Issue 49

E. Abdelouahed et alii, Frattura ed Integrità Strutturale, 49 (2019) 698-713; DOI: 10.3221/IGF-ESIS.49.63 699 standards such as ASME16 .9 [1-3] and the European standard EN 10253- [4] based on experimental tests and analytical calculations. In view of the geometrical configuration of the elbow, the circulating fluid submits it to bending moments. Several researchers are studying the resistance of composite tubes such as Lee et al [5] and Sivakumar Palanivelu et al [6]. They found that its resistance depends on the fiber in its quality, are orientation and its fraction. Research on the combined influence of internal pressure and bending in composite tubular structures has found its way through the work of Natuski et al [7] on the flexural strength of composite tubes. Experimental tests done by Kitching et al [8] on composite bends subjected to bending with and without pressure. A comparison also made by Kochekseraii and. Al. [9] which ends with a good agreement between the experimental and the finite element analysis on a composite tubular structure subjected to a combined loading. The elbow in its geometric configuration will cause a variation of stress along its intrados and the extrados from where the analytical solutions that are possible to be implemented [10]. Several loading conditions are possible giving rise to several types of damage. The study of these tubular composite structures by thermal effect have taken the interest of other researchers as well, Shao [11] evaluated the thermal stresses as well as Kandil et al. [12] by the numerical model. Others such as Bakaiyan et al [13-16] on composite tube responses to combined internal pressure and thermomechanical loading. By their presence, the defects and the temperature, strongly and geometrically destabilize the bends in their resistance, ex; loading mode or misalignment of fibers or orientation anomalies [17]. Matrix cracking and delamination are the main modes that cause the fiber to break [18] and subsequently lead to complete damage. In numerical calculation and composites, most researchers are based on two energy methods. The virtual crack closure technique (VCCT) such as the work of Wimmer et al. [19, 20] on initiation and propagation of delamination and cohesive zone method (CZM) by Gözlüklü and Coker [21,22] who studied the same phenomenon. However, other models of damage exist. The one used by Garnish et al [23] proposed by Padhi et al [24] where the structure rigidity vanishes entirely at the beginning of the failure. It is identified according to the failure criteria of Tsai-Wu [25]. Given these numerous advantages, the Hashin criterion [26] is widely used in composite damage [27]. This criterion uses six modes of failure between fiber and matrix and the separation between them [28]; it is presented by ultimate constraints. The purpose of the present work using the Hashin criterion is to predict the damage under internal pressure and temperature of composite tubular structures caused by a bending moment and by the presence of defect in its quality and location as parameter dangerousness. H ASHIN CRITERION AND INPUT PARAMETER he Hashin criterion is implemented in the standard Abaqus calculation code [29]. The input data given in Tab.(1) are: longitudinal tensile and compressive strengths, transverse tensile and compressive strengths, and longitudinal and transverse shear strengths. All resistance values are assumed to be positive [30]. The damage is continuous in the structure by degradation of rigidity or by removal of the elements. In composites the damage is multimodal, that of fiber and or matrix. In the Hashin criterion, the damage is presented by the following forms: 1. Tensile fiber failure for σ11 ≥ 0 2 2 2 12 13 11 2 12 1 failure 1 no failure T X S                 (1) 2. Compressive fiber failure for σ 11 < 0 2 11 1 failure 1 no failure C X             (2) 3. Tensile matrix failure for σ 22 + σ 33 > 0   13 2 2 2 2 12 22 33 23 22 33 2 2 2 23 12 1 failure 1 no failure T Y S S                  (3) 4. Compressive matrix failure for σ 22 + σ 33 < 0 T