A unified plasticity methodology for rate-and temperature-sensitive alloys exhibiting a non-linear kinematic hardening behavior

In this paper, a novel unified plasticity methodology is proposed to allow the coupling of rate-and temperature-sensitivity of engineering alloys as well as the non-linear kinematic hardening behavior often observed during cyclic loading. The proposed methodology is general in the sense that an arbitrary constitutive model may be chosen for the viscoplastic part, as well as the cyclic part. We adapt our model with a physically-motivated viscoplasticity flow rule and a nonlinear kinematic hardening model. In contrast with other unified plasticity models, the simplified theory involves few material parameters that can be readily calibrated from standard mechanical tests. The capabilities of the proposed theory are demonstrated for a hot rolled annealed 304 L stainless steel supplied by Vimetal Peckover. The model is tested with stress–strain curves obtained from standard tensile and cyclic uniaxial tests at various strain amplitudes and strain-rates, and good accuracy of the response is obtained for strains up to 15%, within a temperature range of 293–673 K. We note that the cyclic plasticity model in our adapted theory can be readily enhanced with ratchetting, mean stress relaxation, strain amplitude history, Masing effects or other complex capabilities.

THE KINEMATIC HARDENING RULES UNDER NONPROPORTIONAL CYCLIC LOADING

A discussion of several kinematic hardening rules based on nonproportional cyclic experiments of 42CrMo steel is presented. They include Prager, Ziegler, Chaboche, Mroz and Tseng Lee hardening rules. It shows that Mroz and Tseng Lee rule related to a two surface model has the latent potentiality to describe the nonproportional cyclic hardening behaviors, and a simple two surface model is presented.

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.

AN EXPERIMENTAL STUDY ON THE KINEMATIC HARDENING RULES FOR NONPROPORTIONAL CYCLIC PLASTICITY

An experimental investigation was cawted out of the cyclic saturated kinematic hardening of the solution treatment stainless steel 316L subjected to cyclic loading for seveml strain paths, such as uniaxial cycling, cireulan elliPtic, diamond, rectangular shapes. The evoluting tndectories of back stresses in deviatoric stress space were obtained, and the evolution of back stress mtes during cyclic saturuted loading was analyzed under the assumption that the yield sudece rudius at cyclic saturation is constant and the direction of plastic stmin rute coincides with the one of the out normal vector Of the yield sudece. Some significant results were obtained.

SHAKEDOWN ANALYSIS OF SHELL STRUCTURES OF KINEMATIC HARDENING MATERIALS

It is of great practical importance to analyze the shakedown of shell structures under cyclic loading, especially of those made of strain hardening materials.In this paper, same further understanding of the shakedown theorem for kinematic hardening materials has been made, and it is applied to analyze the shakedown of shell structures Though the residual stress of a real stale is related to plastic strain, the time-independent residual stress field as we will show in the theorem may be unrelated to the time-independent kinematically admissible plastic strain field For the engineering application, it will lie much more convenient to point this out clearly and definitely, otherwise it will be very difficult. Also, we have proposed a new method of proving this theorem.The above theorem is applied to the shakedown analysis of a cylindrical shell with hemispherical ends. According to the elastic solution, various possible residual sfcss and plastic strain Jlelds, the shakedown analysis of the structure can be reduced to a mathematical programming problem.The results of calculation show that the shakedown load oj strain hardening materials is about 30-40% higher than that of ideal plastic materials. So it is very important to consider the hardening of materials in the shakedown analysis,for it can greatly increase the structure design capacity, and meanwhile provide ascicntific basis to improve the design of shell structures.

A refined deviatoric hardening plastic model for sand

The classical deviatoric hardening models are capable of characterizing the mechanical response of granular materials for a broad range of degrees of compaction.This work finds that it has limitations in accurately predicting the volumetric deformation characteristics under a wide range of confining/consolidation pressures.The issue stems from the pressure independent hardening law in the classical deviatoric hardening model.To overcome this problem,we propose a refined deviatoric hardening model in which a pressure-dependent hardening law is developed based on experimental observations.Comparisons between numerical results and laboratory triaxial tests indicate that the improved model succeeds in capturing the volumetric deformation behavior under various confining/consolidation pressure conditions for both dense and loose sands.Furthermore,to examine the importance of the improved deviatoric hardening model,it is combined with the bounding surface plasticity theory to investigate the mechanical response of loose sand under complex cyclic loadings and different initial consolidation pressures.It is proved that the proposed pressure-dependent deviatoric hardening law is capable of predicting the volumetric deformation characteristics to a satisfactory degree and plays an important role in the simulation of complex deformations for granular geomaterials.

