Buckling of a Near-Surface Parallel Crack Using the Beam Approximation

ABSTRACT: This paper is concerned with the determination of the far-field compressive buckling stress of a near-surface parallel crack, in the limiting case when the crack is situated close to the free surface. In other words, we restrict consideration to the practical case h/l lt; 1, where l is the crack half-length and h is the distance between the crack and boundary. The problem is simplified as the layer between the crack and the free surface can then be treated as a beam under given loads. For the case h/l lt; 1, the critical buckling stress takes a very simple asymptotic form. As buckling is taking place, the crack starts to open asymmetrically, thus causing an increase of both mode I and mode II stress intensity factors. Both K₁, and K_II can be expressed in term of forces and moment at the crack tips. The stress intensity factors in the post-buckling regime can be calculated using a nonlinear analysis.