Issue 38

D. Carrella-Payan et alii, Frattura ed Integrità Strutturale, 38 (2016) 184-190; DOI: 10.3221/IGF-ESIS.38.25 186 was implemented for woven is removed for UD: in woven fabrics, matrix de-cohesion clearly affects the stiffness in longitudinal and transverse directions, whereas in unidirectional plies, the effect of matrix degradation on longitudinal behavior can be neglected. However, the coupling between D 22 and D 12 remains mandatory and has been maintained. Finally, the deletion of this coupling imposes the addition of a propagation term in the formulation of D 12 , so that a pure shear load in a ply remains able to lead to its collapse. With these assumptions applied to the formulations taken from [2], the evolution laws for the damage variables become:     f d d d c exp c c d exp c c dN c d d d c exp c c d exp c dN d d c D dN 2 11 11 1,11 11 2,11 3,11 11 11 5,11 11 4,11 11 3 5,11 2 11 11 1,11 11 2,11 3,11 11 11 11 4,11 11 2 22 1,22 12 ( ) ( ) 3 ( ) 1                                                                     f d exp c c d exp c c D 2 22 22 2,22 3,22 22 22 5,22 22 4,22 2 22 12 1                                f f c d d d c D exp c c d exp c dN D d d d c d exp c c d exp c dN d 3 5,22 2 2 22 22 1,22 22 2,22 3,22 22 22 22 4,22 12 2 22 12 2 2 12 12 1,12 12 12 2,12 3,12 12 12 5,12 2 12 12 ( ) 1 3 1 ( ) 1 2 1                                                                              c d d d c d exp c c d exp c c dN d 12 4,12 2 2 12 12 1,12 12 12 2,12 3,12 12 12 5,12 12 4,12 2 12 12 ( ) 1 2 1                                 (3) where c i,jk are the 15 fatigue material coefficients that must be identified, the fatigue failure indices Σ ij are the ratio between the effective stress and the ultimate strength of the material in the ij component, and ij ij ij cycle ij ij cycle ij ij ij ij ij ij ij max max where ; 0,   0 ,   0                                       (4) ij ij ij ij where 0,   0 ,   0          Accumulated permanent strain In addition to these damage evolution laws, the model takes into account the permanent strain which appears in the ply due to a cyclic shear loading. Some matrix debris formed by the shear stress is accumulated in the opening matrix cracks during tension stress [2], which leads to a non-reversible deformation of the ply. The c 9 parameter drives the fatigue permanent strain accumulation following the formulation: . p t t d dd dd c max c max dN dN dN 12 12 12 9 12 9 12         . (5)