Parameters Calibration of the Combined Hardening Rule through Inverse Analysis for Nylock Nut Folding Simulation

Locking nuts are widely used in industry and any defects from their manufacturing may cause loosening of the connection during their service life.In this study,simulations of the folding process of a nut’s flange made from AISI 1040 steel are performed.Besides the bilinear isotropic hardening rule,Chaboche’s nonlinear kinematic hardening rule is employed with associated flow rule and Hill48 yield criterion to set a plasticity model.The bilinear isotropic hardening rule’s parameters are determined by means of a monotonic tensile test.The Chaboche’s parameters are determined by using a low cycle tension/compression test by applying curve fitting methods on the low cycle fatigue loop.Furthermore,the parameter calibrations are performed in the finite element simulations by using an optimization approach based on the inverse analysis.Dimensional accuracy for the nut is of primary concern due to the tolerance constraints of the nut manufacturers.Experimental diameter and height measurements of the folded locking nut are compared with those obtained from the optimized model.The results reveal that the folding dimensions can be predicted more accurately when the model parameters are determined by using the combined hardening rule.The calibrated parameters are presented for the folding and cycling deformation processes.

AN UPPER DISPLACEMENT BOUND IN DYNAMIC SHAKEDOWN PROBLEMS FOR ELASTOKINEMATIC WORK-HARDENING MATERIALS

A dynamic shakedown theorem for an elasto-kinematic work-hardenlng material with an arbitrary convex yield surface is reviewed. An upper displacement bound for this dynamic shakedown structure is derived. Except for the condition necessary for shakedown of the structure, no other restriction is imposed, which eliminates some of the difficulties appearing in Previous works.

基于晶体塑性有限元法的316LN不锈钢单轴力学行为

为了更准确描述316LN不锈钢单轴力学行为,在率相关晶体塑性理论框架下,以Ahmadzadeh-Varvani(A-V)随动硬化准则为基础,构建了多晶循环塑性本构模型.通过程序UMAT将其移植到有限元软件ABAQUS中,并通过Voronoi图建立二维多晶有限元模型;分别模拟了不同加载率、应变循环和非对称应力循环条件下316LN不锈钢的变形行为.对比模拟结果与实验数据可知:单轴拉伸条件下,两者的应力误差在±0.9%附近波动,最大应力误差仅为1.9%;应变循环条件下,两者的最大应力误差出现在第5圈,拉伸和压缩阶段应力误差分别为11.4%和12.2%,循环稳定后,拉伸和压缩阶段应力误差分别为7.4%和7.9%;应力循环条件下,两者的误差主要体现在滞环宽度上,模拟的滞环面积相对较窄,但滞环演化趋势误差较小.

循环荷载下低屈服点钢材LYP225的力学性能

为了研究低屈服点钢材LYP225的循环本构关系,对18个试件进行单调加载和循环加载,研究其单调曲线、滞回特点、破坏形态等.基于Ramberg-Osgood模型拟合了对称逐级加载下的循环骨架曲线,通过试验滞回数据标定了基于Chaboche模型的等向强化和随动强化参数,并将其输入到Abaqus软件的混合强化模型中,对强化参数的准确性进行验证.结果表明:LYP225钢材的应力-应变关系与加载历史相关;在不同加载制度下LYP225钢材均表现出良好的延性特征;采用Ramberg-Osgood模型能较好地模拟LYP225钢材在循环对称逐级加载下的骨架曲线;将标定的混合强化参数输入到Abaqus软件中,所得结果能准确模拟LYP225钢材的滞回曲线.因此,LYP225钢材在循环荷载下的性能不同于单调荷载,通过试验数据拟合的强化参数可用于整体结构中的地震反应分析.

