Issue 37

M. A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 37 (2016) 138-145; DOI: 10.3221/IGF-ESIS.37.19 141 1 r  fatigue limit surface '    1 '    2 '    3 '    s'  2 r  3 r  4 r  s 1 s 2 Figure 1 : Fatigue limit, damage, and failure surfaces in a 2D deviatoric stress space for three moving nested surfaces, showing the damage backstress vector that defines the location of the fatigue limit surface center, and its three components that describe the relative positions between the centers of consecutive surfaces at each load event. The proposed multiaxial IFD model uses a 5D damage vector D    [D 1 D 2 D 3 D 4 D 5 ] T that acts as an internal variable that stores the current multiaxial fatigue damage state (to account for the damage memory). The scalars D 1 through D 5 are signed damage quantities associated with each one of the directions of the 5D deviatoric stress vector s   , defined in [11]. In this way, the total accumulated damage D (which thus works for multiaxial fatigue problems analogously to the accumulated plastic strain p for multiaxial plasticity problems) is obtained from the length of the path described by the 5D damage vector D   , calculated in either continuous or discrete formulations from D dD dD D D             | | | |   (5) If a given stress state s   is on the fatigue limit surface with a normal unit vector n    , and if its infinitesimal increment ds   is in the outward direction, then T ds n  0       and a fatigue damage increment is obtained from a damage evolution rule (inspired on the analogous Prandtl-Reuss flow rule [10-11]): T MS NP dD D ds n n f f n                    ( 1 ) ( ) ( ) ( , )        (6)