Determination of combined hardening material parameters under strain controlled cyclic loading by using the genetic algorithm method

In this paper, experimental and numerical investigations on mechanical behaviors of SS304 stainless steel under fully reversed strain-controlled, relaxation, ratcheting and multiple step strain-controlled cyclic loading have been performed. The kinematic and isotropic hardening theories based on the Chaboche model are used to predict the plastic behavior. An iterative method is utilized to analyze the mechanical behavior under cyclic loading conditions based on the Chaboche hardening model. A set of kinematic and isotropic parameters was obtained by using the genetic algorithm optimization approach. In order to analyze the effectiveness of this optimization procedure, numerical and experimental results for an SS304 stainless steel are compared. Finally, the results of this research show that by using the material parameters optimized based on the strain-controlled and relaxation data, good agreement with the experimental data for ratcheting is achieved.     

Cyclic loading of beams based on the Prager and Frederick–Armstrong kinematic hardening models

The kinematic hardening theory of plasticity based on the Prager and Frederick–Armstrong models are used to evaluate the cyclic loading behavior of a beam under the axial, bending, and thermal loads. The beam material is assumed to follow non-linear strain hardening property. The material's strain hardening curves in tension and compression are assumed to be both identical for the isotropic material and different for the anisotropic material. A numerical iterative method is used to calculate the stresses and plastic strains in the beam due to cyclic loadings. The results of the analysis are checked with the known experimental tests. It is concluded that the Prager kinematic hardening theory under deformation controlled conditions, excluding creep, results into reversed plasticity. The load controlled cyclic loading under the Prager kinematic hardening model with isotropy assumption results into reversed plasticity. Under anisotropy assumption of tension/compression curve, this model predicts ratcheting. On the other hand, the Frederick–Armstrong model predicts ratcheting behavior of the beam under load controlled cyclic loading with non-zero mean load. This model predicts reversed plasticity under the load controlled cyclic loading with zero mean load, and deformation controlled cyclic loading.     

Evaluation of cyclic plasticity models of multi-surface and non-linear hardening by an energy-based fatigue criterion

This study examines the performance of four constitutive models according to capacity in predicting metal fatigue life under proportional and non-proportional loading conditions. These cyclic plasticity models are the multi-surface models of Mroz and Garud, and the non-linear kinematic hardening models of Armstrong-Frederick and Chaboche. The range of abilities of these models is studied in detail. Furthermore, the plastic strain energy under multiaxial fatigue condition is calculated in the cyclic plasticity models by the stress-strain hysteresis loops. Using the results of these models, the fatigue lives that have set in the energy-based fatigue model are predicted and evaluated with the reported experimental data of 1% Cr-Mo-V steel in the literature. Consequently, the optimum model in the loading condition for this metal is chosen based on life factor.     

General analytical shakedown solution for structures with kinematic hardening materials

The effect of kinematic hardening behavior on the shakedown behaviors of structure has been investigated by performing shakedown analysis for some specific problems. The results obtained only show that the shakedown limit loads of structures with kinematic hardening model are larger than or equal to those with perfectly plastic model of the same initial yield stress. To further investigate the rules governing the different shakedown behaviors of kinematic hardening structures, the extended shakedown theorem for limited kinematic hardening is applied, the shakedown condition is then proposed, and a general analytical solution for the structural shakedown limit load is thus derived. The analytical shakedown limit loads for fully reversed cyclic loading and non-fully reversed cyclic loading are then given based on the general solution. The resulting analytical solution is applied to some specific problems: a hollow specimen subjected to tension and torsion, a flanged pipe subjected to pressure and axial force and a square plate with small central hole subjected to biaxial tension. The results obtained are compared with those in literatures, they are consistent with each other. Based on the resulting general analytical solution, rules governing the general effects of kinematic hardening behavior on the shakedown behavior of structure are clearly.     

Shakedown analysis of beams using nonlinear kinematic hardening materials coupled with continuum damage mechanics

The nonlinear kinematic hardening theory of plasticity based on the Armstrong-Fredrick model and isotropic damage was used to evaluate the cyclic loading behavior of a beam under the axial, bending, and thermal loads. Damage and inelastic deformation were incorporated and they were used for the beam shakedown and ratcheting analysis. The beam material was assumed to follow the nonlinear strain hardening property coupled with isotropic damage. The effect of the damage phenomenon coupled with the elastoplastic nonlinear kinematic hardening was studied for deformation and load control loadings. The Bree's diagram was obtained for two different types of loading, and all numerical results confirmed the reduction of the safe loading domain due to material damage.     

