Issue 49

E. Abdelouahed et alii, Frattura ed Integrità Strutturale, 49 (2019) 698-713; DOI: 10.3221/IGF-ESIS.49.63 704 in all calculations. But depending on the conditions in which they occur, they affect the results. On one side the temperature weakened the structure by accumulating the charges and on the other side the pressure opposes the ovalization. Only the presence of fault conditioned by its quality and location, bending mode and elbow angle, are comparative parameters, hence the resistance capacity of the structure depends on it. The response and the evolution of the system to thermomechanical damage under the evaluative parameters are presented hereinafter by the curves of moments-rotation. Figs. (6 a and b) show that the bend response at bending moment is initially linear and identical for all cases, and take slightly different values just before the maximum moment. This difference is much more caused by the angle of the elbow than by the internal pressure. Figs. (6) also show that during loading, the internal pressure does not delay the damage, in that the bending moment is out of plane. The mode of damage in the out-of-plane bending as shown in Fig. (7), corresponding to a large compression of the matrix on one of the transverse sides of the bend, and tension on the opposite side. The presence of defect has always played the role of amplifying the damage in all the different cases studied. The out-of-plane bending moment causes twists which later give rise to small, 45° oriented wrinkles. This Hashin damage presentation showed us the zone of initiation of damage in compression and tension for the case of fiber and matrix. The dimensionless value 1.00 corresponds to the total damage. In the Hashin criterion, the damage is done by degradation of the rigidity or by the complete suppression of the elements which satisfy the value 1.00 of the structure. It can be seen in all the structures that localized fiber damage occurs only after extensive damage to the matrix in tension and compression. According to the bending mode, the damage is caused either by only the defect (bending in closing) or by the flattening of the cross section of the bend (bending in opening) or by both at the same time as shown in the Figs. (7) (bending out of planes). Figure 7 : Hashin damage representation in structure with elbows of 60° under out-of-plane bending moment. Under the damage by the moment of opening and under the same conditions of internal pressure and temperature, the numerical predictions presented by the Fig. (8) show that the level of damage of the structures is conditioned much more by the type of the moment bending only by the effect of internal pressure and the angle of the elbow. And if we compare the response of the structures to the opening moments, they are very different from those which are submitted to the bending moments out of planes. The response to the bending moments applied is the flattening of the cross section of the bend which takes an orientation in the direction of the bending plane. The mode of elbow failure occurs by a local fiber tension at the central cross section of the elbow. At this point, the critical moment for the 60◦ and 90◦ elbows is 52% and 28% less than the 30° elbow, respectively, see Fig. (8). There is a very weak pressure effect dominated by the rigidity of the composite that appears weakly for structures with a 90° elbow. This effect on response increases as the moment approaches its critical value, as shown in Fig. (8-c). Load responses have almost the same trends as in Fig. (6). It is found in Fig. (10) the same responses up to the critical moment with slightly different levels for the three bends of 30◦, 60◦ and 90◦. The structure with the 30◦ elbow allows a large deformation capacity and a very low pressure effect. Excessive ovality is observed in the case where the structure is subjected to closing bending moments. The flattening is perpendicular to the plane of flexion. The response to the loading of structures leads to the mechanism of their rapid damage due to the additive effect of applied temperature. Failure, therefore, occurs when the composite is solicited by its matrix at high voltages at the extrados of the elbow and by these fibers in tension at the finely localized defect. Localized damage caused by defect positioning may not occur, or with the effect of pressure and temperature. This is illustrated in Fig. (11). The presence of internal pressure has a positive effect on the flexural deformation capacity; it allows the deformation in rotation without breaking because it prevents the structure from becoming ovalized, may remain very weak by the fact that the composite behaves linearly until it is damaged.