应变强化模型的安定准则研究

基于Melan经典的安定理论和von Mises屈服准则,建立了塑性应变强化条件下结构安定的数学模型,根据与时间无关的应力场的特性,对结构中与时间无关的应力场进行了合理的数学变换,将其与载荷变化系数联系起来,推导出与其对应的结构安定极限范围的表达式,给出塑性应变强化模型安定性存在的简化条件.该结论有利于简化应变强化条件下结构的安定分析.     

考虑材料强化的塑性安定性分析

采用较真实的材料本构模型，在Ｐｏｎｔｅｒ和Ｋａｒａｄｅｎｉｚ提出的扩展的安定性理论以及彭得到的考虑混合强化的安定性定量的基础上，发展了计及应变强化和循环强化的结构塑性安定区的分析方法。通过将循环强化和应变强化分别引入子区域ＶＦ和ＶＳ，利用材料安定性假设，得到了较为合理的塑性安定边界，克服了以前的工作中对处于ＶＦ和ＶＳ区中材料分别采用完全各向同性强化（或假设热应力史是弹性应力史）和完全塑性的理想材料     

厚壁圆筒的安定分析

本文讨论了幂强化材料以及弹性—幂强化材料厚壁圆筒在循环内压作用下的安定性;介绍了机动安定定理的推理以及具有部分恒定载荷时的表达式;讨论了厚壁圆筒在恒定内压与循环温度作用下的安定性。     

非线性随动强化条件下的安定定理

基于经典的安定理论与随动强化模型的一般性质,将结构在强化过程中的背应力计入Von Mises屈服准则,建立了随动强化条件下结构的静力安定定理;将背应力与对应的塑性应变率的点积在一个载荷循环内的积分计入塑性耗散功,建立了随动强化条件下结构的机动安定定理,扩展了经典安定理论的应用范围。针对两种定理的存在格式进行了理论证明,并以推论形式给出了结构在随动强化条件下静力安定和机动安定另外两种存在格式。结果表明,随动强化材料的安定状态和安定极限不受强化过程的影响,只取决于材料的初始屈服应力和最终屈服应力。     

影响弹塑性结构安定性的各种因素

安定分析是结构设计或承载能力研究的一个重要方面。本文首先简单介绍了经典安定理论、分析方法及其工程应用,然后从影响安定性的诸因素出发,对安定理论的近期发展进行了综述,包括安定理论在热载荷、几何效应、应变强化效应、动力效应等方面的推广和应用,塑性应变(或残余变形)的限制方法,以及安定性的实验成果等。      

基于圆筒模型的热障涂层安定分析

热载荷作用下,由于热障涂层(thermal barrier coatings, TBCs) 各层材料的热不匹配以及材料参数的温度相关等因素,会使热障涂层界面区域存在复杂的应力应变场,影响系统安定性,并导致涂层开裂和剥落. 将热障涂层外凸和内凹微观界面结构简化为多层圆筒模型,借助经典机动安定定理,利用特雷斯卡(Tresca) 屈服准则和增量破坏准则处理对时间的积分问题,避免了常规安定性分析的数学规划问题,建立了热障涂层安定极限分析方法,将材料屈服强度随温度变化关系简化为双线性关系,利用补偿变换的方法简化求解过程,对典型热障涂层安定性进行了研究. 结果表明,利用基于圆筒的安定极限分析方法,能够方便求解安定极限,便于工程应用;热障涂层安定极限值明显高于弹性设计值,且界面外凸区域安定极限高于内凹区域极限值,结构首先在内凹处失效;圆筒模型基体曲率和涂层厚度越大,结构安定极限越高,分析结果与试验结果一致;所建立的热障涂层安定分析方法,对进一步研究考虑蠕变因素影响的热障涂层安定性具有重要意义.      

冰水浴和自然冷却条件下锂基润滑脂的流变学性能

通过两种不同冷却方式制得锂基润滑脂,采用HAAKE流变仪考察了锂基润滑脂的流变特性,从流变学的角度分析了润滑脂在动态条件下的实时变化,并与其胶体安定性和机械安定性等性能进行了比较.结果表明:锂基润滑脂的流变性能可以很好地反映出润滑脂的胶体安定性和机械安定性;在测试应力范围内,于自然冷却条件下制备的润滑脂结构变化为可逆变化,而冰水浴制备的润滑脂结构容易遭到不可逆的破坏.     

关于幂强化材料旋转圆盘的分折以及安定性的讨论

本文利用四阶 Runge—Kutta 法计算了幂强化材料旋转圆盘的应力(?)和残余应力(?)并计算了应力强度(?)和残余应力强度(?)讨论了满足(?)的安定性问题以及确定安定载荷(ω)的方法。     

拉压性能不同对厚壁圆筒安定性的影响

一些材料在拉伸和压缩时的性能有明显的不同，这一性质会对循环载荷作用下的结构的安定性产生影响．本文以承受内压的厚壁圆筒为例，分析了拉压不同情况下结构安定性的规律．     

三维结构安定分析的直接算法

基于线性随动强化理论和Von. Mises屈服准则,对蒙板结构直接安定分析法进行了扩展,建立了结构的三维安定直接分析法。根据投射原理,推导出结构发生塑性安定的存在条件,便于调整控制加载步长和载荷历程。采用逐次增量加载方式,确定出背应力的偏移范围,克服了原始直接分析法不能获得安定极限的缺陷,并得到安定极限条件下结构中残余应力与应变的分布状况。该数值方法将弹塑性问题分解为弹性问题和特征应变决定的残余问题,节约计算时间,提高计算效率,将该算法应用于相关算例,并与有关数值结果相比较,验证了该算法的有效性。     

