FGM concept used in damage analysis of heat-treated elbows under out-of-plane combined bending moment

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The elbow is presented in pressurized tubular structures as a connecting element, generally subjected to bending moments either out-of-plane or in-plane, in closure or opening. Another mode of bending moment that can also occur in these tubular structures is the combined bending moment between out-of-plane and in-plane in closure, or out-of-plane and in-plane in opening. In this work, to better present the potential severity caused by this loading mode, an elbow structure attached by straight tubular sections made of X60 steel is analyzed and its damage under this combined bending moment with orientations between the plane and out-of-plane of the structure is discussed. A reinforcement proposal will be made in the second part of this work. Indeed, the structure is pretreated thermally at the elbow, resulting in a graded structure along the thickness with two different material constituents: the base metal and the thermally affected zone (HAZ). Based on the concept of Functionally Graded Materials (FGM), the gradation is by volume fraction between the base metal and the HAZ, following a power law function of a volume fraction index (n). This graded property is introduced along the thickness by finite element layers. The elastic-plastic behavior of the HAZ-base metal mixture is modeled using the Voce model and the Von Mises equivalent stress flow theory. Using the XFEM technique(extended finite element method), the damage of the pressurized and thermally treated structure under a combined out-of-plane bending moment shows that these parameters condition the response and the level of damage.