Ratcheting of 304 Stainless Steel Alloys subjected to Stress‐Controlled and mixed Stress‐ and Strain‐Controlled Conditions evaluated by Kinematic Hardening Rules

The present study predicts ratcheting response of SS304 tubular stainless steel samples using kinematic hardening rules of Ohno–Wang (O–W), Chen‐Jiao‐Kim (C–J–K) and a newly modified hardening rule under various stress‐controlled, and combined stress‐ and strain‐controlled histories. The O–W hardening rule was developed based on the critical state of dynamic recovery of backstress. The C–J–K hardening rule further developed the O–W rule to include the effect of non‐proportionality in ratcheting assessment of materials. The modified rule involved terms , and in the dynamic recovery of the Ahmadzadeh–Varvani (A–V) model to respectively track different directions under multiaxial loading, account for non‐proportionality and prevent plastic shakedown of ratcheting data over multiaxial stress cycles. The O–W model persistently overestimated ratcheting strain over the multiaxial loading paths. The C–J–K model further lowered this overprediction and improved the predicted ratcheting curves. The predicted ratcheting curves based on the modified model closely agreed with experimental data under various loading paths.     

Concurrent ratcheting and stress relaxation at the notch root of steel samples undergoing asymmetric tensile loading cycles

The current study intends to develop a framework model to assess ratcheting and stress relaxation at the notch root of 1045 steel samples over asymmetric loading cycles. The framework involves the Ahmadzadeh‐Varvani (A‐V) kinematic hardening rule to control ratcheting progress and Neuber rule to accommodate for local stress and strain components at the vicinity of notch root. Plastic strain at notch root was first coupled with its counterpart in the A‐V model to establish a relation between local stress and backstress components. Calculated local stress and strain values at turning points enabled the A‐V model to assess ratcheting strain over each loading cycle. The stepwise drop in stresses at peak‐valley tips of hysteresis loops at the notch root was associated to coupled framework of the A‐V model and Neuber rule through constancy in local strain while ratcheting progressed over each cycle. This relaxed out the local stresses at tips of hysteresis loops to position on Neuber hyperbolic curve. Predicted ratcheting values at notch root of various diameters closely agreed with those of measured in steel samples over stress cycles.     

Ratcheting assessment of steel alloys under uniaxial loading: a parametric model versus hardening rule of Bower

This study intends to compare ratcheting response of 42CrMo, 1020, SA333 and SS304 steel alloys over uniaxial stress cycles evaluated by a parametric ratcheting model and Bower's hardening rule. The parametric ratcheting equation was formulated to describe triphasic stages of ratcheting deformation over stress cycles. Mechanistic parameters of mean stress, stress amplitude, material properties and cyclic softening/hardening response of materials were employed to calibrate parametric equation. Based on the framework of cyclic plasticity theory, the modified Armstrong–Frederick nonlinear hardening rule of Bower was employed to assess ratcheting response of steel alloys under uniaxial stress cycles. Bower's model was chosen mainly due to simplicity of the model and its lower number of constants required to predict ratcheting strain over stress cycles as compared with other hardening rules. Ratcheting strain values predicted by Bower's model showed good agreements over stage I of stress cycles as compared with experimental values of ratcheting strain. Beyond of stage I stress cycles, Bower ratcheting strain rate stayed constant resulting in an arrest in ratcheting process. The predicted ratcheting strains based on the parametric equation were found in good agreements over three stages of ratcheting as compared with those of experimentally obtained.     

Ratcheting assessment of materials based on the modified Armstrong–Frederick hardening rule at various uniaxial stress levels

The present study evaluates ratcheting response of materials by means of the Armstrong–Frederick (A–F) hardening rule, the modified A–F rule (Bower's model), and further modifications of the hardening rule based on new introduced coefficients. The implemented modifications on the A–F‐based hardening rule aims to address stages of ratcheting over stress cycles. The modified hardening rule predicts the ratcheting strain rate decay over stage I and the constant rate of strain accumulation during stage II. The modified hardening rule consisted of the coefficients of the hardening rule controlling stress–strain hysteresis loops generated over stress cycles during ratcheting process (Bower's modification on A–F rule) plus the coefficients controlling rates over stages of materials ratcheting deformation. Stress–strain‐dependent coefficients in the modified rule are responsible to compromise overprediction of ratcheting of A–F during stage I and the premature plastic shakedown beyond stage I induced by Bower's model. Ratcheting strain rate coefficients improved the hardening rule capability to calibrate and control the rate of ratcheting in stages I and II and enabled the modified hardening rule to predict ratcheting strain over a prolonged domain of stress cycles. The modified hardening rule was employed to assess ratcheting response of 304, 42CrMo, 316L steel and copper samples under uniaxial loading conditions. The predicted ratcheting values based on the modified hardening rule and the experimental ratcheting strains were found in good agreements.     

