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.

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.

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.

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.

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.

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.

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.

Prediction of cyclic large plasticity for prestrained structural steel using only tensile coupon tests

Cold-formed steel members,which experience complicated prestrain histories,are frequently applied in structural engineering.This paper aims to predict cyclic plasticity of structural steels with tensile and compressive prestrain.Monotonic and cyclic tests on hourglass specimens with tensile and compressive prestrain are conducted,and compared with numerical simulations using the Chaboche model.Two approaches are taken in the simulation.The first requires only the monotonic tensile test data from the prestrained steels,and the second requires both the monotonic tensile test data from the virgin steel and the prestrain histories.The first approach slightly overestimates the compressive stress for specimens with tensile prestrain,while the second approach is able to accurately predict the cyclic plasticity in specimens with tensile and compressive prestrain.

Bauschinger Effect of Mn18Cr18N Austenitic Stainless Steel

The experimental study of Bauschinger effect in Mn18Cr18N austenitic stainless steel was presented by compression-tensile cyclic loading tests with the prestrains ranging from 0.005 to 0.1,which was illustrated utilizing stress-strain curves and analysed by TEM images from aspects of microstructural mechanisms.Moreover,the Bauschinger effect and its associated roundness phenomenon in reverse flow curve with respect to different cycles and cyclic strain amplitudes were evaluated in a quantitative manner.The experimental results indicate that Bauschinger effect is apparent during the test.At smaller cyclic strain amplitude,intergranular backstress is the main source of Bauschinger effect.With further increasing of cycles,dislocation density increases and dislocation movement is hindered in the reverse deformation.Therefore,Bauschinger effect is weakened to some extent.At large cyclic strain amplitude,backstress originating from the dislocation pile-up at grain boundaries and the continuous formation of deformation twins dominate the Bauschinger effect.In addition,the backstress results in the roundness of reverse curve during cyclic loading.The larger value ofΔεp*,the more obvious the roundness of the reverse curve,and the more significant the Bauschinger effect.

Damage localization effects of the regeneratively-cooled thrust chamber wall in LOX/methane rocket engines

To investigate the damage localization effects of the thrust chamber wall caused by combustions in LOX/methane rocket engines, a fluid-structural coupling computational methodology with a multi-channel model is developed to obtain 3-demensioanl thermal and structural responses.Heat and mechanical loads are calculated by a validated finite volume fluid-thermal coupling numerical method considering non-premixed combustion processes of propellants. The methodology is subsequently performed on an LOX/methane thrust chamber under cyclic operation. Results show that the heat loads of the thrust chamber wall are apparently non-uniform in the circumferential direction. There are noticeable disparities between different cooling channels in terms of temperature and strain distributions at the end of the hot run phase, which in turn leads to different temperature ranges, strain ranges, and residual strains during one cycle. With the work cycle proceeding, the circumferential localization effect of the residual strain would be significantly enhanced. A post-processing damage analysis reveals that the low-cycle fatigue damage accumulated in each cycle is almost unchanged, while the quasi static damage accumulated in a considered cycle declines until stabilized after several cycles. The maximum discrepancy of the predicted lives between different cooling channels is about 30%.

Thermal-structural analysis of regeneratively-cooled thrust chamber wall in reusable LOX/Methane rocket engines

To predict the thermal and structural responses of the thrust chamber wall under cyclic work,a 3-D fluid-structural coupling computational methodology is developed.The thermal and mechanical loads are determined by a validated 3-D finite volume fluid-thermal coupling computational method.With the specified loads,the nonlinear thermal-structural finite element analysis is applied to obtaining the 3-D thermal and structural responses.The Chaboche nonlinear kinematic hardening model calibrated by experimental data is adopted to predict the cyclic plastic behavior of the inner wall.The methodology is further applied to the thrust chamber of LOX/Methane rocket engines.The results show that both the maximum temperature at hot run phase and the maximum circumferential residual strain of the inner wall appear at the convergent part of the chamber.Structural analysis for multiple work cycles reveals that the failure of the inner wall may be controlled by the low-cycle fatigue when the Chaboche model parameter c3= 0,and the damage caused by the thermal-mechanical ratcheting of the inner wall cannot be ignored when c3〉 0.The results of sensitivity analysis indicate that mechanical loads have a strong influence on the strains in the inner wall.

Constitutive Modeling of Slip, Twinning and Detwinning for Mg Alloy and Inhomogeneous Evolution of Microstructure

To investigate the relationship between macro-plastic behavior and meso-deformation mechanism of Mg alloy AZ31, the mathematical models for various deformation mechanisms of slip, twinning and detwinning are established, respectively. Furthermore, in order to capture the Bauschinger effect under cyclic loading, the back stress is introduced into the three independent deformation mechanisms, respectively. Finally, using the above-mentioned model, a new cyclic plastic constitutive model based on the constitutive theory of crystal deformation for magnesium alloy is established. On this basis, the numerical simulation for AZ31 under cyclic loading with the axial strain amplitude of 1.2% is carried out in accordance with the aforementioned crystal plas- ticity theory associated with the representative volume element model. The comparison between the stress-strain curves obtained from the simulation and the experiments shows that the macro- scopic mechanical responses predicted using the proposed model are in good agreement with the experimental results. In particular, the unique characteristics of cyclic macro-plastic behavior observed in the experiments can be satisfactorily captured by the presented crystal plasticity model. At the mesoscale, these features are caused by the alternate occurrence of twinning and detwinning mechanisms. The further analysis of meso-plastic behavior shows that there are het- erogeneous distributions of twinning, stress-strain and stress triaxiality in polycrystal under cyclic loading.