Analysis of the Beam Approximation Applicability in Problems on Compression of Bodies Along Closely Spaced Cracks

A nonclassical problem of fracture mechanics on compression of bodies along closely spaced parallel cracks is investigated. Cases of a body containing near-surface penny-shaped cracks, parallel to the boundary surface of the body, two parallel penny-shaped cracks, and an array of parallel penny-shaped cracks are considered. The start of fracture process is assumed to begin with stability loss of a part of material surrounding the cracks. By using the approach based on relationships and methods of the three-dimensional linearized theory of stability of deformable bodies for finite and small subcritical strains, the critical loads corresponding to the onset of fracture in highly elastic and composite materials with cracks are calculated. The methodology employed permits the passage to the limit when the separation distance between the parallel cracks or between the near-surface crack and the body boundary tends to zero. On the basis of the results obtained here in the framework of the rigorous three-dimensional linearized approach, we assess the applicability limits of the “beam approach” (“beam approximation”), which is used by other authors and relies on studying stability loss of the respective idealized two-dimensional objects that are “as if separated” by the cracks.