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Scaled rolling contact fatigue tests, used to practically simulate the wear of the wheel and rail material under laboratory conditions, are typically classified into two categories. Tests in the first category use twin-disc stands, while the second group of test rigs use two discs of different diameters considering the rail disc as the larger one. The latter setup is closer to the real situation, but problems can occur with high contact pressures and tractions. The focus of this paper is on two main contributions. Firstly, a case study based on finite element analysis is presented, allowing the optimization of the specimen geometry for high contact pressures. Accumulated plastic deformation caused by cycling is responsible for abrupt lateral deformation, which requires the use of an appropriate cyclic plasticity model in the finite element analysis. In the second part of the study, two laser profilers are used to measure the dimensions of the specimen in real time during the rolling contact fatigue test. The proposed technique allows the changes in the specimen dimensions to be characterized during the test itself, and therefore does not require the test to be interrupted. By using real-time values of the specimen's dimensional contours, it is possible to calculate an instantaneous value of the slip ratio or the contact path width. [ABSTRACT FROM AUTHOR]

Scaled rolling contact fatigue tests, used to practically simulate the wear of the wheel and rail material under laboratory conditions, are typically classified into two categories. Tests in the first category use twin-disc stands, while the second group of test rigs use two discs of different diameters considering the rail disc as the larger one. The latter setup is closer to the real situation, but problems can occur with high contact pressures and tractions. The focus of this paper is on two main contributions. Firstly, a case study based on finite element analysis is presented, allowing the optimization of the specimen geometry for high contact pressures. Accumulated plastic deformation caused by cycling is responsible for abrupt lateral deformation, which requires the use of an appropriate cyclic plasticity model in the finite element analysis. In the second part of the study, two laser profilers are used to measure the dimensions of the specimen in real time during the rolling contact fatigue test. The proposed technique allows the changes in the specimen dimensions to be characterized during the test itself, and therefore does not require the test to be interrupted. By using real-time values of the specimen’s dimensional contours, it is possible to calculate an instantaneous value of the slip ratio or the contact path width.

The second part of the study presents development of the Dirac delta functions framework to modelling of cyclic hardening and softening of material during cyclic loading conditions for the investigated in Part I low carbon S355J2 steel. A new criterion of plastic strain range change is formulated. This provides more certainty in the cyclic plasticity modelling framework compared to classical plastic strain memorization modelling. Two hardening parameters from the developed kinematic hardening rule are written as functions of both plastic strain range and previously accumulated plastic strain. This representation of hardening parameters is able to accurately match experimental results with different types of loading programs including random loading conditions and considering initial monotonic behaviour with yield plateau deformation. Ratcheting behaviour is simulated by the developed cyclic plasticity framework by considering an approximated form of the Dirac delta function for modelling the deviation effect and introducing an additional supersurface for better prediction of ratcheting rate. The proposed cyclic plasticity model requires up to 21 material constants, depending on application. A clear and straightforward calibration procedure, where sets of material constants are determined for each plasticity phenomenon considered, is presented. Application of the model to different materials under various tension-compression and non-proportional axial-torsion cycles shows very close agreement with test results. • New criteria of plastic strain range change provides more certainty in the cyclic plasticity modelling framework. • Approximated form of Dirac delta function simulates the stress deviation effect during the ratcheting phenomenon. • Global and local hardening accurately describe cyclic hardening/softening at various loading programs. • New kinematic hardening model closely matches test results under various cyclic loading programs. [ABSTRACT FROM AUTHOR]

A number of constitutive models have been developed for solid polymers to describe the large deformation behavior. However, most of the existing models rely on a purely elastic or hyperelastic initial response when they are incapable of accurately predicting the cyclic stress-strain hysteresis loops. In this work, therefore, a compact cyclic viscoelastic-viscoplastic constitutive model is proposed to improve the prediction of the loops below the peak yield stress. The proposed approach is based on the distinguished model by Haward and Thackray (1968) for glassy polymers, which is augmented by a few thermodynamically motivated internal state variables able to predict the missing viscous deformation behavior, including the nonlinear cyclic hardening in three dimensions. Based on the comprehensive uniaxial tension experiments, it is demonstrated that this compact formulation, along with a calibration scheme, enables accurate prediction of the shape of the hysteresis loops, as well as the representation of ratcheting behavior. A comparison is also made with state-of-the-art models that are capable of predicting the cyclic stress-strain hysteresis loops. • A compact model suitable for predicting long-term cyclic deformation behavior of solid polymers is proposed. • Pioneering model by Haward and Thackray (1968) is augmented by a few state variables to predict nonlinear cyclic hardening. • Compared with state-of-the-art models, the model requires a reduced set of internal variables and material parameters. • It is demonstrated that the model, along with a calibration scheme, predicts well the hysteresis loops and ratcheting. [ABSTRACT FROM AUTHOR]

