304不锈钢室温和高温单轴循环塑性的实验研究

对304不锈钢进行了室温和高温单轴应变控制和应力控制下的系统循环试验。揭示和分析了循环应变幅值、平均应变及其历史和温度历史对材料应变循环特性的影响以及应力幅值、平均应力及其历史以及温度对循环棘轮行为的影响。也讨论了应变循环和应力循环间交互作用对材料循环塑性行为的影响。研究表明,无益单轴应变循环特性还是非对称单轴应力循环下的棘轮效应不仅取决于当前温度和加载状态,而且强烈依赖于其加载历史。研究得到了一些有助于304不锈钢室温和高温单轴循环行为本构描述的结果。     

Uniaxial and non-proportionally multiaxial ratcheting of SS304 stainless steel at room temperature: experiments and simulations

The uniaxial and non-proportionally multiaxial ratcheting behaviors of SS304 stainless steel at room temperature were initially researched by experiment and then were theoretically described by a cyclic constitutive model in the framework of unified visco-plasticity. The effects of cyclic stress amplitude, mean stress, and their histories on the ratcheting were experimentally investigated under uniaxial and different multiaxial loading paths. The shapes of non-proportional loading paths were linear, circular, elliptical and rhombic, respectively. In the constitutive model, the rate-dependent behavior of the material was reflected by a viscous term; the cyclic flow and cyclic hardening behaviors of the material under asymmetrical stress-controlled cycling were reflected by the evolution rules of kinematic hardening back stress and isotropic deforming resistance, respectively. The effect of loading history on the ratcheting was also considered by introducing two fading memorization functions for maximum inelastic strain amplitude and isotropic deformation resistance, respectively, into the constitutive model. The effect of multiaxial loading path on the ratcheting was reflected by a non-proportional factor defined in this work. The predicting ability of the developed model was proved to be good by comparing the simulations with corresponding experiments.     

退火和调质42CrMo合金钢单轴循环塑性行为的实验研究

在室温下对退火和调质42CrMo合金钢进行了单轴应变控制和应力控制的系统循环实验,并对它们的应变循环和应力循环特性进行比较.揭示和分析了应变幅值、平均应变及其历史对材料应变循环特性的影响以及应力幅值、平均应力及其历史对棘轮行为的影响.讨论了应变循环和应力循环间的交互作用以及不同热处理工艺下材料循环变形行为间的区别.研究发现材料的热处理工艺、平均应力和应力幅值及其历史对材料的棘轮行为都有很大的影响.得到了一些有助于进行合理本构描述的结果.     

Uniaxial ratcheting of SS304 stainless steel at high temperatures: visco-plastic constitutive model

The uniaxial ratcheting of SS304 stainless steel at high temperatures (300, 600 and 700 °C) were analyzed experimentally, and described by a cyclic constitutive visco-plasticity model. The rate dependence of the material was accounted for by introducing a viscous term. The cyclic hardening and cyclic flow behavior of the material under asymmetrical stress-controlled cycling were described by the evolution rules of kinematic hardening back stress and isotropic deforming resistance. Under the isothermal condition, temperature effect was included by terms involving temperature in the evolution equations of isotropic deforming resistance. The effect of load history on ratcheting was also considered by introducing a fading memory function of the maximum inelastic strain amplitude and isotropic deformation resistance. After the material constants were determined from the experimental data, the uniaxial ratcheting of SS304 stainless steel was numerically simulated and compared with the corresponding experimental results at high temperatures. The predicted results agree well with the experimental ones.     

循环软化45碳钢和循环硬化304不锈钢的棘轮行为实验研究

对循环软化45碳钢的单轴应力循环下的平均应力、应力幅值以及先前应变循环对棘轮效应的影响进行了实验研究;并对循环硬化的304不锈钢进行了多种非比例循环加载路径下路径形状、路径等效应力幅值、平均应变与平均应力对材料棘轮变形行为的影响实验．发现平均应力和应力幅值及其历史对于材料的棘轮行为都有很大的影响．     