GS-20Mn5钢非对称循环应力-应变本构模型及其应用

在实际工程中,机械结构件承受反复载荷时,内部往往是非对称的应力应变状态。在非对称循环加载条件下,材料不仅会表现出循环软/硬化特性,还会表现出平均应力松弛行为。这会影响其在循环稳定状态下的力学性能,进而影响结构在相应工况下承载服役的强度安全性。针对大型压机本体结构常用GS-20Mn5钢进行了单向拉伸及应变比R为0.5,应变幅0.20%、0.25%、0.27%、0.30%和0.40%的非对称应变循环加载试验研究,分别构建了基于单向拉伸试验结果的A-F随动硬化模型,以及基于非对称循环加载的Landgraf模型来描述其平均应力松弛特性,将其应用到Ramberg-Osgood公式中,结合A-F非线性随动硬化模型,建立了非对称循环加载条件下对应于循环应力-应变曲线的本构模型,并确定了相应模型参数。针对承受非对称循环载荷的某大型锻造液压机上横梁,应用所建立的本构模型分别进行了安定性数值分析,评估了其在循环载荷下的弹塑性强度安全性。结果显示,与采用单向拉伸条件下的A-F模型时的计算结果相比,采用非对称循环应力-应变本构模型时上横梁的安定极限载荷提高了约7%。     

变幅单/多轴混合加载下GH4169光滑件的弹塑性有限元分析

对承受变幅单轴和变幅非比例多轴加载的镍基合金GH4169光滑薄壁管进行了有限元分析。使用ANSYS有限元分析软件进行有限元建模,采用Von Mises屈服准则和多线性随动强化准则来描述变幅弹塑性特性。结合三角波加载,在柱坐标系下对试样一端加载轴向位移和周向位移来实现拉扭应变加载。通过对光滑薄壁管件的有限元分析结果与试验结果进行比较,说明此方法对变幅单多轴加载弹塑性分析的正确性和实用性。     

Discussion of cyclic plasticity and viscoplasticity of single crystal nickel-based superalloy in large strain analysis: comparison of anisotropic macroscopic model and crystallographic model

The inelastic behavior of nickel-based superalloy is investigated in detail by application of a macroscopic anisotropic plasticity model developed here, and the results are compared to predictions based on crystal plasticity, which incorporates the kinematic hardening. Uniaxial deformation processes and simple shear deformations at large strain are considered. The plastic spin concept coupled with an anisotropic Chaboche model is provided in the framework of macroscopic viscoplasticity. The plastic spin formulation used here is based on the concept of the noncoaxiality between the stress and plastic rate of deformation. The present model succeeds in reproducing the inelastic behavior during large deformation. It is shown that the plastic spin associated with the anisotropic flow rule plays a key role in the macroscopic model. Simulation results find these two different scale models provide similar predictions under uniaxial deformation for [0 0 1] and [1 1 1] orientation, while their predictions for simple shear deformation at large strain exhibit quantitative difference, but their trends are the same. The interpretations for simulation results are pursued in detail.     

Finite element simulation of springback for a channel draw process with drawbead using different hardening models

The objective of this work is to predict the springback of Numisheet’05 Benchmark#3 with different material models using the commercial finite element code ABAQUS. This Benchmark consisted of drawing straight channel sections using different sheet materials and four different drawbead penetrations. Numerical simulations were performed using Hill's 1948 anisotropic yield function and two types of hardening models: isotropic hardening (IH) and combined isotropic-nonlinear kinematic hardening (NKH). A user-defined material subroutine was developed based on Hill's quadratic yield function and mixed isotropic-nonlinear kinematic hardening models for both ABAQUS-Explicit (VUMAT) and ABAQUS-Standard (UMAT). The work hardening behavior of the AA6022-T43 aluminum alloy was described with the Voce model and that of the DP600, HSLA and AKDQ steels with Hollomon's power law. Kinematic hardening was modeled using the Armstrong-Frederick nonlinear kinematic hardening model with the purpose of accounting for cyclic deformation phenomena such as the Bauschinger effect and yield stress saturation which are important for springback prediction. The effect of drawbead penetration or restraining force on the springback has also been studied. Experimental cyclic shear tests were carried out in order to determine the cyclic stress-strain behavior. Comparisons between simulation results and experimental data showed that the IH model generally overestimated the predicted amount of springback due to higher stresses derived by this model. On the other hand, the NKH model was able to predict the springback significantly more accurately than the IH model.     