Highlights • Ratcheting strain behavior tends to decrease after the application of overload which explains the retardation effect in FCG. • The compressive zone of crack-tip residual stress field increases with the decrease in R ratio. • The compressive zone of crack-tip residual stress field increases with the increase of overload. • The compressive part of crack-tip residual stress field increases with the increase of overload ratio and SIF range value. Abstract The present study deals with the investigation of cyclic plastic deformation behavior near crack-tip with/without overload. The effect of overload is studied on single edge notch tension SENT specimen in an elasto-plastic finite element FE analysis. Three different stress ratios, two different overload ratios and a selected stress intensity factor SIF range Δ K value are used. Chaboche model is used for characterizing SA333 Gr 6 C-Mn steel material behavior. Crack-tip cyclic stress/strain hysteresis loops, crack-tip residual stress field and crack-tip ratcheting strain accumulation are simulated with/without overload. Moreover, the effect of overload ratio, stress ratio, background Δ K -level and crack size on controlling the compressive residual stress field, generated near crack-tip after overloading, are discussed. The results show that the progressive accumulation of plastic strain in the crack-tip cyclic plastic zone tends to decrease after overloading. It is also noticed that the maximum magnitude and the size of compressive residual stress zone following a single overload increase with the increase in the overload crack size and the decrease in the background R r a t i o. The finding results provide insight into the understanding of cracked metallic parts' fatigue response under variable amplitude loading. [ABSTRACT FROM AUTHOR]

Abstract Z2CND18.12N austenitic stainless steel elbow pipes were studied experimentally under reversed in-plane load of 20 kN and constant pressure of 17.5 MPa after thermal aged 1000 h and 2000 h respectively at the same thermal aging temperature of 500 centigrade degrees (oC). The ratcheting behaviors of pressurized elbow pipes were analyzed compared with original elbow pipe. The results indicate that the ratcheting behavior of pressurized elbow pipe is prominently affected by thermal aging. The uniaxial tensile properties of Z2CND18.12N austenitic stainless steel were also studied under the same condition of thermal aging. It is shown that yield stress of material decreases obviously with the increase of thermal aging period. Chen-Jiao-Kim (CJK) kinematic hardening model was used to evaluate the ratcheting behaviors of pressurized elbow pipes under different thermal aging periods. Simulation results are perfectly agreement with experimental data. Ratcheting shakedown boundaries of thermal aged elbow pipes were determined by CJK model. Highlights • Thermal aging will reduce the yield strength of Z2CND18.12N austenitic stainless steel. • The ratcheting strain of the elbow increases with the increase of thermal aging period. • The ratcheting shakedown boundary decreases with the increase of thermal aging period. • Chen-Jiao-Kim (CJK) kinematic hardening model can evaluate the ratcheting behavior of the elbow aged. [ABSTRACT FROM AUTHOR]

Highlights • Ratcheting is a rate-independent elastoplastic phenomenon. • Ratcheting should not be confused with creep, cyclic softening and fatigue damage. • Within the small strain assumption conditions, ratcheting is not significant for 304L SS. • Outside the small strain assumption conditions, ratcheting is observed in 304L SS under large stress amplitudes. Abstract In this work our goal is to better understand the origin of the cyclic accumulation of the inelastic strain (often called ratcheting) observed in 304L SS subjected to uniaxial cyclic stress control at room temperature. Recent works performed in the frame of small strain assumption attribute this phenomenon essentially to creep (Taleb, 2013). However, outside this frame, it seems that creep is not the only contributor in this phenomenon (Facheris, 2014). New experiments are performed here in order to investigate the role played by creep, cyclic softening, fatigue damage, the mode of control (engineering or true stress) and ratcheting in this observation. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

Unidirectional plastic strain accumulation (ratcheting) is one of the main causes of surface crack nucleation in rails and wheels in dry condition. It is related to frictional forces which develop at the contact interface due to sliding, especially in curve and in braking. Surface cracks generated by ratcheting can subsequently lead to severe damage when environmental fluid contaminants (such as rain or snow) are added at the contact interface, due to the complex solid-fluid interaction, which can enhance crack growth. In dry condition, wear and ratcheting can reach an equilibrium, such that the strain field and the crack depth are stationary. Understanding such steady-state deformation regime can be a key factor for predicting the expected crack depth and scheduling a correct maintenance programme. In this paper a model for predicting the strain field at steady-state regime is proposed. Such model, based on an integral equation, allows predicting the strain field and crack morphology at high cycle number with no need of iterative numerical simulation. The potentiality of the model was proven both in characterizing the cyclic plasticity behaviour of materials and in predicting the maximum expected crack depth in full scale railway wheels. [ABSTRACT FROM AUTHOR]

Strain-life methodologies are commonly employed for fatigue estimation in military aircraft structures. These methodologies rely on models describing the elastoplastic response of the material under cycling. Despite the numerous advanced plasticity models proposed and utilised in various engineering problems over the past decades, the Masing model remains a popular choice in fatigue analysis software, mainly due to its simplicity. However, in the case of military aircraft load spectra including scattered overloads the Masing model fails to represent adequately transient cyclic phenomena, such as mean stress relaxation and strain ratcheting. In this study, four well-known constitutive plasticity models have been selected as potential substitutes for the Masing model within a defence organisation in-house developed fatigue analysis software. These models assessed were the well-known Multicomponent Armstrong–Frederick Model (MAF) and three of its derivatives: MAF with threshold (MAFT), Ohno–Wang (OW) and MAF with Multiplier (MAFM). The models were calibrated with the use of existing experimental data, obtained from aircraft aluminium alloy tests. Optimisation of the parameters was performed through a genetic algorithm-based commercial software. The models were incorporated in the fatigue analysis software and their performance was evaluated statistically and compared against each other and with the Masing model for a series of different flight load spectra for a military aircraft. The results show that all four models have achieved a drastic improvement in fatigue analysis, with the MAFT model giving a slightly better performance. [ABSTRACT FROM AUTHOR]

