Zone of influence in Hertzian contacts and stress analysis in a finite-width body

Abstract

Zone of influence has been defined as a region beyond which stresses due to loads applied on an elastic half-space are below a given fraction of the peak stress. These zones are significant since the half-space assumption is valid if the width of contacting body is beyond these zones of influence, while it may need correction if the width is less than the zone width. Further, the half-space solution for stresses needs revision at certain depths since they do not integrate up to the corresponding applied loads within the finite body width, thus violating equilibrium. This paper presents analytical solutions for zones of influence for different stresses and peak percentages and the revised stress distribution at various depths of the contacting body, for Hertzian contacts under: (a) normal loading only; and (b) full-sliding condition. They are found to match with solutions from finite element analysis.