Experimental evaluation of incremental theories for nonproportionate loading of thin-walled cylinders

An experimental investigation was undertaken to evaluate incremental-strain theories which have been proposed in the literature to predict the loads on thin-walled cylinders subjected to nonproportionate loading which follow prescribed strain histories. Test data were obtained for two materials, annealed SAE 1035 steel and normalized 4340 steel. Material-property tests for the SAE 1035 steel indicated that the stress-strain diagram was flat topped and the material followed the Tresca flow condition. Similar tests for the SAE 4340 steel indicated that this steel was a linear strain-hardening material that followed the von Mises flow condition. Two incremental-strain theories were developed for thin-walled cylinders made of SAE 1035 steel. Both were based on the Tresca flow condition. One theory called the Tresca-Tresca theory used the stress-strain relations for the Tresca theory. The other theory called the Tresca-Mises theory used the Prandtl-Reuss stress-strain relations. In general, the test data fell between the two theories. The incremental theory developed for thin-walled cylinders made of the SAE 4340 steel, called the Mises-Mises theory, was based on the von Mises flow condition and the Prandtl-Reuss stress-strain relations. The agreement between theory and experiment was poor.     

Evaluation of finite-plasticity theories for torsion-tension members made of tresca materials

Finite-incremental Tresca and von Mises theories are developed for solid circular-section torsion-tension members subjected to proportionate and nonproportionate loading. The materials are assumed to be isotropic and even. Two Tresca theories and a von Mises theory are compared with test data obtained from torsion-tension members. Three different kinds of steels were tested; they are hot-rolled mild steel, annealed mild steel, and hot-rolled SAE 1017 steel. The fully plastic values of axial load and torque predicted by the Tresca theories agree with the experimental results; however, the deformations, in the strain-hardening region, predicted by both of the Tresca theories were greater than observed. The von Mises theory is nonconservative in predicting the fully plastic loads of torsion members and torsion-tension members and in predicting the deformations of torsion members in the strain-hardening region, but gives good correlation between predicted and experimental deformations for the torsion-tension members in the strain-hardening region.     

Evaluation of multiaxial theories for room-temperature plasticity and elevated-temperature creep and relaxation of several metals

Based on the assumption that the material satisfies the condition of isotropic hardening for either a von Mises or a Tresca material, finite-strain theories are derived for solid circular torsion members for the conditions that the inelastic deformations are either time independent or time dependent. In the latter case, both creep and relaxation theories are derived. At room temperature the theories are evaluated for each of eight metals using finite-strain data from tension, compression and torsion members. Of the six metals that are found to satisfy the condition required for the isotropic-hardening model, two are von Mises, one is Tresca, and the other three are between von Mises and Tresca. At elevated temperatures, the theories are evaluated for each of five of the latter six metals, using data from tension and torsion members. Material properties obtained from the tension specimens are used to predict creep and relaxation curves for the torsion members. Contrary to the results at room temperature, creep curves for the torsion members do not all fall within the region bounded by von Mises and Tresca theories. In the case of relaxation, either excellent agreement is obtained between the von Mises strain-hardening theory and experimental data or the theory is conservative.     

Generalized stress/strain rate relations for creep of thin shells; a comparison of “exact” and approximate relations

A set of approximate generalized stress/strain rate relations which has been used for the stationary creep analysis of thin shells is compared with the corresponding ‘exact’ relations. The comparison is made by computing the functions from which the relations are derived and plotting the corresponding surfaces. Results are included for a limiting condition in which the stress/strain rate relations become those for a rigid-plastic material obeying the von Mises yield condition and associated flow rule. Although the comparison is made only for conditions valid in a cylindrical shell under rotationally symmetric loading, it indicates the errors which are likely to occur when the approximate relations are used in stationary creep analysis.     

Elevated-temperature creep and relaxation of torsion-tension members

Based on the assumption that each material satisfies the condition for isotropic hardening for a von Mises material, an incremental solution is developed to predict axial-strain creep curves and maximum shearing-strain creep and relaxation curves for solid circular torsion-tension members subjected to proportionate and nonproportionate stepped loading including creep in tension and relaxation in torsion. Test data are obtained from torsion-tension members made either of annealed OFHC copper at 800°F (427°C) or hot-rolled SAE 1045 steel at 950°F (510°C). The loading histories include either four stepped proportionate load changes, four stepped nonproportionate load changes, or torsion-tension loading in which the axial load remains constant and the torsional load is allowed to relax during two loading periods of the test. Each test duration is about 100 h. Good agreement is indicated between the predicted and measured creep and relaxation curves.     

