In recent years, significant patents have been devoted to developing non-destructive techniques for damage identification in structures. A crack in a structural member induces a local flexibility which affects the dynamic and static behavior of the whole structure. In this paper, an approach that is able to derive the flexibility parameters in beams with an edge crack based on the strain energy density theory is presented. The method takes into account that the crack in a beam does not propagate in a collinear manner, but due to the presence of the mixed mode, it changes its direction. This allows a description of the phenomenon of the non collinear propagation of the crack similar to the experimental evidence. The crack is assumed to be vertical before the loading, and then it runs in the direction of the minimum of the strain energy density. Then, the crack is supposed to follow the direction of the principal tensile stress in the section. Comparisons are made to the evaluation of the energy released during the whole crack process in the case of incorrect collinear propagation of the crack in mixed mode. Preliminary results are presented for different positions and initial length of the crack.
Keywords: Castigliano theorem, edge crack, energy released, flexibility parameter, mixed mode, principal stress, Strain energy density, three-point bending, collinear propagation of the edge-crack, non-collinear propagation of the edge-crack
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