Hertz Contact Solution of Elastic Theory for Concave to Convex Shapes

[vdash103]

For the equation:

contact stress = {(1 / (pi[((1-v1^2)/E1)) + ((1-v2^2)/E2))) ^ 0.5} * {((Fn/b) * (Sum (1/pi)))^0.5}

Where Sum (1/pi) = [(1/p1) - (1/p2)] for concave shapes in contact with convex shapes

Sum (1/pi) approaches 0 as the two radii get closer, however when the two radii equal each other, the second part of the equation equals 0 from multiplication and the entire equation will equal 0. This is confusing to me. How could the stress be 0?

 

[Mapes]

If the two radii are equal, wouldn't the contact area by the entire surface area of each object? Then the contact stress would be very small, as the constant load would be spread over a very large area.

 

[vdash103]

I believe that is correct. That was the assumption I had come to.