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.     

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。     

Modeling of uniaxial and biaxial ratcheting behavior of 1026 Carbon steel using the simplified Viscoplasticity Theory Based on Overstress (VBO)

Summary.  Hassan and Kyriakides [1], Hassan et al. [2], and Corona et al. [3] performed uniaxial and biaxial ratcheting experiments on heat-treated 1026 Carbon steel. The loading histories performed with uniaxial and tubular specimens were selected to simulate those encountered in nuclear reactor vessels. The stress-strain diagram of 1026 Carbon steel was used to determine the material constants in a simplified version of VBO. Small rate dependence was allowed. The model represents some nonlinear rate dependence, kinematic hardening and cyclically neutral behavior. The set of material constants determined only from uniaxial tests was used throughout the paper. Numerical experiments included are: (i) uniaxial stress-controlled cycling with various mean stresses, (ii) strain-controlled axial tests with tubular specimens under constant and variable internal pressure, and (iii) examination and variation of certain material constants of the VBO model that can influence ratcheting. Very good agreement with the experiments is found for the uniaxial case. However the ratchet strain accumulation during biaxial cycling is over-predicted by VBO and other constitutive models. Received November 5, 2001; revised June 12, 2002 Published online: January 16, 2003     

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.     

Experimental Study on Uniaxial and Multiaxial Strain Cyclic Characteristics and Ratcheting of 316L Stainless Steel

An experimental study was carried out on the strain cyclic characteristics and ratcheting of 316L stainless steel subjected to uniaxial and multiaxial cyclic loading. The strain cyclic characteristics were researched under the strain-controlled uniaxial tension-compression and multiaxial circular paths of loading. The ratcheting tests were conducted for the stress-controlled uniaxial tension-compression and multiaxial circular, rhombic and linear paths of loading with different mean stresses, stress amplitudes and histories. The experiment results show that 316L stainless steel features the cyclic hardening, and its strain cyclic characteristics depend on the strain amplitude and its history apparently. The ratcheting of 316L stainless steel depends greatly on the Values of mean stress, stress amplitude and their histories. In the meantime, the shape of load path and its history also apparently influence the ratcheting.     

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.     

Stabilized cyclic stress-strain calculation for metals under multiaxial loading

A simple plasticity model for modeling the stabilized cyclic stress-strain responses is developed to consider the effect of non-proportional additional hardening. In the proposed model, the plastic modulus for uniaxial loading is extended to multiaxial loading by introducing the non-proportionality factor and the additional hardening coefficient. The two introduced factors take into account the effects of non-proportional additional hardening, not only on the shape of the loading path, but also on the material and its microstructure. And then, the basic Armstrong-Frederick nonlinear hardening rule is modified to model the evolution of the back stress. The consistency condition is enforced to obtain the relationship between the back stress and plastic modulus. The proposed model requires only six material constants for estimating the stabilized responses. Comparisons between the test results (30CrNiMo8HH steel, SA 333 Gr.6 steel, and 1 %CrMoV steel) and model predictions show that the proposed model predicts relatively accurate stress responses under both proportional and non-proportional loading paths.     

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.     

A plasticity model for multiaxial cyclic loading and ratchetting

Summary The nonlinear behavior of metals when subjected to monotonic and cyclic non-proportional loading is modeled using the proposed hardening rule. The model is based on the Chaboche [1], [2] and Voyiadjis and Sivakumar [3], [4] models incorporating the bounding surface concept. The evolution of the backstress is governed by the deviatoric stress rate direction, the plastic strain rate, the backstress, and the proximity of the yield surface from the bounding surface. In order to ensure uniqueness of the solution, nesting of the yield surface with the bounding surface is ensured. The prediction of the model in uniaxial cyclic loading is compared with the experimental results obtained by Chaboche [1], [2]. The behavior of the model in multiaxial stress space is tested by comparing it with the experimental results in axial and torsional loadings performed by Shiratori et al. [5] for different stress trajectories. The amount of hardening of the material is tested for different complex stress paths. The model gives a very satisfactory result under uniaxial, cyclic and biaxial non-proportional loadings. Ratchetting is also illustrated using a non-proportional loading history.     

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.     

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.     

Parameter determination of Chaboche kinematic hardening model using a multi objective Genetic Algorithm

Chaboche model is a powerful tool to evaluate the cyclic behavior under different loading conditions using kinematic hardening theory. It can also predict the ratcheting phenomenon. To predict the ratcheting, it is required to determine the material parameters under strain control conditions. Although, these parameters can model the hysteresis loop fairly accurately, their ratcheting prediction does not have the same quality. A set of material parameters that could accurately predict both ratcheting and hysteresis loop is of great importance. The available models, generally for low cycle fatigue, are mostly complex and nonlinear. Therefore, an optimization procedure can be used for parameter determination and consequently improving the prediction of these models.Genetic Algorithm is a numerical approach for optimization of nonlinear problems. Using a multi objective Genetic Algorithm for Chaboche model, a set of parameters was obtained which improved both ratcheting prediction and hysteresis loop model. Two fitness functions were used for this approach. The proposed model was verified using Hassan and Corona’s experimental data conducted on CS 1026 low carbon steel. The model indicated a very good agreement in the case of uniaxial loading with the experimental data. The results of proposed model for biaxial loading histories are similar to the model by Hassan and his co-workers.     

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.     

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.     

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

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

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。     

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

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

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.