On shakedown of three-dimensional elastoplastic strain-hardening structures

The present article considers the shakedown problem of structures made of either kinematic or mixed strain-hardening materials. Some basic and useful shakedown properties of elastoplastic strain-hardening structures are proved mathematically. It is impossible for a kinematic strain-hardening structure to be involved in incremental plastic collapse, and so its only possible failure mode is that of alternating plasticity. A time-independent self-equilibrium stress field has no influence on the shakedown of a kinematic strain-hardening structure although it contributes to the magnitude of plastic deformation. The sufficient shakedown conditions for either kinematic or mixed strain-hardening structures are deduced, from which the lower bound of shakedown load domain can be obtained via a mathematical programming problem. It should be pointed out that, to guarantee the safety of an elastoplastic strain-hardening structure, the damage analysis is also necessary to determine the maximum load factor the structure can bear. The shakedown analysis of strain-hardening structures can be simplified by the conclusions obtained in this article, as is illustrated by two simple examples.     

棘轮安定曲线在不锈钢压力容器应变强化技术中的应用

应变强化是不锈钢压力容器结构实现轻型化的重要途径,而应变强化内压的确定则是应变强化技术的核心。为了能够更准确有效地达到结构应变强化的目的,对循环加载的应变强化方式进行了研究。通过304不锈钢材料的室温单轴棘轮试验,建立了应力比R0条件下的棘轮安定曲线。根据Mises等效原理,利用该曲线通过一次弹塑性有限元分析直接获得结构在循环载荷作用下的强化内压和产生的塑性应变,与试验结果吻合较好,说明运用循环加载的应变强化方式可以有效地达到应变强化的目的。在达到相同的应变强化程度要求下,该方法降低了强化内压,因此可以减小过载加压的风险。     

On shakedown analysis in hardening plasticity

The extension of classical shakedown theorems for hardening plasticity is interesting from both theoretical and practical aspects of the theory of plasticity. This problem has been much discussed in the literature. In particular, the model of generalized standard materials gives a convenient framework to derive appropriate results for common models of plasticity with strain-hardening. This paper gives a comprehensive presentation of the subject, in particular, on general results which can be obtained in this framework. The extension of the static shakedown theorem to hardening plasticity is presented at first. It leads by min-max duality to the definition of dual static and kinematic safety coefficients in hardening plasticity. Dual static and kinematic approaches are discussed for common models of isotropic hardening of limited or unlimited kinematic hardening. The kinematic approach also suggests for these models the introduction of a relaxed kinematic coefficient following a method due to Koiter. Some models for soils such as the Cam-clay model are discussed in the same spirit for applications in geomechanics. In particular, new appropriate results concerning the variational expressions of the dual kinematic coefficients are obtained.     

SIMPLE SHAKEDOWN OF STRUCTURES UNDER VARIABLE MULTI-LOADINGS

The shakedown analysis of structures under variable multi-loadings is considered, and the corresponding simple shakedown condition is presented in this paper. Distribution of fixed stresses field is given, and the self-equilibrium of fixed stresses field is analyzed. Elastic shakedown and plastic shakedown conditions are presented based on the fixed stresses field. The theorem is convenient to evaluate the shakedown limit of structures under cyclical variable multiloadings through solving positive scalar fields and fixed stresses field factors at a series of dangerous positions of the structure, and tedious computations are avoided. Finally the theorem is applied to a thick-walled cylindrical tube under variable pressure and temperature, and the rolling contact problem. The results are in good agreement with some computational results.     

Shakedown of an Elastic-Plastic Arch Under Moving Load

Abstract

The problem considered consists in calculating the maximum value of a shakedown load which moves slowly across an arch according to a prescribed loading program. Sandwich cross section of the arch and elastic-plastic material with linear strain-hardening and ideal Bauschinger effect are assumed. Both current residual stress distribution and yield limits are evaluated for selected cross sections and for every load crossing.

In most cases the first crossing is decisive, and shakedown loads can be computed on the basis of the results of the first and second crossing     

Bounding solutions for creeping structures subjected to load variations above the shakedown limit

For load variations above the shakedown limit, cyclic plasticity solutions are defined for yield criteria of perfect-plasticity and of kinematic strain-hardening. The cyclic plasticity solutions are used to provide upper bounds on the work, displacements and creep energy dissipations which occur in the cyclic stationary state of a creeping structure.     

Shakedown analysis of engineering structures with limited kinematical hardening

We present a numerical method for the computation of shakedown loads of engineering structures with limited kinematical hardening under thermo-mechanical loading. The method is based on Melan’s statical shakedown theorem, which results in a nonlinear convex optimization problem. This is solved by an interior-point algorithm recently developed by the authors, specially designed for lower bound shakedown analysis of large-scale problems. Limited kinematical hardening is taken into account by use of a two-surface model, such that both alternating plasticity and incremental collapse can be captured. For the yield surface as well as for the bounding surface the von Mises criterion is used. The proposed method is validated by two examples, where numerical results are compared to those of literature where available.     

Shakedown analysis of structures made of materials with temperature-dependent yield stress

In this work, the shakedown of structures made of materials with temperature-dependent yield stress is considered. Under some restrictions on the thermal loading condition the yield stress is linearized and shakedown theorems are established. Based on these linearized shakedown theorems, the shakedown limit is formulated as a problem of convex optimization. An algorithm is built to compute shakedown limits. Numerical tests show good agreement with analytic solutions and experimental data.