A rigid-plastic finite-element formulation for the analysis of general deformation of planar anisotropic sheet metals and its applications

General three-dimensional deformation of a planar anisotropic rigid-plastic sheet metal which obeys Hill's quadratic yield function is considered in the present analysis. The explicit expressions of the yield criterion and the related equations are given in the surface curvilinear co-ordinate system. A convective co-ordinate system is used in order to take into account the effect of geometric change during one step in the incremental analysis. The expression of the effective strain increment during one step is obtained in closed form by introducing assumptions on the deformation path and by proper consideration of the rotation of the axes of anisotropy during deformation. Considering the equilibrium at the deformed state, a variational formulation is derived to determine the deformation during a step. The corresponding finite-element equations are found in order to analyze the general deformation of planar anisotropic sheet metals. Two computational examples are chosen and computed by using the developed FEM program in order to verify the present formulation. The flange deformation in deep drawing of a circular diaphragm of planar anisotropy is analyzed and compared with the existing solution. The effects of planar anisotropy in the circular diaphragm bulge test are also investigated.     

板材冲压成形的晶体塑性有限元模拟

将率相关晶体塑性本构理论引入Mindlin曲壳单元模型与动力显式有限元法,采用切线系数法计算剪切应变率,根据晶体取向正态分布规律在单元积分点处分配晶体取向,按各晶体取向体积分数的加权平均计算多晶体应力,开发晶体塑性动力显式有限元程序,实现板材冲压成形过程模拟和晶体取向演化预示.以主要初始织构为铜织构和S织构的轧制铝板为对象,对方盒件冲压成形过程及织构演化进行数值模拟,计算结果与试验结果呈现出较好的一致性.通过晶体弹塑性有限元法不仅可以预示板材宏观成形构形变化,而且能够预测板材织构的演化情况.模拟结果显示在方盒件冲压成形过程中,铜织构和S织构为不稳定取向,变形后逐渐转到其他取向.     

成形极限曲线的新概念

失稳理论是成形极限曲线（ＦＬＣ）的理论基础。本文论述了ＦＬＣ理论研究中存在的问题。研究指出：一般出厂板的表面状况不会影响板料的集中失稳；板内损伤平面应变时最严重；双拉时，板内损伤的积累、发展，导致应力状态向平面应变漂移；拉压时，载荷失稳后引起的双拉，也会导致平面应变。因此平面应变状态的出现是板料集中失稳的共同原因。在此基础上，建立了ＦＬＣ左右两半部统一的模型。新模型与试验结果符合良好，优于Ｍ－Ｋ理论。     

复合变形路径下的板材冲压成形极限应变(Ⅰ)——冲压成形极限应变的立论与解析

从4个方面就变形路径对成形极限图影响的研究现状进行综述,并进一步论述了复杂变形路径和单一变形路径的概念,以及基于Hill'48屈服准则的塑性应变几何关系.为了在任意复杂变形路径下计算冲压板材的失稳极限应变,提出"任意复杂变形路径均可简化为线性复合变形路径"、"板材的冲压成形能力亦即板材允许的极限厚度应变",以及"板材在线性复合变形路径下的冲压成形能力取决于其最终变形路径的应变比值"等3个工程简化假设,并对它们进行立论和诠释.同时基于这些假设,在板材承受线性复合变形路径和前后变形路径的应变主轴发生转动的条件下,解析和推导出计算冲压成形极限应变的理论公式.利用这些简化假设和理论公式,可以在任意复杂变形路径下计算板材的冲压成形极限应变并绘制其冲压成形极限图.     

Numerical simulations on reducing the unloading springback with multi-step multi-point forming technology

Multi-point forming (MPF) is an innovative flexible manufacturing technology for three-dimensional sheet metal forming. It replaces the conventional solid dies with a set of height-adjustable discrete punches, called the “punch group”. A set of punches can construct various three-dimensional curved surfaces freely and conveniently, through adjusting the relative position of each punch. MPF technology not only saves a significant amount of money and time in the design, manufacture, and adjusting of the dies but it can also be applied to change the deformation path and to improve the forming quality. Unloading springback is an inevitable phenomenon in sheet metal forming using MPF. To control and reduce springback, numerical simulations for the MPF process and the unloading springback are carried out using the explicit-implicit coupled finite element method. Subsequently, influencing factors such as thickness, deformation amount, and material properties of MPF springback are researched to investigate the MPF springback tendency. Next, the multi-step MPF technology is introduced to reduce MPF springback. Based on numerical simulation analysis, it is obviously validated that the unloading springback is decreased when the multi-step MPF method is applied. Finally, it is verified that the equidifferent deformation path and small deformation amount of each forming step can improve the workpiece stress state and minimize the unloading springback effectively by an evaluation result of the deformation path effect on the multi-step MPF.     

基于增量理论的板材轴对称成形直接积分解法

对一般轴对称曲面零件成形,在平面应力假设和增量理论等条件下,以初始构形为参考构形,采用参数分析方法,得到了等效应变增量的微分方程。由于该微分方程包含了等效应变增量和等效应变增量的一阶导数项,一般情况下,等效应变增量的一阶导数以隐函数的形式存在,难以采用理论方法进行求解,因此,将等效应变增量的一阶导数表示成其自身、等效应变增量以及参变量的函数,根据泰勒级数展开式和积分的定义给出了逐步积分解法,可用于求解轴对称胀形、翻边、拉深等板材成形问题。以圆筒形件和圆锥形件的拉深成形为例,采用增量理论,将总变形分成若干个增量步,逐步加载,跟踪变形质点,累加应变,求解得到了法兰区和凹模圆角区等的应变分布。对分别采用比例加载条件、增量理论计算得到的结果与实验值进行了比较,结果表明,采用增量理论得到的结果更接近实验值。     

