Cyclic Pure Bending Research Articles

Damage behaviour of full-scale straight pipes under extreme cyclic bending conditions

Requirements of industrial piping and pipelines to withstand extreme cyclic loading conditions have been motivating increasing interest on a particular extreme fatigue regime: the ultra-low cycle fatigue (ULCF). This damage domain corresponds to a transition between low-cycle fatigue and monotonic ductile damage. Albeit better understanding of this damage regime is required, very few studies are available covering full-scale testing. This study aims at investigating the performance of X60 and X65 piping steels, subjected to extreme cyclic loading conditions resulting in a reduced number of fatigue cycles (Ni<100). Experimental tests were carried out on full-scale straight pipes subjected to cyclic pure bending, which were performed under the framework of the ULCF RFCS/EU project. Additionally to the large-scale tests, plain material was also tested under monotonic and ULCF conditions, supported by small-scale smooth and notched specimens. Large-scale tests were simulated by means of elastoplastic finite element models in order to reproduce the local plastic instability (buckling) where fatigue cracking was verified. Classical Coffin-Mason relation and a modified Xue relation were calibrated using small-scale testing data, the latter relation accounting for triaxiality and Lode angle stress tensor dependencies. The referred models were applied in the damage prediction of the full-scale pipes and results compared with code based procedures such as the ones proposed in the ASME VIII, Div.2. In general, the incorporation of the stress state parameters in the computation of ULCF damage produced improved predictions with respect to the pure strain range based models as the Coffin-Manson or ASME VIII, Div.2 code.

Applying a new constitutive model to analyse the springback behaviour of titanium in bending and roll forming

This paper is an extension to previous work that dealt with the development of a strain path dependent constitutive model to describe the inelastic behaviour of Ti-6Al-4V at room temperature based on the homogenous yield function combined with the anisotropic hardening characteristics, the so-called HAH model. The present work is to apply and verify the accuracy of the proposed model in the finite element (FE) analysis of springback in bending dominated forming processes such as the V-die bending and the roll forming process. In addition, the model is applied to develop a greater insight into the nature of springback in the roll forming process where springback is generally lower compared to that found for simple bending. For this the hardening characteristics of Ti-6Al-4V were identified applying an inverse analysis approach in Abaqus Standard and the model used to describe the evolution of the anisotropic yield surface during non-proportional strain path deformation; this included the cyclic pure bending and cyclic tension–compression tests to generate experimental target curves. The constitutive model parameters were optimised to capture the cyclic behaviour of Ti-6Al-4V in both the pure bending and tension—compression and incorporated into the numerical models of a V-die bending test and a roll forming procedure to analyse springback.The model achieved good agreement with experimental results and reproduced the lower springback observed in roll forming compared to simple bending. In contrast to this a conventional isotropic hardening model significantly overestimated springback for the roll forming process. This suggests that the lower level of springback observed in roll forming compared to V-die bending may be due to kinematic hardening effects. In addition, a lower level of accumulated effective stress and the presence of redundant shear strain was numerically observed in the bending regions of the roll formed section which also may have contributed to the reduction of springback. The results of this study suggest that for the accurate numerical prediction of springback in roll forming kinematic hardening effects need to be accounted for. For this the study presents an effective numerical approach and prove its applicability by numerical roll forming and V-die bending studies performed on high strength Ti-6Al-4V at room temperature and verified with experimental results.

Surface crack growth subject to bending and biaxial tension-compression

Fatigue surface crack growth and the in-plane and out-of-plane constraint effects are studied through experiments and computations for aluminium alloy D16T. Subjects for studies are cruciform specimens under different biaxial loading and bending central notched specimens with external semi-elliptical surface crack. Both the optical microscope measurements and the crack opening displacement (COD) method are used to monitor and calculate both crack depth and crack length during the tests. The variation of crack growth rate and surface crack paths behaviour is studied under cyclic pure bending and biaxial tension-compression fatigue loading. This work is centered on the relations between crack size on the free surface of specimen considered configurations, COD and aspect ratio under different fatigue loading conditions. For the experimental surface crack paths in tested specimens the T-stress, the local triaxiality parameter h, the out-of-plane TZ factor and the governing parameter for the 3D-fields of the stresses and strains at the crack tip in the form of In-integral were calculated as a function of aspect ratio by finite element analysis to characterization of the constraint effects along semi-elliptical crack front. The plastic stress intensity factor approach is applied to the fatigue crack growth on the free surface of the tested bending and cruciform specimens as well as the deepest point of the semi-elliptical surface crack front. As result fatigue surface crack paths or crack front positions as a function of accumulated number of cycle of loading are obtained.

