Hertzian contact pressure & shear stress

[curiousPep]

TL;DR Summary

Direction of shear stress due to Hertz pressure

Hello,
I am trying to get some intuition about the direction of the shear stress caused by the Hertz contact pressure.
Once I exert some pressure downwards on a spherical object the direction of the Hertz pressure will be upwards.
However, this case some shear stress to exist, but I can't see where the sirection of the shear stress is. Can someone provide a simple sketch it is for visualisation and intuition porpuses.
Thank you

 

[FEAnalyst]

From what I know, Hertz contact theory assumes that only normal stresses exist. If you want to visualize the shear stress in the contact area, finite element analysis is the best way.

Which case of Hertz contact is of your interest ?

 

[jrmichler]

There is compressive stress directly under the center of the contact pressure, and shear stress under the surface and off to each side. This diagram, from http://mechdesigner.support/cam-contact-stress-hertz-equations.htm?toc=0&printWindow&, nicely shows it:

This reversing shear stress is the root cause of spalling failures in rolling element bearings and gear teeth. Good search term to learn more is hertz contact stress.

 

[FEAnalyst]

There is compressive stress directly under the center of the contact pressure, and shear stress under the surface and off to each side.

Yes, but Hertz equations account only for the normal stress. Shear stress is mentioned as an addition to that theory.

 

[Baluncore]

The applied pressure radiates out from under the contact and is attenuated as depth increases.
The shear stress is the differential pressure between those successive layers.

This reversing shear stress is the root cause of spalling failures in rolling element bearings and gear teeth.

True. A very small lubricant filled pit, in the surface of a ball or roller, can rapidly spall the surface by providing a very high differential fluid pressure at the edge of the contact area.

 

[PSMotion]

There are three principal Stresses below the surface: sigma-x, sigma-y, and sigma-z.
- they are all compressive.
These stresses are in the direction of rolling, across the direction of rolling, and vertically down, respectively.

When they are plotted, from '0mm' at the surface to below the surface, they are all different, and 'decay' at different rates to a very small value at about 4 x the width of contact below the surface.
Because the stress functions are different, you can plot, at each 'slice' below the surface, the difference in sigma-x and sigma-y (for line contact) their values, which is the Shear-Stress, as (Sigma-x - Sigma-y)/2. This difference reaches a maximum of about 0.78 x the width of the contact.