstressorstra.html
What's the importance of the distinction? My understanding: Stress and strain are directly related; though anisotropy makes it more difficult to transform your stresses into different, possibly more convenient, coordinate systems.

here's a reference that may be useful for you: http://solidmechanics.org/text/Chapter3_2/Chapter3_2.htm

What is the problem you're trying to solve? Loading condition? General material properties of arterial tissue? Can you assume any material symmetry for the tissue?
 
  • #5
5,439
7
My understanding: Stress and strain are directly related
Strain is possible without stress.
 
  • #6
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Strain is possible without stress.
Yes, this is true I did overlook that important bit in Hooke's Law. This isn't necessarily true for the shear stress-strain problem presented though, correct?
 
  • #7
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Yes, this is true I did overlook that important bit in Hooke's Law. This isn't necessarily true for the shear stress-strain problem presented though, correct?
Stress free strain has nothing to do with Hookes law.
An example would be unrestricted thermal expansion. Stress is only developed in thermal expansion in the event of external restraint.

Nor was the OP about shear in particular. If the pressure inside a blood vessel increase, this is countered by and increase in circumferential tension in the vessel wall, as in any membrane. I take the reference to shear as the possibility that the wall material may fail in shear in a direction roughly 45 degrees to the principal stress in the normal manner.
 
  • #8
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Stress free strain has nothing to do with Hookes law.
An example would be unrestricted thermal expansion. Stress is only developed in thermal expansion in the event of external restraint.

Nor was the OP about shear in particular. If the pressure inside a blood vessel increase, this is countered by and increase in circumferential tension in the vessel wall, as in any membrane. I take the reference to shear as the possibility that the wall material may fail in shear in a direction roughly 45 degrees to the principal stress in the normal manner.
I've got all kinds of overlooking shenanigans going on here.

Though, I did get the impression the OP was talking about shear in particular; if that's the proper thing to be be investigating I guess could depend on the application studied, which wasn't mentioned.

I'm picturing a mechanical test and trying to visualize how the shear strain will be/was developed without stressing the sample simultaneously. Maybe I'll also take a look at that bread dough situation you mentioned March 11th.
 
  • #9
Though, I did get the impression the OP was talking about shear in particular
Sorry I didn’t jump in earlier but , the question actually does pertain to shear specifically, I’m sorry I didn’t make that more apparent. However, I think that as far as failure theory goes, the same general principles should apply to both normal and shear stress.

I think the largest issue I’ve run into while testing is the viscoelastic nonlinear nature of the tissue. Biological Materials in general, (a link is shown below) appear to exhibit nonlinear properties; this has been partially confirmed by the few tests I have run. From what I’ve read, viscoelastic materials don’t obey Hooke’s law, which makes characterizing the material failure and the stress-strain relationship much more difficult.

http://www.loci.wisc.edu/files/loci/NLV.pdf
 
  • #10
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Sorry I didn’t jump in earlier but , the question actually does pertain to shear specifically, I’m sorry I didn’t make that more apparent. However, I think that as far as failure theory goes, the same general principles should apply to both normal and shear stress.

I think the largest issue I’ve run into while testing is the viscoelastic nonlinear nature of the tissue. Biological Materials in general, (a link is shown below) appear to exhibit nonlinear properties; this has been partially confirmed by the few tests I have run. From what I’ve read, viscoelastic materials don’t obey Hooke’s law, which makes characterizing the material failure and the stress-strain relationship much more difficult.

http://www.loci.wisc.edu/files/loci/NLV.pdf
Have you considered applying any ASTM (or other) standards for viscoelastic polymers to your situation? Is this not possible or does one not exist?
 
  • #11
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Perhaps if you were to elaborate on where your investigations have got to we could help further?
 
  • #12
Have you considered applying any ASTM (or other) standards for viscoelastic polymers to your situation? Is this not possible or does one not exist?
I hadn't thought of that, it appears that there aren't any standards that match my situation exactly, but I will definitely investigate further and see if there is anything I can use.

Perhaps if you were to elaborate on where your investigations have got to we could help further?
Could you rephrase the question, I'm having difficulty understanding exactly what you are asking? I'm attempting to describe the general failure of artery tissue. I'm currently performing direct shear tests on small (6mm x 6 mm) samples using a shear rheometer that my supervising professor designed. If you want more details on the rheometer I will send you a paper we used as a model during the design process. So far I have only run a few successful tests, but I'm just trying to get a good theoretical basis down for any conclusions I might reach.
 
  • #13
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Are you also investigating the artery tissue's failure in relation to shear rate?
 

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