Review on cyclic plasticity of magnesium alloys:Experiments and constitutive models

Fatigue analysis has always been a concern in the design and assessment of Mg alloy structure components subjected to cyclic loading,and research on the cyclic plasticity is fundamental to investigate the corresponding fatigue failure.Thus,this work reviews the progress in the cyclic plasticity of Mg alloys.First,the existing macroscopic and microscopic experimental results of Mg alloys are summarized.Then,corresponding macroscopic phenomenological constitutive models and crystal plasticity-based models are reviewed.Finally,some conclusions and recommended topics on the cyclic plasticity of Mg alloys are provided to boost the further development and application of Mg alloys.

AN EXPERIMENTAL STUDY ON THE KINEMATIC HARDENING RULES FOR NONPROPORTIONAL CYCLIC PLASTICITY

An experimental investigation was cawted out of the cyclic saturated kinematic hardening of the solution treatment stainless steel 316L subjected to cyclic loading for seveml strain paths, such as uniaxial cycling, cireulan elliPtic, diamond, rectangular shapes. The evoluting tndectories of back stresses in deviatoric stress space were obtained, and the evolution of back stress mtes during cyclic saturuted loading was analyzed under the assumption that the yield sudece rudius at cyclic saturation is constant and the direction of plastic stmin rute coincides with the one of the out normal vector Of the yield sudece. Some significant results were obtained.

A microstructure-based analysis of cyclic plasticity of pearlitic steels with Hill's self-consistent scheme incorporating general anisotropic Eshelby tensor

A pearlitic steel is composed of numerous pearlitic colonies with random orientations, and each colony consists of many parallel lamellas of ferrite and cementite. The constitutive behavior of this kind of materials may involve both inherent anisotropy and plastic deformation induced anisotropy. A description of the cyclic plasticity for this kind of dual-phase materials is proposed by use of a microstructure-based constitutive model for a pearlitic colony, and the Hill＇s self-consistent scheme incorporating anisotropic Eshelby tensor for ellipsoidal inclusions. The corresponding numerical algorithm is developed. The responses of pearlitic steel BS 11 and single-phase hard-drawn copper subjected to asymmetrically cyclic loading are analyzed. The analytical results agree very well with experimental ones. Compared with the results using isotropic Eshelby tensor, it is shown that the isotropic approximation can provide acceptable overall responses in a much simpler way.

CONSTITUTIVE MODELLING OF NONPROPORTIONAL CYCLIC PLASTICITY

A multiplicative hardening function and a unified evolution rule of the hardening factors are proposed.The hardening factor f_1 is introduced to describe cyclic hardening with respect to the plastic strain range,while f_2 and f_3 describe,respectively,instantaneous and hereditary additional hardening with respect to the nonproportionality of the plastic strain path.Two material dependent memory parameters α_1 and α_3 are introduced to keep the memory of the largest cyclic and additional hardening in the previous plastic deformation history.Different hardening mechanisms are then embedded into a thermomechanically consistent constitutive equation through the hardening function.The constitutive response of 304 and 316 stainless steels subjected to biaxial nonproportional cyclic loading is analyzed and the proposed model is critically verified by comparing the results with experimental results obtained by Tanaka et al.,and Ohashi et al.

A MICROSTRUCTURE-BASED ANALYSIS FOR CYCLIC PLASTICITY OF DUAL-PHASE PEARLITIC RAIL STEELS

Based on the assumption that a representative element of apearlitic steel is an aggregate of numerous spherical pearliticcolonies with randomly distributed orientations, and that each colonyis com- posed of many parallel fine lamellas of ferrite andcementite, a description for the dual-phase pearlitic steel isobtained by making use of a microstructure-based constitutiveequation for a single dual-phase pearlitic colony and the Hill'sself-consistent scheme. The elastoplastic response of dual-phasepearlitic steel BS11 subjected to asymmetrically cyclic loading isanalyzed, and a comparison with the experimental results showssatisfacto- ry agreement. The non-proportional cyclic plasticity ofBS11 is also analyzed, in which stress develops along a semi-circlein a biaxial tension/compression and shear stress plane, as istypically experienced by the sur- face elements in rolling andsliding contact.

