Simulating Pipeline Rupture with Finite Element Analysis
FEA predicts the initiation and evolution of damage in metals, providing an alternative to laboratory structural testing.
Figure 1. Geometry of pipeline model and gouge in pipe. All images: Simulia
Although metal pipelines are manufactured to be durable, they are still susceptible to damage. A common example is a gouge from a backhoe bucket or other heavy equipment. The resulting deformation needs to be comprehensively evaluated to determine whether the pipeline is still functional, or requires repair or replacement.
A body of assessment guidelines for determining the fitness-for-purpose of a damaged pipeline has been developed. Many of these methods rely on experimental results and semi-empirical procedures; as such, their validity may be limited when considering loadings, materials, or specific damage configurations that are outside the scope of their assumptions.
Computer modeling of pipeline damage with finite element analysis (FEA) can complement the existing methodologies by predicting the effects of such outside variables. Simulation can provide important information about the performance of different materials and pipe geometries being considered.
To study how FEA could predict damage initiation in an internally pressurized pipe of API X65 steel with a gouge defect, a team from Simulia reproduced an experiment published by Oh in the International Journal of Pressure Vessels and Piping in 2007 using Abaqus FEA software, which provides two types of damage initiation criterion: ductile, based on the nucleation, growth, and coalescence of voids; and shear, based on shear band localization. The team focused on the use of the ductile criterion.
Figure 2: Quarter symmetric mesh of the pipe, with close-up of detailed mesh at the gouge.
The geometry of the model under consideration is shown in Figure 1. A simulated gouge, 100 mm long, was introduced into the pipeline.
A quarter-symmetric mesh of second order hex elements was generated, and internal pressure loading was applied. End forces were applied to simulate experimental closed-end conditions, and the loads were increased linearly with time. In general, the specification of damage initiation is included in the material definition and must be used in conjunction with a plasticity model. In this analysis the Mises plasticity formulation was used. The mesh is shown in Figure 2.
The ductile damage initiation criterion is a phenomenological model. This criterion was included in the analysis by specifying the equivalent plastic strain at damage initiation as a function of stress triaxiality and strain rate. Stress triaxiality is known to play a role in damage growth.
Figure 3: Abaqus FEA simulation of damage initiation in a pipe gouge.
To calibrate the FEA models, test data from the Oh study was compared to a corresponding FEA model. The test specimens were round, notched bars, loaded in tension until complete fracture was achieved. Each test was compared against a corresponding FEA model. It was noted that as notch radius decreased, yield and tensile strengths increased, but strain to failure decreased. This behavior is consistent with the increasing triaxiality of the stress state as the notch radius decreased.
An FEA contour plot of the damage initiation output variable is shown in Figure 3. Damage has initiated when this variable is greater than 1.0. From the contour, it can be seen that the critical element in the mesh is in the root of the notch at the intersection of the symmetry planes. Further x-y plotting of the initiation criterion in the critical element provided a more precise determination of the failure pressure: The simulation demonstrated that the threshold of 1.0 was crossed at a pressure of 24.97 MPa. The experimentally determined burst pressure was 24.68 MPa.
Simulia’s FEA results compare favorably with the full-scale experimental burst test data collected by Oh. While laboratory results remain valuable for validating computer models, simulation can provide a lower-cost alternative to extensive structural testing.