低屈服点钢材LYP100循环加载试验

为了准确模拟低屈服点钢材LYP100的弹塑性地震反应,需要对材料的循环本构关系进行研究.采用16种不同加载制度对LYP100的20个试件进行试验,分析单调曲线、滞回曲线、破坏形态、延性特点等.基于Ramberg-Osgood模型对逐级加载下的循环骨架曲线进行拟合.利用试验数据标定LYP100钢材的等向强化和随动强化参数,通过ABAQUS有限元数值模拟进行参数数值的验证.结果表明,LYP100钢材表现出明显的循环硬化特征;LYP100经历过循环荷载加载以后仍具有良好的延性;采用Ramberg-Osgood模型可以较好地模拟LYP100在逐级循环加载下的骨架曲线;标定的强化模型参数,应用到ABAQUS有限元软件中时,计算结果与试验结果接近.

剪胀和破坏耦合的节理岩体本构模型的研究

根据节理岩体切向加载作用下的变形机制,把微凸体在磨损破坏过程中引起的剪胀软化现象和伴随的强化现象分开考虑,提出一种新的本构模型。试验结果表明,在法向和切向载荷共同作用下,由于微凸体的爬坡和啃断作用,节理岩体均会发生一定程度的剪胀和磨损,累积到一定程度就产生软化现象,在此引入一个初始剪应力概念体现上述特征。另一方面,由于破碎颗粒的碾压和迁移作用,使得抗剪力学行为由微凸体粗糙度控制逐渐转变为由结构面上形成的紧密夹层的力学行为所控制,抗剪强度提高,在此通过弹塑性随动强化模型来体现这一变形行为。当随动强化模型与初始剪应力相结合时,即为节理岩体切向加载作用下的剪应力–切向位移本构关系。通过对各种已有试验曲线的对比分析,验证该模型的正确性。

热疲劳裂纹开裂过程的有限元模拟

用有限元方法并考虑材料的多线性随动强化性质对带有裂纹的简单试件模型进行热疲劳分析,研究热疲劳裂纹张开的过程和规律。在升温半循环中材料受热膨胀,热疲劳裂纹保持闭合,两裂纹面相互挤压,当压缩应力达到材料的屈服极限,产生压缩塑性变形;在降温半循环中试件有恢复原有形状的趋势,但由于升温半循环中生成的压缩塑性变形不可恢复,裂纹逐渐张开.热疲劳裂纹张开的一个必要条件是高温侧材料在升温过程产生压缩塑性变形,这与普通疲劳裂纹不同.

材料强化模型对板料回弹量的影响

基于Lemaitre and Chaboche非线性随动强化理论、等向强化和Mises屈服准则,建立了复杂加载模式下非线性混合强化材料模型的弹塑性应力应变本构关系,并采用Backward Euler切向预测径向返回算法计算应力应变增量.基于ABAQUS开发式程序接口,编写了非线性混合强化材料模型用户子程序.以Numisheet’93板料U型弯曲考题为例,分析了不同材料强化模型对板料回弹量的影响.结果表明,线性随动强化因模拟板料成形后的应力最小而低估了回弹量,各向同性强化因模拟成形后的应力最大而使预测的回弹量偏大.与Numisheet’93实验值的比较可知,对于复杂加载问题,采用非线性混合强化材料模型预测板料回弹量的精度最高.

基于包辛格效应的回弹仿真分析

金属材料在一个方向上的应变硬化降低了反方向的屈服强度,材料包辛格效应的存在对车身成形仿真精度产生了重要影响,尤其现今高强钢和铝合金的大量应用,使车身成形件的回弹问题日益突出,车身模具制造对有限元回弹预测的准确性提出更高的要求。为了提高回弹的仿真精度有必要对材料的包辛格效应进行研究,利用一套夹具对DC06和DP600两种材料的薄板进行拉伸压缩试验,获得不同预应变下的位移加载曲线,通过拉伸压缩试验结果与仿真结果的对比分析,得到能反映材料包辛格效应的非线性混合硬化模型材料参数。开展U形件成形试验,并建立试验的仿真模型,计算DC06和DP600薄板的U形件成形回弹量,分析等向强化、混合强化和随动强化本构模型对回弹预测精度的影响,针对回弹仿真结果和试验结果的差别,对影响仿真精度的材料模型因素进行分析。结果表明,DC06和DP600的包辛格效应大小存在差别,考虑包辛格效应有助于回弹仿真精度的提高,但小曲率弯曲成形回弹计算对材料本构模型的敏感性,限制了回弹仿真精度的提高。

