Implementation of the Tresca yield criterion in finite element analysis of burst capacity of pipelines

摘要

The Tresca and von Mises criteria are two classic yield criteria for metals. While the von Mises criterion has been widely implemented in commercial finite element analysis (FEA) software package, the Tresca yield criterion in the context of the associated-plastic flow rule is not available in any well-known FEA packages such as ABAQUS and ANSYS. In this study, the Tresca yield criterion as well as the associated plastic flow and hardening rules are implemented in a user-defined material model (UMAT) in commercial FEA package ABAQUS based on the return-mapping technique. The consistent tangent operator for the Tresca criterion is also implemented in the UMAT model to facilitate the computation of the tangent stiffness matrix during the Newton-Raphson iteration for solving the nonlinear global equilibrium equations in the plastic domain. The constitutive integration algorithm for the Tresca UMAT is written in the principal stress space, which markedly simplifies the implementation. The implemented Tresca UMAT model is validated by theoretical solution and full-scale burst tests of both pristine and defected pipes. Furthermore, based on the Tresca-based and von Mises-based FEA predictions, a new formula is proposed to accurately predict burst pressure of thin-walled corroded pipes.