Benchmark experiments and characteristic cyclic plasticity deformation

Key issues in cyclic plasticity modeling are discussed based upon representative experimental observations on several commonly used engineering materials. Cyclic plasticity is characterized by the Bauschinger effect, cyclic hardening/softening, strain range effect, nonproporitonal hardening, and strain ratcheting. Additional hardening is identified to associate with ratcheting rate decay. Proper modeling requires a clear distinction among different types of cyclic plasticity behavior. Cyclic hardening/softening sustains dependent on the loading amplitude and loading history. Strain range effect is common for most engineering metallic materials. Often, nonproportional hardening is accompanied by cyclic hardening, as being observed on stainless steels and pure copper. A clarification of the two types of material behavior can be made through benchmark experiments and modeling technique. Ratcheting rate decay is a common observation on a number of materials and it often follows a power law relationship with the number of loading cycles under the constant amplitude stress controlled condition. Benchmark experiments can be used to explore the different cyclic plasticity properties of the materials. Discussions about proper modeling are based on the typical cyclic plasticity phenomena obtained from testing several engineering materials under various uniaxial and multiaxial cyclic loading conditions. Sufficient experimental evidence points to the unambiguous conclusion that none of the hardening phenomena (cyclic hardening/softening, strain range effect, nonproportional hardening, and strain hardening associated with ratcheting rate decay) is isotropic in nature. None of the hardening behavior can be properly modeled with a change in the yield stress.     

Uniaxial ratcheting and fatigue failure of tempered 42CrMo steel: Damage evolution and damage-coupled visco-plastic constitutive model

Uniaxial ratcheting and fatigue failure of tempered 42CrMo steel were observed by the tests under the uniaxial stress-controlled cyclic loading with non-zero mean stress [G.Z. Kang, Y.J. Liu, Mater. Sci. Eng. A 472 (2008) 258–268]. Based on the obtained experimental results, the evolution features of whole-life ratcheting behavior and low-cycle fatigue (LCF) damage of the material were discussed first. Then, in the framework of unified visco-plasticity and continuum damage mechanics, a damage-coupled visco-plastic cyclic constitutive model was proposed to simulate the whole-life ratcheting and predict the fatigue failure life of the material presented in the uniaxial stress cycling with non-zero mean stress. In the proposed model, the damage was divided into two parts, i.e., elastic damage and plastic damage, which were described by the evolution equations with the same form but different constants, since the maximum applied stresses in most of loading cases were lower than the nominal yielding strength of the material. The ratcheting of the material was still described by employing a nonlinear kinematic hardening rule based on the Abdel-Karim–Ohno combined kinematic hardening model [M. Abdel Karim, N. Ohno, Int. J. Plast. 16 (2000) 225–240] but extended by considering the effect of damage. The maximum strain criterion combined with an elastic damage threshold was employed to determine the failure life of the material caused by two different failure modes, i.e., fatigue failure (caused by low-cycle fatigue due to plastic shakedown) and ductile failure (caused by large ratcheting strain). The simulated whole-life ratcheting behavior and predicted failure life of tempered 42CrMo steel are in a fairly good agreement with the experimental ones.     

304不锈钢室温单轴循环棘轮行为的粘塑性本构描述

在统一粘塑性循环本构模型的框架下对循环硬化的304不锈钢的单轴棘轮行为进行了本构描述。模型中通过随动硬化背应力演化和各向同性变形阻力演化对304不锈钢在非对称应力循环下的循环附加硬化和循环流动特性进行了分析，同时考虑了加载历史对循环棘轮行为的影响。将模型应用于304不锈钢室温单轴循环棘轮行为及其对加载历史依赖性的描述中，预言结果与实验结果吻合较好。     

考虑塑性应变记忆恢复的循环棘轮本构模型研究

在统一粘塑性循环本构理论框架下,以Ohno-Abdel-Karim非线性随动硬化模型为基础,建立了一个循环本构模型。模型通过引入塑性应变幅值记忆效应,并在塑性应变记忆项中加入恢复系数,提高了对循环硬化材料单轴棘轮行为的预言能力。将模型应用于316L不锈钢单轴棘轮行为的描述中,模拟不同平均应力、应力幅值下的棘轮应变,均与实验数据吻合较好,证明本文改进的本构模型能合理地描述循环硬化材料的单轴棘轮行为。     

