A universal approach to ratcheting problems of bree type incorporating arbitrary loading and material nonlinearity conditions. (August 2020) - Pei, Xianjun
Abstract: A universal solution procedure has been developed for solving a wide range of thermal ratcheting problems beyond those covered by Bree Diagram or modified Bree Diagrams. Both thermal and pressure cyclic loading histories considered can be in-phase or out-of-phase with a prescribed phase shift. Material strain hardening behavior is modeled through a modified Ramberg-Osgood stress-strain relationship which can recover the elastic-perfect-plastic material response as an idealized case considered originally by Bree. The universal procedure is made possible through a unified analytical treatment of the associated thermoplasticity phenomena in an incremental form. In addition to elucidating some specific mechanics aspects of ratcheting phenomena under realistic loading and material hardening conditions of interest, the procedure can be used to automate the Bree Diagram generation process under conditions beyond those available to design engineers today. Validations are performed by comparing with brute force finite element solutions for selected thermal ratcheting problems and recovering the original and modified Bree Diagrams used by Codes and Standards currently used by the pressure equipment industry. One key finding is that by considering strain hardening effects, Bree diagram actually "evolves", primarily in the form of an expanded "shakedown" region, as cyclic thermal and pressure loading continues until a limiting condition is reached. This suggests that existing ratcheting design criteria can be overly conservative. Highlights: A numerical procedure is provided to solve thin pipe ratcheting problem of Bree type. The procedure can automatically generate Bree diagram for different loading conditions. A modified Ramberg-Osgood equation is used to address strain hardening effect in Bree diagram generation.