S. Baste / Composites Science and Technology 61(2001)2285-2297 strain is simply the effective density of transverse matrix B=FB microcracks multiplied by their aspect ratio, Eq.(4). Then, the predicted total strain is the sum of the pre- where B is the density of cracks that have been accumu- dicted elastic and inelastic parts of the strain. The com- lated during monotonic loading. The opening-closure parison between the experimental strains and their variable F is the proportion of cracks that remains open predictions(Fig 19), allows us to validate the choice of during unloading and thus represents the damage deac the evolution laws of the two internal variables, B and 8, tivation and, so, of the description of this micro level damage mechanism [24] 5. Cyclic loading When cyo clic loading is performed, as the stress decreases during unloading, the transverse cracks that have been created during the monotonic loading are prone to close(Fig. 20). They are still present anyway but their closure simulates an increase of stiffness as if the material could recover its mechanical properties The cracks that remain open represent the active part of the microcracking. An apparent state of damage seems to decrease while the damage accumulated is greater. The closing effect induces damage deactivation leading to unilateral behaviour [26-28]. The internal variable is then representative of a damage that can be qualified as apparent damage [14]. It is necessary to make a dif- ference between the apparent state of cracking and the number of cracks that has been created effectively. Just as the active cracks were defined we can define an active Fig. 18. Stiffness changes (in GPa) during a tensile test in fibres or apparent crack density direction 3. 2D C-SiC inelastic elastic [B-4.2,2x,/ 300 080160240320 b如01624x Stress(MPa) 00.10.20.30.40.50.60.70.8 Fig. 16. Variation of the crack density parameter and of the thickness Strain(%) crack aspect ratio for the transverse matrix microcracking as a func- Fig. 19. Variation of the total strain, of the elastic strain and of the tion of applied stress inelastic strain as a function of the applied stress. 4104 Debonding crack Transverse Matrix Crau 210+ t 2u (Crack Ope 200300400 Stress(MPa) Fig. 17. Variation of the volume concentration of the three cracks laI nnen Fig. 20. States of the transverse cracks.strain is simply the effective density of transverse matrix microcracks multiplied by their aspect ratio, Eq. (4). Then, the predicted total strain is the sum of the pre￾dicted elastic and inelastic parts of the strain. The com￾parison between the experimental strains and their predictions (Fig. 19), allows us to validate the choice of the evolution laws of the two internal variables,  and , and, so, of the description of this micro level damage mechanism [24]. 5. Cyclic loading When cyclic loading is performed, as the stress decreases during unloading, the transverse cracks that have been created during the monotonic loading are prone to close (Fig. 20). They are still present anyway but their closure simulates an increase of stiffness as if the material could recover its mechanical properties. The cracks that remain open represent the active part of the microcracking. An apparent state of damage seems to decrease while the damage accumulated is greater. The closing effect induces damage deactivation leading to unilateral behaviour [26–28]. The internal variable b is then representative of a damage that can be qualified as apparent damage [14]. It is necessary to make a dif￾ference between the apparent state of cracking and the number of cracks that has been created effectively. Just as the active cracks were defined, we can define an active or apparent crack density:  ¼ F ð19Þ where  is the density of cracks that have been accumu￾lated during monotonic loading. The opening-closure variable F is the proportion of cracks that remains open during unloading and thus represents the damage deac￾tivation. Fig. 16. Variation of the crack density parameter and of the thickness crack aspect ratio for the transverse matrix microcracking as a func￾tion of applied stress. Fig. 17. Variation of the volume concentration of the three cracks arrays. Fig. 18. Stiffness changes (in GPa) during a tensile test in fibres direction 3, 2D C–SiC. Fig. 19. Variation of the total strain, of the elastic strain and of the inelastic strain as a function of the applied stress. Fig. 20. States of the transverse cracks. S. Baste / Composites Science and Technology 61 (2001) 2285–2297 2291