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.     

Isotropic‐kinematic hardening framework to assess ratcheting response of steel samples undergoing asymmetric loading cycles

The present study intends to characterize ratcheting response of several steel alloys subject to asymmetric loading cycles through coupling the Ahmadzadeh‐Varvani kinematic hardening rule with isotropic hardening rules of Lee and Zavrel, Chaboche, and Kang. The Ahmadzadeh‐Varvani kinematic hardening rule was developed to address ratcheting progress over asymmetric stress cycles with relatively a simple framework and less number of coefficients. Inclusion of isotropic hardening rules to the framework improved ratcheting response of materials mainly over the first stage of ratcheting. Lee and Zavrel model (ISO‐I) developed an exponential function to account for accumulated plastic strain as yield surface is expanded over stage I and early stage II of ratcheting. Isotropic models by Chaboche (ISO‐II) and Kang (ISO‐III) encountered yield surface evolution in the framework by introducing an internal variable that takes into account the prior maximum plastic strain range. The choice of isotropic hardening model coupled to the kinematic hardening model is highly influenced by material softening/hardening response.     

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.     

McDowell模型改进及1070钢棘轮效应的预测

利用McDowell 模型对1070 钢比例和非比例循环加载条件下的棘轮效应进行了预测,通过对McDowell模型的修正,为McDowell 模型中的单轴参数Ai引入了与塑性应变累积相关的演化方程,改进后的McDowell 模型能精确的预测具有拉压平均应力的单轴棘轮效应,具有平均应力的拉扭比例加载,常轴向应力的扭转循环,非比例循环载荷以及多重步骤加载条件下单轴平均应力变化的棘轮效应,改进的模型对较大循环数的棘轮效应也能给予较好的描述。     

Kinematic hardening rules for modeling uniaxial and multiaxial ratcheting

Ratcheting, which is the strain accumulation observed under the unsymmetrical stress controlled loading and non-proportional loadings, is modeled using the simplified viscoplasticity theory based on overstress (VBO). The influences of kinematic hardening laws on the uniaxial and multiaxial non-proportional ratcheting behavior of CS 1026 carbon steel have been investigated. The following kinematic hardening rules have been considered: the classical kinematic hardening rule, the kinematic hardening rules introduced by Armstrong–Frederick, Burlet–Cailletaud and the modified Burlet–Cailletaud. The investigated loading conditions include uniaxial stress controlled test with non-zero mean stress, and axial strain controlled cyclic test of thin-walled tubular specimen in the presence of constant pressure. Numerical results are compared with the experimental data obtained by Hassan and Kyriakides [Hassan T, Kyriakides S. Ratcheting in cyclic plasticity, part I: uniaxial behavior. Int J Plast 1992;8:91–116] and Hassan et al. [Hassan T, Corona E, Kyriakides S. Ratcheting in cyclic plasticity, part I: multiaxial behavior. Int J Plast 1992;8:117–146]. It is observed that all investigated kinematic hardening rules do not improve ratcheting behavior under multiaxial loading, but over-prediction still exists.     

Ratcheting assessment of steel alloys under step-loading conditions

The present study examines the capability of a recently modified hardening rule to characterize ratcheting response of materials subjected to multi-step uniaxial stress cycles. The modified hardening rule was developed based on Armstrong–Frederick (A–F) hardening rule through implementing new ratcheting rate dependent coefficients γ₂ and δ. These coefficients were estimated by means of calibrated curves for any given stress levels defined from the uniaxial single-step ratcheting response at various cyclic stress levels. At a constant mean stress, ratcheting strain progressively increased as stress amplitude over steps of loading history increased. Similar response was also evident for step-loading with constant stress amplitude while the values of mean stress increased. For high–low histories, the trend of predicted ratcheting strain from higher to lower magnitudes found agreeable with that of experimental data. The discrepancy of the predicted and experimentally ratcheting strain values in the high–low step loading however was due to constancy in the shape and size of translating yield surface in the modified kinematic hardening rule. The modified hardening rule was employed to assess ratcheting response of SS316L, SA333, SS316L(N) and 1070 steel alloys under various step-loading conditions. Predicted ratcheting data at various stress level were found in good agreements as compared with the experimental ratcheting strains.     