Surface topography changes in aluminum alloy sheet during large plastic straining under cyclic pure bending

This study consists of the experimental assessment of the surface topography of aluminum alloy AA 6022 sheet during large cyclic tensile and compressive plastic straining such as those present in the flow through drawbeads and small corner radii. Uniaxial and cyclic bending tests were used to measure the effects of such strains on the substrate layers of the sheet. All testing was performed without tool contact to ensure surface roughness changes were exclusively the result of the straining evolution of the free outer layers. The three-dimensional average surface roughness (Sa) was measured using optical interferometry. Changes in Sa were evaluated for two sheet textures: mill finish (MF) and electro discharge texture (EDT), along longitudinal and transverse rolling directions. Texture pattern, test direction, and bending/unbending strain are all shown to be significant contributors to variations in Sa. The magnitude of the initial surface roughness was also an important factor of the resultant %Sa variation, ranging from 40% ΔSa for EDT, to approximately 350% ΔSa for MF. Unbending the sample to its flat state considerably altered the Sa, disturbing any monotonic Sa trend. This made it unfeasible to assess the effects of strain history on a formed part based only on Sa values. The non-linear relationship between Sa and strain was more significant at medium and large strains. Effects on Sa due to bending/unbending of the substrate layer presented in this study must be taken into account in the modeling of more complex phenomena involving tool radii contact and friction.

Discrete dislocation plasticity analysis of single crystalline thin beam under combined cyclic tension and bending

The cyclic plastic response of a single crystalline thin beam subject to combined cyclic tension and bending is analyzed using two-dimensional discrete dislocation plasticity. In this contribution, special attention is paid to the difference in the inherent mechanism of the size effect for different cyclic loads. Results show that the cyclic plastic response has a strong size effect for both cyclic pure tension–compression and pure bending. However, the inherent mechanisms are different. The dislocation starvation mechanism dominates the cyclic tension–compression while the geometrically necessary dislocation dominates the cyclic pure bending. When the combined cyclic tension and bending are applied to the thin beam, the cyclic moment–rotation response shows strong size effect while the stress–strain response shows weak or even no size effect. In addition, it is also found that the cyclic loading paths have considerable influences on the shape of the cyclic stress–strain loops.

Plastic mechanism analyses of circular tubular members under cyclic loading

This paper presents plastic mechanism analyses of circular tubular members under cyclic loading. In particular, it provides new methods of analyses for circular hollow sections subjected to a constant amplitude cyclic pure bending (CCPB) and a large axial compression–tension cycle (ACTC). The procedure described herein for CCPB considers both prebuckling deformation and local buckling. The prebuckling deformation was simulated using a progressively deforming elliptical cross-section which was observed during the test. The local buckling analysis was performed using a rigid plastic mechanism analysis. Good agreement was found between the predicted and measured hysteresis. However, the present model over-estimates the strength and absorbed energy. For the ACTC, good agreement was found between the predicted and measured collapse curves within the compression half-cycle. More work is needed to model the effect of tension developed during the remaining of the loading cycle. The present models consider the actual local buckling deformation of the cross-section and also avoid the complexity involved in the numerical analyses since they provide the most commonly used closed-form solutions.

Concrete-filled cold-formed circular steel tubes subjected to variable amplitude cyclic pure bending

This paper describes an experimental investigation of the cyclic inelastic flexural behaviour of concrete-filled tubes (CFT). Controlled-rotation, symmetrical cyclic bending tests were performed using a variable amplitude loading history on different sizes of CFT with different section slenderness. The CFT beams exhibited stable hysteresis behaviour up to local buckling and then showed considerable degradation in strength and ductility depending on the D / t ratio. Seismic capacity parameters are presented including strength, hysteresis curves and modes of failure for the specimens. Peak moments obtained in the cyclic tests were compared with design moments predicted using a number of steel and concrete specifications. New section slenderness limits suitable for design and construction of seismic resisting structural systems were determined. A comparison is made between these seismic slenderness limits and the limits available in the design codes.

Variable amplitude cyclic pure bending tests to determine fully ductile section slenderness limits for cold-formed CHS

This paper describes an experimental investigation of the cyclic inelastic flexural behaviour of cold-formed circular hollow section (CHS) beams. Controlled-rotation, symmetrical cyclic bending tests were performed using a variable amplitude loading history on different sizes of compact CHS with diameter-to-thickness ( D / t ) ratios ranging from 20 to 40. The CHS beams exhibited stable hysteresis behaviour up to local buckling and then showed considerable degradation in strength and ductility depending on the D / t ratio. Seismic capacity parameters are presented including strength, stiffness, hysteresis loops and modes of failure for each specimen. Peak moments obtained in the cyclic tests were compared with those obtained in monotonic and cyclic tests published previously and also with design moments predicted using a number of steel specifications. New section slenderness limits suitable for the design and construction of seismic resisting structural systems were determined. A comparison is made between these seismic slenderness limits and the limits available in the design codes. The effect of the number of cycles on ductility and energy absorption is examined.

Analysis of circular cross-section element, loaded by static and cyclic elastic–plastic pure bending

Data of theoretical and experimental investigation of a circular cross-section element subjected to monotonic and cyclic elastic–plastic pure bending is presented in the paper. Linear approximation of monotonic and cyclic tension–compression curves was applied, what allowed to simplify analysis and to obtain satisfactory conformance of theoretical data with experimental results. Grade 45 structural steel specimens were subjected to low cycle stress or strain-controlled reversed tension–compression and cyclic pure bending. In case of strain-controlled loading low cycle fatigue life curves for both loading models (tension–compression and bending) coincide. In case of stress-controlled bending elastically deformed internal fibers of the element impede the plastic–strain accumulation in the external fibers, and in such a way decrease the quasi-static damage accumulation, and increase the lifetime. In this research specimens lifetime was calculated by use of fatigue damage fraction and quasi-static damage fraction summation rule. The damage calculations allowed to establish the increase of fatigue life at stress-controlled low cycle bending.

