Interactions among cracks and rigid lines near a free surface

Abstract

Cracks and rigid-line inclusions, or anticracks, are commonly observed in many engineering materials, such as intermetallics and ceramic composites. Interactions among these cracks and rigid lines can significantly affect the strength of these materials. Strength degradation due to finishing operations, such as grinding, also depend to a large extent on these interactions near a free surface and their associated surface and subsurface damage evolutions. Accordingly, modeling of interactions among general systems of cracks and rigid lines in the vicinity of a free surface, subject to general loading conditions, is the main thrust of this paper. An integral equation approach based on the fundamental solutions due to point loads and point dislocations in an elastic half plane is utilized for this purpose. The integral equations are reduced to a system of linear equations consisting of the distributions of Burger's dislocation vectors and forces on the cracks and the anticracks, respectively. The proposed solution procedure also allows direct determination of the rigid-body rotations for the rigid lines. The results obtained from the present analysis are first verified against existing results for a single crack or rigid line near a free surface. The amplification and shielding effects on stress intensity factors due to interactions among various distributions of cracks and rigid lines are then investigated. Such interactions near a free surface play crucial roles in surface and subsurface damage evolutions during high-speed machining of ceramic materials.