Shakedown Limit Loads for 90 Degree Scheduled Pipe Bends Subjected to Steady Internal Pressure and Cyclic Bending Moments

A simplified technique for determining the shakedown limit load for a long radius 90 deg pipe bend was previously developed (Abdalla, H. F., et al., 2006, "Determination of Shakedown Limit Load for a 90 Degree Pipe Bend Using a Simplified Technique, "ASME J. Pressure Vessel Technol., 128, pp. 618-624; Abdalla, H. F., et al., 2007, "Shakedown Limits of a 90-Degree Pipe Bend Using Small and Large Displacement Formulations," ASME J. Pressure Vessel Technol., 129, pp. 287-295). The simplified technique utilizes the finite element (FE) method and employs the small displacement formulation to determine the shakedown limit load (moment) without performing lengthy time consuming full cyclic loading finite element simulations or utilizing conventional iterative elastic techniques. The shakedown limit load is determined through the calculation of residual stresses developed within the pipe bend structure. In the current paper, a parametric study is conducted through applying the simplified technique on three scheduled pipe bends, namely, nominal pipe size (NPS) 10 in. Sch. 20, NPS 10 in. Sch. 40 STD, and NPS 10 in. Sch. 80. Two material models are assigned, namely, an elastic perfectly plastic (EPP) material and an idealized elastic-linear strain hardening material obeying Ziegler's linear kinematic hardening (KH) rule. This type of material model is termed in the current study as the KH-material. The pipe bends are subjected to a spectrum of steady internal pressure magnitudes and cyclic bending moments. The cyclic bending includes three different loading patterns, namely, in-plane closing, in-plane opening, and out-of-plane bending moment loadings of the pipe bends. The shakedown limit moments outputted by the simplified technique are used to generate shakedown diagrams of the scheduled pipe bends for the spectrum of steady internal pressure magnitudes. A comparison between the generated shakedown diagrams for the pipe bends employing the EPP- and the KH-materials is presented. Relatively higher shakedown limit moments were recorded for the pipe bends employing the KH-material at the medium to high internal pressure magnitudes.

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