Blunting of a Plane Strain Crack Tip Into a Shape With Vertices

Abstract

When monotonically increasing tensile opening loads are applied to a cracked, plane strain, elastic-plastic body, the crack tip will blunt until fracture occurs. At least within the rigid-plastic model for nonhardening material, the shape of the blunted tip is not unique. The blunted tip shape may have two or more sharp corners, or be smoothly curved. When the shape involves corners, the opening is predominantly accommodated by shearing of the material at the corners. This shearing transports material from the interior of the body onto the crack surface. In contrast, the smoothly blunted crack tip involves no such transfer of material points from the interior. However, the smoothly blunted crack, which was originally sharp, involves infinite strains on the crack tip surface. The crack with corners on the tip has large but finite strains on the crack tip surface. The stress and deformation field in front of a crack with two corners and with three corners on the tip, as calculated using the slip line method, is presented for the nonhardening, fully plastic, deeply cracked, double edge-notched thick panel. As in the case of the smoothly blunted crack tip, the elevated stress between the crack tips cannot be maintained very close to the crack tip, due to a lack of constraint. The stress distribution in the case of the crack tip with vertices on it differs from that of the smoothly blunted crack tip case. In particular, immediately in front of the crack tip with three corners, the stress is higher than that immediately in front of the smoothly blunted crack tip. An approximation for a power law hardening material indicates that the maximum stresses near the blunted crack tip is much the same for a crack with vertices on the tip as for a smoothly blunted crack tip. The details of the stress distribution, though, will depend on the mechanism by which the crack blunts. These results for stress and strain and some calculations of the growth of voids near the crack tips indicate the same fracture process could lead to different fracture toughnesses, depending on the type of mechanism by which the crack blunts.