ON NONPROPORTIONAL CYCLIC PLASTIC BEHAVIOR OF STEEL 40

An experimental investigation was carried out on the flow characteristic and hardening of steel 40 subjected to complex combined axial-torsional cyclic straining. For a specific cyclic strain path, the steel has mainly cyclic softening behavior when the strain amplitude is small. While with an increase of the effective strain amplitude, the softening becomes small, but there is the cyclic softening even though the steel is subjected to the cyclic loading by a square strain path. However, the steel has cyclic additional hardening by a nonproportional path, compared with the proportional cycling. Generally, the additional hardening is small and its historical effect is not obvious at small strain amplitude. The additional hardening is remarkable by a cross-triangular strain path of large strain amplitude. The memory of the history of nonproportional cyclic loading, the direction of plastic flow and the plastic modulus of the steel were also studied.

A new method to predict fatigue crack growth rate of materials based on average cyclic plasticity strain damage accumulation

By introducing a fatigue blunting factor, the cyclic elasto-plastic Hutchinson-Rice-Rosengren （HRR） field near the crack tip under the cyclic loading is modified. And, an average damage per loading-cycle in the cyclic plastic deformation region is defined due to Manson-Coffin law. Then, according to the linear damage accumulation theory-Miner law, a new model for predicting the fatigue crack growth （FCG） of the opening mode crack based on the low cycle fatigue （LCF） damage is set up. The step length of crack propagation is assumed to be the size of cyclic plastic zone. It is clear that every parameter of the new model has clearly physical meaning which does not need any human debugging. Based on the LCF test data, the FCG predictions given by the new model are consistent with the FCG test results of Cr2Ni2MoV and X12CrMoWVNbN 10-1-1. What＇s more, referring to the relative researches, the good predictability of the new model is also proved on six kinds of materials.

THERMO-ELASTIC-PLASTIC RESPONSE AND OPTIMUM DESIGN OF CERAMIC-METAL FGMS-CYCLIC THERML LOADING PROBLEM

The materials are made with a graded composition and microstructure in the thickness direction from the ceramic side to the metal side. The cyclic thermal loading and high temperasure gradient environment are simulated by heating the ceramic surface with a cyclic hear flux input and cooling the metal surface with a flowing liquid niterogen. The thermal and themo-elastic-plastic response of the materials is calculated using the isotropic hardening model and kinetic hardening model. Emphasis is placed on the response analysis under the different graded compositional distributions. Through the response analysis, the optimum design process of the graded composition under the dynamic case is established, which is bused on a unified viewpoint of the heat insulation property, thermal stress relaxation property and stress history feature.

Efficiency of employing fiber-based finite-length plastic hinges in simulating the cyclic and seismic behavior of steel hollow columns compared with other common modelling approaches

The accuracy and effi ciency of the modelling techniques utilized to model the nonlinear behavior of structural components is a signifi cant issue in earthquake engineering. In this study, the suffi ciency of three diff erent modelling techniques that can be employed to simulate the structural behavior of columns is investigated. A fi ber-based fi nite length plastic hinge (FB-FLPH) model is calibrated in this study. In order to calibrate the FB-FLPH model, a novel database of the cyclic behavior of hollow steel columns under simultaneous axial and lateral loading cycles with varying amplitudes is used. By employing the FB-FLPH model calibrated in this study, the interaction of the axial force and the bending moment in columns is directly taken into account, and the deterioration in the cyclic behavior of these members is implicitly considered. The superiority of the calibrated FB-FLPH modelling approach is examined compared with the cases in which conventional fi ber-based distributed plasticity and concentrated plasticity models are utilized. The effi ciency of the enumerated modelling techniques is probed when they are implemented to model the columns of a typical special moment frame in order to prove the advantage of the FB-FLPH modelling approach.

深冷循环热处理下锆基金属玻璃的回春行为调控

研究Zr_(55)Cu_(30)Ni_(5)Al_(10)(摩尔分数,%)金属玻璃在深冷循环处理过程中的回春行为。实验发现,随着循环次数的增加,样品的回春程度更高,表现为更高的弛豫焓与更低的密度。回春程度经200次循环后逐渐饱和,这可能与非晶结构中有限的自由体积含量有关。同时,高循环次数下的样品硬度更低,塑性更好,这与其剪切转变区体积增大有关。此时,更低的剪切面形成能有利于多重剪切带的形成。此外,还发现自由体积含量与样品塑性应变及剪切转变区体积呈线性关系。分子动力学模拟结果还表明,在高冷速下回春程度高的样品会发生原子体积的饱和。