Macro versus micro-scale constitutive models in simulating proportional and nonproportional cyclic and ratcheting responses of stainless steel 304

A recent study by Hassan et al. [Hassan, T., Taleb, L., Krishna, S., 2008. Influences of nonproportional loading paths on ratcheting responses and simulations by two recent cyclic plasticity models. Int. J. Plasticity, 24, 1863–1889.] demonstrated that some of the nonproportional ratcheting responses under stress-controlled loading histories cannot be simulated reasonably by two recent cyclic plasticity models. Two major drawbacks of the models identified were: (i) the stainless steel 304 demonstrated cyclic hardening under strain-controlled loading whereas cyclic softening under stress-controlled loading, which depends on the strain-range and which the existing models cannot describe; (ii) the change in biaxial ratcheting responses due to the change in the degree of nonproportionality were not simulated well by the models. Motivated by these findings, two modified cyclic plasticity models are evaluated in predicting a broad set of cyclic and ratcheting response of stainless steel 304. The experimental responses used in evaluating the modified models included both proportional (uniaxial) and nonproportional (biaxial) loading responses from Hassan and Kyriakides [Hassan, T., Kyriakides, S., 1994a. Ratcheting of cyclically hardening and softening materials. Part I: uniaxial behavior. Int. J. Plasticity, 10, 149–184; Hassan, T., Kyriakides, S., 1994b. Ratcheting of cyclically hardening and softening materials. Part II: multiaxial behavior. Int. J. Plasticity, 10, 185–212.] and Hassan et al. [Hassan, T., Taleb, L., Krishna, S., 2008. Influences of nonproportional loading paths on ratcheting responses and simulations by two recent cyclic plasticity models. Int. J. Plasticity, 24, 1863–1889.] The first model studied is a macro-scale, phenomenological, constitutive model originally proposed by Chaboche et al. [Chaboche, J.L., Dang-Van, K., Cordier, G., 1979. Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel. In: Proceedings of the Fifth International Conference on SMiRT, Div. L, Berlin, Germany, L11/3.]. This model was systematically modified for incorporating strain-range dependent cyclic hardening–softening, and proportional and nonproportional loading memory parameters. The second model evaluated is a polycrystalline model originally proposed by Cailletaud [Cailletaud, G., 1992. A micromechanical approach to inelastic behavior of metals. Int. J. Plasticity, 8, 55–73.] based on crystalline slip mechanisms. These two models are scrutinized against simulating hysteresis loop shape, cyclic hardening–softening, cross-effect, cyclic relaxation, subsequent cyclic softening and finally a broad set of ratcheting responses under uniaxial and biaxial loading histories. The modeling features which improved simulations for these responses are elaborated in the paper. In addition, a novel technique for simulating both the monotonic and cyclic responses with one set of model parameters is developed and validated.     

Visco-plastic constitutive modeling on Ohno-Wang kinematic hardening rule for uniaxial ratcheting behavior of Z2CND18.12N steel

Experimental results of monotonic uniaxial tensile tests at different strain rates and the reversed strain cycling test showed the characteristics of rate-dependence and cyclic hardening of Z2CND18.12N austenitic stainless steel at room temperature, respectively. Based on the Ohno-Wang kinematic hardening rule, a visco-plastic constitutive model incorporated with isotropic hardening was developed to describe the uniaxial ratcheting behavior of Z2CND18.12N steel under various stress-controlled loading conditions. Predicted results of the developed model agreed better with experimental results when the ratcheting strain level became higher, but the developed model overestimated the ratcheting deformation in other cases. A modified model was proposed to improve the prediction accuracy. In the modified model, the parameter m_i of the Ohno-Wang kinematic hardening rule was developed to evolve with the accumulated plastic strain. Simulation results of the modified model proved much better agreement with experiments.     

