13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- where V and S are the volume and surface of the region analyzed, and Ti are the specified surface tractions. (a) (b) Figure 1. (a) Geometry used to model the problem: r=100mm, Rs=200mm, tk=19 mm, α=10°. (b) A detail of the mesh used. 2.1 The Dang Van criterion A brief introduction to the basis of the fatigue criterion used will be given (see further details in [16]). The Dang Van criterion is a stress based multiaxial fatigue criterion. It relates the variation of the stress state in a material point to a critical parameter, that should not be reached: f [σij(t)] ≤ λ (5) The critical value λ is usually function of the fatigue limits in pure torsion, w, and the fatigue limit in pure bending, σw, and its choice is essential in a multiaxial criterion since it establishes which is the most important stress component that is assumed to have influence on the failure. The Dang Van criterion, in particular, can be formulated as: max(t)+αDVσH(t) ≤ w (6) where αDV= 3 ( w σw - 1 2 ) (7) is a constant that depends on the material fatigue limits previously mentioned, σH(t) is the instantaneous hydrostatic component of the stress tensor and max(t) is the instantaneous value of the Tresca-like shear stress max(t)= σIෝ(t)-σIIIෞ(t) 2 (8) The stress deviator is obtained by the usual definition: sij(t)=σij(t)- δijσ H (t) (9) Then a constant tensor, sij m, is calculated by solving the minmax problem
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