This paper is concerned with the ratcheting prediction for steels. The yield surface evolution is integrated in the elastoplasticity analysis by a new proposed model. First, the new proposed model of Distortional Yield Surface (DYS) is developed and then ratcheting under different uniaxial and multiaxial cyclic loadings is investigated. The capabilities of the DYS model is assessed by using the results of various stress-controlled and strain-controlled tests under uniaxial loading condition and the cyclic uniaxial experimental results of Hassan and Kyriakides (1994a). In addition, the model prediction under multi-steps uniaxial loadings is also studied. Effects of DYS consideration in different uniaxial loadings are shown. Strain or stress controlled tests and combined stress-strain control experimental tests (Hassan and Kyriakides, 1994b) are used to be modeled by the present distortional yield surface approach. The biaxial experiments on CS 1018 thin-walled tubes (Hassan and Kyriakides, 1994b) are chosen to be compared with the present model results. With the incorporation of DYS, The new proposed model shows better prediction of uniaxial and multiaxial ratchetting in all ranges of experimentally tested parameters. [ABSTRACT FROM AUTHOR]

The paper compares numerical solution with results of experimental solution of pipeline under cyclic loading in elastoplastic domain. The pipeline was subjected to internal pressure and bending moment. Firstly material parameters were estimated (for Besseling model, Chaboche model and Modified AbdelKarim-Ohno model) on the basis of uniaxial loading. The possibility of parameter identification of assumed models using multiaxial tests was tested too. FE program ANSYS was used for all computations. Modified AbdelKarim-Ohno model was implemented by writing own user subrutin in FORTRAN language. Chaboche model usually overpredicts ratcheting under multiaxial stress state in confrontation with experiments, when it is calibrated by uniaxial tests only. Modified AbdelKarim-Ohno model makes possible better calibration for both uniaxial and multiaxial loading cases.

Correct determination of ratcheting strain is very important in cyclic loading. A new simple yield surface distortion model is presented and its effect on cyclic loading and ratcheting prediction is investigated in this research. Model of Baltov and Sawczuk was modified in order to be able to consider directional distortion of the yield surface. Movement of the yield surface center is modeled by Chaboche's nonlinear kinematic hardening model. Isotropic hardening was also considered. A triangular function is used and necessary cyclic plasticity relations are developed. Convexity of the proposed model is discussed and verified. Performance of the proposed model in ratcheting strain prediction is investigated in multiaxial non proportional loadings under different paths. Experimental results with stress, strain and combined stress-strain control paths are compared with the proposed model results. Incorporation of the yield surface distortion of this new model, predicts better ratcheting strain for different stress, strain and stress-strain paths. [ABSTRACT FROM AUTHOR]

The paper presents a new type of experiment focused on investigation of the influence of mean stress and stress amplitude on steady state ratcheting realized in ST52 steel at the Technical University of Ostrava. Therefore, a new cyclic plasticity model based on the AbdelKarim–Ohno kinematic hardening rule, Jiang–Sehitoglu memory surface, and modified Calloch isotropic hardening rule is described. The model allows correct description of the stress–strain behavior of ST52 steel, including ratcheting, non-Masing behavior, and cyclic hardening under proportional as well as non-proportional loading. The model was implemented in the commercial FE code ANSYS using a Fortran subroutine. The results of all simulations focusing on the uniaxial and biaxial ratcheting prediction correspond with experiments very well. The AbdelKarim–Ohno nonlinear kinematic hardening rule in its original form gives an accurate prediction of ratcheting even for the non-proportional loading, when the additional hardening is correctly described by the isotropic hardening rule. [ABSTRACT FROM AUTHOR]

This contribution presents a new methodology of fatigue tests evaluation based on digital image correlation application. The full-field strain analysis brings the possibility of 3D strain measurement evaluation on a curved part of specimen standardly used under axial-torsional loading. Resulting strain response curves can subsequently serve for evaluation of cyclic plasticity model predictions. The crucial idea is the way of FE model creation to can evaluate simulation in the same points of the structure as in the DIC measurement. The new methodology saves amount of material and leads to a shorter experimental time.

