Issue 46

M. Hack et alii, Frattura ed Integrità Strutturale, 46 (2018) 54-61; DOI: 10.3221/IGF-ESIS.46.06 55 challenge is related to the variability of those conditions: non proportional and variable amplitude loading leading to multi- axial local stress states and long duration fatigue loading. This is why Siemens PLM software [2] has developed an innovative composite fatigue CAE methodology (patent pending) keeping track of the material degradation under such conditions. Sevenois and van Paepegem [3] reviewed and compared the state of the art for fatigue model techniques of woven and UD composite. The study concluded that out of the four modelling methodology  fatigue life (SN curve based),  residual strength,  residual stiffness  (micro-)mechanics model the residual stiffness models are most suitable for mechanical performance using experimental data and can also be combined with a residual strength approach. The presented methodology is based on residual stiffness fatigue laws combined with an efficient damage operator approach to calculate the progressive damage and residual stiffness. This approach is able to perform fatigue simulations for variable amplitude loads and allows ply-stacking optimization without additional testing or material characterizations. I NTRA - LAMINAR F ATIGUE S OLUTION : T HE MODEL n the following sections, the fatigue model strategy will be presented from the load definition, stiffness degradation theory, calculation optimisation algorithm to the parameter identification procedure. Fatigue damage laws The damage evolution law is based on the work of van Paepegem [1] for woven glass fibres that has been verified in several projects (e.g. [4][5]). Three intra-laminar damage variables 11 D , 22 D and 12 D are defined at ply level and linked to the stress tensor by the following behaviour law, Eqn.(1)   p HCH      (1) where C is the stiffness tensor, p  is a permanent strain tensor and H is defined as 11 22 12 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 D D H D                         (2) In [1] the damage variables ij D were split into a positive and a negative part ( ij d  and ij d  ), where the positive part increases when the stress is positive, and the negative one when it is negative. At the end the two parts were added, including a crack closure coefficient for the combination of tension and compression. In this work, only positive stress ratios are used, which means that there is no switch between tension and compression over a cycle and simplifies the problem. Either the stress is always positive and the damage ij D is equal to ij d  ; or it is always negative and it is equal to ij d  , Eqn.(3) . Furthermore, the formulations of Van Paepegem [1] must be adapted to unidirectional plies. First of all, to account for the high in-plane orthotropic behaviour of unidirectional plies, independent i c parameters are defined for the three components of the damage. Therefore, fifteen parameters are used ( , i jk c ) instead of five. For the same reason, the coupling between 11 D and 22 D which was implemented for woven is not included for UD: in woven fabrics, matrix de-cohesion clearly affects I