Cyclic Bending Moment Research Articles

Damage analysis in welded steel pipe elbow under strong cyclic loading

According to cyclic loading modes, highly pressurized tubular elements, such as those in elbows, differ from other straight tubular structures in their modes of stress and damage. This work aims to perform a numerical prediction of a tubular structure. It consists of an X52 steel elbow welded to X65 grade ends by straight tubular sections. This pressurized structure is subjected to strong cyclic loading in bending moment applied until damage occurs. The bending moment is combined with different orientations between the closing or opening moment and the out-of-plane moment, presenting a possible but rarely analyzed situation. This cyclic loading mode is taken as an evaluative parameter in its various amplitudes, orientations, and patterns. The cyclic hardening of the elbow and straight tubular sections, including those of the welded joints, are all formulated by the combined isotropic and kinematic model introduced in the ABAQUS calculation code with parameters calibrated according to the Voce model and experimental results, using plasticity by the Von Mises equivalent stress flow theory. The appropriate XFEM (Extended Finite Element Method) technique is used in conjunction with the hardening model to overcome numerical calculation difficulties and predict damage in traction laws, separation by crack initiation and propagation. The results, in the form of hysteresis curves in cyclic bending moment and angular displacement, have shown a strong dependency that conditions the structure’s response as well as the level of its damage.

Mathematical model of dry stack structural elements with geometric imperfections under a cyclic bending moment

Dry stack structural elements are characterized by nonlinear stiffness that arises from geometric imperfections of their components and the absence of any bonding between them. Moreover, such elements dissipate energy under cyclic loading because of their internal structure. The authors considered dry stack structural elements loaded with a bending moment to propose a relatively simple mathematical model of dry stacks composed of only three elements. The model consists of a linear spring, a nonlinear spring, and a spring with hysteresis in series. In this model, the first element describes the idealized properties of a dry stack element, while the second and third elements correspond to the influence of geometric imperfections and the behaviour of dry joints. Furthermore, the authors described a procedure for determining the parameters of the model based on test results. The proposed solution was verified via experimental studies of temporary support structures consisting of a stack of cuboid elements and a hydraulic jack typically used in the process of building rectification. This study showed that the proposed model adequately describes both the nonlinearity and the energy dissipation under a cyclic bending moment.

Nonlinear Slippage of Tensile Armor Layers of Unbonded Flexible Riser Subjected to Irregular Loads

The unbonded flexible riser has been increasingly applied in the ocean engineering industry to transport oil and gas resources from the seabed to offshore platforms. The slippage of helical layers, especially the tensile armor layers of unbonded flexible risers, contribute to the nonlinear hysteresis phenomenon, which is a research hotspot and difficulty. In this paper, on the basis of a typical eight-layer unbonded flexible riser model, the nonlinear slippage of a tensile armor layer and the corresponding nonlinear behavior of an unbonded flexible riser subjected to irregular external loads are studied by numerical modeling with detailed cross-sectional properties of the helical layers, and are verified through a theoretical method considering the coupled effect of the external loads on the unbonded flexible riser. Firstly, the balance equation of each layer considering the effect of external loads is established based on functional principles, and the overall theoretical model of the unbonded flexible riser is set up in consideration of the contact between adjacent layers. Secondly, the numerical modeling of each separate layer within the unbonded flexible riser, including the actual geometry of the carcass and pressure armor layer, is established, and solid elements are applied to all the interlayers, thus simulating the nonlinear contact and friction between and within interlayers. Finally, after verification through test data, the behavior of the unbonded flexible riser under the cyclic axial force, torsion, bending moment, and irregular external and internal pressure is studied. The results show that the tensile armor layer can slip under irregular loads. Additionally, some suggestions related to the analysis of unbonded flexible risers under irregular loads are drawn in the end.