板材通过拉深筋时的循环塑性变形机理分析

板材通过拉深筋的变形具有明显的循环加载特征,因反向加载时存在包申格效应,所以目前对不同反向加载阶段板材的变形特征还不明确。为研究板材在拉深筋中的循环变形机理,明确不同加载阶段的变形特征及包申格效应的具体体现,考虑板材方向性、加工硬化特性和包申格效应,建立基于Hill正交各向异性屈服条件和Ziegler随动硬化法则的材料模型。分别采用Mises屈服条件的各向同性硬化、Hill屈服条件的随动硬化两种材料模型,对板材通过半圆形拉深筋的循环塑性变形过程进行数值模拟对比分析,并通过试验验证所建材料模型的有效性。分析随动硬化模型下计算所得板材经过拉深筋时的循环变形特征及各加载阶段应力应变的对应关系;揭示包申格效应对应力-应变循环关系的影响规律。对应力应变历程关系曲线的分析显示,不同于现有的分析结果板材在半圆筋中经历了两次弯曲、卸载与反向弯曲的塑性变形过程;板材同一截面上不同积分点在同一加载分支的包申格效应参数不同,同一积分点在不同加载分支的包申格效应参数也不同;随循环加载次数增加,反映不同加载分支硬化情况的切线模量呈显著下降趋势。

考虑土石料颗粒破碎和密度变化的次塑性本构模型建模方法

试验和现场观测都发现高土石坝的坝料在高压及湿化作用下会发生显著的颗粒破碎,颗粒破碎会改变土石料的级配曲线和密度,因而影响其后继力学行为,因此,土石料的颗粒破碎是当前岩土工程领域的研究热点。为了模拟土石料在高压及湿化作用下发生显著的颗粒破碎现象,以及循环加载中的颗粒破碎与应力诱导各向异性随动硬化共同影响下土石料的变形,本文提出了一个建模方法,考虑土石料颗粒破碎和密度变化的影响。所建议的次塑性本构模型在经过试验资料的验证后可用于动力有限元数值计算。

钢管混凝土拱桥在车辆荷载作用下的非线性动力响应分析

根据随动硬化理论和钢管混凝土组合材料恢复力模型 ,提出了复杂应力状态下钢管混凝土组合材料的弹塑性应力应变关系。采用非线性有限元法 ,对一钢管混凝土拱桥进行移动车辆荷载作用下车—桥体系的动力响应分析 ,并进一步研究钢管混凝土组合材料进入塑性后对体系振动的影响 ,取得了较满意的结果 ,为钢管混凝土拱桥动力性能评价提供参考。

混凝土桥梁结构非线性地震损伤演化

采用基于断裂能的损伤变量表达式,以单位体积材料当前耗能与断裂能的比值定义损伤变量,考虑了混凝土的拉压异性效应。引入了地震损伤的整体演化指标,通过有限元方法利用材料塑性损伤模型模拟桥梁结构在地震激励下的非线性损伤演化过程。数值计算过程中考虑了混凝土后继屈服的随动强化效应,采用损伤型本构关系及相应的Drucker-Prager型屈服函数,并通过算例验证了混凝土结构的非线性地震损伤特性。

旋转硬化与统一硬化参量在修正剑桥模型中的应用

针对修正剑桥模型不能模拟土体剪胀性、应力路径转折时土体的应力应变特性以及应力引起的各向异性,将旋转运动硬化理论引入到修正剑桥模型中,给出了椭圆屈服面的旋转运动硬化机制,把等向硬化的修正剑桥模型扩展为旋转运动硬化模型.同时,为了能够反映砂土和超固结土的剪胀等本构特性,用统一硬化参量H代替修正剑桥模型中的等向硬化参数—塑性体积应变pvε,建立了一个新的基于旋转硬化与统一硬化参量的改进的修正剑桥模型.对修正剑桥模型、旋转运动硬化修正剑桥模型和新模型进行了定性对比,结果表明,新模型不但能够反映应力路径转折时土体的特性,也能描述土体的剪缩和剪胀.