The yield-point loads of symmetrically-notched metal strips

Theoretical plastic yield-point loads are calculated for symmetrically-notched metal strips in plane stress, assuming that the material obeys the von Mises yield criterion. Deep-notch solutions due to R. Hill are extended to cover all notch depths. The numerical results are presented in simple empirical formulae. The purpose of the work is to provide a way of discriminating between metals that obey the Tresca or the von Mises yield criteria.     

简支圆板在复杂荷载作用下的塑性极限荷载统一解析解

本文采用双剪统一屈服准则对受线性荷载和边缘弯矩联合作用下的简支圆板进行了塑性极限分析，考虑了联合作用的两种形式，分别给出了统一的解析解。得到了极限荷载随不同屈服准则的变化曲线。对于不同的材料，本文均能给出相应的极限荷载。已有的Tresca准则、Von Mises准则、双剪应力准则的解答是文中解答的特例或逼近。本文得到的一系列有规则变化的解析解，可以适用于各种拉压强度相同材料的简支圆板的塑性极限荷载求解。文中统一解大于Tresca单剪理论解，它可以更好地发挥材料的强度潜力，工程应用可以取得明显的经济效益。     

Stress Analysis of an Orthotropic Work-Hardening Cylinder with Body Force*

ABSTRACT

An elastoplastic analysis of an axisymmetric cylinder subjected to linear body forces is presented. The effect of reinforcement and anisotropy are also included. Classical plasticity and familiar assumptions of plane stress and strain are used to arrive at closed-form solutions for the case of linear body forces. The problem is solved for the general case in which orthotropy is considered in the elastic range. For the case of plasticity, first the isotropic yield functions (von Mises and Tresca) are used and then the problem is extended to the case of Hill's yield criterion. Closed-form solutions are found for both the von Mises (plane strain) and Tresca (plane stress and strain) cases.     

考虑拉压强度差效应的厚壁圆筒承载能力分析

应用双剪统一强度理论，考虑材料的拉压异性和同性，推导了在内压力和轴力联合作用下的厚壁圆筒的塑性极限载荷表达式．在该表达式中，当反映中间主应力效应的系数取不同的值时，就能得到按Tresca屈服准则、线性逼近的Mises屈服准则和双剪应力屈服准则的计算结果，并且绘制了在相应准则下的极限应力线图．从而可知：在三维应力状态下，应用该理论，可以获得极限载荷分析的精确解；极限载荷线图与三种屈服准则的屈服曲线是相吻合的；计算的结果可以用于拉压异性和同性的材料，为工程应用提供了理论依据．     

内压作用下弯管的塑性极限载荷分析

在变壁厚椭圆截面弯管应力分析的基础上,运用Tresca 和von Mises 屈服准则,对承受内压作用的钢制弯管进行了极限载荷分析,推导出考虑弯管截面壁厚变化和弯管椭圆度的变壁厚椭圆弯管的塑性极限压力计算式. 弯管的极限载荷随着弯管的壁厚和弯管的椭圆度的不同而变化.     

An experimental study on subsequent yield surface after finite shear prestraining

An equimodulus surface is introduced and the subsequent yield surface after large finite shear prestraining is experimentally investogated. Fully annealed, thin-walled copper tubular specimens were subjected to large torsional loading and partial unloading; strain gages were carefully mounted on the specimen after the application of pure shear loading. Specimens were then subjected to various combined tension-torsion loadings. Influences of he von Mises and Tresca equivalent offset strains on the subsequent yield surfaces are studied. On examining the experimental results reported in this article, it was found that the smaller the offset strains, the more distorted are the subsequent yield surfaces. At the torsional preloading point, a rounded corner was developed, whereas in the region opposite to the preloading point, the subsequent yield surface was flattened. When large von Mises offset strains were used, the corresponding subsequent yield surfaces passed through the von Mises loading surface. But this was not the case when Tresca offset strains were used. The subsequent yield surface determined by the back extrapolation method was almost completely outside the von Mises loading surface. On the other hand, the subsequent yield surface determined by the back extrapolation method was close to the Tresca loading surface. It is also found that the equimodulus surface is distorted and cannot simply be described by the combined kinematic and isotropic hardening rule.     

