In the framework of the J-A_2 fracture theory, the crack driving force J and the crack tip constraint parameter A_2 are used to describe the near crack tip stress and deformation fields. These two parameters, J and A_2, were calculated from three-dimensional finite element results for semi-elliptic surface cracks with various lengths and depths in X100 pipeline steel. It was found that, under a uniform far field tensile loading, A_2 increases rapidly to a nearly constant value along the crack front from the free surface to the deepest part of the crack. A similar trend was found for the J-integral distribution except in the case of a semi-circular crack. In addition, for a given elliptic crack configuration, A_2 showed significant J-integral dependence when the crack front approached the free surface, where a strong three-dimensional effect is apparent. On the other hand, at the deepest part of the crack, A_2 converged to a constant value. Two-dimensional plane strain calculations were also performed for single edge-notched tension specimens (SENT), where the crack length corresponds to the depth of the surface crack. The constraint of these two configurations (semi-elliptic crack and SENT) were compared under the same crack driving force (J-integral). In general, the constraint at the deepest crack front of an elliptic crack is higher than that of the corresponding SENT, especially in mid- to large scale yielding condition where J-integral is relatively large. It can be concluded that using fracture toughness determined from SENT specimens to predict surface flaw stability may lead to non-conservative result.
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