Plastic behavior and shakedown limit of defected pressurized pipe under cyclic bending moment

Pipelines subjected to thermal or mechanical loads may fail due to plastic strain accumulation which leads to ratcheting. In this research, cyclic plastic behavior and shakedown limit are investigated experimentally and numerically for a defected pressurized pipe under cyclic bending moment. In the numerical model, the combined isotropic/kinematic hardening model based on the Chaboche model is adopted to represent the cyclic plastic flow of the material. The hardening parameters are determined experimentally and used in the finite element (FE) model. A four-point bending test rig is manufactured to test a pressurized API 5L steel pipe under cyclic bending. An elliptical defect is created by machining to depict corrosion pits in pipes. The plastic strains are measured experimentally and the results are used to tune the parameters of the FE model. The shakedown limit of the defected pipe is determined numerically by tracking the critical points behavior and the results are verified experimentally. Furthermore, the plastic work dissipated energy (PWD) is estimated within the defective structure to study the behavior of the pipe. By running this compatible model, it is found that the yield and the shakedown limits are lowered by mean values of 55% and 25% respectively due to the presence of metal loss defect occupying almost half of the pipe thickness.

An optimised equivalent modelling approach for LMRP/BOPs in the global dynamic analysis of deepwater risers

ABSTRACT Lower marine riser package/blowout preventers (LMRP/BOPs) play a crucial role in transferring the dynamic loads from the slim drilling risers to the subsea wellhead (SW). Generally, the LMRP/BOPs are usually modelled as the combination of pipe and mass elements in the finite element analysis. In this paper, an optimised equivalent modelling approach for LMRP/BOPs was proposed to improve the calculation accuracy of dynamic cyclic bending moment of SW. In the proposed methodology, the equivalent model of LMRP/BOPs was established based on the deformation analysis of the local fine model of LMRP/BOPs. Using the Newton–Raphson method, the equivalent model was optimised to acquire the optimal equivalent model of LMRP/BOPs. A case study indicated the modelling accuracy of LMRP/BOPs was improved by 14.6% compared to the conventional approach by using the proposed approach, thus the calculation accuracy of the dynamic cyclic bending moment of SW was improved accordingly.

A methodology to calibrate the PICSI cyclic p-y model using experimental results and optimisation

Fatigue life estimation of the components of a drilling conductor system is often a critical design consideration. The analysis is usually performed using a coupled system, with the soil-conductor interaction modelled using p-y springs that remain constant throughout the analysis. This means that shifts in bending moment profile that occur due to degradation and recovery of the soil during or after cycling are not accurately modelled. While the PICSI framework (White et al., 2022) can model changes in stiffness and strength of p-y curves due to cycling and pore-pressure dissipation, guidance has not yet been provided on how to calibrate its parameters. This paper presents an experimental methodology for this calibration process based on centrifuge and p-y model testing in reconstituted carbonate silt and kaolin clay. The procedure uses numerical optimisation, and the calibrated parameters are validated against results from an independent set of centrifuge tests on carbonate silt using a flexible pile of similar dimensions to a conductor. It is found that the calibrated model is able to match the changes in cyclic bending moment through a sequence of different packets of cyclic loading. This calibration procedure provides an objective approach for more accurate modelling of conductor fatigue.

Damage investigation of a pressurized elbow pipe using the XFEM technique under severe cyclic loading

Given the various loading cases possible in tubular structures, cyclic bending moment is one of the frequent cases presented in bent structures attached by straight tubular parts, as in straight tubular structures or a connecting tubular element; their loading is under various cyclic modalities; analyzing these pressurized tubular structures or unlocking the difficulties of numerically predicting or approximating to possible and actual fatigue behavior is of interest to several researchers, this work opts to use 316LN stainless steel, also known as Z2CND18.12 N of an elbow attached by straight parts, the study of the cyclic response up to the damage of the pressurized bend is aimed at evaluating the behavior under the effects of the parameters analyzed, namely the amplitude and the pattern of the cyclic bending moment, The fatigue behavior of the steel is formulated as a combined isotropic and kinematic Ohno-Wang model introduced into the ABAQUS calculation code by parameters calibrated to the experimental, using the finite element method. The damage to the structure under a high cyclic bending moment is introduced into the structure mesh. Of the cyclic accumulation of stress, the damage will occur in the structure by crack initiation and propagation, hence using the XFEM technique. The non-linear behavior, independent of the strain rate, is based on the Von Mises equivalent stress flow theory by mode effect at high cyclic bending moment; the results presented by moment-rotation curves show a significant effect on the response, as well as the level of damage. That damage by crack initiation and propagation precedes excessive ovalization at the level of the elbow cross-section. The approach followed in this analysis and the reliability of the results obtained were previously based on a validation of experimental results, which showed good agreement with the numerical model used.

