Functionally Graded Materials (FGMs) have become a vast field of research, due to their wide range of applications and numerous advantages. The use of FGMs has recently expanded, particularly in the reinforcement of tubular structures. Pipe elbows are among the most important elements in a piping system, responsible for reducing stresses and balancing pressure inside pipes. However, due to significant deformations, most frequently caused by bending moment loads, elbows are more prone to exceeding their stress limits. It is for this reason that the analysis of these tubular structures has attracted the interest of many researchers. As a result, the study of their reinforcement can only be carried out through the study of their damage. In other words, to unlock the difficulties of numerically predicting their responses. The aim of our study is to use the finite element method with the proposed meshing technique in the ABAQUS calculation code, to analyze the behavior of a 90° elbow tubular structure, attached to two straight sections, made of functionally graded FGM Al/SiC (Aluminum/Silicon Carbide) material, with a continuous gradual variation of properties in the direction of wall thickness, per row of finished elements along the entire geometry of the tubular structure, in order to simulate a real pipe system installation. The structure is loaded by two modes of in-plane bending moment (Closing and Opening), with an imposed rotational displacement. The aim of this analysis is to evaluate, firstly, the effects of different grading concepts for the FGM Al/SiC material couple in the model geometry (Simple and Symmetrical Concepts), and secondly, the effect of different power exponent indices (n) of the volume fraction, on the elasto-plastic response up to the damage of the tubular structure. The constitutive behavioral law of our model is based on Von Mises’ equivalent stress flow theory with a hardening variable in incremental form. In addition, the TTO (Tamura-Tomota-Ozawa) model was used to describe the elastic-plastic behavior of the FGM, and the XFEM technique was also applied for crack initiation and propagation. The results obtained under moment-rotation conditions show a significant effect on the response as well as on the level of damage, the effect is also remarkable on the ovalization at the bend cross-section. The approach and reliability of the results obtained were based on a comparison with experimental results, which show good agreement, compared with our numerical model.