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.     

Influence of hardening rule on the elasto-plastic behaviour of a simple structure under cyclic loading

The modes of cyclic elasto-plastic deformation of a two-bar structure with unequal areas and lengths under the simultaneous action of sustained mechanical load and cyclic thermal history are investigated analytically using three types of elasto-plastic material models: perfectly plastic, linear kinematic hardening and linear isotropic hardening. This simple structure is shown to exhibit much of the behaviour of interest in design of structural components subjected to repeated thermal loads: viz, elastic shakedown, reversed plasticity and ratcheting. The cyclic plastic behaviour of the structure is developed in closed form and the effects of strain hardening, hardening rule and geometrical parameters of the two-bar assembly on the deformation modes are critically examined.     

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.     

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.     

Ratcheting behavior of cylindrical pipes based on the Chaboche kinematic hardening rule

In this study, cyclic loading behavior of thick cylindrical pipes are described. Effects of internal pressure level and axial strain amplitude on the ratcheting rate under different types of loading histories are investigated. The kinematic hardening theory based on the Chaboche model is used to predict the plastic behavior of the structures. An iterative method is developed to analyze the structural behavior under cyclic loading conditions based on the Chaboche kinematic hardening 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.     

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。     

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.     

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%。     

高强钢变模量随动强化本构模型匹配与解耦标定策略研究

高强钢通过微观组织调控获得高强度,但不同牌号高强钢微观的不均匀变形和微观诱导塑性机理不同,使得高强钢卸载及反向加载行为更加复杂,并且牌号间差异增大,为此给出模型自适应匹配及参数解耦匹配的系统化策略,实现了高强钢回弹精确预测。首先建立幂函数和指数函数混合硬化模型,基于混合模型给出自由弯曲加载的弯矩平衡方程和曲率约束方程,基于变模量模型构建截面弹性弯矩的积分方程,基于加载和卸载解析模型建立逆向识别卸载参数的子优化模型。确定变模量线性随动强化、变模量非线性随动强化模型和含边界面的变模量随动强化模型的匹配策略。基于自由弯曲、单向拉伸和拉压试验数据,确定相应本构的子优化模型参数的优化次序,最终形成本构匹配及其参数解耦标定的系统化策略,并基于Fortran语言开发标定程序库。建立U形弯曲件和弧形弯曲件预测模型,分别对DP980和DH980两种高强钢不同应变水平下的识别结果及回弹预测结果进行对比分析,验证了解耦标定策略不仅提高了不同牌号数据的相关度,而且大幅度提升了同一牌号下的模型精度和稳定性,为基于数据的材料性能统一自辨识方法研究奠定了基础。     

不同材料的室温单轴应变循环特性和棘轮行为研究

通过对U71Mn轨道钢和316L不锈钢室温下单轴应变控制和应力控制循环的实验研究，就两种材料的应变循环特性和棘轮行为进行研究和比较。讨论应变循环下应变幅值和平均应变的大小及其历史对应变循环特性的影响以及应力循环下应力幅值和平均应力的大小及其历史对棘轮行为的影响，同时还讨论了应变循环与应力循环间的交互作用。研究中着重对两种材料的循环特性进行比较，得到一些有助于进行合理本构描述的结果。     

内压弯管受对称面外弯曲时的棘轮应变有限元分析

利用有限元法，采用弹性理想塑性模型，对受对称面外弯曲的内压弯管进行循环塑性分析。计算结果表明，在一定载荷作用下，弯管中部两顶线与内缘线之间有较大的塑性应变累积，且塑性应变区域随加载次数增加而增大。分析发现，棘轮应变沿多个方向发生，但以径向与环向为主，棘轮应变可用等效塑性应变描述。通过计算不同载荷下棘轮应变速率，得出结构的棘轮应变边界。由于采用弹性理想塑性模型，棘轮应变速率恒定，所得棘轮应变边界偏于安全，可供工程设计参考。     

对塑性诱导裂纹闭合几种影响因素的计算研究

基于塑性诱导裂纹闭合原理,通过弹塑性有限元方法的大规模数值计算分析,考察几何构形(带中心裂纹矩形板和中心孔双边裂纹矩形板)、材料强化模型(线性随动强化和非线性随动强化)、加载方式(等幅循环加载和等应力强度因子K循环加载)和应力比R等因素对疲劳裂纹张开、闭合规律的影响。结果表明,等幅加载中裂纹张开、闭合应力水平随裂纹长度变化且无明确规律可循。而在等K(给定应力比下保持最大应力强度因子不变)加载中,无论是使用不同材料强化模型,还是对应不同几何构形,用瞬时最大应力正则化的裂纹张开、闭合应力水平与裂纹长度无关。相同等K加载条件下,两种几何构形的裂纹张开应力强度因子均保持恒定且大小相近。两种随动强化模型对应的裂尖局部循环特性有差异,所获得的裂纹张开应力水平大小不同,但变化规律相似。文中结果可为更深入地理解疲劳裂纹扩展的驱动力机理提供帮助。     