Redesign of a Failed Hoisting Shaft of a Vertical Transfer Device

The redesign of a failed hoisting shaft belonging to a 10 m stroke vertical transfer device (VTD) is presented. Firstly, the operation of the VTD is thoroughly analysed, the variation of loads and moments along the operating cycle is characterised, and transients such as emergency stop loads are calculated. The selection of safety factors and duty cycle factors was followed by the shaft sizing. After an initial rough sizing, the high-cycle fatigue (HCF) design for cyclic bending moments was performed, first considering constant torque and then considering cyclic torque. The number of bending and torsion cycles performed by the hoisting shaft over 10 years was shown to exceed 106, and an infinite life design is mandatory. The analyses showed that the initial shaft diameter was insufficient, thus justifying the failures observed before the present redesign. A classical fatigue model combining torsional shear stresses with bending stresses was used to take into account reversed torsional loading and ensure infinite fatigue life. This work highlights the need to thoroughly understand a machine’s operating cycle so that the wrong premises for fatigue design calculations are not assumed.

Influence of corrosion fatigue on the fatigue strength of an AlSi10MgMn high‐pressure die‐casting alloy with regard to the surface condition

AbstractThis study investigates the influence of corrosion fatigue on the fatigue strength of an AlSi10MgMn high‐pressure die‐casting alloy with regard to the surface condition. Two different surface conditions are compared. First, an unmachined surface condition with a rough surface () and second a machined and polished surface condition with a smooth, polished surface () are tested. The specimens are loaded with a cyclic bending moment at a constant stress ratio of R = 0 till failure. A 5 wt% NaCl solution enables the corrosion fatigue tests. Corrosion fatigue leads to a significant reduction of the endurable stresses along the whole load spectrum independent from the surface condition. The applied corrosive solution prevents the formation of a pronounced long‐life fatigue strength limit within the tested load cycle range. Hence, the reduction of the endurable stresses increases with the increasing number of load cycles, reaching approximately 37% at load cycles. No significant influence of the surface condition, independent of the environment (air, 5 wt% NaCl), on the fatigue behaviour is found.

Effect of Thinning on Fatigue Life Estimation of Elbows under In-Plane Cyclic Bending Moment

The safety of the piping systems used in any nuclear or thermal power plant is essential to the environment and also to the people involved. Pipe bends are one of the critical components of the piping system. Hence, fatigue life estimation becomes primary focus when the designing pipe bends for their safety limits. The current study uses finite element analysis and the revised manson universal slope method to estimate the life of elbows under in-plane opening and closing cyclic bending moment. The estimated fatigue life was compared with low-cycle fatigue tests in the literature. The displacement of 20 mm was given as input to estimate the number of cycles. The principal stresses were obtained on the highly strained node of the finite element model to locate the crack and its direction accurately. The elbows with thinning have a reduction in the fatigue life of about 19%.