晶体塑性模型在单晶铜低周疲劳行为中的应用

关注循环载荷作用下晶体滑移变形中的非线性硬化现象,用改进的晶体塑性模型刻画单晶金属在循环载荷作用下的变形机理.通过试验和数值模拟,研究单晶铜在循环载荷作用下的Bauschinger效应、滞回特性和循环硬化等循环塑性现象.所得结果表明,文中提出的模型可以有效地描述单晶金属在循环载荷下的非线性变形过程,可以与有限元方法结合,用数值模拟再现试样在循环加载中的Bauschinger效应、滞回特性和循环硬化等塑性变形行为.     

不同强化模型下的板料成形极限

介绍Hill48屈服准则下基于不同强化模型的屈服方程。推导出能够用来确定随动强化模型和混合强化模型中参数的方程。采用单向拉伸曲线上所取得的数据,对所得方程进行拟合,得到参数值,并使用所得参数值得出三种强化模型下的单向拉伸曲线。结果表明采用上述方法能够准确地确定强化模型中的参数。给出随动强化模型和混合强化模型下成形极限的计算方法。基于三种强化模型,针对分散性失稳准则、Hill集中性失稳准则、凹槽失稳准则和平面应变漂移失稳准则,得到简单加载路径下的成形极限图和成形极限应力图。从这些图中可以看出,强化模型对成形极限图和成形极限应力图影响明显。因此应当确定板料在成形过程中的强化规律,选择合适的强化模型进行成形极限预测。     

Inelastic constitutive models for the simulation of a cyclic softening behavior of modified 9Cr-lMo steel at elevated temperatures

In this paper, the inelastic constitutive models for the simulations of the cyclic softening behavior of the modified 9Cr-1Mo steel, which has a significant cyclic softening characteristic especially in elevated temperature regions, are investigated in detail. To do this, the plastic modulus, which primarily governs the calculation scheme of the plasticity, is formulated for the inelastic constitutive models such as the Armstrong-Frederick model, Chaboche model, and Ohno-Wang model. By implementing the extracted plastic modulus and the consistency conditions into the computer program, the inelastic constitutive parameters are identified to present the best fit of the uniaxial cyclic test data by strain-controlled simulations. From the computer simulations by using the obtained constitutive parameters, it is found that the Armstrong-Frederick model is simple to use but it causes significant overestimated strain results when compared with the Chaboche and the Ohno-Wang models. And from the ratcheting simulation results, it is found that the cyclic softening behavior of the modified 9Cr-1Mo steel can invoke a ratcheting instability when the applied cyclic loads exceed a certain level of the ratchet loading condition.     

304不锈钢两阶段载荷模式下的疲劳寿命

对304不锈钢进行一系列单轴、扭转、比例和非比例循环载荷变化的两阶段低周疲劳实验,比较各阶段载荷下的循环特性.结果表明在第一阶段载荷下,材料在开始几个循环表现出软化特性,在路径转化时有交错强化现象,而在圆路径下产生明显的附加强化.试验结果表明,这种强化对疲劳寿命有明显影响,使两段载荷的总疲劳损伤小于1.文中比较了线性损伤律和几个非线性损伤律(Manson的双线性损伤律、损伤曲线方法、Morrow模型)的寿命预测结果,表明对寿命的预测各模型都给出了不安全的结果.     

小变形循环载荷下Q235材料特性的试验研究

为进一步挖掘材料的承载能力,以焊接结构常用材料Q235为研究对象,通过应变控制下的循环加载试验,得到了Q235在小变形量循环载荷作用下的应力应变曲线及特征,应力随循环周次的变化规律,并给出了相应的数学模型。试验结果表明,Q235在小应变对称循环载荷作用下表现出循环硬化特性和包申格效应,随循环周次的增加,循环硬化速率和包申格能量参数变化率最终均会达到一个稳定值;Q235在小应变非对称循环载荷作用下的变形特征,可以看作是其对应变初值和对称应变循环载荷叠加作用的响应,且随循环周次的增加,材料响应应力峰值与屈服应力逐渐回归于相同幅值对称应变作用下的相应数值。     

低周循环应力-应变关系和损伤

引入硬化状态变量表征微结构变化对材料循环变形行为的影响，提出应变控制下材料的循环应力一应变关系，由此导出的疲劳损伤演变方程与材料的损伤和硬化状态有关，考虑加载历史的影响。其结果可以为分析多级疲劳加载时，损伤演变过程和剩余寿命估算提供新的思路。     