Concrete-filled steel circular tubes subjected to constant amplitude cyclic pure bending

This paper describes an experimental investigation of the cyclic inelastic flexural behaviour of concrete-filled tubular (CFT) beams made of cold-formed circular hollow sections and filled with normal concrete. Cyclic bending tests were performed using a constant amplitude loading history on different CFT specimens with diameter-to-thickness ratios ( D/ t) ranging from 20 to 162. The CFT beams exhibited stable hysteresis behaviour up to the formation of plastic ripples and then showed considerable degradation in stiffness, strength, and ductility depending on the D/ t ratio. Seismic capacity parameters are presented including strength, stiffness, rotation capacity, hysteresis loops and modes of failure of the specimens. Peak moments obtained in the cyclic tests are compared with those obtained previously in monotonic tests and also with design moments predicted using the available design rules for composite beams. The deformation ductility demand was determined and used to derive new fully ductile section slenderness limits suitable for seismic design.

Degradation and Buckling of I-Beams under Cyclic Pure Bending

This paper presents experimental and numerical results of the elasticplastic response and buckling of S3 x 5.7 steel and aluminum I-beams subjected to cyclic pure bending. A special 4-point bending device was designed and built for this purpose. The emphasis of the work is on the description of the response and buckling of the beams. The numerical results were obtained using a commercial finite element program that implements the nonlinear kinematic hardening plasticity model. Results indicate that the beams considered, most of which had length-to-height ratio of 5, buckled first in a global mode involving either twisting or lateral deflections of the beams. The prevailing deflection mode seems to be determined by the nature of the initial geometric imperfections. The deformations induced by the global deflections could induce a local buckle at mid-span. The finite element predictions yield results that qualitatively reproduce the development of most of the aspects of the response of the beams, but generally at a slower rate.

Buckling of T-beams under cyclic bending

This paper presents the results of an experimental study of the response and stability of elastic-plastic T-beams under cyclic pure bending, with emphasis on local buckling. The objectives of the study were to determine the evolution of instabilities and to find parameters useful to determine the degree of damage incurred during cycling. All specimens were subjected to a quasi-static curvature symmetric loading history of constant amplitude. The results indicate that, in the range of curvature amplitudes considered, structural degradation was mainly due to progressive growth of a ripple in the lateral deflection of the web. The unstable growth of one of the features of this ripple led to the formation of a local buckle, which caused a marked reduction in the moment capacity of the specimens. Further cycling resulted in fracture of the web at the local buckle. The best indicator of degradation was a measure of the amplitude of the ripple in the lateral deflection of the web. This measure could be used to generate a criterion for assessing the current state of the specimens in relation to their useful life under cyclic bending.

Degradation and collapse of square tubes under cyclic bending

This paper presents the results of an experimental investigation of the elastic–plastic degradation and collapse of steel tubes with square cross-section under cyclic pure bending in a curvature symmetric fashion. The results indicate that the structural performance of the tubes degrades due to the growth of periodic, transverse deflections in their flanges. The wavelength of these deflections is equal to the wavelength of the buckling mode of the tubes under monotonic pure bending. Persistent cycling induces localization of the amplitude of these deflections and leads to the formation of a kink in one of the flanges. This causes collapse of the tube.

Installation for fatigue testing during cyclic pure bending : Dolgushev, A.A., Kurteev, V.F. Dubrov, V.N. and Vasilevich, D.I. Industrial Laboratory (Russia) (Sept. 1993) 59 (3), 320–322

A finite element methodology for thermo-mechanical fatigue analysis of a subcritical power plant outlet header under realistic loading conditions is presented. The methodology consists of (i) a transient heat transfer model, (ii) a sequential anisothermal cyclic viscoplastic model and (iii) a multiaxial, critical-plane implementation of the Ostergren fatigue indicator parameter. The methodology permits identification of the local thermo-mechanical stress–strain response at critical locations and prediction of fatigue life and cracking orientation for complex transient, anisothermal, cyclic elastic–plastic-creep material behaviour. Measured plant data, in the form of steam and pipe temperature transients and steam pressure data, are employed to identify heat transfer constants and validate the predicted thermal response, with particular attention given to plant start-up and attemperation effects. The predictions indicate out-of-phase temperature-strain response at the header inside surface and in-phase response on the outside surface. Cooling transients are predicted to control damage and crack initiation at the inner bore, whereas heating transients are predicted to have a more damaging effect at weld locations. A representative test cycle is presented, which is shown to capture the salient thermo-mechanical cyclic damage of the realistic cycle. The predicted results correlate well with industrial experience in terms of crack (initiation) orientation, location and life.