Ratcheting response and boundary of austenitic stainless steel in a pressurized straight pipe subjected to in-plane bending cycles

Ratcheting behavior of pressurized straight pipes made of Z2CND18.10 austenitic stainless steel alloy was evaluated under in-plane bending cycles and under displacement- and force-controlled conditions by means of the Ahmadzadeh-Varvani (A-V) kinematic hardening rule. Ratcheting tests were conducted on straight pressurized steel pipes under bending cycles. Ratcheting response of steel pipes was also numerically simulated through inclusion of the A-V framework into ABAQUS software. The simulated ratcheting results along the axial and circumferential directions were found in good agreement with those of experimental values in the pressurized steel pipes. It was found that variables including the magnitude of internal pressure, cyclic bending moments, loading spectra, material properties, and FE element types, size and numbers noticeably impacted simulated ratcheting values. Ratcheting boundaries were further determined through coupling design codes of KTA/ASME and RCC-MR plus committee of three-dimensional finite element stress evaluation (C-TDF) with the A-V model. Both experimentally obtained ratcheting boundaries and those determined by design codes agreeably revealed the shakedown occurrence.

Shakedown and limit analyses of a pressurised water reactor vessel nozzle under cyclic thermo-mechanical loadings

This paper has investigated cyclic plasticity of a reactor pressure vessel (RPV) nozzle subjected to cyclic thermo-mechanical loads thoroughly: cyclic thermal loads, cyclic bending moments, and cyclic internal pressures. By utilising an advanced direct numerical method known as the Linear Matching Method, elastic shakedown limit boundaries of the RPV nozzle are constructed to evaluate the effects of different load combinations on the cyclic plasticity behaviours. In additions, limit load boundaries of the RPV nozzle are constructed to confirm whether alternative plasticity or ratchetting response appear under the same loading combinations. Through comprehensive numerical studies, the effects of geometric parameters of the nozzle geometries on the cyclic plastic behaviour are identified and the parametric study results are formulated as semi-empirical equations to predict both limit load and elastic shakedown limit boundaries. Ultimately, this research provides reactor design engineer insight into the design of the RPV nozzle in consideration of cyclic plasticity.

Effect of loading patterns on in-plane flexural hysteretic performance of CHS X-connections

This paper presents an experimental investigations to study the hysteretic behavior of circular hollow section (CHS) X-connections which widely applied in various tubular structures. Cyclic in-plane bending moment (IPBM) loading patterns and geometric parameter of brace-to-chord diameter ratio (β) were varied in testing four connection specimens, to evaluate the influence of load patterns on the hysteretic behavior of the connections. Test results shown that regardless of load patterns and connection details, all specimens showed plump and no pinching effect for the hysteresis curve before cracking occurred, all specimens shared similar final failure modes (the chord wall near the intersection teared) and similar energy dissipation modes (mainly rely on the plastic deformation of the chord wall near the intersection). However, the influence of loading patterns on the hysteretic behavior of the X-connections with varied β is different. For the CHS X-connections with large β, it developed higher flexural strength, better ductility and more energy dissipation performance under synchronized down and up IPBM (SDUI) loading pattern than that under take turns to align clockwise and counterclockwise IBPM (TCCI) loading pattern; while for the X-connections with small β, it is opposite. This experimental observation result was further affirmed by a simplified analytical model and FE analysis results. The test results also indicated that regardless of the load patterns, increasing β trend to significantly improve the strength, ductility ratio and energy dissipation behavior of CHS X-connections under cyclic IPBM, and the current specification trend to give conservative prediction on the in-plane flexural strength of the X-connections.

Influence of brace-to-chord angle on the seismic behavior of circular hollow section X-joints under in-plane bending

