On the Effect of Grading Elastic Modulus in Frictional Line Contacts

Abstract

We study the effect of elastic material grading close to the surface in line contacts with friction on internal stresses, particularly to quantify the reduction of tensile principal stresses due to grading. We observe that for the classical indentation by a parabolic indenter and power-law material grading, tensile stresses are reduced, but both dilatational and deviatoric strain energy are increased, which points to a possible decrease of strength at the surface. We then move to the more realistic case of exponential grading, for a sinusoidal form of pressure and shear traction, which is taken as representative of a wide class of contact conditions. We observe that tensile stresses can be removed completely if friction is not too high and Poisson's ratio is not too low, but anyway, the effect is likely to be sufficiently strong to remove surface cracks. Dilatational strain energy is also decreased for this type of functional elastic grading, while deviatoric strain energy is not increased much at the surface. We thus confirm in a more general way than previously known the possible advantages of using functional elastic grading to increase resistance to contact loading and provide a general set of results to quantify this for engineering purposes.