• Monotonic and cyclic softening modeling in viscoplasticity. • Softening carried by back stress. • Monotonic and cyclic softening kinetics dependent on strain rates. • Cyclic softening modeling sensitive to the strain ratio. • Qualitative analysis of ratcheting with cyclic softening. A phenomenological model is proposed to predict both monotonic and cyclic softening in Inconel 718 superalloy at 650 °C. Contrary to the current cyclic softening models consisting of a modified isotropic hardening variable, an internal state variable acting on the amplitude of the back stress is proposed and implemented in a crystal-plasticity model. Crystal-plasticity finite-element simulations are performed to validate quantitatively the model on uniaxial strain-controlled monotonic and cyclic loading for several plastic strain rates and strain amplitudes as well as to gain insights on the ratcheting phenomenon depending on the mean stress and stress amplitude values when cyclic softening occurs. [Display omitted] [ABSTRACT FROM AUTHOR]

This article presents an evaluation of the performance of conventional constitutive models in modelling the structural ratcheting of an austenitic stainless steel structure subjected to a thermomechanical loading. This work highlights the influence of monotonic and cyclic behaviour in ratcheting responses. Propositions on how to determine constitutive models and which ones are able to reproduce ratcheting responses are also presented. Models employing only a few kinematic hardening are found to be inadequate in predicting structural ratcheting. Results predicted by a simplified version of Chaboche model proposed here are found in good agreement as compared to experimental measurements. • Structural thermal ratcheting of a pressurized pipe heated by Joule effect is evaluated. • Three constitutive models are evaluated in predicting ratcheting responses. • Model's determination is discussed. • The simplified version of Chaboche model seems to be more adequate to simulate ratcheting. • Cyclic hardening has a significant effect in ratcheting modelling. [ABSTRACT FROM AUTHOR]

One of the main failure indications in rolling bearings subjected to rolling contact fatigue (RCF) is premature subsurface cracking accompanied by white etching areas (WEAs). The cracks that are linked with WEAs are called white etching cracks (WECs). The formation mechanisms of WEAs/WECs are still highly debatable according to international state of art. Often SAE 52100 steel is used for bearing rings. Its microstructure consists of a martensitic or bainitic matrix and homogeneously distributed chromium rich cementite precipitations. There are two main hypotheses based on what forms first, the cracks or WEAs (hypothesis 1 & 2 respectively). There are many numerical studies that examine non-metallic inclusions as a source of cracks that leads to WEAs (hypothesis 1), but none that considers carbides as the source of severe plastic deformation subjected to RCF that leads to WEAs and, eventually WECs (hypothesis 2). In this study, the testing was conducted on a ZF-type modified RCF test rig with hydrogen charged samples to reproduce WEAs/WECs formation. Later the influence of the microstructural features of the carbides on the steel matrix, during the formation of WEAs was investigated by microstructural investigations and multiscale finite element modelling. It was found that carbides can contribute to severe local plastic deformation which leads to formation of WEAs. Thus, it also supported the likelihood of hypothesis 2. Additionally, the surface traction and microstructural characteristics of carbides are correlated with the wide range of WEAs formation depths and timescales. • Influence of slip and Hertzian pressure on WEA/WEC failures under diffusible hydrogen. • Microstructural investigations SEM BSE, SE imaging and SEM EBSD measurements: shearing of carbides, WEA/WECs. • Simulation models enable a detailed understanding of the impact of carbides under RCF during formation of WEAs. • Multi-scale simulation model: RCF, Influence of the microstructural features of the carbides, ratcheting effect. • Carbide shearing simulation during formation of WEAs under adiabatic and non-adiabatic conditions. [ABSTRACT FROM AUTHOR]

An existing cyclic plasticity constitutive model is enhanced to simulate low-cycle fatigue and ratcheting responses of 304 stainless steel (SS) under proportional and various nonproportional loading cycles. Nonproportional loading and multiaxial ratcheting parameters, and strain range dependent cyclic hardening/softening modeling features are incorporated into a modified Ohno–Wang model to enhance its uniaxial and multiaxial loading responses. The improved constitutive model is incorporated in the commercial Finite Element Code ABAQUS through its user defined subroutine UMAT and the responses of 304 SS tubular specimen from literature have been simulated. The proposed model has demonstrated good correlation with uniaxial and different types of multiaxial fatigue and ratcheting responses. Two types of multiaxial loading cycles are studied; the first included axial and torsion cycles along different loading paths, and the second included steady internal pressure and axial strain or stress cycles. The axial–torsional loading cycles demonstrated axial and/or shear strain ratcheting, whereas the internal pressure-axial cycles demonstrated axial and/or circumferential strain ratcheting. Complex interactions between ratcheting strains in different directions along with the rate of ratcheting are simulated well by the improved Ohno–Wang model. [ABSTRACT FROM AUTHOR]

The paper shows results of experiments focused on the influence of loading frequency on ratcheting as well as interesting results obtained from uniaxial tests and biaxial tests with rectangular and circular loading paths under variable amplitude loading realized on the ST 52 steel at the VŠB-Technical University of Ostrava. The model based on the AbdelKarim-Ohno kinematic hardening rule and Calloch isotropic hardening rule was used for stress-strain behavior description in finite element analysis using commercial software Ansys. The material model was implemented into the FE code using a fortran subroutine. Results of simulations containing ratcheting and cyclic hardening effects correspond with experiments very well. [ABSTRACT FROM AUTHOR]