Experimental Study on Non-proportional Multiaxial Strain Cyclic Characteristics and Ratcheting of U71Mn Rail Steel

An experimental study was carried out on the strain cyclic characteristics and ratcheting of U71Mn rail steel subjected to non-proportional multiaxial cyclic loading. The strain cyclic characteristics were researched under the strain-controlled circular load path. The ratcheting was investigated for the stress-controlled multiaxial circular, elliptical and rhombic load paths with different mean stresses, stress amplitudes and their histories. The experiment shows that U71Mn rail steel features the cyclic non-hardening/softening, and its strain cyclic characteristics depend greatly on the strain amplitude but slightly on its history. However, the ratcheting of U71Mn rail steel depends greatly not only on the values of mean stress and stress amplitude, but also on their histories. In the meantime, the shape of load path and its history also apparently influence the ratcheting. The ratcheting changes with the different loading paths.

THE STRAIN CYCLIC CHARACTERISTICS AND RATCHETING OF U71Mn RAIL STEEL UNDER UNIAXIAL LOADING

An experimental study was carried out of the cyclic behavior of U71Mn rail steel subjected to uniaxial strain and stress. The effects of cyclic struin amplitude, mean struin,strain loading rate and their histories on the strain cyclic characteristics were studied.Under the asymmetrical stress cycling, the effects of stress amplitude, mean stress,stress loading rate and their histories on the ratcheting were analyzed. The interaction between strain cycling and stress cycling was also discussed. It is shown that either the cyclic characteristics under strain cycling or the ratcheting under asymmetrical stress cycling depends not only on the cumnt loading state, but also on the previous loading history. Some significant results are obtained.

A CRYSTALLOGRAPHIC MODEL FOR THE ORIENTATION DEPENDENCE OF LOW CYCLIC FATIGUE PROPERTY OF A NICKEL-BASE SINGLE CRYSTAL SUPERALLOY

Fully reversed low cyclic fatigue (LCF) tests were conducted on [0 0 1], [0 1 2], [(1) over bar 1 2], [0 1 1] and [(1) over bar 1 4] oriented single crystals of nickel-bared superalloy DD3 with different cyclic strain rates at 950 degrees C. The cyclic strain rates were chosen as 1.0 x 10(-2), 1.33 x 10(-3) and 0.33 x 10(-3) s(-1). The octahedral slip systems were confirmed to be activated on all the specimens. The experimental result shows that the fatigue behavior depends an the crystallographic orientation and cyclic strain rate. Except [0 0 1] orientation specimens, it is found from the scanning electron microscopy(SEM) examination that there are typical fatigue striations on the fracture surfaces. These fatigue striations are made up of cracks. The width of the fatigue striations depends on the crystallographic orientation and varies with the total strain range. A simple linear relationship exists between the width and total shear strain range modified by an orientation and strain rate parameter. The nonconformity to the Schmid law of tensile/compressive flaw stress and plastic behavior existed at 95 degrees C, and an orientation and strain rate modified Lall-Chin-Pope ( LCP) model was derived for the nonconformity. The influence of crysrallographic orientation and cyclic strain rate on the LCF behavior can be predicted satisfactorily by the model. In terms of an orientation and strain rate modified total strain range, a model for fatigue life was proposed and used successfully to correlate the fatigue lives studied.

Experimental Study on the Uniaxial Cyclic Deformation of 25CDV4.11 Steel

The strain cyclic characteristics and ratcheting behavior of 25CDV4.11 steel were studied by the experiments under uniaxial cyclic loading with relatively high cyclic number and at room temperature. The cyclic hardening/softening feature of the material was first observed under the uniaxial strain cycling with various strain amplitudes. Then, the ratcheting behavior of the material was researched in detail, and the effects of stress amplitude and mean stress on the ratcheting were discussed under uniaxial asymmetrical stress cycling. Comparing with the experimental results of SS316L stainless steel, it is concluded that the material exhibits remarkable cyclic softening feature, and then a special ratcheting behavior is caused. Some conclusions useful to establish corresponding constitutive model are obtained.

