I believe the formula for the b (width of contact) is incorrect in two ways, firstly if b is the whole width it contradicts the diagram of the two cylinders in contact which shows 2b. So if it is the full width it should be b=2*(sqrt((4*F*R)/(pi*L*E’))) with a 4 instead of a 2 in the formula, OR if b is the half width as implied by the diagram it should be b=(sqrt((4*F*R)/(pi*L*E’))
Thank you for a comment. So b is the half-width, as shown in Figure 2. The equation for b that you posted in your comment assumes a different definition of the reduced elastic modulus (1/E’=…, while the equations posted in the wiki, assume 2/E’=…, see its definition after equation 1). If you substitute this formula to the equation in the article, you will get your equation.
if we assume Steel material ,its ultimate strength is ~500MPa. if we calculate the contact pressure for a two sphere(0.1m) under contact in both elastic & plastic regime , the hertz contact pressure is reaching around 11.66E3 MPa. I have analytical & numerically(using abaqus) validated it. my concern is if the obtained contact pressure is so huge and crossing the ultimate strength of the material ,can i consider it for my design ?
Should Contact pressure or hertz contact stress be LESS than Ultimate stress ?
I believe, if the Hertzian stress exceeds the ultimate strength of the material in your design, it cannot be a good sign. You will get a lot of plastic deformation and probably a failure in a short term. So it is good to rethink the design.