PSI - Issue 61

Ilias Gavriilidis et al. / Procedia Structural Integrity 61 (2024) 315–321 Gavriilidis et al. / Structural Integrity Procedia 00 (2024) 000–000

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segments, while the kinematic parameters correspond to the components’ initial positions, displacements and the number of punching steps along the plate width. The simulation starts with crimping of the plate edges and continues with simulating the J-C-O steps where the plate is subjected to several punching steps, which mainly force locally the plate to deform under bending and unloading conditions. The plate bending starts at the right crimp edge (“J steps”), continues to the left crimp edge (“C steps”), and ends with the final punching that occurs at the middle of the plate width (“O step”). In case of thick-walled pipes, extra punching steps are induced by a “finishing press” to reduce the gap and continue with the welding process. In the present analysis, welding is not performed due to its negligible e ff ect on the collapse pressure of the pipe, as reported by Antoniou (2021). The semicircular configuration obtained after gap closing is referred to as “JCO” pipe, and the analysis proceeds with the expansion step to improve the circularity of the pipe, and obtain the “JCO-E” final product. In the following, uniform external pressure is applied on the outer surface of the pipe, using the modified Riks’ algorithm, which is available in ABAQUS, to capture the maximum pressure at the onset of collapse and trace the post-buckling response. In the present two-dimensional finite element model, the forming tools (punch, finishing press) and dies are modelled using analytical rigid surfaces, while the deformable steel plate with 2242 mm width and 39 mm wall thickness is modelled using four-node reduced-integration generalized plane strain continuum elements (denoted as CPEG4R in ABAQUS), which allows out-of-plane deformation, so that the conditions are similar to those imposed in the pipe mill. The contact between the plate and the rigid surfaces is modelled using a “master-slave” algorithm with frictionless contact property. The steel plate is subjected to severe bending during the forming process, while circumferential tensile strain is induced in pipe wall during expansion. Subsequently, the pipe material is subjected to reverse loading due to external pressurization of the pipe, therefore the Bauschinger e ff ect should be taken into account. A J 2 (von Mises) cyclic plasticity model with non-linear kinematic / isotropic hardening is employed to describe e ff ectively the elastic-plastic properties of the plate material and capture both the Bauschinger e ff ect and the plastic plateau upon first yielding. The nonlinear kinematic hardening rule, which is initially proposed by Armstrong and Frederick (1966), is enhanced for the purposes of the present work. Furthermore, the constitutive model is modified to capture the plastic plateau upon first yielding and the Bauschinger e ff ect, following the modification proposed by Ucak and Tsopelas (2011). The capability of describing both the plastic plateau and the Bauschinger e ff ect is not available in built-in models of commercial software. The material model is implemented in a user-subroutine (UMAT) for ABAQUS / Standard. The formulation and the implementation of the constitutive model are presented in detail by Chatzopoulou et al. (2016). The material model is calibrated based on a series of experiments, which involve tension-compression-tension loading path on coupon specimens extracted from the X60 steel plate at di ff erent locations and orientations. Fig. 1 shows the experimental stress-strain curve of the X60 steel plate material and the corresponding numerical fit of the plasticity model. The yield strength ( σ y ) of the plate material is 440 MPa, the Young’s modulus (E) is 200 GPa and the Poisson’s ratio ( ν ) is 0 . 3. 2.2. Material model

3. Numerical results

3.1. Simulation of JCO-E manufacturing process

Fig. 2a presents the plate configurations at di ff erent stages of the JCO-E manufacturing process for the initial crimping step and the following punching steps (“J”, “C” and “O”), while fifteen punching steps are applied to the plate. After removal of forming tool (JCO punch), a secondary forming tool refereed to as “finishing press” is used by imposing one extra punching step on each crimped side of the plate after the O-step, as shown in Fig. 2b. The final gap, which is shown in Fig. 2b (stage “IV”), is significantly lower than the one obtained at the end of the O-step and both gap values at the beginning and at the end of the finishing press are in accordance with measurements with actual 30-inch-diameter pipe provided by the pipe mill. Once the final gap is closed the two plate edges are kept in contact using a “no separation” contact algorithm and the “JCO” pipe is obtained, as shown in Fig. 2c. The analysis proceeds with the expansion of the JCO pipe, using twelve expander segments (also called as “mandrels”) which move radially