Elasto‐plastic analysis of thin‐walled tube under cyclic bending

Abstract

The elasto‐plastic endochronic theory is extended to describe the material behavior of tubes under cyclic bending. Experimental data of cyclic bending of 6061‐T6 aluminum and 1018 steel was used for comparison. It is shown that by using the complete differential equations of the theory and by assuming a linear relation between the strain and the curvature, the theory is capable of predicting the moment‐curvature response.     

Uniaxial ratchetting in steels with different cyclic softening/hardening behaviours

The cyclic deformation of three structural steels, SS316L stainless steel, 40Cr3MoV bainitic steel and 25CDV4.11 steel, were studied experimentally by uniaxial cyclic straining or stressing tests at room temperature. The cyclic softening/hardening behaviours of the steels were discussed first by cyclic straining tests; and then the effects of cyclic softening/hardening behaviours on the uniaxial ratchetting of the materials were investigated by asymmetrical cyclic stressing tests. It is concluded from the experimental results that the ratchetting greatly depends on the cyclic softening/hardening behaviours of the materials, as well as the loading history. Different ratchetting and failure behaviours are observed for the prescribed steels. It is also stated that the proposed unified visco‐plastic constitutive model can provide a fairly reasonable simulation of the uniaxial ratchetting of SS316L stainless steel and 25CDV4.11 steel; but cannot simulate the ratchetting of 40Cr3MoV bainitic steel since the dependence of cyclic softening behaviours on the applied inelastic strain amplitude cannot be reasonably described in the discussed constitutive model. Some significant conclusions are obtained, which are useful to construct constitutive model to describe the ratchetting of the materials with different cyclic softening/hardening behaviours.     

Collapse of elliptical-notched circular tubes under cyclic bending

In this paper, an experimental investigation of the response and collapse of elliptical-notched tubes subjected to cyclic bending is discussed. It was found from moment-curvature curves that the loops show cyclic hardening and gradually steady after a few cycles. The ovalization-curvature curves show an unsymmetrical, ratcheting and increasing manner with the number of cycles. Based on the experimental relationship between the controlled curvature and the number of cycles necessary to produce buckling, the empirical formulation proposed by Kyriakides and Shaw in 1987 was modified for simulating the aforementioned relationship. In addition, it was found that the experimental curve of the ovalization and the number of cycles could be divided into three stages. The empirical relationship proposed by Chang and Pan in 2009 was modified for simulating the aforementioned curve of the initial and secondary stages. It has been shown that the simulations were in good agreement with the experimental data.     

Study on bending fretting fatigue of LZ50 axle steel considering ratchetting by finite element method

Based on the finite element simulation, the crack nucleation location and failure life of bending fretting fatigue are analysed and predicted for LZ50 axle steel, respectively. In the simulation, a simplified two‐dimensional finite element model with an equivalent normal force is proposed and the role of ratchetting is also considered by using a new cyclic elastoplastic constitutive model. The crack nucleation location and fatigue life are finally predicted by Smith–Watson–Topper (SWT) critical plane criteria referring to the finite element calculation. It is shown that the predicted results are in fairly good agreement with the experimental ones.     

Growing and critical ovalization for sharp-notched 6061-T6 aluminum alloy tubes under cyclic bending

In this paper, we present results from experiments dealing ovalization in 6061-T6 aluminum alloy tubes which have been notched and subjected to cyclic bending are presented. It was discovered that the tubes continuously ovalized to a critical quantity when they buckled. Tubes with a smooth surface and five different notch depths were considered. The ovalization–curvature curve exhibited a symmetrical and ratcheting increase with the number of bending cycles. Deeper notch depths caused greater ovalizations. In addition, the trend of the ovalization at negative extreme curvature and number of bending cycles relationship was distinguished into three stages. Finally, the empirical form proposed by Lee, Hung, and Pan in 2010 was employed for describing the above-mentioned correlation in the first two stages. It was found that the experimental and simulated data agreed quite well.     

