Semi-analytical solutions of kinked edge cracks
Yijie Si, Yujie Wei
Abstract
A surface crack may advance either by further penetrating inward or by kinking out in response to possible variations in driving force or material properties. This paper provides a general approach to solve the planar elastic boundary value problem (BVP) of a kinked edge crack in a half-space. Semi-analytical solutions to BVPs with far-field uniform tension and concentrated loads on the free surface are given. The solution enable us to derive related information for reliability analysis, including stress fields, stress intensity factors (SIFs), and crack opening displacement (COD). An extension to the Cotterell–Rice formula (Cotterell and Rice, 1980) on SIFs for infinitesimal kinks is supplied, which is applicable to cracks with kinked segments of arbitrary length. Zooming in on a broadly concerned BVP of a cross-coating crack in a coating–substrate with a kink in the interface, we show the SIFs of the kink tip following an empirical formula K ∗ = α exp ( − β a h ) + K ∞ ∗ as a / h > 0 . 2 , where a is the length of the interface segment and h the coating thickness, and K ∞ ∗ is the asymptotic solution by Thouless et al. (1987, 1989). The formula is in accord with existing solutions on the two asymptotic limits of the kinked part.