Cyclic plastic deformation and cyclic hardening/softening behavior in 304LN stainless steel

Low cycle fatigue experiments have been conducted on 304LN stainless steel in ambient air at room temperature. Uniaxial ratcheting behavior has also been studied on this material and in both engineering and true stress controlling modes. It is shown that material’s cyclic hardening/softening behavior in low cycle fatigue and in ratcheting is dependent not only on material but also on the loading condition. Improvement of ratcheting life and mean stress dependent hardening are observed in the presence of mean stress. A method based on the strain energy density (SED) is used to represent cyclic hardening/softening behavior of the material in this work. The decrease of SED with cycles is an indication that the life in low cycle fatigue and in ratcheting is improved. The SED represents the area of the hysteresis loops.     

316L不锈钢随动强化模型改进研究

本文对316L不锈钢进行了单轴与多轴非比例路径下的应力控制棘轮试验,考察了应力幅值、平均应力和加载历程对棘轮特性的影响。同时进行了应变控制循环试验以研究材料的应力松弛特性。试验结果表明轴向棘轮效应在对称剪切荷载下效果明显,同时棘轮应变随应力幅值和平均应力的增加而增加。研究了Chen-Jiao随动强化模型与Jiang-Sehitoglu随动强化模型采用的单轴与多轴参数对背应力分量增量方向的影响,将Chen-Jiao模型中的多轴系数替换为界面饱和率,并在此基础上引入新的参数对塑性模量系数进行修正,计算结果表明修正后的模型能提升应力控制下多轴棘轮的预测精度,并能很好的预测应力松弛现象,表明了新模型的正确性与有效性。     

An experimental study on the ratcheting behavior of pure aluminium under uniaxial cyclic stressing

An experimental study was carried out for the cyclic properties of pure aluminium subjected to uniaxial cyclic straining and stressing. For a material of pure aluminium the effects of the cyclic strain amplitude history and mean strain on the cyclic deformation behavior were investigated, and the influences of stress amplitude, mean stress and their histories on cyclic creep (i. e., ratcheting) were analyzed. It is shown that either uniaxial cyclic property under cyclic straining or ratcheting behavior under asymmetric uniaxial loading depends not only on the current loading, but also on the previous loading history. Some significant results were obtained.Financial support from NFSC is acknowledged.     

Reconcile the perfectly elastoplastic model to simulate the cyclic behavior and ratcheting

Perfectly elastoplastic constitutive model is modified through a smoothing factor introduced by Liu [Liu, C.-S., 2003. Smoothing elastoplastic stress–strain curves obtained by a critical modification of conventional models. Int. J. Solids Struct. 40, 2121–2145]. The new model allows plasticity to happen in a non-zero-measure yield volume in stress space, rather than that of conventional zero-measure yield surface, and within the yield volume the plastic modulus is varying continuously. It endows a specific strain-hardening rule of flow stress and is able to describe the phenomena of strain hardening, cyclic hardening, the Bauschinger effect, mean-stress relaxation, strain ratcheting, out-of-phase hardening, as well as erasure-of-memory. In order to suppress the over prediction of ratcheting we consider a scalar function of smoothing factor, which can simulate the saturation behavior of uniaxial/multiaxial strain ratcheting. These effects are demonstrated through numerical examples. The existence of stress equilibrium point and limiting surface is a natural result without requiring an extra design. Moreover, the non-linear constitutive equations can be converted into a linear system for augmented stress in the Minkowski space, of which the symmetry group is a proper orthochronous Lorentz group SO_o(5, 1). The augmented stress is a time-like vector, moving on hyperboloids inside the cone. When taking the Prager kinematic hardening rule into account we can simulate some cyclic behaviors of SAE 4340 and grade 60 steels within a certain accuracy through the use of only three material constants and a fixed smoothing factor. To simulate the ratcheting behaviors of SS304 stainless steel we allow the smoothing factor to be an exponential decaying function of λ.     