Deformation analysis of notched components and assessment of approximate methods

Finite element modelling was conducted on notched members subjected to proportional and non-proportional loading. A recently developed cyclic plasticity model capable of accurately describing cyclic material behaviour was implemented into a finite element code. A plate with a central hole and a shaft with a circumference groove were studied. Approximate methods for the notched problems were critically evaluated using the finite element results.     

Non-proportional multiaxial transformation ratchetting of super-elastic NiTi shape memory alloy: Experimental observations

Experimental observations are reported for the non-proportional multiaxial transformation ratchetting of super-elastic NiTi shape memory alloy performed under the stress-controlled cyclic tension–torsion loading conditions and at room temperature. The effect of axial mean stress on the evolutions of transformation ratchetting strain and dissipation energy per cycle during the cyclic tests is discussed firstly; and then the dependence of multiaxial transformation ratchetting on the different non-proportionally loading paths (e.g., linear, square, hourglass-typed, butterfly-typed, rhombic and octagonal paths) is investigated. The results show that the multiaxial transformation ratchetting occurs mainly in the axial direction because only the non-zero axial mean stress is used and the mean shear stress is set to be zero in the all prescribed multiaxial loading paths; and the axial peak and valley strains increase with the increasing axial mean stress and also depend significantly on the shapes of loading paths. Comparison with the corresponding uniaxial ones illustrates that the multiaxial stress states are more helpful to promote the development of transformation ratchetting, especially for the non-proportional ones.     

钢管混凝土轴压构件耗能计算及单位体积耗能公式建立

提出了计算钢管混凝土轴压构件材料阻尼的新方法,根据Lazan材料阻尼与应力关系的理论研究,计算弹性阶段钢管混凝土构件在轴向重复荷载下的滞回曲线包围面积,得到钢管混凝土材料单位体积损耗能量。结果表明,单位体积损耗能量随最大应力幅值的提高而增大,且随混凝土强度和截面含钢率增大而减小。通过SPSS统计分析软件回归建立了钢管混凝土构件在轴向重复荷载下材料单位体积耗能与最大应力幅值、混凝土强度和截面含钢率的关系式。为进一步准确分析钢管混凝土结构动力性能及进行钢管混凝土结构的抗震分析打下了基础。     

Limit load analysis of strength undermatched welded T-joints under bending

An increasing amount of laser beam welded T‐joints (e.g. skin‐stringer) of aluminium alloys are now in use in advanced fuselage applications designed as ‘integral structures’ for weight and cost savings. It is known that weld joints generally show lower strength (undermatching) than base metal in both laser beam and friction stir welded joints of 6xxx series Al‐alloys. Damage tolerance considerations in terms of the residual strength of such joints require limit load solutions to be used in engineering fitness‐for‐service (FFS) analysis. The paper, therefore, provides an upper bound limit load solution in closed form for welded T‐joints (idealized) with strength undermatching and subject to a bending moment. In addition to the necessary requirements of the upper bound theorem, the kinematically admissible velocity field chosen leads to a stress field, which satisfies the equilibrium equations and some stress boundary conditions in the plastic zone. This is an advantage of the solution and, therefore, it is expected that the upper bound obtained is close to the exact limit load of such joints.     

Nonlinear fatigue crack propagation in a baffle module of Wendelstein 7‐X under cyclic bending loads

Simulation of the fatigue crack propagation in a Wendelstein 7‐X baffle module is performed in this study using both a finite element method‐based software and the UniGrow nonlinear model for small‐scale yielding (SSY) conditions. Some experimental fatigue tests of several cracked baffle modules have been performed through a servo‐hydraulic machine. One of these experimental tests has been considered to simulate fatigue crack propagation in the baffle module. Before starting the experimental test, a first crack partly contained in the welding seam and partly in the steel pipe is found. Subsequently, owing to the applied load, the crack propagated both into the welding seam and into the steel pipe until the plastic zone in the near field attains SSY conditions. Finally, owing to the increase in the extension of the plastic zone, SSY conditions are not more valid, and the breakage of the steel pipe is produced by plastic collapse.     

