Load Interaction Diagram of Pressure and Cyclic Bending for Elastic-Plastic Tubes

Tubes operating with internal pressure can be under cyclic bending. In this work we used the Prager and Armstrong-Frederick models to analyze plastic deformations in tubes under the above loading. We used the von-Mises yield criteria as the yield surface model. The yield surface shape is assumed constant. With the aid of this criteria and using appropriate simplifications on geometry elements, the loading region in which plastic deformation occurs is distinguished from the elastic region. While increasing the pressure, the transition from elastic to plastic deformation happens in lower cyclic bending. The two kinematic hardening models are used for plastic calculations. The stressstrain equations are solved by the return mapping method. In different pressures and bending the plastic strains are calculated. Finally a region of loading in which the elastic shakedown occurs is plotted. In the two models a slight variation is observed for the elastic shakedown limit. Reduction of the elastic shakedown limit with increasing the pressure is observed. In each pressure after the elastic shakedown limit, increasing the bending causes plastic shakedown and ratcheting. Prager model predicts plastic shakedown. The Armstrong-Frederick predicts almost linear ratcheting rate. All the above inspections are plotted in a load interaction diagram.

کلیدواژه ها:

kinematic hardening ، ratcheting ، elastic shakedown ، plastic shakedown ، load interaction diagram ، cyclic bending