Hertzian Static Contact Stress Acceptance Criteria

In summary, the conversation is discussing the use of a formula from the book "Mechanical Engineering Design, Shigley, 5th Edition" to calculate a static contact stress, and the lack of an acceptance criteria for the calculated value. The question of whether a 2.5 * yield value can be used for pass criteria is raised, and a reference for this value is provided from the book "Mechanics of Materials, 2nd Edition, E.J. Hearn". The use of this approach for ductile materials is confirmed, but caution is advised for more brittle materials. Surface roughness can also affect the calculated stresses. The individual sharing the conversation offers a freeware program to calculate Hertzian stresses.
  • #1
crobb
6
0
I have calculated a static contact stress of 670 N/mm2 using formula from Mechanical Engineering Design, Shigley, 5th Edition.

My problems lies that there is no acceptance criteria. I'm using Grade 5 Structural Steel (yield~355 N/mm2).

Previous threads have stated that a 2.5 * yield can be used for pass criteria but i can't this referenced in any code or book.

Can anyone provide a reference or justification for 2.5 * yield?
 
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  • #2
I have now found a reference for this value:

Mechanics of Materials, 2nd Edition, E.J. Hearn. page 779 states 'uncontained plastic flow' commences when contact stress --> yield * 2.8
 
  • #3
Hello crobb and welcome to Physics Forums.

Yes grade5 structural steel is sufficiently ductile for this approach to work.

High strength more brittle steels (and other materials) need more careful consideration - the outcome depends upon service factors such as grit or corrosion in rollers initiating a crack.

Post again if you want more.
 
  • #4
crobb said:
I have now found a reference for this value:

Mechanics of Materials, 2nd Edition, E.J. Hearn. page 779 states 'uncontained plastic flow' commences when contact stress --> yield * 2.8

Usually, Hertz contact stresses are judged by the shear stress just below the surface. It will be ~211 N/mm2 in your case. Using Tresca's criterion, a minimum yield stress of ~422 N/mm2 will be required (for ductile materials). But yes, in static cases you can often allow for higher stress.

Note that surface roughness can drastically reduce the stresses.

You can use my freeware program to quickly calculate the Hertzian stresses at http://en.vinksda.nl under 'Toolkit'.

Jaap
 

1. What is Hertzian static contact stress?

Hertzian static contact stress refers to the pressure or force that is exerted on a material when it is in contact with another material. This type of stress is typically seen in mechanical systems where two surfaces are in contact and experience compression due to the applied load.

2. How is Hertzian static contact stress calculated?

Hertzian static contact stress is calculated using the Hertz contact theory, which takes into account the material properties, geometry, and applied load of the two contacting surfaces. The formula used to calculate Hertzian stress is σ = (3FL)/(2ab√R), where σ is the contact stress, F is the applied load, L is the contact length, a and b are the radius of curvature of the two surfaces, and R is the radius of contact.

3. What is the significance of Hertzian static contact stress acceptance criteria?

Hertzian static contact stress acceptance criteria are important in determining the maximum allowable stress that a material can withstand without experiencing failure. This is especially crucial in engineering and design, where components need to be able to withstand certain levels of stress to ensure safe and reliable operation.

4. What are some commonly used Hertzian static contact stress acceptance criteria?

Some commonly used Hertzian static contact stress acceptance criteria include the maximum shear stress theory, maximum distortion energy theory, and maximum principal stress theory. These criteria take into account different aspects of stress distribution and are used to determine the acceptability of a material under specific loading conditions.

5. How do Hertzian static contact stress acceptance criteria differ from dynamic contact stress criteria?

Hertzian static contact stress acceptance criteria are specifically used for situations where the loading is constant and the contact stress is applied over a long period of time. Dynamic contact stress criteria, on the other hand, take into account the changing nature of the applied load and how it affects the material's stress distribution. This is important in situations where there is rapid movement or vibration, which can lead to fatigue and failure in the material.

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