Creep and shrinkage analysis of composite systems under axial load and biaxial bending

The instantaneous and creep and shrinkage behaviour of composite steel-concrete sections subjected to axial load and biaxial bending is examined analytically using the age-adjusted effective modulus method and a stress relaxation procedure. Any cross-section that can be discretized in rectangular elements can be analysed using the approach described in this study. Material non-linearities (concrete cracking and crushing as well as steel yielding) are included in the formulation by empolying an interative numerical procedure. The analytical method was implemented in a computer program and case studies demonstrate that composite columns under complex loads experience a considerable redistribution of stresses and strains, causing the degree of cracking and the secondary load effects (P-delta) to increase.     

Techniques for the investigation of the ratchetting behaviour of piping components under internal pressure and simulated seismic loading

The ratchetting behaviour of piping components under internal pressure and simulated seismic loading has been investigated using special fixtures and a standard laboratory universal testing machine fitted with a fatigue module. Experimental arrangements are presented for testing plain pipes with or without thinned sections, elbows and tee branch junctions under in-plane dynamic bending; similar fixtures and arrangements could be used for reducers and flanged connections and other types of loadings. Input accelerations up to 5g have been achieved and the results demonstrate that a great deal can be learnt about piping component behaviour from such simple arrangements and without resorting to sophisticated or expensive experimental techniques. The necessary instrumentation and algorithms for the analysis of results are described. Some sample results are included and discussed in terms of overall piping component behaviour. Two recommendations are suggested to more realistically simulate typical earthquake input spectra.     

Linear matching method on the evaluation of plastic and creep behaviours for bodies subjected to cyclic thermal and mechanical loading

On the basis of the previously proposed Linear Matching Method (LMM), a new LMM model and its corresponding numerical procedure are developed in this paper to allow for the evaluation of plastic, creep and ratchet strains of structures subjected to a general load condition in the steady cyclic state. The constant and varying residual stress fields associated with differing mechanisms are obtained as well as the steady cyclic stress state of the whole component for further structural design and assessment. The total strain range for use in fatigue assessment, including the effect of creep and plastic strains, is obtained. A typical example of 3D holed plate subjected to cyclic thermal load and constant mechanical load is analysed here in detail to verify the applicability of the proposed numerical technique. The LMM results in the paper are compared with those obtained by ABAQUS step‐by‐step inelastic analyses. This comparison demonstrates that the LMM has both the advantage of programming method and the capacity to be implemented easily within a commercial finite element code, in this case ABAQUS. The LMM provides a general‐purpose technique for the evaluation of creep/fatigue interaction in the steady cyclic state. Copyright © 2006 John Wiley & Sons, Ltd.     

基于三维梁理论的复合材料层合管等效抗弯刚度

针对任意铺层形式和任意壁厚复合材料圆形层合管件,提出一种等效抗弯刚度的计算方法。此方法采用符合复合材料圆形管件梁真实变形的变形理论,考虑横向剪切变形,非均匀扭转效应,主、次挠曲效应和层合材料的三维弹性效应,按照壳壁中实际应力状态,建立了复合材料圆形管件等效抗弯刚度的计算模型。通过与4种铺层管件的三点弯曲实验结果以及经典层合板理论计算的等效抗弯刚度进行对比,验证了计算模型的正确性。通过退化与各向同性材料抗弯刚度的计算方法进行对比,分析了计算模型的适用性。      

Experimental study on the whole‐life heterogeneous ratchetting and ratchetting‐fatigue interaction of SUS301L stainless steel butt‐welded joint

Uniaxial fatigue tests of butt‐welded joint, made from SUS301L stainless steel, were carried out under asymmetric stress‐controlled cyclic loading conditions in this work. The effects of stress amplitude and mean stress on the whole‐life heterogeneous ratchetting and fatigue life of the butt‐welded joint were investigated, respectively, for the specified subzones. The experimental observations show that the whole‐life inhomogeneous ratchetting strain concentrating in a specific fusion zone (denoted as the FZ‐1 subzone) of the welded joint becomes more significant as the stress level increases; the fatigue failure also occurs in the FZ‐1 subzone, and the fatigue life depends on both the applied mean stress and stress amplitude and is determined by the combination of ratchetting damage and fatigue one in the localized FZ‐1 subzone.     

