The American Petroleum Institute sponsored a research program starting in 1996 to determine the effects of smooth dents and rock dents on the integrity ofliquid pipelines. Fort-four different dent configurations were used in the course of testing. While the primary thrust of the work was experimental, analytical efforts were made to address dent mechanics using finite element methods. A test matrix using seventy-two test cases was developed to assess the effects of pipe D/t, dent profie and depth, level of constraint and different pressure cycles on the fatigue life of dented pipelines. Results were examined in terms of stress changes resulting from denting, pressurization, and the associated residual stress states. The shell model finite element results permitted the development of stress concentration factors for use in calculating fatigue lives for the respective dent configurations. Favorable results were obtained in comparing the calculated values to the experimentally-determined fatigue lives. The project had two primary contributions to the study of dent mechanics. First, the program ilustrates how finite element methods can be used to compare the effects of different size dents involving different pipe geometries. Secondly, as in-line inspection technology evolves, there wil be an increased need to assess dents based upon their size and shape. The analytical results and methods of this research program can serve as the foundational basis for this type of correlation. INTRODUCTION While a considerable amount of experimental research on dents and mechanical damage have been conducted (Fowler et aI., 1995 and Kiefner et aI., 1996), use of finite element models permits quantitative assessment of dents not specifically addressed in experimental research programs. This benefit is derived by studying the dents in terms of stress changes resulting from denting, pressurization and the associated residual stress-states. Information is presented herein relating to the following topics of discussion, Finite Element Methodology (brief background on finite element modeling and its application) Analysis Test Matrix (basis for selected pipe and dent geometries) Analytical Results (results for each defect combination) Verification and Application of Analytical Results (correlation with experimental work and usage of finite element data in assessing defect severity) Discussion of Results (meaning, comparison, and implications) FINITE ELEMENT METHODOLOGY A detailed description of the principles associated with finite element analyses is outside the scope of this paper; however, the basic components and variables involved wil be discussed. Certain parameters are required as input into the finite element model, Boundary conditions Model configurations (element types, loading sequence, and contact issues) Material modeL. Boundary Conditions The boundary conditions are selected based upon the specific model geometry. To minimize computational time in the analysis phase, a quarer-symmetry model was used. Shown in Figure 1 is a mesh for the 12-in nominal diameter pipe models used in the analysis. As ilustrated in this figure, a dense mesh is applied locally to the dented region of the pipe. Also shown are the associated boundary conditions for each of the exposed edges of the modeL. The model was constructed using the PATRAN modeling package (version 3.1) and analyzed using the ABAQUS (version 5.4) general-purpose finite element program. Model Configuration The complex geometry created by the dents under review prevented a plane-strain formulation (two-dimensional), hence a three-dimensional shell model was used. Solid continuum elements were not required because of the high radius to wall thickness ratio (on the order of34). Shell elements are permitted whenever this ratio is 10 or higher. The ABAQUS S4R5 first-order quadrilateral shell elements were employed. These elements permit calculation of membrane strain in addition to the associated bending strains which var as functions of thickness in the direction of the element normal vector. Transverse shear strains were also calculated, although for piping models these are rather inconsequential in comparison to the hoop and axial strains resulting from pressure and denting. In constructing the models, all elements were oriented so that their normals projected radially outward from the axis of the pipe. In the application of pressure, a corresponding pressure was applied to the inside face of each element (due to the orientation of the element normals this corresponds to the inside of the pipe). Because of the large strains and displacements associated with denting a pipe, the analysis accounted for stress stiffening and employed the formulation for large displacements and rotations. As one would expect, the model was highly nonlinear because of the large displacements and rotations, the nonlinear aspects of the material data, and the use of contact elements at the intedace between the pipe and testing apparatus. An elastic modulus of 29 X 106 psi and a Po iss ion’s ratio of 0.3 were used. The dimensions for the pipe models were 12.75-in outer diameters, wall thicknesses ofO.188-in and 0.375-in, and the lengths of the pipes were 30 inches total (approximately 2.5 diameters from the center of the dent). The longitudinal length of the pipe was selected in order to minimize any interaction between the dent area and the end of the pipe. The basic components ofthe model from a constrction standpoint were: Pipe material Indenter Saddle. The geometry for the indenters was equivalent to those used in the experimental work (Alexander and Kiefner, 1997). Refer to the information provided in Table 1 for dimensions on the indenters. As ilustrated in Figure 1, the saddle supports the bottom portion ofthe pipe and is similar to the saddle arangement that exists with the experimental dent set-up.. The radius of curvature for the saddle was larger than the pipe radius to prevent any over-constraining the bottom of the pipe. Contact elements were generated in all areas where contact was expected. The two areas of contact in the pipe were the dent regions between the pipe and indenter, and at the bottom of the pipe where contact with the saddle is made. As implied by its name, the contact element is used where two or more bodies come in contact. A load transfer occurs and the bodies deform based on the relative compliance of the members involved. For our application, the relative stiffness of the indenter and saddle are much greater than pipe. This means that the pipe deformed locally in relation to these contact surfaces that possess greater stiffnesses. When the indenter displacement was removed, the pipe body maintained a shape based upon the level of indentation and plasticity-level induced in the pipe. This stress configuration in the pipe is known as the residual stress state and performs a critical role in determining the alternating stresses induced in the process of cycling with internal pressure. Both smooth and rock dents were studied in the analysis phase of this research program. The smooth dents were allowed to reround after being installed in the pipe; however, the rock dents were not permitted to reround. The latter indention remains constant during the course of pressure cycling. The terms used to describe these two dent configurations are unconstrained and constrained, respectively. In conducting the analysis, the load steps employed in denting, rebounding, and pressurizing were identical to the steps used in the experimental work. The four basic load steps for the unconstrained smooth dents were as follows: Indent to a depth specified as a percentage of pipe diameter Remove indenter and allow elastic rebound of the pipe Apply pressure inside the pipe Remove internal pressure (determination of final residual dent depth). The three basic load steps for the constrained rock dents are as follows: Indent to a depth specified as a percentage of pipe diameter Apply pressure inside the pipe Remove internal pressure (determination of final residual dent depth). Material Model In order to accurately model the behavior of the piping material in response to denting, elastic rebound, and response to cyclic pressurization, a material model incorporating plasticity was used with an assumption of isotropic hardening. Values for the true stress/true strain input were based upon conversion of lab test data for X52 grade materiaL. The following sections present information relating to the matrix selected for analysis, correlation with experimental data, and usage of analytical results in predicting fatigue life. Analysis Test Matrix Because the experimental efforts were started prior to the finite element work, an analysis matrix was developed based upon the insights gained in the course of testing. The selection ofthe 12-in nominal pipe diameter was for purposes of comparison with the experimental test samples. Additional variables were also selected based upon interests not necessarily addressed in the experimental work. Table 1 provides a complete listing of these variables and description of the indenters. The analysis matrix provided for a total of 72 test cases. While only one pipe diameter was considered, the effects of diameter to wall thickness were addressed in considering D/t values of 34 and 68. While typical fatigue data would lead one to believe that increased mean stress has a detrimental effect on fatigue life, experimental work ilustrated the benefits associated with cycling dented pipes at upper range of the MOP. The benefit resides primarily in the removal of the associated indentations which then lowers the alternating stresses of the dented region. In light of this information, the test matrix presented in Table 1 shows 3 cyclic pressure ranges based upon percentages of MOP (where MOP corresponds to 72% SMYS).
