Plastic collapse moment equations of throughwall axially cracked elbows subjected to combined internal pressure and in-plane bending moment

Plastic collapse moment (PCM) equations of throughwall axially cracked (TAC) elbow subjected to in-plane closing/opening bending moment were previously proposed by the present authors. However, in actual situation, an elbow may often be subjected to combined internal pressure and bending moment loading. The present work investigates the effect of internal pressure on the in-plane plastic collapse moment of throughwall axially cracked elbows through 3-D elastic-plastic finite element analysis. Equations of un-pressurized cases are recommended where it is conservative and in other cases new equations are proposed.     

Plastic collapse moment equations of throughwall axially cracked elbows subjected to in-plane bending moment

A throughwall axial crack may develop in an elbow or pipe bend due to service related degradation mechanism. It is very important to know the plastic collapse moment (PCM) of an elbow in the presence of a throughwall axial crack. The existing PCM equations of throughwall axially cracked (TAC) elbows are based on very few test data points of Griffiths without detailed analyses and also the range of applicability of their proposed equations are limited. Further, they do not differentiate between closing and opening modes of bending although deformation characteristics under these two modes are completely different. Therefore, the present study has been undertaken to investigate through 3D elastic-plastic finite element analysis. A total of 84 elbows with various sizes of axial cracks (a/D_m = 0-1), different wall thickness (R/t = 5-20), different elbow bend radii (R_b/R = 2, 3) and two different bending modes, namely closing and opening have been considered in the analysis. Elastic-perfectly plastic stress-strain response of material has been assumed. Both geometric and material non-linearity are considered in the analysis. Crack closing is observed in most of the cases. To capture the crack closure effect, contact analysis has been performed. Plastic collapse moments have been evaluated from moment-end rotation curves by twice-elastic slope method. From these results, closed-form equations are proposed to evaluate plastic collapse moments of elbows under closing and opening mode of bending moment. The predictions of these proposed equations are compared with the test data available in the literature. Matching between predictions and experimental results is found to be satisfactory.     

Elastic-plastic J and COD estimation schemes for throughwall circumferentially cracked elbow under in-plane closing moment

Leak-before-break (LBB) assessment of primary heat transport piping of nuclear reactors involves detailed fracture assessment of pipes and elbows with postulated throughwall cracks. Fracture assessment requires the calculation of elastic-plastic J-integral and crack opening displacement (COD)¹ for these piping components. Analytical estimation schemes to evaluate elastic-plastic J-integral and COD simplify the calculations. These types of estimation schemes are available for pipes with various crack configurations subjected to different types of loading. However, no such schemes are available for throughwall circumferentially cracked elbow (or pipe bend), an important component for LBB analysis. In this paper, simple J and COD estimation schemes are proposed for throughwall circumferentially cracked elbow subjected to closing bending moment. The ovalisation of elbow cross-section has a significant bearing on its fracture behavior. Therefore, unlike conventional deformation theory plasticity analysis, incremental flow theory is adopted considering both material and geometric non-linearities in the development of the proposed estimation schemes. Although it violates Ilyushin’s theorem, it has been shown that the resulting estimation schemes is still reasonably accurate for engineering purposes. Finally, experimental/numerical validation has been provided by comparing the J-integral and COD between numerical/test data and predictions of the proposed estimation schemes.     

Effect of internal pressure on plastic loads of 90° elbows with circumferential part-through surface cracks under in-plane bending

This paper quantifies the effect of internal pressure on plastic loads for elbows with circumferential through-wall and constant-depth part-through surface cracks under in-plane bending. Results are based on FE limit analyses using elastic-perfectly plastic materials and the non-linear geometry option. It is found that, for larger values of r/t, the pressure effect on plastic loads is more pronounced and plastic loads for combined loading cases could be much higher than those for pure bending cases. Full FE data of plastic loads are tabulated, and effects of crack geometries on interaction curves are discussed.     

Closed-form plastic collapse loads of pipe bends under combined pressure and in-plane bending

Based on three-dimensional (3-D) FE limit analyses, this paper provides plastic limit, collapse and instability load solutions for pipe bends under combined pressure and in-plane bending. The plastic limit loads are determined from FE limit analyses based on elastic-perfectly-plastic materials using the small geometry change option, and the FE limit analyses using the large geometry change option provide plastic collapse loads (using the twice-elastic-slope method) and instability loads. For the bending mode, both closing bending and opening bending are considered, and a wide range of parameters related to the bend geometry is considered. Based on the FE results, closed-form approximations of plastic limit and collapse load solutions for pipe bends under combined pressure and bending are proposed.     

Finite element plastic loads for circumferential cracked pipe bends under in-plane bending

This paper proposes plastic loads (limit load and twice-elastic-slope (TES) plastic load) for pipe bends with circumferential through-wall and part-through surface cracks under in-plane bending, based on three-dimensional FE limit analyses. The material is assumed to be elastic-perfectly plastic, and both the geometrically linear (small strain) and nonlinear (large geometry change) effects are considered. Regarding a crack location, both extrados and intrados cracks are considered. Based on the FE results, closed-form approximations of limit and TES plastic loads are proposed for practical applications, and compared with corresponding solutions for straight pipes.     

Plastic loads of pipe bends under combined pressure and out-of-plane bending

This paper provides plastic limit and TES (twice-elastic-slope) plastic load solutions for 90° pipe bends under combined pressure and out-of-plane bending, via three-dimensional non-linear FE analyses using elastic-perfectly plastic materials. Without internal pressure, a closed-form approximation is given. For combined pressure and out-of-plane bending, tabulated data are given, from which TES plastic loads can be interpolated. It is found that TES plastic loads for pipe bends under out-of-plane bending are lower than those under in-plane opening bending, but are higher than those under in-plane closing bending. It suggests that the in-plane closing bending mode is the most critical loading mode for 90° pipe bends, which is fully consistent to existing findings.     

Dynamic analysis of multi-layered filament-wound composite pipes subjected to cyclic internal pressure and cyclic temperature

Based on the three-dimensional anisotropic elasticity, the stress analysis of multi-layered filament-wound composite pipes subjected to cyclic internal pressure and temperature loading is conducted in this article. The time-dependent stress, strain and deformation distributions are numerically obtained by the use of the finite difference technique. The pressure and temperature are considered to be symmetrical about the axis of the cylinder and independent of the axial coordinate. Each layer of the pipes is made of a homogeneous, anisotropic and linearly elastic material and it is assumed that the material properties do not change with increasing the temperature. The shear extension coupling is also considered because of lay-up angles. Numerical results obtained from the present model are compared with other published results and good agreement has been achieved.     

Support-induced restraint effect of thin-walled tube in a steam generator subjected to combined pressure and bending load

The restraint effects of support plates on limit load (LL) are evaluated for thin-walled tubes subjected to combined internal pressure and bending loads. To achieve this goal, three-dimensional (3D) finite element (FE) analyses assuming elastic-perfectly plastic material behaviour are carried out for tubes with various sizes of circumferential cracks. Two crack locations, both the top of the tube sheet (TTS) and transition regions, where circumferential cracks have been found in many steam generators during operation, are considered. FE analysis results show that LLs for the circumferential cracks are significantly affected by the boundary conditions of the tube and that the resulting LL solutions can be simply applied to the practical integrity assessment of steam generator tubes, because the comparison between experimental data and FE analysis results shows a good agreement.