Corroded pipes for oil transportation can eventually undergo ratcheting after several years of operation. Evaluation of the defects caused by corrosion in these pipes is important when deciding either to repair the line or to continue its operation. Under normal operational conditions, these pipes are subjected to constant internal pressure and cyclic loading due to bending and/or tension. Under such loading conditions, regions in the pipes with a reduction in thickness due to corrosion could experience a phenomenon known as ratcheting. The objective of this paper is to study the effect of a loss in thickness due to the corrosion through combined numerical models and experiments. Three constitutive models capable of representing the ratcheting phenomenon were selected and assessed. Experimental tests were developed to verify the eventual occurrence of ratcheting in corroded pipes under typical operational load conditions. In parallel small-scale cyclic tests were performed to obtain the material parameters necessary to calibrate the constitutive models that were adopted to simulate the phenomenon. The results reveal the existence of loading combinations that cause ratcheting in the defect region, but for the intact pipe, would result in elastic behavior. Numerical and experimental results were compared and showed that a good prediction of the plastic strain along the cycles can only be achieved with the model that requires a more complex calibration, but the shakedown/ratcheting occurrence can be accurately predicted with a model calibrated solely with uniaxial tests. [ABSTRACT FROM AUTHOR]

Cyclic plastic deformation characteristics of 304LN stainless steel material have been studied with two proposed cyclic plasticity models. Model MM-I has been proposed to improve the simulation of ratcheting phenomenon and model MM-II has the capability to simulate both cyclic hardening and softening characteristics of the material at various strain ranges. In the present paper, strain controlled simulations are performed with constant, increasing and decreasing strain amplitudes to verify the influences of loading schemes on cyclic plasticity behaviors through simulations and experiments. It is observed that the material 304LN exhibits non Masing characteristics under cyclic plastic deformation. The measured deviation from Masing is well established from the simulation as well as from experiment. Simulation result shows that the assumption of only isotropic hardening is unable to explain the hardening or softening characteristics of the material in low cycle fatigue test. The introduction of memory stress based cyclic hardening coefficient and an exponentially varying ratcheting parameter in the recall term of kinematic hardening rule, have resulted in exceptional improvement in the ratcheting simulation with the proposed model, MM-II. Plastic energy, shape and size of the hysteresis loops are additionally used to verify the nature of cyclic plasticity deformations. Ratcheting test and simulation have been performed to estimate the accumulated plastic strain with different mean and amplitude stresses. In the proposed model MM-I, a new proposition is incorporated for yield stress variation based on the memory stress of loading history along with the evolution of ratcheting parameter with an exponential function of plastic strain. These formulations lead to better realization of ratcheting rate in the transient cycles for all loading schemes. Effect of mean stress on the plastic energy is examined by the simulation model, MM-I. Finally, the micro structural investigation from transmission electronic microscopy is used to correlate the macroscopic and microscopic non Masing behavior of the material. [ABSTRACT FROM AUTHOR]

To investigate the material behavior of a stainless steel grade AISI 316L, subjected to loading conditions typical for the primary cooling circuit of a light water nuclear reactor, a set of uniaxial, torsional and multiaxial low cycle fatigue and strain-controlled ratcheting tests has been carried out. The main goal of these experiments is to analyze how the cyclic deformation response is influenced by strain amplitudes, loading paths and ratcheting, and to estimate how fatigue life is affected by these elements. Finally, the performance of three advanced multiaxial fatigue criteria (i.e. Smith-Watson-Topper, Fatemi-Socie and Jiang) has been critically evaluated for all the considered loading cases. [ABSTRACT FROM AUTHOR]

Highlights: [•] Modeling of cyclic plastic and ratcheting deformation behavior of AISI 316L. [•] Capability to reproduce the effect of strain amplitude, temperature and ratcheting. [•] Internal variable dependent Chaboche-type model. [•] Calibration procedure characterized by reduced complexity allowing the application in an industrial context. [•] Straightforward implementation in a commercial finite element code. [Copyright &y& Elsevier]

Highlights: [•] Elegant formulation of cyclic hardening is proposed with new memory function. [•] Low cycle fatigue simulation shows good co-relation with the experiments. [•] Influence of loading history and magnitude of SA333 C–Mn steel are demonstrated. [•] Effect of mean strain on mean stress and non Masing characteristics are simulated. [•] In all load cases, prediction of ratcheting strain is improved in transient cycles. [ABSTRACT FROM AUTHOR]

Abstract: Cyclic plastic deformation phenomena include the Bauschinger effect, cyclic hardening/softening, strain range effect, loading history memory, ratcheting, mean stress dependent hardening, mean stress relaxation and non-proportional hardening. In this work, different cyclic plastic deformation responses of piping materials (SA333 C–Mn steel and 304LN stainless steel) are experimentally explored. Cyclic hardening/softening is depends upon loading types (i.e. stress/strain controlled), previous loading history and strain/stress range. Pre-straining followed by LCF and mean stress relaxation shows similar kind of material response. Substantial amount of non proportional hardening is observed in SA333 C–Mn steel during 90° out of phase tension-torsion loading. During ratcheting, large amount of permanent strain is accumulated with progression of cycles. Permanent strain accumulation in a particular direction causes cross-sectional area reduction and which results uncontrollable alteration of true stress in engineering stress controlled ratcheting test. In this work, true stress control ratcheting on piping materials has been carried out in laboratory environment. Effects of stress amplitude and mean stress on the ratcheting behaviors are analyzed. A comparison has also been drawn in between the true and engineering stress controlled tests, and massive difference in ratcheting life and strain accumulation is found. [Copyright &y& Elsevier]