A model of one-surface cyclic plasticity and its application to springback prediction

This paper presents an elasto-plastic constitutive model based on one-surface plasticity, which can capture the Bauschinger effect, transient behavior, permanent softening, and yield anisotropy. The combined isotropic-kinematic hardening law was used to model the hardening behavior, and the non-quadratic anisotropic yield function, Yld2000-2d, was chosen to describe the anisotropy. This model is closely related to the anisotropic non-linear kinematic hardening model of Chun et al. [2002. Modeling the Bauschinger effect for sheet metals, part I: theory. International Journal of Plasticity 18, 571-95.]. Different with the model, the current model captures in particular permanent softening with a constant stress offset as well as the Bauschinger effect and transient behavior under strain path reversal. Inverse identification was carried out to fit the material parameters of hardening model by using uni-axial tension/compression data. Springback predicted by the resulting material model was compared with experiments and with material models that do not account for permanent softening. The results show that the resulting material model has a good capability to predict springback.     

内压弯管在面内循环弯曲载荷作用下棘轮效应的研究

利用多轴试验机研究了内压及面内循环弯曲载荷作用下低碳钢弯管的棘轮效应。试验研究表明最大棘轮应变发生在顶线位置的环向。对于个别试件,内缘线位置也发现了环向棘轮应变,但所有试件的外缘线位置均未发现棘轮应变。内压不变时棘轮应变速率随面内循环弯曲载荷的增大而增大;面内循环弯曲载荷不变时,棘轮应变速率随内压的增大而增大。通过用户编程,采用Chen—Jiao—Kim随动强化模型,利用弹塑性有限元法对弯管进行了循环塑性分析。与试验结果相比,Chen—Jiao—Kim随动强化模型能给出较好的预测。采用C—TDF提出的等效塑性应变增量控制法确定了结构的棘轮边界。     

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.     

内压直管对称循环弯曲棘轮效应实验研究

利用多轴疲劳实验机及自行设计的准三点弯曲实验装置，对20钢直管在不同内压与不同循环弯曲载荷下进行棘轮应变测试。棘轮应变由应变计检测，直管径向变形由自行设计的径向位移引伸计检测。实验发现，内压直管在一定循环弯曲载荷作用下，将首先沿环向产生棘轮应变，随着载荷的增加，轴向也将产生棘轮应变，但较环向小。随着棘轮应变的产生，直管圆截面变为椭圆截面。无论是不同试件，还是同一试件的多载荷步实验，均发现相同内压下，循环弯曲载荷增大，棘轮应变速率增大；相同循环弯曲载荷下，内压增大，棘轮应变速率增大。多载荷步加载时，以往棘轮应变会降低应有的棘轮应变速率，尤其在较大的载荷下先发生棘轮应变后，这种影响十分明显。利用直管准三点弯曲实验装置，确定内压直管循环弯曲的棘轮边界。     

Effect of kinematic hardening on localized necking in biaxially stretched sheets

For elastic-plastic sheets under biaxial stretching localized necking is investigated assuming that the material follows a kinematic hardening rule. The investigation is mainly based on the plane stress approximation, but includes a few results obtained in the context of the three-dimensional theory. It is found that the forming limit curves predicted by kinematic hardening are in far better agreement with experimental results than the similar curves predicted by standard flow theory with isotropic hardening. For a high hardening material quite good agreement is obtained with predictions of deformation theory of plasticity, which may be considered as a simple model of a solid that develops a vertex on the yield surface.     

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.     

多种循环加载制度下Q235材料性能试验

对Q235钢进行了变应力载荷幅值及不同预变形和载荷保持时间等条件下的循环加载试验,并分析了其力学响应和材料性能。研究结果表明：Q235钢在应力控制的循环加载过程中表现出明显的循环软化特性和棘轮效应,棘轮应变的大小主要取决于载荷水平;当循环载荷逐级增大时,前期的变形会导致后期的棘轮应变增大;而当循环载荷逐级减小时,后期的棘轮应变值取决于最大载荷时的棘轮应变,且棘轮应变率接近于零;当预变形的响应应力峰值小于后期控制应力峰值时,预变形对材料的棘轮效应具有抑制作用,且预变形量越大,抑制效果越明显;载荷保持时间延长会使材料的棘轮应变增大,棘轮应变率增大,从而加速材料失效。