The state of stress induced by the plane frictionless cylindrical contact. I. The case of elastic similarity

The contact problem between cylindrical conformal surfaces, modelling for instance a fastener joint, is studied. A closed form solution is obtained in Part I of the paper for the case of elastic similarity, improving (i) the solution obtained by Persson (On the Stress Distribution of Cylindrical Elastic Bodies in Contact, Ph.D. dissertation, 1964), which was also limited to identical materials, and (ii) the results of Noble and Hussain (Int. J. Engng. Sci. 7 (1969) 1149), which were limited to the case of perfect fit of contacting materials. The variation of the contact area, pressure distribution and maximum sustainable load is given for the complete range of possible dimensionless loading parameter Ep₁ ^*ΔR/Q and first Dundurs' material parameter, α. Under conditions of initial clearance, the contact area arc, ε, increases with load from zero to a limiting value, ε_lim, which depends only on the material parameter α. Vice versa, under conditions of initial interference, the contact is complete until there is detachment and the contact area starts to decrease with load up to the same limiting value, ε_lim, which is also the only possible value of contact area for neat-fit conditions, under any applied load. Finally, a complete assessment of the strength of the contact is given for the entire range of working conditions. As expected, the strength of the joint decreases rapidly if the extent of the contact area reduces, and finally tends to the limit predicted by the Hertzian theory when the arc of contact is smaller than about 30°. The optimal conditions for avoiding yielding are reached for a contact arc smaller than the limiting arc ε_lim: This means that it is not possible to reach the optimum from a configuration of initial interference.