Closure of circular arc cracks under general loading: effects on stress intensity factors

The two-dimensional circular arc crack solution of Muskhelishvili (Some basic problems of the mathematical theory of elasticity, P. Noordhoff Ltd, Groningen, Holland, 1953) has been used widely to study curved crack behavior in an infinite, homogeneous and isotropic elastic material. However, for certain orientations and magnitudes of the remotely applied loads, portions of the crack will close. Since the analytical solution is incorrect once the crack walls come into contact, the displacement discontinuity method is combined with a complementarity algorithm to solve this problem. This study uses stress intensity factors (SIFs) and displacement discontinuities along the crack to define when the analytical solution is not applicable and to better understand the mechanism that causes partial closure under various loading conditions, including uniaxial tension and pure shear. Closure is mainly due to material from the concave side of the crack moving toward the outer crack surface. Solutions that allow interpenetration of the crack tips yield non-zero mode I SIFs, while crack tip closure under proper contact boundary conditions produce mode I SIFs that are identically zero. Partial closure of a circular arc crack will alter both mode I and II SIFs at the crack tips, regardless of the positioning or length of the closed section along the crack. Friction on the crack surfaces in contact changes the total length and positioning of closure, as well as generally decreases the magnitude of opening along the portions of the crack that are not closed.