Experimental investigations into the influence of cyclic phenomena of metals on structural ratchetting behaviour

The results of experiments on 2-bar structures of 99.9% copper are compared with the prediction of classical plasticity models for loading histories which simulate the effects of thermal cycling in the presence of constant primary loading. Two material phenomena, cyclic hardening and material ratchetting, are shown to have important effects upon cyclic strain growth. Neither of these effects are contained in classical plasticity models. The steady state growth of strain due to material ratchetting is modelled in a simple way. An approximate solution method, based on the “rapid cycle” method for creep analysis, is shown to give a good prediction of the experimental data.     

Influence of hardening rule on the elasto-plastic behaviour of a simple structure under cyclic loading

The modes of cyclic elasto-plastic deformation of a two-bar structure with unequal areas and lengths under the simultaneous action of sustained mechanical load and cyclic thermal history are investigated analytically using three types of elasto-plastic material models: perfectly plastic, linear kinematic hardening and linear isotropic hardening. This simple structure is shown to exhibit much of the behaviour of interest in design of structural components subjected to repeated thermal loads: viz, elastic shakedown, reversed plasticity and ratcheting. The cyclic plastic behaviour of the structure is developed in closed form and the effects of strain hardening, hardening rule and geometrical parameters of the two-bar assembly on the deformation modes are critically examined.     

Kinematic hardening analysis of ratchet strain in the “pulley test”

The classical Bree problem—which represents an uniaxial model of a thin tube subjected to combined internal pressure and cyclic thermal stress across its wall—can be simulated by means of the pulley test in which a wire or strip specimen is subjected to combined steady tensile stress and cyclic bending stress. In this paper, accumulation of ratchet strain in the pulley test is investigated using a linear kinematic hardening material model from which perfect plasticity can be generated as a special case. The results of the investigation show that asymptotic ratchet strains are linearly related to the excess in mean stress σ_D above its value σ*_D at the ratchetting limit regardless of the thermal stress amplitude. Comparisons with test results on copper wire specimens—which exhibit non-linear hardening rate—confirm the qualitative validity of this simple relation. Deviations between theory and experiment are attributed to metallic cyclic creep. Further, perfect plasticity results are shown to be well predicted by a linearized lower bound estimate.     

A two surface plasticity model for the simulation of uniaxial ratchetting response

In this study, a two surface plasticity model was developed and used to simulate the uniaxial ratchetting response of CS 1026 steel. Most cyclic plasticity models used in ratchetting simulations are Chaboche-type nonlinear kinematic hardening models, which deal with dynamic recovery terms considering the back stress tensor. This paper describes the ratchetting simulation of steel by the two surface model based on yield theory following both isotropic and kinematic hardening rules in order to obtain enhanced ratchetting response. The parameters used in the simulation were obtained from a parametric study and were determined from the initial range and stabilized range of CS 1026 steel. In addition, the two surface model was validated by comparing the results of a ratchetting simulation with experimentally determined maximum axial strain per cycle. The ratchetting responses obtained from the two surface model are an improved simulation results compared with results from bilinear and kinematic hardening models.     

Cyclic loading of beams based on the Prager and Frederick–Armstrong kinematic hardening models

The kinematic hardening theory of plasticity based on the Prager and Frederick–Armstrong models are used to evaluate the cyclic loading behavior of a beam under the axial, bending, and thermal loads. The beam material is assumed to follow non-linear strain hardening property. The material's strain hardening curves in tension and compression are assumed to be both identical for the isotropic material and different for the anisotropic material. A numerical iterative method is used to calculate the stresses and plastic strains in the beam due to cyclic loadings. The results of the analysis are checked with the known experimental tests. It is concluded that the Prager kinematic hardening theory under deformation controlled conditions, excluding creep, results into reversed plasticity. The load controlled cyclic loading under the Prager kinematic hardening model with isotropy assumption results into reversed plasticity. Under anisotropy assumption of tension/compression curve, this model predicts ratcheting. On the other hand, the Frederick–Armstrong model predicts ratcheting behavior of the beam under load controlled cyclic loading with non-zero mean load. This model predicts reversed plasticity under the load controlled cyclic loading with zero mean load, and deformation controlled cyclic loading.     

