13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- While the large-size asymptote is always physically meaningful, the small-size asymptote could become only theoretical if mode II prevails for sizes too small for the asymptotic approach to hold true. In fact, when the finite crack extension is not negligible with respect to the other geometrical dimensions (e.g. for very small sizes), disregarding higher order terms in the asymptotic stress field is not acceptable. Similarly to LEFM, the asymptotic approach to V-notched structures leads to an infinite strength for vanishing sizes, i.e. to a result that, within the present coupled Rankine-Griffith criterion and under constant remote tensile stresses (see Fig. 4), must be regarded as physically unacceptable. Figure 5. Size effect on nominal stress at failure: (a) pure mode I loading; (b) pure mode II loading; (c) mixed mode loading. 6. Conclusions In the present paper we applied the FFM criterion provided in Cornetti et al. [14] to determine the critical load in V-notched structures under combined Mode I and Mode II loadings. With respect to simple Mode I loadings [5], the mixed mode problem is more complex since, beyond the failure load, also the direction of the crack onset at the re-entrant corner tip is unknown. Nevertheless, exploiting suitable weight functions for the SIFs of a V-notch-emanated crack [12], we were able to formulate the model as a standard minimization-under-constraint problem and to solve it by means of the Lagrange multiplier technique. A comparison with a broad set of experimental data (for both the failure load and the crack orientation) can be found in the recently published paper [16]. In mixed-mode loading cases, we showed that our model is able to explain the growing relevance of the mode II contribution for increasing material lengths lch, while it is negligible if lch tends to zero. Nevertheless, since the present approach is based on the asymptotic stress field, it yields accurate results only for sufficiently small lch values (with respect to the other geometrical dimensions). If this condition is not met, it is necessary to consider further terms in the stress field asymptotic expansions [17] or to tackle the problem numerically [18]. ln b ln σf ln b 1 1−λII ln σf ln b 1 1−λII ln σf 1 1−λI (a) (b) (c) 1 1−λI
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