Multiple Crack Analysis in Finite Plates

• Published in: AIAA journal 2006-11, Vol.44 (11), p.2535-2541
• Main Authors: Yavuz, A. Kadir, Phoenix, S. Leigh, TerMaath, Stephanie C
• Format: Article
• Language: English
• Subjects: Aircraft; Cracks; Exact sciences and technology; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Linear equations; Physics; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Studies
• ISSN: 0001-1452; 1533-385X
• DOI: 10.2514/1.17919

In this study, interactions of multiple cracks in finite rectangular plates are analyzed. A finite plate is treated as a polygon-shaped plate which can be created by contiguous crack segments embedded in an infinite plate forming an enclosed region so there are no true crack tips remaining around the plate. This boundary value problem is solved with the superposition approach based on the dislocation distributions requiring the determination of crack opening displacement profiles that satisfy the traction-free condition on interior crack faces and the given boundary tractions on four exterior cracklike segments defining the outside boundary of the rectangular plate. A new point allocation scheme that reduces the number of evaluation points leads to a set of linear algebraic equations in terms of unknown weighting coefficients of opening displacement profiles involving polynomial terms and wedge terms whose exponents are approximated as rational numbers to represent irrational wedge eigenvalues, thus permitting evaluation of the integrals in closed form. Then, stress and displacement fields on the entire body, as well as the usual stress intensity factors at the crack tips and kinks, are calculated. The accuracy of the method and the strong interactions of multiple cracks are demonstrated with figures and tables. [PUBLICATION ABSTRACT]