Sensitivity calibration of post-yield strain gauges under cyclic plastic straining

A plastic sensitivity calibration procedure is outlined for strain gauges under cyclic, four point bending. Tests show that the gauge resistance changes in an approximately linear manner with longitudinal strain for the first quarter cycle of loading. Calibration curves for subsequent reversals to the direction of deformation display zero-shift and non-linearity. Under balanced strain cycling, there is evidence of a cyclically-stable, sensitivity calibration loop. Theoretical considerations are given in which it is proposed that separate sensitivity factors apply to the elastic and plastic components of strain. It is shown that the plastic sensitivity factor is a function of (i) plastic strain induced hardening and softening in the gauge foil and (ii) any apparent change to the gauge resistivity due to imperfect bonding. The elastic component sensitivity factor equals the manufacturer's value only in the absence of hardening. The two sensitivities may be combined to give a total sensitivity factor when a post-yield strain gauge suffers elastic-plastic straining.     

格栅夹层梁的热弯曲变形

考虑内部热传导,研究了格栅夹层梁一侧受热后的弯曲变形.认为变形后夹层结构中间腹板无弯曲.利用格栅夹层梁结构上的周期性,通过胞元结构的内力平衡方程和变形协调关系,得到了胞元两端内力和位移的关系.引入传递矩阵,建立了夹层梁内力和变形随温度变化的表达式.应用所建立的模型计算了悬臂格栅夹层梁在其上表面受热后的变形.在格栅夹层梁包含的胞元数量较多、腹板高度较小且厚度与表板厚度相近的情况下,由本文模型计算得到的挠度结果与有限元结果吻合较好.     

Effects of grain size on cyclic plasticity and fatigue crack initiation in nickel

Fatigue experiments were conducted on polycrystalline nickel of two grain sizes, 24 and 290 μm, to evaluate the effects of grain size on cyclic plasticity and fatigue crack initiation. Specimens were cycled at room temperature at plastic strain amplitudes ranging from 2.5×10⁻⁵ to 2.5×10⁻³. Analyses of the cyclic stress–strain response and evolution of hysteresis loop shape indicate that the back stress component of the cyclic stress is significantly affected by grain size and plastic strain amplitude, whereas these parameters have little effect on friction stress. A nonlinear kinematic hardening framework was used to study the evolution of back stress parameters with cumulative plastic strain. These are related to substructural evolution features. In particular, long range back stress components are related to persistent slip bands. The difference in cyclic plasticity behavior between the two grain sizes is related to the effect of grain size on persistent slip band (PSB) morphology, and the effect this has on long range back stress. Fine grain specimens had a much longer fatigue life, especially at low plastic strain amplitude, as a result of the influence of grain size on fatigue crack initiation characteristics. At low plastic strain amplitude (2.5×10⁻⁴), coarse grain specimens initiated cracks where PSBs impinged on grain boundaries. Fine grain specimens formed cracks along PSBs. At high plastic strain amplitude (2.5×10⁻³), both grain sizes initiated cracks at grain boundaries.     

Sickle-shaped surface crack in a notched round bar under cyclic tension and bending

A sickle-shaped surface crack, also called crescent-moon (or crescent) crack, is assumed to exist at the root of a circular-arc circumferential notch in a round bar under tension and bending. For different notch sizes (i.e. different values of the stress concentration factor), the stress intensity factor along the crack front is computed through a three-dimensional finite-element analysis. The effect of the stress concentration factor on the stress intensity factor values is examined for several crack configurations. Finally, the surface crack growth under cyclic loading is analysed through a numerical procedure that employs the stress intensity factor values obtained. Some results of the present study are compared with those by other authors.