BSTRACT [ABSTRACT FROM AUTHOR]

The present study aims to evaluate the capabilities of a class of models that take into account non-linear isotropic and kinematic hardening. The purpose is to predict the behaviour of a 'Bi-tube' structure when submitted to a cyclic thermo-mechanical loading. The first part consists of an overview of the methods of describing different kinematic hardening variables. In the second part, the studied structure and the results of numerical simulation of the models used are presented, with an emphasis on the sensitivity of the analysis with regard to the choice of the element type, using a FE software 'Code-Aster', developed by Electricité de France. This study constitutes a first step in the validation of the models of cyclic behaviour with respect to tests on structures, limited in this first case to Bi-tube structure. The comparison between numerical predictions and the experimental results demonstrates that the model of Taheri seems to be the best adapted to the study of 'Bi-tube' structures because it leads to stabilisation around 1%, which is comparable to the experimental results. [ABSTRACT FROM AUTHOR]

Abstract: Asymmetric cyclic loading in the plastic region can leads to progressive accumulation of permanent strain. True stress controlled uniaxial asymmetric cycling on SA333 steel is conducted at various combinations of mean stress and stress amplitude in laboratory environment. It is investigated that fatigue life increases in the presence of mean stress. Plastic strain amplitude and hysteresis loop area are found to decrease with increasing mean stress. A huge difference of life and ratcheting strain accumulation is found in engineering and true stress controlled tests. [ABSTRACT FROM AUTHOR]

Abstract: Cyclic plasticity deals with non-linear stress–strain response of materials subjected to external repetitive loading. An effort has been made to describe cyclic plastic deformation behavior of the SA333 C–Mn steel by finite element based plasticity model. The model has been developed on the framework using a yield surface together with Armstrong–Frederick type kinematic hardening model. No isotropic hardening is considered and yield stress is assumed to be a constant in the material. Kinematic hardening coefficient and kinematic hardening exponent reduces exponentially with plastic strain in the proposed model. The proposed model has been validated through experimental results. [Copyright &y& Elsevier]

Abstract: The first objective of this paper investigates the influence of the previous strain history on ratcheting. New tests were performed where different strain-controlled histories have been applied prior to ratcheting tests. It is demonstrated that under the same conditions, one can observe ratcheting, plastic shakedown or elasticity according to the prior strain-controlled history. The second objective points out the correlation between the experimental data base devoted to the identification of the material parameters and the quality of the predictions in cyclic plasticity. The results suggest that the choice of the tests should be closely linked to the capabilities of the model. In particular, the presence of non proportional strain-controlled tests in the data base may be not a good choice if the model itself is not able to represent explicitly such a character. All tests considered here were performed on 304L SS at room temperature. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: This work follows a series of experiments carried out earlier at INSA of Rouen (Hassan, T., Taleb, L., Krishna, S., 2008. Influence of non-proportional loading paths on ratcheting responses and simulations by two recent cyclic plasticity models. Int. J. Plast. 24, 1863–1889). It investigates the elastoplastic cyclic behavior of a 304L stainless steel at room temperature. In a first step the cross path effect on ratcheting is confirmed, as well as the crucial role of the loading path non-proportionality. Strain controlled tests are also conducted for different strain amplitudes and loading paths. Cross-hardening effect appears more important when the shearing sequence is followed by the axial one. Moreover for alternating axial and shearing cycles, this phenomenon occurs after each crossing sequence leading to a very significant strain hardening, at least of the same order as the one obtained after a circular strain path. Yet, the magnitude of the observed over hardening does not necessarily seem a function of the cumulated plastic strain. The relative contributions of the isotropic and kinematic parts of the cyclic strain hardening are also very different in the axial direction. The material generally exhibits a transient period of cyclic hardening followed by cyclic softening. Under tension-compression, the importance of the cyclic strain hardening period seems to increase with the strain amplitude. Microstructural investigations have been performed in order to understand the main physical phenomena responsible for this macroscopic behavior. The additional cyclic hardening observed in cross paths may be explained by the high defect density generated: multiple slip systems, intersecting stacking faults and twins, formation of dislocation heterogeneous structures. Furthermore, it is shown that martensite nucleation takes place at the intersections between micro-shear bands or twin faults; the quantity of martensite being estimated through magnetic measurements. After the application of a magnetic field, the material anisotropy induced by the loading path is evaluated; the martensitic needles and platelets seem to develop in the axial direction. [Copyright &y& Elsevier]

Abstract: This paper evaluates seven cyclic plasticity models for structural ratcheting response simulations. The models evaluated are bilinear (Prager), multilinear (Besseling), Chaboche, Ohno–Wang, Abdel Karim–Ohno, modified Chaboche (Bari and Hassan) and modified Ohno–Wang (Chen and Jiao). The first three models are already available in the ANSYS finite element package, whereas the last four were implemented into ANSYS for this study. Experimental responses of straight steel pipes under cyclic bending with symmetric end rotation history and steady internal pressure were recorded for the model evaluation study. It is demonstrated that when the model parameters are determined from the material response data, none of the models evaluated perform satisfactorily in simulating the straight pipe diameter change and circumferential strain ratcheting responses. A detailed parameter sensitivity study with the modified Chaboche model was conducted to identify the parameters that influence the ratcheting simulations and to determine the ranges of the parameter values over which a genetic algorithm can search for refinement of these values. The refined parameter values improved the simulations of straight pipe ratcheting responses, but the simulations still are not acceptable. Further, improvement in cyclic plasticity modeling and incorporation of structural features, like residual stresses and anisotropy of materials in the analysis will be essential for advancement of low-cycle fatigue response simulations of structures. [Copyright &y& Elsevier]