Prediction of asymmetric cyclic‐plastic behaviour for cyclically stable non‐ferrous materials

Investigation on asymmetric cyclic‐plastic or ratcheting behaviour of non‐ferrous materials has received relatively little attention compared with ferrous materials. Ratcheting behaviour of materials is generally simulated using isotropic‐kinematic hardening models; however, for materials showing cyclically stable response, isotropic hardening is often not accounted for the constitutive modelling. A methodology based on Chaboche's isotropic‐kinematic hardening (CIKH) model with the consideration of genetic algorithm for optimization of initial estimates of the CIKH parameters is used in this study. The investigated plastic responses incorporate both symmetric strain‐controlled hysteresis loops and ratcheting behaviour. The suggested approach satisfactorily predicts the reported plastic response of cyclically stable non‐ferrous alloys based on aluminum, zirconium, and titanium.     

Ratcheting progress at notch root of 1045 steel samples over asymmetric loading cycles: Experiments and analyses

The present study examines ratcheting response of steel samples with various notch diameters through conducting several cyclic tests. Ratcheting strain values were measured through strain gauges mounted at different distances from the notch root. Local ratcheting at the notch region was highly influenced by notch diameter, notch shape, distance from the notch root, and magnitude of the nominal mean/amplitude of loading cycles. Nominal force‐controlled cycles were kept below the yield point and the Neuber's rule accommodated for the maximum/minimum local stress components along those local strains measured through the strain gauges at the notch region. Plastic strains at the vicinity of notch root over loading cycles were further accumulated by means of the Chaboche hardening model. The local ratcheting strain while progressed at the notch root plastic zone over loading cycles resulted in mean stress relaxation controlled by the model.     

Simulation of low cycle fatigue stress‐strain response in 316LN stainless steel using non‐linear isotropic kinematic hardening model—A comparison of different approaches

Cyclic stress‐strain response of 316LN stainless steel subjected to low cycle fatigue at strain amplitude of ±0.4% and at 873 K is simulated using finite element analysis with non‐linear isotropic‐kinematic hardening Chaboche model. Four different approaches have been used in simulating cyclic stress response and hysteresis loops: 3 based on Chaboche model‐parameters and the fourth on direct experimental data (stabilized loop and cyclic stress‐strain curve [CSSC]). Among them, simulations performed with direct experimental data have not yielded expected initial cyclic response. The source of data used for evaluation of kinematic‐hardening (KH) parameters determined the extent of closeness between experimental results and Chaboche‐model predictions. KH parameters determined from first‐cycle loop and modified‐CSSC predicted the overall stress‐strain response (from initial to stabilized condition) with reasonable fit, compared with other approaches. All 4 approaches though predicted stabilized response, simulations based on “KH‐parameters from stabilized‐cycle” accurately described stabilized response with coefficient of determination (r²) 0.995.     

Cyclic loading of beams based on the Chaboche model

The time independent non-unified version of the Chaboche constitutive model for the cyclic loading which includes the kinematic and isotropic hardening is discussed in detail. The performance of the Chaboche constitutive model in predicting ratcheting response of CS1026 steel for a broad set of mechanical uniaxial and biaxial loading histories is considered. A numerical iterative method is used to calculate the stresses and strains in beams due to cyclic loading. The reported experimental data of the stainless steel, available in the literature, is used for the verification of the results. It is concluded that the Chaboche model performs quite well in predicting the uniaxial ratcheting or shakedown responses. In addition, imposing the isotropic hardening effect to the constitutive equations results to lower ratcheting rate at initial cycles. While the kinematic hardening effect remains the major factor in prediction of the ratcheting response.     