This paper studied the influence of brace-to-chord angle (BCA) on the in-plane flexural behavior of circular hollow section (CHS) tubular X-joints. The study begins with three CHS tubular X-joint specimens (one orthogonal joint with BCA of 90°, two skew joints with BCA of 70° and 55° respectively) under cyclic in-plane bending moment (IPBM). The test results showed that specimens mainly failed in tearing of the chord wall near the brace/chord intersection after experienced large plastic development, and the crack propagation rate of the chord wall of the skew specimens under negative IPBM is obviously faster than that under positive IPBM, while the propagation rates of the orthogonal specimen under two IPBM is similar. The ductility, strength and energy dissipation of the X-joints are deeply affected by BCA. Decreasing BCA is beneficial to the ductility ratio under positive IPBM, but it is not conducive to the ductility ratio under negative IPBM; decreasing BCA can increasing the flexural strength; both the skew joint with large BCA and the orthogonal joint exhibit higher energy dissipation behavior than that of the skew joint with small BCA. These observations is further confirmed by a simple load transferring model proposed in this study. Finite element (FE) parametric analysis is then carried out to verify test and the load transferring mechanism analysis results. Moreover, FE and test results showed that the negative strength Miu− (under negative IPBM) and the positive strength Miu+ (under positive IPBM) of the orthogonal joints are close, but Miu− of the skew joints are larger than the counterpart of Miu+, and the ratio of Miu− /Miu+ is increased (from slightly more than 1.0 to above 1.2) as BCA decreased (from 70° to 35°).

Ultimate strength assessment of cracked stiffened box girders subjected to extreme cyclic bending moments

This paper aims at obtaining insight on the ultimate strength characteristic of stiffened box girder under extreme cyclic bending. Nonlinear finite element analysis is performed to investigate the ultimate bending moment of cracked stiffened box girder. It is presumed that the preset crack is a through-thickness and transverse crack on the deck, the corresponding five types of cracked models are analyzed. The effects of crack type, crack length and crack location under cyclic loads are examined. Two load patterns are considered in this study, and crack propagation under bi-directional cyclic bending is simulated by applying the element erosion approach. The individual and coupling effects of fatigue crack damage and accumulated plastic damage on the ultimate bending moment of stiffened box girders are discussed. The mechanism of ultimate strength reduction under extreme cyclic bending is analyzed, it could be concluded that ultimate strength reduction is attributed to the coupling effect of these two damages and its applicability is verified by other stiffened box girders.

Experimental and numerical investigations on the collapse behaviour of box type hull girder subjected to cyclic ultimate bending moment

This paper presents experimental and finite element analyses of the ultimate strength and buckling collapse behaviours of a single- and a double-hull girder with a large deck opening subjected to cyclic ultimate bending moments. The cyclic ultimate bending moments here means that the external load in every cycle exceed the ultimate load bearing capacity of the specimens; the aim is to understand how the structures behave under this kind of extreme but not unusual load condition. The results showed that, in general, the plastic deformation would be accumulated under the cyclic loads, and the buckling collapse would expand from the deck plates to the broadside plates in both specimens. However, even if overall buckling occurred on both specimens, the specimens still preserved most of the load bearing capacity for the next ultimate loading cycles, but the double-hull specimen had a higher safety stock. In addition, the different behaviours of these two types of specimens were recorded, and the reasons behind were deeply analysed, which has helped us gain a deeper understanding of how these complex engineering structures perform under this kind of extreme but not well-studied load condition. The conclusions drawn in this works would be beneficial to improve the structural safety of ship hull girders and other similar thin-walled structures.

Implant-abutment screw removal torque values between customized titanium abutment, straight titanium abutment, and hybrid zirconia abutment after a million cyclic loading: an in vitro comparative study

PurposeThe aim of this study was to compare removal torque values after mechanical cyclic loading and bending moment after the static compression testing of customized titanium abutment compared with prefabricated and hybrid abutments.Materials and methodsThe study was developed according to ISO 14801:2016. Sixty implants were divided into three groups equally: Straight titanium abutment group, Customized titanium abutment group, and Hybrid zirconia abutment group. Abutments were fabricated with zirconia restoration. Forty five implants underwent for cyclic loading. The removal torque values were measured after a fatigue test was conducted at 0 cycles (control), 50,000 cycles and 1,000,000 cycles. In the second experiment, 15 implants were divided into the same groups. Then, bending moments were investigated.ResultsThe mean initial removal torque value was significantly higher than 50,000 cycles and 1,000,000 cycles (P < 0.001). The comparison of mean removal torque value between types of abutments was not significantly different (P > 0.05), and the bending moments of all abutments were not significantly different (P > 0.05).ConclusionsFrom the boundary of this in-vitro study, it could be concluded that customized titanium abutment and hybrid abutment were not significantly different in terms of removal torque values after the fatigue test. The bending moment between types of abutment were not significantly different. Thus, it could be concluded that abutment type does not significantly influence abutment stability or fracture strength.