A model of one-surface cyclic plasticity and its application to springback prediction

This paper presents an elasto-plastic constitutive model based on one-surface plasticity, which can capture the Bauschinger effect, transient behavior, permanent softening, and yield anisotropy. The combined isotropic-kinematic hardening law was used to model the hardening behavior, and the non-quadratic anisotropic yield function, Yld2000-2d, was chosen to describe the anisotropy. This model is closely related to the anisotropic non-linear kinematic hardening model of Chun et al. [2002. Modeling the Bauschinger effect for sheet metals, part I: theory. International Journal of Plasticity 18, 571-95.]. Different with the model, the current model captures in particular permanent softening with a constant stress offset as well as the Bauschinger effect and transient behavior under strain path reversal. Inverse identification was carried out to fit the material parameters of hardening model by using uni-axial tension/compression data. Springback predicted by the resulting material model was compared with experiments and with material models that do not account for permanent softening. The results show that the resulting material model has a good capability to predict springback.     

The effect of axial loading and axial restraint on the thermal ratchetting of thin tubes

The finite element method has been used to investigate the thermal ratchetting behaviour of thin tubes subjected to steady, internal pressure and cyclic, linear, through-thickness temperature distributions. An elastic-perfectly plastic material behaviour model was used and uniaxial behaviour was related to multiaxial behaviour via the von Mises yield criterion and the Prandtl-Reuss flow rule. Results for a tube without axial stress, a tube with axial stress (corresponding to a tube with an end closure) and a tube constrained to have no axial strain, are presented. Correlations with a simplified analytical solution were attempted. Good correlations were obtained for the tubes without axial restraint. The correlation for the axially constrained tube was poor because the thermal loading is essentially different. In the case of the axially constrained tube, if the thermal load is high enough, yielding occurs through the whole of the wall thickness simultaneously in each half cycle. This is not possible in the other two cases considered.     

Evaluation of cyclic plasticity models of multi-surface and non-linear hardening by an energy-based fatigue criterion

This study examines the performance of four constitutive models according to capacity in predicting metal fatigue life under proportional and non-proportional loading conditions. These cyclic plasticity models are the multi-surface models of Mroz and Garud, and the non-linear kinematic hardening models of Armstrong-Frederick and Chaboche. The range of abilities of these models is studied in detail. Furthermore, the plastic strain energy under multiaxial fatigue condition is calculated in the cyclic plasticity models by the stress-strain hysteresis loops. Using the results of these models, the fatigue lives that have set in the energy-based fatigue model are predicted and evaluated with the reported experimental data of 1% Cr-Mo-V steel in the literature. Consequently, the optimum model in the loading condition for this metal is chosen based on life factor.     

The effect of ‘material ratchetting’ on the incremental growth of beams subjected to steady axial loads and cyclic bending

An elastic-plastic material behaviour model capable of predicting material ratchetting, cyclic relaxation and cyclic hardening has been incorporated into finite element programs. The resulting programs have been used to predict the behaviour of beams subjected to the steady axial loads and cyclic bending. The results are compared with experimental data obtained from three tests performed on beams made from a model material. Overall, the predictions were found to be good; discrepancies in the results for the most highly loaded beam were attributed to creep effects in the experiment.The results indicate that an elastic-perfectly plastic material behaviour model, with an equivalent yield stress, does not allow acceptable prediction of the beam behaviour to be obtained.     

Effect of kinematic hardening on localized necking in biaxially stretched sheets

For elastic-plastic sheets under biaxial stretching localized necking is investigated assuming that the material follows a kinematic hardening rule. The investigation is mainly based on the plane stress approximation, but includes a few results obtained in the context of the three-dimensional theory. It is found that the forming limit curves predicted by kinematic hardening are in far better agreement with experimental results than the similar curves predicted by standard flow theory with isotropic hardening. For a high hardening material quite good agreement is obtained with predictions of deformation theory of plasticity, which may be considered as a simple model of a solid that develops a vertex on the yield surface.     

小变形循环载荷下Q235材料特性的试验研究

为进一步挖掘材料的承载能力,以焊接结构常用材料Q235为研究对象,通过应变控制下的循环加载试验,得到了Q235在小变形量循环载荷作用下的应力应变曲线及特征,应力随循环周次的变化规律,并给出了相应的数学模型。试验结果表明,Q235在小应变对称循环载荷作用下表现出循环硬化特性和包申格效应,随循环周次的增加,循环硬化速率和包申格能量参数变化率最终均会达到一个稳定值;Q235在小应变非对称循环载荷作用下的变形特征,可以看作是其对应变初值和对称应变循环载荷叠加作用的响应,且随循环周次的增加,材料响应应力峰值与屈服应力逐渐回归于相同幅值对称应变作用下的相应数值。     

Inelastic behaviour of rectangular beams subjected to steady axial load and cyclic bending

Analytical and numerical solutions are given for the inelastic behaviour of a rectangular cross-section beam, subjected to a steady axial load and cyclic, fully reversed load-controlled bending. Elastic-perfectly plastic, linear isotropic and kinematic materials are examined and solutions for the strain accumulation and cyclic reverse plastic strains obtained. Also the effect of introducing a creep dwell period into the cycle is considered.     