Prediction of history-dependent forming limits by applying different hardening models

The loading history-dependent forming limits have been computed for sheet metals undergoing various combinations of plane-stress loading conditions. The analysis method is essentially an extension of Marciniak and Kucźynski's inhomogeneous model, except that the roles of isotropic and Prager-Ziegler kinematic hardening have been examined in detail while the flow theory of plasticity is applied. A suitable modification of the constitutive equations for the kinematic hardening model converts the rate form of the constitutive equations into the finite-increment form which satisfies the yield criterion precisely. Representative combinations of strain history consisted of an initial proportional straining to either a fixed strain state or different levels of strain state followed by continued loading under different conditions of strain ratios. Comparison of computed forming limits with available experimental data shows that the ultimate choice of either an isotropic or a kinematic hardening model is dependent on a specific combination of strain history and the material properties.     

缺口件两轴循环弹塑性有限元分析及寿命预测

利用弹塑性有限元模拟,对高温两轴比例与非比例拉扭应变循环加载下的光滑薄壁管件与缺口轴类件进行研究.材料弹塑性特性用Von Mises屈服准则、多线性运动硬化准则和高温单轴循环加载的应力应变数据来描述.采用柱坐标系下在试样一端加轴向和周向位移来实现拉扭应变加载.对光滑薄壁管件的后处理结果与试验结果比较,证实了这种方法的正确性和可用性,进而应用到缺口件,得到缺口根部局部的循环应力应变响应.基于有限元数据,采用Kandil-Brown-Miller法和Smith-Watson-Topper法预测了缺口件疲劳裂纹萌生寿命.     

复杂循环载荷条件下金属的应力、应变规律

在各向同性循环强化模型基础上 ,通过屈服面及极限面形状、方向及面积的变化 ,分析了拉 -扭非比例循环载荷下金属的双表面各向异性强化模型 [1 ] ,并用BT9钛合金 [3 ] 及 30 4不锈钢 [3～ 5] 的试验结果检验了该模型的可行性。采用了塑性应变历程非比例参数来描述非比例载荷下材料的循环强化程度。研究了材料的横向强化及附加强化效应。结果表明 :本模型能很好地描述非比例载荷下金属的一系列主要应力、应变规律     

双相不锈钢各组相循环变形行为的纳米压痕试验和有限元表征方法研究

对双相不锈钢的奥氏体相和铁素体相,分别开展了不同加载模式（接触载荷和压入位移）和不同加载波形下的单向、循环纳米压痕试验,对比分析了两相的基本力学性能和压痕循环变形行为的演化规律。基于压痕试验结果和修正ABDEL-KARIM-OHNO非线性随动硬化准则的弹塑性本构模型,提出一套双相不锈钢奥氏体相和铁素体相的塑性和循环塑性行为的本构模型参数表征方法。通过对微结构代表性体积单元整体拉伸和循环变形行为进行模拟,并与宏观试验结果对比,验证了参数表征方法的合理性。研究结果表明,铁素体相的强度、硬度和抗棘轮变形的能力均高于奥氏体相,两相之间通过晶界产生一定的交互作用;在接触载荷控制的循环加载条件下,奥氏体相与铁素体相均产生明显的压痕棘轮现象,且载荷水平越高压痕棘轮变形程度越大;所发展的本构模型参数表征方法可为研究多相材料各组相、小体积材料的循环变形行为提供借鉴和参考。     

Influence of hardening rule on prediction of cyclic plasticity in pressurized thin tubes subjected to cyclic push-pull

The paper considers the cyclic plastic behaviour of a thin-walled tube subjected to steady internal pressure and cyclic reversed axial push-pull. Tubes under such a loading combination are known to exhibit continued strain growth in the hoop direction. The steady-state behaviour of the tube is investigated using a number of hardening rules within the framework of time-independent plasticity theory. Isotropic hardening and Prager kinematic hardening are considered first and shown to yield no strain growth at the steady state. When a kinematically hardened yield surface is assumed to translate in the direction of the stress rate vector, considerable steady-state strain growth is predicted in the hoop direction. Consideration of two-surface plasticity theory yields also large steady-state strain growth. Closed-form analytical expressions are derived for growth rates and ranges of cyclic plasticity for all hardening rules considered. Contours of strain growth are plotted for practical ranges of primary and secondary stresses using representative material properties. Comparison with limited test data indicate that the predicted steady growth rate is larger than about four times observed rate.