Abstract: Aubin and her coworkers conducted a unique set of experiments demonstrating the influence of loading non-proportionality on ratcheting responses of duplex stainless steel. In order to further explore their new observation, a set of experiments was conducted on stainless steel (SS) 304L under various biaxial stress-controlled non-proportional histories. This new set of data reiterated Aubin and her coworkers’ observation and illustrated many new responses critical to model development and validation. Two recent and different classes of cyclic plasticity models, the modified Chaboche model proposed by Bari and Hassan and the version of the multi-mechanism model proposed by Taleb and Cailletaud, are evaluated in terms of their simulations of the SS304L non-proportional ratcheting responses. A modeling scheme for non-proportional ratcheting responses using the kinematic hardening rule parameters in addition to the conventionally used isotropic hardening rule parameter (yield surface size change) in the modified Chaboche model is evaluated. Strengths and weaknesses of the models in simulating the non-proportional ratcheting responses are identified. Further improvements of these models needed for improving the non-proportional ratcheting simulations are suggested in the paper. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: The basic innovation proposed in this work is to consider one of the two coefficients of the Armstrong and Frederick (AF) evolution equation for the back stress, function of another dimensionless second order internal variable evolving also according to an AF equation in what can be called a multiplicative AF kinematic hardening rule. Introducing the foregoing modification into some of the components of the back stress additive decomposition model proposed by Chaboche et al. [Chaboche, J.L., Dang-Van, K., Cordier, G., 1979. Modelization of strain memory effect on the cyclic hardening of 316 stainless steel. In: Transactions of the 5th International Conference on Structural Mechanics in Reactor Technology, Berlin, no. Div L in 11/3], one obtains a refined model with improved performance in partial unloading/reloading and ratcheting. In many respects the multiplicative AF kinematic hardening scheme plays a role equivalent to that of the back stress with a threshold scheme introduced by Chaboche [Chaboche, J.L., 1991. On some modifications of kinematic hardening to improve the description of ratcheting effects. Int. J. Plasticity 7, 661–678] to improve ratcheting simulations. The basis equations are presented for both uniaxial and multiaxial stress spaces and the calibration of the model constants is addressed in detail. Numerical applications are executed for uniaxial cyclic loading only, and indicate that the proposed refinement can perform quite well in simulating uniaxial experimental data, including ratcheting, while the potential to simulate successfully multiaxial loading data is an issue to be addressed in the future. [Copyright &y& Elsevier]

Abstract: Phase transformational shakedown of a structure refers to a status that plastic strains cease developing after a finite number of loading cycles, and subsequently the structure undergoes only elastic deformation and alternating phase transformations with limited magnitudes. Due to the intrinsic complexity in the constitutive relations of shape memory alloys (SMA), there is as yet a lack of effective methods for modeling the mechanical responses of SMA structures, especially when they develop both phase transformation and plastic deformation. This paper is devoted to present an algorithm for analyzing shakedown of SMA structures subjected to cyclic or varying loads within specified domains. Based on the phase transformation and plastic yield criteria of von Mises-type and their associated flow rules, a simplified three-dimensional phenomenological constitutive model is first formulated accounting for different regimes of elastic–plastic deformation and phase transformation. Different responses possible for SMA bodies exposed to varying loads are discussed. The classical Melan shakedown theorem is extended to determine a lower bound of loads for transformational shakedown of SMA bodies without necessity of a step-by-step analysis along the loading history. Finally, a simple example is given to illustrate the application of the present theory as well as some basic features of shakedown of SMA structures. It is interesting to find that phase transformation may either increase or decrease the load-bearing capacity of a structure, depending upon its constitutive relations, geometries and the loading mode. [Copyright &y& Elsevier]

A series of multiaxial ratcheting experiments has been conducted on 63Sn-37Pb solder alloys. It is shown that the ratcheting rate in each loading step keeps constant under constant axial stress and cyclic shear strain range. However, the ratcheting rate is sensitive to the shear strain rate. Based on the Edmunds-Beer (E-B) equation, a simple constitutive model is proposed to predict the ratcheting rate of each loading step. The results have shown that the model can predict the experimental data well. [ABSTRACT FROM AUTHOR]

Abstract: A series of uniaxial and multiaxial ratcheting experiments have been conducted on 63Sn–37Pb solder alloys. It is shown that eutectic tin–lead solder is cyclic softening under uniaxial, pure torsional and axial/torsional ratcheting loading. Even low-level stress can cause high ratcheting strain. The rate of ratcheting strain remains steady and does not decay rapidly. Under constant axial stress and cyclic shear strain, the axial ratcheting strain and its rate rise with increase of the axial stress and shear strain range, but loading history and its sequence have no clear influence on the ratcheting behavior. The axial ratcheting strain rate is found to be strongly dependent on applied shear strain rates in axial/torsional ratcheting experiments. Axial ratcheting strain rates increase with decreasing shear strain rates. [Copyright &y& Elsevier]

