# Hertzian Static Contact Stress Acceptance Criteria

by crobb
Tags: acceptance, contact stress, hertzian stress, static
 P: 6 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 cant this referenced in any code or book. Can anyone provide a reference or justification for 2.5 * yield?
 P: 6 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
 P: 5,462 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.
P: 4

## Hertzian Static Contact Stress Acceptance Criteria

 Quote by crobb 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

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