Abstract
Asymptotic forms are a useful way of representing the state of stress at a contact edge, allowing us to characterise the region in which cracks nucleate. The asymptotes must match the behaviour implied by the local geometry. In this paper, we study the behaviour of a flat contact with a circular arced edge (i.e. a flat and rounded contact); a geometry that has extensive applications. We show explicitly how the very convenient closed-form solution for this problem, derived from half-plane theory, may be collocated into the more realistic three-quarter plane far field solution, obtained from Williams’ solution. This provides a closed-form representation of the edge, correctly geared to the far-field solution, for the first time.
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