Abstract: The strain cyclic characteristics, ratcheting and failure behaviors of 25CDV4.11 steel and SS304 stainless steel were experimentally studied under uniaxial cyclic tests and at room temperature. The cyclic hardening/softening features of the materials were first observed under uniaxial strain cycling; and then the ratcheting and failure behaviors of the materials were researched in detail under cyclic stressing. The effects of stress amplitude and mean stress on the ratcheting and failure were discussed under uniaxial asymmetrical stress cycling. It is concluded that the ratcheting and failure behaviors of the materials depend greatly on the cyclic softening/hardening features of the materials and the stress values of cyclic loading. Some conclusions useful to understand the fatigue failure of the materials presented under asymmetrical cyclic stressing are obtained. [Copyright &y& Elsevier]

This paper evaluates the performance of four Ohno–Wang type constitutive models in predicting ratcheting responses of medium carbon steel S45C for a set of axial/torsional loading paths. Suggestions are also made for further modification. The four models are the Ohno–Wang model, the McDowell model, the Jiang–Sehitoglu model and the AbdelKarim–Ohno model. It is shown that the Ohno–Wang model and the McDowell model overestimate the multiaxial ratcheting. Whereas, the Jiang–Sehitoglu model yields good predictions for most loading conditions used in this study with an appropriate modification of the dynamic recovery term. The AbdelKarim–Ohno model gives acceptable predictions for all considered multiaxial conditions when used with an evolution function for μi, but gives poor predictions of uniaxial ratcheting if the parameter μi is determined from a multiaxial ratcheting response. A new modified Ohno–Wang hardening rule is proposed for better adaptability under diverse situations by multiplying a factor to the dynamic recovery term, which is dependent on noncoaxiality of the plastic strain rate and back stress. This new model predicts ratcheting strain reasonably well for the test cases. [Copyright &y& Elsevier]

A visco-plastic constitutive model was proposed to simulate the uniaxial/multiaxial ratcheting of cyclically stable materials (such as U71Mn rail steel), and its finite element implementation was also achieved. The kinematic hardening rule used in the proposed model is similar to that developed by Abdel-Karim and Ohno [Int. J. Plast. 16 (2000) 225], except for a modification to the dynamic recovery term. The proposed model is verified by simulating the uniaxial/multiaxial ratcheting of U71Mn rail steel at room temperature. In the finite element implementation of the proposed model, based on radial return method and backward Euler integration, a new implicit stress integration algorithm is proposed by combining the successive substitution method developed by Kobayashi and Ohno [Int. J. Numer. Meth. Engng. 53 (2002) 2217] with Newton–Raphson solving method of non-linear scalar equation. Simultaneously, a new expression of consistent tangent modulus is also derived for rate-dependent plasticity. Numerical examples are given to verify the advantage of the implementation and the capability of the model in simulating ratcheting and cyclic stress relaxation. [Copyright &y& Elsevier]

A modified kinematic hardening rule is proposed in which one biaxial loading dependent parameter δ′ connecting the radial evanescence term [(α:n)ndp] in the Burlet–Cailletaud model with the dynamic recovery term of Ohno–Wang kinematic hardening rule is introduced into the framework of the Ohno–Wang model. Compared with multiaxial ratcheting experimental data obtained on 1Cr18Ni9Ti stainless steel in the paper and CS1026 steel conducted by Hassan et al. [Int. J. Plasticity 8 (1992) 117], simulation results by modified model are quite well in all loading paths. The simulations of initial nonlinear part in ratcheting curves can be improved greatly while the evolutional parameter δ′ related to plastic strain accumulation is added into the modified model. [Copyright &y& Elsevier]

• Extensions were proposed for constitutive modeling of cyclic plasticity involving pre-loading and ratcheting. • Evolution equations of cyclic hardening and PSR surface were extended by considering maximum plastic strain. • Cyclic tests of 316 stainless steel involving pre-loading and ratcheting were performed at 600 ∘ C. • The cyclic tests were simulated well using a constitutive model with the extensions. • The extended evolution equation of cyclic hardening was discussed considering previous experiments. An extended evolution equation of cyclic hardening is proposed to include the effect of maximum plastic strain due to pre-loading and ratcheting. A set of extended evolution equations is also proposed for a plastic strain surface to properly evaluate the cyclic plastic strain range in the presence of pre-loading and ratcheting. These extensions are verified by performing uniaxial cyclic experiments of 316 stainless steel at 600°C. The experiments are accurately simulated using a constitutive model with the extensions in addition to the resetting scheme of the plastic strain surface recently proposed by the authors. The extension for the plastic strain surface allows fairly good simulation of the experiments without recourse to the resetting scheme if the strain range does not markedly decrease with the number of cycles. The extended equations are further used to discuss the effect of maximum plastic strain considering previous experiments. [ABSTRACT FROM AUTHOR]