Study of hardening and cyclic plastic behaviour around the crack tip of C(T) specimen made by as‐received and annealed copper

The purpose of this research is determining experimentally the characteristics of tension and cyclic plastic behaviours of as‐received and annealed coppers and studying distribution of stress/strain field near the crack tip. Samples made by pure copper were annealed at 420°C for 40 minutes in electric furnace. To determine the properties of the cyclic plastic behaviour, proper tests with symmetric strain‐controlled conditions were performed on standard samples. Chaboche nonlinear hardening model was used to determine the cyclic plastic behaviour of both materials. According to results, annealing process creates isotropic hardening in the copper and also changes its initial kinematic hardening behaviour. Effects of the annealing and hardening on the variations of the stresses and strains around the crack tip were investigated. Also, ratcheting and mean stress relaxations versus number of cycles, inside the plastic region, were studied.     

Particle swarm optimization procedure in determining parameters in Chaboche kinematic hardening model to assess ratcheting under uniaxial and biaxial loading cycles

As parameters in Chaboche model are difficult to be determined from experimental data, a single objective particle swarm optimization procedure was employed to obtain them. Hysteresis loop and uniaxial and biaxial ratcheting simulations were conducted to validate the determined models. Chaboche models determined by particle swarm optimization give more accurate simulation of ratcheting compared with the model determined by trial and error method. Chaboche models containing different backstress components were studied. Models determined considering uniaxial ratcheting can only predict uniaxial ratcheting precisely, while giving very bad simulation of biaxial ratcheting. The linear hardening rule in the N3L1 model clearly decreases the rate of the accumulation of ratcheting strain, and the N3L1 model gives the best simulations. For biaxial ratcheting, the fourth backstress component can decrease the rate of the accumulation apparently, while it has a little influence on prediction of uniaxial ratcheting.     

Numerical and experimental study of ratcheting in cold expanded plate of Al‐alloy 2024‐T3 in double shear lap joints

In this paper strain ratcheting in cold expanded flat plate of Al‐alloy 2024‐T3 in double shear lap joints was studied both experimentally and numerically. In the experimental part, two types of symmetric strain‐controlled and asymmetric stress‐controlled cyclic tests were performed. Also, the cold expanded double shear lap joints subjected to cyclic stress‐controlled tests. The required parameters for simulating the cyclic plastic behaviour of Al‐alloy 2024‐T3 were obtained on the basis of the experimental responses. In the numerical part, a combination of nonlinear isotropic and nonlinear kinematic hardening model (Chaboche) was implemented in the commercial finite element code of ABAQUS, using the subroutine UMAT written in FORTRAN. The results of simulations give an accurate prediction of ratcheting for all types of loading. The obtained results show that increasing the mean stress increases the strain ratcheting. It is clearly shown that the cold expansion process decreases the magnitude of strain ratcheting remarkably compared with “as drilled” specimens and the decrease is bigger for larger cold expansion sizes. Also, it is shown that the middle plane has the highest amount of ratcheting compared to the pin entrance plane and exit plane of the plate hole.     

Experimental and numerical analyses of mean stress relaxation in cold expanded plate of Al‐alloy 2024‐T3 in double shear lap joints

In this paper, the mean stress relaxation behavior of simple Al‐alloy 2024‐T3 specimens and also the mean stress relaxation around the hole of cold expanded specimen are studied. The analyses are performed through the combination of the nonlinear isotropic hardening and Chaboche nonlinear kinematic hardening model accompanied by the results of experimental tests. The strain‐controlled axial tests are performed at two different strain amplitudes, while the stress‐controlled tests of cold expanded specimens are performed for three different imposed load amplitudes. The constitutive equations of the hardening model are coded as a UMAT subroutine in FORTRAN programming language and implemented in the commercial finite element code of ABAQUS. The accuracy of the hardening model has been proved in two steps: first by simulations of mean stress relaxation during the uniaxial strain‐controlled cyclic tests and second by simulation of strain ratcheting during the stress‐controlled cyclic loading. The stress and strain distributions after cold expansion process are examined as well as the mean stress relaxation due to cyclic loading. The results show the influences of imposed stress amplitude on increasing mean stress relaxation and also the effect of cold expansion level on reducing the mean stress relaxation.     