循环加载下压实黄土的边界面塑性本构模型

压实黄土的动应力应变关系预测是黄土高原平山填方工程长期运营涉及的关键问题之一,已有模型预测压实黄土的动本构关系难度较大。该文在边界面塑性框架下,引入动态映射法则,提出了一个反映应变累积的循环加载塑性模量表达式,构建了循环加载条件下压实黄土边界面塑性本构模型,分析了循环应力比与围压对应力应变关系与模量的影响规律,采用压实粉质黄土动三轴试验结果进行了验证。结果表明,该循环加载塑性模量基本反映了压实黄土的应变累积行为,所构建的本构模型考虑了循环应力比对动应力应变关系与模量的影响,可为填方压实黄土长期变形分析提供参考。

A DAMAGE FUNCTION USED FOR PREDICTION OF LOW CYCLIC FATIGUE LIFE

In this paper, the cyclic plastic strain energy is acted as damage variable and its mathematical model of transient response is established. The nonlinear fatigue damage function is given by means of the damage mechanical method. The formula used for prediction of low cyclic fatigue life is obtained from this damage function which takes into account the cyclic relativity of cyclic plastic strain energy. The low cyclic fatigue life predicted by this formula is in correspondence with the experimental result.

A NONCLASSICAL CONSTITUTIVE MODEL FOR CRYSTALPLASTICITY AND ITS APPLICATION

A nonclassical constitutive description for a slip system is formulated by using a simple mechanical model consisting of a spring and a plastic dashpot-like block. The corresponding constitutive model for a single crystal and the analysis for polycrystalline response is proposed based on the KBW's self-consistent theory. The constitutive model contains no yield criterion, so the corresponding numerical analysis is greatly simplified because it involves no additional process to search for the activation of slip systems and slip direction. A mixed averaging approach is proposed to obtain the response of polycrystalline material, which consists of the Gaussian integral mean for the omega which varies continuously within each face of the isosahedron and arithmetic mean for the spatially uniformly distributed twenty sets of 0 and phi determined by the normal of each face of the isosahedron. The main features 316 stainless steel subjected to typical biaxial nonproportional cyclic strain paths are well described. Calculation also shows that the developed model and the corresponding analytical approach are of good accuracy and efficiency.

Fractional-order visco-plastic constitutive model for uniaxial ratcheting behaviors

This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional(fractional-order)derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic(FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain properly.The capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature(KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Timedependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894(2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.

Effects of axial cyclic loading at constant confining pressures on deformational characteristics of anisotropic argillite

Triaxial cyclic loading tests have been performed to assess the influence of plastic deformation on inelastic deformational properties of anisotropic argillite with bedding planes which is regarded as a kind of transversely isotropic media.Considering argillite's anisotropy and inelastic deformational properties,theoretical formulae for calculating oriented elastic parameters were deduced by the unloading curves,which can be better fitted for the description of its elasticity than loading curves.Test results indicate that with the growth of accumulated plastic,strain,the apparent elastic modulus of argillite decreases in a form of exponential decay function,whereas the apparent Poisson ratio increase in a form of power equation.A ratio of unloading recoverable strain to the total strain increment occurred during a loading cycle is defined to illustrate the characteristic relations between anisotropic coupled elasto-plastic deformation and plastic strain.It is significant to observe that high stress level and plastic history have an inhibiting effect on argillite anisotropy.

CYCLIC HARDENING BEHAVIOR OF POLYCRYSTALS WITH PENETRABLE GRAIN BOUNDARIES:TWO-DIMENSIONAL DISCRETE DISLOCATION DYNAMICS SIMULATION

A two-dimensional discrete dislocation dynamics （DDD） technology by Giessen and Needleman （1995）, which has been extended by integrating a dislocation-grain boundary interaction model, is used to computationally analyze the micro-cyclic plastic response of polycrystals containing micron-sized grains, with special attentions to significant influence of dislocationpenetrable grain boundaries （GBs） on the micro-plastic cyclic responses of polycrystals and underlying dislocation mechanism. Toward this end, a typical polycrystalline rectangular specimen under simple tension-compression loading is considered. Results show that, with the increase of cycle accumulative strain, continual dislocation accumulation and enhanced dislocation-dislocation interactions induce the cyclic hardening behavior; however, when a dynamic balance among dislocation nucleation, penetration through GB and dislocation annihilation is approximately established, cyclic stress gradually tends to saturate. In addition, other factors, including the grain size, cyclic strain amplitude and its history, also have considerable influences on the cyclic hardening and saturation.