A generalized anisotropic hardening rule based on the Mroz multi-yield-surface model for pressure insensitive and sensitive materials

In this paper, a generalized anisotropic hardening rule based on the Mroz multi-yield-surface model for pressure insensitive and sensitive materials is derived. The evolution equation for the active yield surface with reference to the memory yield surface is obtained by considering the continuous expansion of the active yield surface during the unloading/reloading process. The incremental constitutive relation based on the associated flow rule is then derived for a general yield function for pressure insensitive and sensitive materials. Detailed incremental constitutive relations for materials based on the Mises yield function, the Hill quadratic anisotropic yield function and the Drucker–Prager yield function are derived as the special cases. The closed-form solutions for one-dimensional stress–plastic strain curves are also derived and plotted for materials under cyclic loading conditions based on the three yield functions. In addition, the closed-form solutions for one-dimensional stress–plastic strain curves for materials based on the isotropic Cazacu–Barlat yield function under cyclic loading conditions are summarized and presented. For materials based on the Mises and the Hill anisotropic yield functions, the stress–plastic strain curves show closed hysteresis loops under uniaxial cyclic loading conditions and the Masing hypothesis is applicable. For materials based on the Drucker–Prager and Cazacu–Barlat yield functions, the stress–plastic strain curves do not close and show the ratcheting effect under uniaxial cyclic loading conditions. The ratcheting effect is due to different strain ranges for a given stress range for the unloading and reloading processes. With these closed-form solutions, the important effects of the yield surface geometry on the cyclic plastic behavior due to the pressure-sensitive yielding or the unsymmetric behavior in tension and compression can be shown unambiguously. The closed form solutions for the Drucker–Prager and Cazacu–Barlat yield functions with the associated flow rule also suggest that a more general anisotropic hardening theory needs to be developed to address the ratcheting effects for a given stress range.     

Thermal ratcheting of solder-bonded elastic and elastoplastic layers

The cyclically growing deflection of solder-bonded elastic and elastoplastic layers subjected to cyclic thermal loading is studied. Finite element analysis of a Si/Sn–95Pb/OFHC-Cu layered structure is performed by taking into account the temperature-dependent viscoplastic behavior of Sn–95Pb as well as the uniaxial ratcheting behavior of OFHC-Cu. A temperature-dependent power law is employed for the viscoplasticity of Sn–95Pb, while a combined nonlinear kinematic and isotropic hardening model is assumed for the cyclic plasticity of OFHC-Cu. It is shown that the temperature-dependent viscoplasticity of Sn–95Pb and the uniaxial ratcheting of OFHC-Cu are the controlling factors for the cyclic growth of deflection of the layered structure under temperature cycling. It is also shown that cyclic hardening of OFHC-Cu plays an important role for the cyclic growth of deflection, and that elastic stress in the Si layer cyclically develops noticeably if the cyclic growth of deflection is significant.     

奥氏体不锈钢高温循环棘轮行为的实验研究

对两种不锈钢材料（316L和304）进行了高温应力控制下的系统循环试验。对该类材料在应力循环下的平均应力、应力幅值及其历史对循环蠕变（棘轮效应）的影响进行了分析,同时也分析了环境温度的变化以及先前应变循环对后继应力循环的棘轮行为的影响。研究表明,两种不锈钢材料在高温非对称循环下的单轴棘轮行为基本相同,不但依赖于当前温度和加载状态,而且还依赖于先前加载历史。研究得到了不锈钢材料高温单轴循环棘轮行为的一些有意义的结果。     

内压循环下薄壁圆筒的环向棘轮应变预测

对单轴和比例加载下的棘轮应变进行预测目前仍有较大困难。本文考虑将移动极限面加入材料双面本构模型中，对原提出的叠加型随动强化律进行了修正，可以对较多循环数的1Crl8Ni9Ti不锈钢薄壁圆管的环向棘轮应变做出预测。     

ON NONPROPORTIONAL CYCLIC PLASTIC BEHAVIOR OF STEEL 40

An experimental investigation was carried out on the flow characteristicand hardening of steel 40 subjected to complex combined axial-torsional cyclicstraining. For a specific cyclic strain path, the steel has mainly cyclic softeningbehavior when the strain amplitude is small. While with an increase of the effectivestrain amplitude, the softening becomes small, but there is the cyclic softening eventhough the steel is subjected to the cyclic loading by a square strain path. However, thesteel has cyclic additional hardening by a nonproportional path, compared with theproportional cycling. Generally, the additional hardening is small and its historicaleffect is not obvious at small strain amplitude. The additional hardening is remarkableby a cross-triangular strain path of large strain amplitude. The memory of the historyof nonproportional cyclic loading, the direction of plastic flow and the plastic modulusof the steel were also studied.