Prediction of ductile fracture using isotropic and kinematic hardening rules including void nucleation

A formulation combining kinematic translation and isotropic expansion for a yield surface based on Gurson–Tvergaard function is used to describe void growth. By adopting a criterion of internal necking of the ligaments between voids, fracture strains for tensile bars made of conventional alloys and powder metal compacts—with micromechanical parameters mostly identified from experiments—are predicted according to kinematic, isotropic and mixed hardening models. Fracture strains predicted by the kinematic‐hardening model are in closer agreement with experiments whereas those estimated according to isotropic‐hardening model are overestimated. The consideration of either step‐like or continuous void nucleation models indicates its great influence on fracture strains and emphasizes a further need to quantify the statistical parameters involved in these models.     

Visco-plastic constitutive model considering non-proportional hardening at elevated temperature under multiaxial loading

Based on the Chaboche unified visco-plastic constitutive model, a visco-plastic constitutive model which can take into account non-proportional hardening was proposed for nickel-base alloy at elevated temperature under multiaxial loading. In the proposed multiaxial visco-plastic constitutive model, the non-proportional hardening is considered as a change of kinematic hardening property. The kinematic hardening parameters which can evolve exponentially with the cumulative plastic strain and rotation factor resulted from loading path were proposed to take into account the non-proportional hardening at high temperature under non-proportional loading. Experimental verification showed that the proposed model can accurately predict the peak stresses and the hysteresis loop compared with the original model during the tension-torsion loading process for nickel-base alloy at elevated temperature under non-proportional loading.     

Development of new cyclic plasticity model for 304LN stainless steel through simulation and experimental investigation

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.     

Modeling of ratcheting behavior under multiaxial cyclic loading

Summary.  A two-surface plasticity theory is used to predict ratcheting strain under multiaxial loading. A kinematic hardening rule that combines the Mroz and Ziegler hardening rules is employed along with the plastic modulus given as an exponential function of the distance between the yield surface and the bounding surface. Model results are compared with the experimental data obtained on medium carbon steel under proportional and nonproportional axial-torsional loading. The model predicts reasonably well the experimental ratcheting behavior at relatively low cycles. Predictions overshoot the actual ratcheting strains at high cycles, yet the results look favorable compared with other data found in the literature. Received July 29, 2002; revised January 15, 2003 Published online: May 20, 2003 The authors gratefully acknowledge financial support for this work, in part from Brain Korea 21 Program at Pohang University of Science and Technology, and in part from National Natural Science Foundation of China and TRAPOYT.     

高强轨道钢双轴压-扭棘轮行为的实验和模拟

在室温下对高强轨道钢进行了单轴和非比例双轴压-扭循环变形行为的实验,讨论了不同加载路径对轨道钢棘轮变形行为的影响。结果显示:该轨道钢呈现出明显的循环软化效应和压缩方向的棘轮行为,且棘轮行为的演化表现出强烈的加载路径相关性;在椭圆路径下,棘轮应变较其他四种路径更小。进而建立了基于Abdel Karim-Ohno非线性随动硬化律的非比例多轴循环棘轮本构模型,并通过在随动硬化和各向同性软化律中引入非比例因子来考虑非比例路径对双轴压-扭棘轮行为的影响。实验结果和模拟结果的对比表明:该本构模型能够较好地模拟高强度轨道钢的非比例双轴压-扭棘轮行为。     

Cyclic uniaxial and multiaxial loading with yield surface distortion consideration on prediction of ratcheting

In this study, the yield surface distortion was incorporated in the cyclic plasticity modeling as well as its center movement. The combination of Chaboche’s model and the yield surface distortion model of Baltov was used in a set of uniaxial and multiaxial loadings. The variation of the stress amplitude and the mean stress and different multiaxial loadings such as tension-torsion tests were studied. It was shown that the consideration of the distortion of the yield surface via the distortion parameter and its sign in modeling has an important effect on the plastic strain increment determination and so on the ratcheting rate. The combined model was applied to the experimental results. It was shown that the combination of the nonlinear kinematic hardening model of Chaboche and the yield surface distortion leads to a good estimation of the ratcheting strain increment in different uniaxial and multiaxial tests.