Contact Mechanics 6

[OptiEng]

Hello all,

I would like to clarify something about the the stress distribution of contact between two bodies. I have seen many references show the maximum shear stress (Tmax) to be below the contact surface. e.g. seem the image shown in wiki below

http://en.wikipedia.org/wiki/Contact_(mechanics)

However, the contact pressure and maximum normal stress is maximum at the surface, and my FE analysis also shows the maximum stress to be at the surface of contact. Can anyone provide some further explanations on this.

Thanks

 

[GregLocock]

You seem to be confusing maximum shear stress, and maximum normal stress. I rather suspect the famous Irish analyst Tim O'Shenko has something useful to say about that.



Cheers

Greg Locock


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[OptiEng]

Hi Greg,

Thanks for your feeback, I am not getting confused between the two, I just don't think I have explained my questions clearly enough.

My original question in another way is:

I am looking for an explanation of why shear stress is maximum at a point below the surface. Any theories, equations to explain why.

Thanks

 

[btrueblood]

Opti,

Greg's suggestion is that you get a copy of Timoshenko's Theory of Elasticity and study it.

I can give you a trite answer that the boundary condition at the point of contact is a normal force, therefore there can be no shear stress at that point, and the maximum shear must then occur somewhere else.

But that doesn't really fully explain it.

 

[GregLocock]

Push hard on a surface. The material at the surface is keen to push back at you, but you are attempting to shear the material as well. If you draw lines of force radiating away from the contact point it is obvious that far away they will be parallel, at the surface they are parallel, but at some point some expansion sideways will occur, a bit like membrane forces.

I have a strong feeling that Timoshenko is clearer than the above handwavy description!

Cheers

Greg Locock


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[TERIO]

Equations for the stress distribution are given on page 62 of Contact Mechanics by Ken Johnson.

http://books.google.com/books?id=oy...AA#v=onepage&q=principal shear stress&f=false

 

[tbuelna]

GregLocock,

The guy that formulated the theory behind contacts between elastic bodies was not the Irishman Tim O'Shenko, it was the German Herr Ztian.

Technically, OptiEng is correct. The absolute max stress in his two contacting bodies is at the surface. But most materials will fail due to sub-surface shear fatigue long before they fail due to surface bearing. The classic contact failure mode is a sub-surface shear initiated fracture that propagates up through the case and creates a surface spall.

Regards,
riff raff

 

[GregLocock]

If only i could find some way to reward your witty reply.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[ione]

Take a look at this

 

[GregLocock]

ione's graphs are classic.

But i wonder if they actually answer the OP's question? My gut feeling is that there is a natural wedge angle for a material.

This turns normal forces into shear.

Slightly silly question, if you model this with an element size of the order of 0.02r, does it show the same sort of effect?






Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[btrueblood]

"The guy that formulated the theory behind contacts between elastic bodies was not the Irishman Tim O'Shenko, it was the German Herr Ztian. "

Well, ACTUALLY...Herr Ztian figured out the maximum stresses, but the guy who figgered out the equations for the max shear stress (ocurring below surface) for contact problems, Belajef it or not...was some kinda Eastern European, always in trouble for Rushin' around or something. Tim O'Shenko, between bouts of drinking and dart throwing at the pub, cites that work in the reference given earlier, which is probably a good thing, because Irish is easier to puzzle out than Russian.

 

[OptiEng]

Hello all,

Thanks for all your input, its very useful. Great discussion too. With a bit more digging I also found that Shigley gives a nice summary of cylinder or sphere contact but doesnt really answer the question of normal and shear stress states. Ione's upload is useful though.

Thanks again.

OptiEng

 

[TERIO]

Maybe this is already clear to everyone, but when they are discussing maximum shear stress it is the maximum shear stress on any plane (i.e., the radius of Mohr's circle).

I suspect if you plot stress intensity or von Mises stress in your FE model you would see that it is maximum below the surface.

 

[OptiEng]

Thanks TERIO, That's why I was confused about my FE model, it shows the max von mises to be at the surface. Any comments on this?

OptiEng

 

[ione]

The attached paper shows some practical cases, examining principal stresses and shear stresses.
As already pointed out above (tbuelna) a critical section is located at a certain distance from the surface and the maximum shear stress is responsible for the surface fatigue failure.

 

[TERIO]

I'm not sure all the details of your model (elements, contact, formulation, material props, etc), but your mesh is probably too coarse to capture it. If you look at the paper posted by ione it has equations to calculate the size of the contact area. I think you would probably need to have multiple elements within the width of the contact patch to really pick up the max shear stress below the surface.

 

[TERIO]

Also, the depth where the shear stress is maximum is only a fraction of the radius of the contact patch.

 

[OptiEng]

Very good points Terio, I will try remodelling with a finer mesh, and review the points you also suggested thanks.