Using Functionally Graduated Materials Concept to Predict the Damage of Heat-Treated Elbows Under Bending and Pressure Loading

Elbows in pressurized tubular structures are increasingly stressed by loadings with radial and tangential stresses. These stresses are completely different from those of straight tubular structures. Through the finite element method and using the ABAQUS computer code, the damage of a tubular structure in X60 of an elbow attached by straight parts stressed in internal pressure and in the moment of bending in closing is analyzed in this work. As a proposal for reinforcement, this structure is previously heat-treated and partially at the level of the elbow. The formulation of the heat-treated X60 material is based on the concept of functional graded materials (FGM), where the graduation by volume fraction between the metal in its base and that previously heat-affected named heat affected zone (HAZ) is under a power function of a parameter named volume fraction index (n). The graded properties of HAZ in the base metal along the thickness of the tubular structure are introduced by a row of finite elements using a proposed meshing technique. The elastic–plastic behavior of the HAZ-base metal mixture under the Voce model follows the equivalent stress flow theory of Von Mises. The technique of extended finite element technique (XFEM) in the damage and the mesh proposed in the graduation, were used to evaluate the various parameters, such as: the internal pressure and the heat treatment (surface and index n). The latter condition the response of the structure and the level of its damage.