Approximate analytical expression for elastic stresses in flat punch problems

摘要

A simple approximate closed form expression is presented for finding the normal traction distribution under a finite stiffness thick flat punch being pressed without bending into another flat elastic contact body. The correct corner singularity known from elasticity solutions is built into the new expression. The traction expression is validated by an extensive parametric finite element study that shows that the maximum error in predicted tractions is less than 4% for thick contact bodies. Limits of applicability of the expression as the contact body becomes thinner are explored. The stresses and stress intensity factors are readily found from the tractions using well known integral expressions which can be evaluated in seconds numerically. Example applications to fretting crack growth are also presented.