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For steels with Poisson's ratio v = 0.3 the maximum shear stress is then:

at a depth of half the radius of the contact surface.

The maximum tensile stress set up within the contact zone occurs at the edge of the contact zone in a radial direction with a value of:

The circumferential stress at the same point is equal in value, but compressive, whilst the stress normal to the surface is effectively zero since contact has ended. With equal and opposite principal stresses in the plane of the surface, therefore, the material is effectively in a state of pure shear.

The maximum octahedral shear stress which is also an important value in consideration of elastic failure, occurs at approximately the same depth below the surface as the maximum shear stress. Its value may be obtained from eqn (8.24) by substituting the appropriate values of crx, oy and oz found from Fig. 10.5 which shows their variation with depth beneath the surface.

The relative displacement, e, of the centres of the two spheres is given by:

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