屈服准则及切线模量修正的弹塑性计算模型

为提高不同应力状态下金属弹塑性行为的模拟精度,采用含应力三轴度修正的von Mises屈服准则,材料弹塑性本构关系在等效应力$\!$-$\!$-$\!$等效应变曲线基础上,提出一个切线模量为主应力函数的理论修正项. 将这两个修正项结合,以子程序形式编程嵌入ABAQUS主程序,以此模拟几种不同形状试样的弹塑性行为,并将其他屈服准则在单一曲线假设下编程与之对比. 模拟结果与真实试验结果对比发现,对于屈服而言,含应力三轴度修正的vonMises屈服准则比其他屈服理论准确;对于弹塑性阶段计算而言,提出的切线模量为主应力函数这一假设比单一曲线假设更加接近真实试验.      

部分均匀荷载作用下圆板塑性极限统一解

本文采用俞茂宏双剪统一屈服准则求解部分均匀荷载下简支圆板的塑性极限，已有的最大主应力准则、Ｔｒｅｓｃａ准则，Ｍｉｓｅｓ准则的解答均是该解答的特例或线性逼近。该解答可以适合于多种工程材料，具有普遍性和适用性，从得出的解析解和图示中可得出一些新的有益的认识     

Localization in elasto-plastic materials: Influence of the plasticity yield surface in biaxial loading conditions

The influence of the plasticity yield surface on the development of instabilities in plane plates in biaxial loading is analyzed in order to understand and simulate the localization pattern observed in an expanding hemisphere experiment. First, a criterion for the activation of slip bands is formulated in the form of a critical hardening coefficient: it is particularized to the Von Mises and Tresca surfaces. In the Von Mises case, the criterion gives a strongly negative hardening coefficient in biaxial loading conditions different from the ones of plane strain. In the Tresca case, the criterion is fulfilled for a perfectly plastic material in uniaxial and biaxial loading; besides, in equi-biaxial loading, two possible orientations for slip bands are exhibited; this can be understood, with a few approximations, by the existence of a vertex point on the Tresca yield surface which give additive degrees of freedom for the direction of the plastic strain rate. Second, the development of localization in the loading conditions met in an expanding hemisphere experiment is simulated using both plasticity yield surfaces; whereas the Von Mises simulation does not localize, the Tresca simulation exhibits a pattern composed of a network of shear bands of different orientations; this pattern is not far from the pattern observed experimentally.     

塑性力学教学中Mises屈服准则几何轨迹证明

本文针对塑性力学教学中学生难以理解的屈服准则几何轨迹,从教学角度出发,利用坐标变换和空间几何投影关系分析证明了Mises屈服准则的平面椭圆和空间圆柱面轨迹。基于Tresca和Mises屈服准则简化形式,分析了两个准则几何轨迹的内接和外接关系,当用拉伸屈服应力${\sigma _{\rm{s}}}$表示时,Mises椭圆外接于Tresca六边形,当用剪切屈服强度k表示时,正好相反。

     

Limit loads of edge-restrained shallow shells

Limit analysis of edge-restrained rigid, perfectly plastic shallow spherical shells under external pressure is considered. A numerical solution, based on the von Mises yield criterion, is shown to be in good agreement with existing approximate solutions based on the Tresca yield criterion.     

Effect of creep prestrain on subsequent plastic deformation

The effect of creep prestrain on subsequent plastic deformation is experimentally investigated. The experiments are performed by subjecting thin-walled tubular specimens of stainless steel SUS 304 after creep prestraining to combined axial load and torsion at room temperature to 600°C. The stress-strain relations subsequent to creep prestrain are determined under combined stress state with and without temperature changes in prestraining and subsequent plastic straining. On the experimental results, the plastic hardening effects by creep prestrain are discussed under various temperature conditions. The subsequent stress-strain relations are compared with the calculated results on the equi-plastic strain surfaces.     

基于双剪应力屈服准则的受内压管道爆破压力分析

采用双剪应力屈服准则,对在内压作用下的无缺陷管道进行了塑性极限分析,得到了管道爆破压力的计算公式;并且将结果与基于Tresca、Mises、平均剪应力屈服准则得到的爆破压力进行了比较.研究结果表明:爆破压力随着管道材料的应变硬化指数的增大而减小,随着管道厚径比的增大而增大;此外,基于双剪应力屈服准则得到的管道爆破压力为爆破压力的上限,而基于Tresca屈服准则得到的爆破压力为管道爆破压力的下限.