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T-stresses for short and long cracks

John Dempsey (Clarkson University)

Crack initiation and growth: methods, applications, and challenges

Tue 10:45 - 12:15

Sayles Auditorium

An edge-cracked half-plane and a half-plane with a semi-infinite crack perpendicular to the boundary are discussed. Uniform crack-face loading is first examined, with a review of the Koiter (1956) Wiener-Hopf approach; an analytical expression for the corresponding T-stress is obtained. For the additional cases of (i) non-uniform edge-crack crack-face loading, (ii) concentrated loading at the edge-crack crack mouth, the Wiener-Hopf solutions and analytical T-stress expressions are provided. A Green's function for the edge-crack T-stress is developed. The differing developments made by Koiter (1956), Wigglesworth (1957) and Stallybrass (1970) for the case of an edge-cracked half-plane are enhanced by deducing a quantitative relationship between the three different Wiener-Hopf type factorizations. An analytical universal T-stress expression for edge-cracks is derived. Finally, the case of a vanishing uncracked ligament in a half-plane is examined, and the associated Wiener-Hopf solution and analytical T-stress expression are provided. Several limiting cases are examined.