CHAPTER 10 CONTACT STRESS,RESIDUAL STRESS AND STRESS CONCENTRATIONS Summary The maximum pressure po or compressive stress oc at the centre of contact between two curved surfaces is: 3P P0=-0c= 2πab where a and b are the major and minor axes of the Hertzian contact ellipse and P is the total load. For contacting parallel cylinders of length L and radii R:and R2, maximum compressive stress,oc=-0.591 R2 L△ =一P0 1 with△= 1-响+E,-1 and the maximum shear stress,tmax=0.295 po at a depth of 0.786b beneath the surface,with: P△ contact width, b=1.076 R R2 For contacting spheres of radii R and R2 maximum compressive stress, 0e=-( =-p0 maximum shear stress, rmax =0.31 po at a depth of 0.5b beneath the surface with: P△ contact width (circular) b=0.88 (+ For a sphere on a flat surface of the same material PE2 maximum compressive stress, 0c=-0.62 4R2 381CHAPTER 10 CONTACT STRESS, RESIDUAL STRESS AND STRESS CONCENTRATIONS Summary The maximum pressure po or compressive stress a, at the centre of contact between two curved surfaces is: 3P po = -0, = - 21rab where a and b are the major and minor axes of the Hertzian contact ellipse and P is the total load. For contacting parallel cylinders of length L and radii RI and R2, - -Po LA maximum compressive stress, a, = -0.591 and the maximum shear stress, rmax = 0.295~0 at a depth of 0.7861, beneath the surface, with: contact width, PA b = 1.076 For contacting spheres of radii RI and R2 maximum compressive stress, maximum shear stress, rmax = 0.31 po at a depth of 0.56 beneath the surface with: PA contact width (circular) b = 0.88 For a sphere on ajat sulface of the same material maximum compressive stress, a, = -o.ti*$lg 38 1