60 M. Taherzadehboroujeni and S. W. Case A bucket of water Pump DIC Solenoid Valve Gas regulator Speckled sample Water + Nitrogen Reservoir LabView DIC Pressure Transducer Nitrogen Tank S PI Fig. 6.1 A schematic chart of the internal pressurization tests [8] Fig. 6.2 Modeled pipe in the internal pressurization (burst) test 6.4 Numerical Modeling In this study, the developed plastic flow model along with initial elastic response of the material are utilized to simulate long-term internal pressurization tests and evaluate the lifetime of the pressure pipes under different working conditions. The finite element creep analysis is performed using ABAQUS CAE software, version 6.10. The pipes are modeled as a deformable axisymmetric shell with the same dimensions as used in the internal pressurization tests. Because of the symmetry in the axial direction of the pipe, only a half of the pipe is modeled and appropriate constrains are applied. Figure 6.2 shows the modeled pipe. In order to use the developed plastic flow model in the simulation, a user creep subroutine is developed which is called at all integration points. The subroutine code is provided in Appendix. We assume that the total deformation has both linear elastic and plastic creep components. Thus, ε =εe +εcr (6.4) For an isotropic material the linear elastic portion of the deformation can easily be calculated using a temperaturedependent elastic modulus and Poisson’s ratio. We used the developed plastic flow model to calculate the plastic creep portion of the deformation. The eight parameters used in the plastic flow model and elastic modulus evaluated at different temperatures and the Poisson’s ratio are reported in Table 6.1. At each time increment and for each integration point, the equivalent plastic flow rate associated with the local updated equivalent Mises stress, Sy, equivalent pressure stress, p, and the
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