Key issues in cyclic plastic deformation: Experimentation

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.     

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。     

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.     

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.     

Uniaxial and non-proportionally multiaxial ratcheting of U71Mn rail steel: experiments and simulations

The ratcheting and strain cyclic characteristics of U71Mn rail steel were experimentally researched under uniaxial and non-proportionally multiaxial cyclic loading at room temperature. The effects of cyclic strain, stress and their histories on strain cyclic characteristics and ratcheting were studied, respectively. It is shown that: U71Mn rail steel exhibits a cyclic stabilization and non-memorization for previous loading history under strain cycling; however, the ratcheting of the material depends greatly not only on the current values of mean stress and stress amplitude, but also on their histories; the non-proportionality of multiaxial loading path only causes a negligible additional hardening for the material. Based on the Ohno–Wang non-linear kinematic hardening model [Int. J. Plast. 9 (1993) 375, 391], the uniaxial and multiaxial ratcheting behaviours of the material were simulated by a visco-plastic constitutive model. The simulated results are in good consistence with the experimental ones.     

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.     

1Cr18Ni9不锈钢高温单轴时相关棘轮行为研究

在室温、250℃、500℃和650℃四种温度下对1Cr18Ni9不锈钢材料的单轴应变循环特性及其时相关棘轮行为进行了实验研究,以讨论不同加载速率、加载波形和峰值应力保持时间对材料棘轮行为的影响。实验结果表明:在室温下,材料呈现出弱的循环软化特性和渐进型棘轮变形行为,并对加载速率和峰值应力保持时间具有强烈依赖性;在250℃、650℃下,因材料的循环硬化加快而使其棘轮行为较快趋于安定,但棘轮变形大小仍一定程度依赖于加载速率和保持时间;在500℃温度下则由于动态应变时效的影响没有明显的棘轮行为发生。研究得到一些有助于后续建立时相关本构模型的结论。     

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.     

A plastic shakedown constitutive curve based on uniaxial ratcheting behavior of 304 stainless steel at room temperature

On the basis of the Bauschinger effect, a relationship between the elastic space defined in this study and the accumulated plastic strain is measured in uniaxial ratcheting tests of 304 stainless steel at room temperature. According to this relationship, a new model of uniaxial ratcheting is established and used to simulate uniaxial ratcheting behavior. The results of simulation agree well with the experimental results. These results demonstrate that the relationship between the elastic space and the accumulated plastic strain plays an important role in uniaxial ratcheting simulation. Furthermore, by taking into account the interaction of ratcheting and viscoplasticity, the relationships among elastic space, accumulated plastic strain and loading cases are discussed. It can be seen that, when the stress ratio R of valley stress versus peak stress is not less than zero, the accumulated plastic strain is a function of the peak stress. So, a constitutive curve is obtained to describe the stable states of plastic shakedown for 304 stainless steel material under the stress ratio R ≥ 0. It can be used to determine the accumulated plastic strain of engineering structures under cyclic loading only by an elastic–plastic analysis.     

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.     

Thermal ratcheting of solder-bonded layered plates: cyclic recovery and growth of deflection

This paper describes computational analysis of the thermal ratcheting of solder-bonded layered plates subjected to cyclic thermal loading following solder-bonding. Finite element computations of Si/solder/Cu layered plates are performed by taking into account mechanical ratcheting of the copper as well as temperature-dependent creep of the solder. A sophisticated non-linear kinematic hardening model is used for appropriately representing mechanical ratcheting of the copper; a temperature-dependent power-law creep model is assumed for the solder. It is shown that the layered plates can exhibit either the cyclic recovery or the cyclic growth of deflection depending on the extent of plastic yielding in the copper layer, and that the cyclic recovery always occurs if the copper layer is elastic. It is also demonstrated that the cyclic recovery of deflection can be much greater than the static recovery of deflection at a constant temperature.