内压弯管在面内循环弯曲载荷作用下棘轮效应的研究

利用多轴试验机研究了内压及面内循环弯曲载荷作用下低碳钢弯管的棘轮效应。试验研究表明最大棘轮应变发生在顶线位置的环向。对于个别试件,内缘线位置也发现了环向棘轮应变,但所有试件的外缘线位置均未发现棘轮应变。内压不变时棘轮应变速率随面内循环弯曲载荷的增大而增大;面内循环弯曲载荷不变时,棘轮应变速率随内压的增大而增大。通过用户编程,采用Chen—Jiao—Kim随动强化模型,利用弹塑性有限元法对弯管进行了循环塑性分析。与试验结果相比,Chen—Jiao—Kim随动强化模型能给出较好的预测。采用C—TDF提出的等效塑性应变增量控制法确定了结构的棘轮边界。     

Surface instabilities on statically strained plastic solids

An exploratory study is carried out of various aspects of the development of instabilities of traction-free surfaces of statically strained, rate-independent elastic-plastic solids. Existence of surface instabilities as predicted by either a bifurcation analysis or a quasi-static, imperfection-growth analysis, is found to be strongly dependent on the type of constitutive law assumed. In most instances no instabilities are found using the standard plastic flow law based on a smooth yield surface and isotropic hardening. Instabilities are predicted when a finite strain deformation theory is assumed. These are documented for a full range of proportional overall straining histories using a bifurcation analysis. A finite element analysis employing a corner theory of plasticity is used to study the non-linear growth of the instabilities starting from small initial surface undulations for the case of plane strain deformation. Some experimental observations of surface irregularities which may be due to surface instabilities are reported and discussed.     

Influence of reverse yielding on residual stresses induced by autofrettage

The paper investigates the influence of reverse yielding on residual stresses induced by autofrettage. On the basis of reverse loading tests, a material model is developed and implemented into analytical procedures capable of treating the elasto-plastic deformation behaviour of thick-walled tubes during both loading and unloading phases. The results show that residual hoop stresses are drastically reduced near the tube bore as compared with residual stresses obtained from conventional isotropic hardening analysis. Pure kinematic hardening analysis is also shown to overestimate residual hoop stress induced by autofrettage.     

Stress analysis of the strain rate hardening materials in axially symmetric field

This paper presents an analysis of a circular hollow cylinder composed of strain rate hardening plastic material subjected to a sudden internal pressure loading. Materials satisfying the constitutive relation, and Levy-Mises equation are considered in the analysis. Dynamic and static analyses of axially symmetric material loaded under plane strain condition are described. The paper discusses the effect of strain rate hardening exponent, m, on the dynamic and static plastic response in the axially symmetric medium. A method is presented for the determination of the strain rate hardening exponent by measuring the hoop stress on the outer surface of a thin cylindrical specimen using the static solution.     

Reproducing hoop stress–strain behavior for tubular material using lateral compression test

Identification of material properties in the hoop direction, such as stress–strain behavior, is essential in tube hydroforming processes. Conventional tests such as uniaxial tension and compression tests have some drawbacks and limitations. In the current investigations a simple technique to identify the stress–strain behavior in the hoop direction for tubular material is introduced, based on the experimental data obtained from tube lateral compression test. In the proposed technique, an assumed stress–strain curve is used in finite element simulation to predict the load deflection curve of the tube lateral compression. An iterative algorithm is used to compare the calculated and experimental load deflection curves until a good agreement with a percentage deviation less than 4% is obtained. The suggested technique was used to obtain the material properties of Cu–40%Zn brass tube. The predicted stress–strain curve was compared with that obtained from uniaxial compression test. Comparison between the experimental and predicted stress–strain curve showed that the proposed technique is effective in the prediction of the material properties from the tube lateral compression test with percentage deviation less than 1%.