The state of stress induced by the plane frictionless cylindrical contact. II. The general case (elastic dissimilarity)

In Part I of the paper, the authors have studied the contact problem between a pin and an infinite plate containing a conforming hole, in the absence of friction and in the case of elastic similarity, obtaining a closed form result which generalizes the identical materials analysis of Persson (On the stress distribution of cylindrical elastic bodies in contact, Ph.D. dissertation, 1964). Here, in Part II, the general case of contacting materials is first studied numerically, finding that the effect of elastic dissimilarity (i.e. the second Dundurs' constant not being zero) is negligible for the dimensionless pressure distribution, the maximum influence being less than 2%. Vice versa, the influence on the relation between the contact area arc semi-width, ε, and the dimensionless loading parameter E₁ ^*ΔR/Q is indeed significant; however, considering as an approximate pressure distribution the one of the elastically similar case, an extremely good approximation is obtained for the general relation ε vs. E₁ ^*ΔR/Q which can now take into account of both Dundurs' elastic parameters. In particular, the limiting value for ε_lim, towards which the contact tends under very high loads both under initial clearance or interference (or for any load for the perfect fit limiting case) is given as a function of both Dundurs' elastic parameters, α, β as well as the load when complete contact is lost in an interference contact, ε_compl. Hence, a complete assessment of the strength of the contact can be obtained directly from the results of Part I of the paper, given that for a certain contact area extension, the correct value of load is used.