Issue 38

D. Carrella-Payan et alii, Frattura ed Integrità Strutturale, 38 (2016) 184-190; DOI: 10.3221/IGF-ESIS.38.25 187 Initial degradation of the ply It is also important to consider the effect of the first static loading of the ply on its fatigue damage and strain behavior, as it is not included in the fatigue degradation. Therefore, the static damage and permanent strain are evaluated with a static damage model [2] by running a first non-linear analysis up to the peak load of the cyclic fatigue analysis. The resulting initial damage and permanent strain are imposed as initial state of the fatigue analysis and the first cycle can be computed with a correct stress distribution. The fatigue damage tensor D f is then added to the initial damage tensor D s D = D s + D f (6) The same operation is done with the permanent strain. Calculation optimization: from N-Jump to Damage Jump Block loading: N-Jump The purpose of the N-Jump algorithm is to avoid running a full FE analysis at each load cycle and to deliberately choose a few relevant load cycles only. The cycles with no significant damage growth are “jumped”. From a first FE analysis, at each Gauss point of the FE model, the theoretical number of cycles to jump NJUMP1 is estimated by extrapolating the damage, Eq. (1) and applying to Eq. (7) N NJUMP N if D D D D D if D if D 20 1 10   0  0.5  0 0.2 0.1   0.2                (7) A global cycle jump NJUMP is defined such that P% of Gauss points verify NJUMP1 < NJUMP for the three components. The value of P has been set to 5% in this study. The damage is finally extrapolated after NJUMP, using again the progressive damage formulations Eq.(3). To validate this algorithm and the value of P, three similar fatigue analyses (three points bending) have been run on the first 100 loading cycles with a 45 degrees layup; one without NJUMP, one with P=1% and one with P=5%. Fig. 1 compares the stiffness degradation observed in the three analyses and validates the accuracy of the NJUMP algorithm. Figure 1: Effect of the N-Jump algorithm on stiffness degradation. V ARIABLE AMPLITUDE : DAMAGE ACCUMULATION JUMP AND DAMAGE HYSTERESIS OPERATOR n automotive industry, the synthesis of realistic fatigue loading involves complex load schedules for different roads with variable loading (Fig. 2). The aforementioned jump algorithm is given for block loading. Also, the N-Jump is calculating the damage status by extrapolation (Eq. 7). Here, the damage accumulation jump aims to accurately calculate locally the progressive damage and stiffness degradation. I