Structural performance evaluation of square hollow section column under compressive axial force with bending moment having different width‐thickness ratio

AbstractThe square hollow section (SHS) is commonly used for the column of the steel building structures in Japan. The moment‐resisting frame will resist the lateral force with the flexural manner of the columns. Under the seismic event, the bending moment will be significant, and the plastic hinge may be formed in the columns. It is crucial to understand the structural behavior at the component level to capture the structure system's ultimate limit state by computational simulation. Understanding the strength and the ductility is one of the essential aspects, but it is also crucial to know the structural elasto‐plastic behavior until the ultimate limit state. It is worthwhile to conduct the testing of the members under combined loading conditions. In this paper, the test results obtained from the different width‐thickness ratio SHS were reported. The forces subjected to the specimen were axial force and cyclic bending moment; therefore, the member was under combined loading condition. Collapse mode, maximum bending moment, and plastic deformation capacity were evaluated in consideration of the effect of the width‐thickness ratio; comparison study between the current design recommendation was also shown.

Shakedown and Limit Analysis of Kinematic Hardening Piping Elbows Under Internal Pressure and Bending Moments

Abstract In this paper, the stress compensation method (SCM) adopting an elastic-perfectly plastic (EPP) material is further extended to account for limited kinematic hardening (KH) material model based on the extended Melan's static shakedown theorem using a two-surface model defined by two hardening parameters, namely, the initial yield strength and the ultimate yield strength. Numerical analysis of a cylindrical pipe is performed to validate the outcomes of the extended SCM. The results agree well with ones from literature. Then the extended SCM is applied to the shakedown and limit analysis of KH piping elbows subjected to internal pressure and cyclic bending moments. Various loading combinations are investigated to generate the shakedown limit and the plastic limit load interaction curves. The effects of material hardening, elbow angle, and loading conditions on the shakedown limit and the plastic limit load interaction curves are presented and analyzed. The present method is incorporated in a commercial finite element simulation software and can be considered as a general computational tool for shakedown analysis of KH engineering structures. The obtained results provide a useful information for the structural design and integrity assessment of piping elbows.

Cyclic behavior of wood-frame shear walls with vertical load and bending moment for mid-rise timber buildings

In light wood-frame buildings, the gravitational and lateral force-resisting systems are composed of floor diaphragms and shear walls. During an earthquake, these walls are subjected to the simultaneous action of in-plane vertical force, shear force, and in-plane bending moment. In a mid-rise building, these internal forces can reach large magnitudes, especially on the lower stories, and could have an important influence on the lateral behavior of the walls. The historical use of light wood-frame construction has been in low-rise buildings. Consequently, few investigations have analyzed the effects of high gravitational forces or in-plane bending moment on the lateral behavior of wood shear walls designed for multi-story buildings. This paper presents an investigation of the cyclic lateral behavior of light wood-frame shear walls, designed for mid-rise buildings, subjected to large axial compressive load and in-plane bending moment. Eight wall specimens were experimentally tested with a cyclic lateral displacement protocol, a constant compressive load, and a cyclic in-plane bending moment. The effects of axial compressive load and in-plane bending moment were analyzed. Also, the wall length and the spacing of sheathing nails were varied to study the effects of these variables on the response. A numerical study was performed to show how these effects could influence the response of mid-rise timber buildings. An improvement in the lateral performance of the walls was observed compared to walls tested without compressive force nor bending moment, showing an increase in stiffness, load-carrying capacity, and dissipated energy.