Higher order terms of the crack tip asymptotic field for a notched three-point bend beam

The coefficients of the first five terms of the crack tip asymptotic field of three-point bend single edge notched beams (TPBs) with span to depth ratios widely used in testing are computed using a hybrid crack element (HCE), which has the potential to directly calculate not only the stress intensity factor (SIF) but also the coefficients of the higher order terms of the crack tip asymptotic field. The general approximate closed-form expression for SIF proposed by Guinea et al. (1998) and the available numerical results for the second T-term are calibrated by the results of the HCE. Approximate analytical expressions for the second, third, fourth and fifth terms for a TPB with a span to depth ratio of 4 and for a single edge notched beam subjected to pure bending are obtained by fitting the computed data. These approximations are then used to predict the general expressions for coefficients of the higher order terms of a TPB with arbitrary span to depth ratio β. The accuracy of these general expressions is studied for TPBs with β=6, 8 and 12.

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