基于滑移线理论计算板料弯曲变形力

板料弯曲变形力一般都是根据材料力学方法计算,而滑移线法常用作分析理想刚塑性材料平面变形问题。通过对板料弯曲变形区应力状态分析,利用滑移线理论建立滑移线场,并根据滑移线场推导变形区的应力分布方程。基于变形区应力分布方程计算板料弯曲变形力,进一步对变形力进行修正,修正后的计算结果与根据弯矩求得的结果吻合较好。     

Determining the critical deformations during the forming of sheet metal

The plastic deformation of a uniform sheet workpiece loaded with normal stresses along the edges is considered. Critical deformations corresponding to two states of equilibrium bifurcation are determined. The first state corresponds to the formation of a neck, the second, to the appearance of a band of a concentrated necking. The deformations depend on the parameters of the stress or strain states and the mechanical characteristics of the sheet metal. A comparison of the obtained theoretical results with experimental data is carried out, and their good agreement is shown.     

A new model for springback prediction in which the Bauschinger effect is considered

Springback prediction is an important issue for the sheet metal forming industry. Most sheet metal elements undergo a complicated cyclical deformation history during the forming process. For an accurate prediction of springback, the Bauschinger effect must be considered to determine accurately the internal stress distribution within the sheet metal after deformation. Based on the foundations for isotropic hardening and kinematic hardening, Mroz multiple surface model, plane strain assumptions, and experimental observations, a new incremental method and hardening model is proposed in this paper. This new model compares well with the experimental results for aluminum sheet metal undergoing multiple-bending processes. As is well known, aluminum is one of the most difficult sheet metals to simulate. The new hardening model proposed in this paper is not only a generic model for springback prediction but also a hardening model for sheet metal forming process simulation.     

非回转对称拉深变形规律的研究 ——薄板矩形盒形件拉深的形状特性

为了研究非回转对称成形中材料的变形规律及其成形性 ,根据薄板的矩形盒件 (3 6mm× 72mm)拉深实验 ,针对法兰特定部位进行了应力、应变解析。在此基础上 ,着重分析了法兰变形及直边部的变形缓和作用随形状特性的变化 ,指出rc/l2 为 0 1左右时 ,与正方形盒件相同可以获得较大的极限拉深高度。另外 ,根据rc/l2 适当地切除板坯的角部材料或调整板坯长短边变形尺寸 ,可以有效地减轻法兰曲边或短边的变形抵抗 ,从而相应地提高拉深极限。     

A general forming limit criterion for sheet metal forming

The forming limit of sheet metal is defined to be the state at which a localized thinning of the sheet initiates during forming, ultimately leading to a split in the sheet. The forming limit is conventionally described as a curve in a plot of major strain vs. minor strain. This curve was originally proposed to characterize the general forming limit of sheet metal, but it has been subsequently observed that this criterion is valid only for the case of proportional loading. Nevertheless, due to the convenience of measuring strain and the lack of a better criterion, the strain- based forming limit curve continues to play a primary role in judging forming severity. In this paper it is shown that the forming limit for both proportional loading and non-proportional loading can be explained from a single criterion which is based on the state of stress rather than the state of strain. This proposed criteria is validated using data from several non-proportional loading paths previously reported in the literature for both aluminum and steel alloys. In addition to significantly improving the gauging of forming severity, the new stress-based criterion is as easy to use as the strain-based criterion in the validation of die designs by the finite element method. However, it presents a challenge to the experimentalist and the stamping plant because the state of stress cannot be directly measured. This paper will also discuss several methods to deal with this challenge so that the more general measure of forming severity, as determined by the state of stress, can be determined in the stamping plant.     

罗德系数的一点推广及应用

为了深入研究罗德系数的物理意义及应用,利用理论分析方法,推导出罗德系数与应力场特征量J2不变量、应变增量关系的表达式,直观地给出罗德系数与二者间的定量变化规律.对罗德系数与塑性变形复杂程度、变形类型的关系进行表征,揭示应力状态与金属瞬时变形流动行为的内在联系.并以典型塑性工艺过程为例,通过罗德系数的数值分布确定了工件全场的应变类型,进而为金属塑性变形流动行为的定量分析提供理论依据,这对于分析金属塑性成形问题及其在实际中应用具有重要意义.     

板材粘性介质压力成形粘性附着力影响因素试验研究

针对粘性介质压力成形过程是粘性介质与板材耦合的变形过程,不易确定板材在粘着应力作用下变形行为的情况,自行设计了粘性附着力拉伸试验装置,将粘着应力作为板材拉伸力,直接测量粘着应力对板材变形的作用。采用聚甲基乙烯基聚合物作为成形传力介质,初步研究了粘性附着力拉伸过程板材受到的粘性介质粘性附着力对板材变形的影响以及粘性附着力的影响因素。试验结果表明,增大板材表面压力差、提高粘性介质流动速度及提高粘性介质压力有利于提高粘性附着力的作用。研究结果可为合理利用粘性附着应力作用,提高板材成形性提供理论基础。     

数字图像相关法测量金属薄板焊接的全场变形

提出了一种基于数字图像相关法和双目视觉技术的全场三维变形测量方法来测量金属薄板焊接过程中的高温变形.首先,提出一种基于种子点的高精度图像匹配算法求解相关匹配非线性优化初值.然后,介绍了三维坐标重建以及三维位移、三维应变的求解算法.最后,借助于VC+ +6.0开发环境,研制了用于薄板焊接全场变形测量的实验系统.为验证本文方法在材料力学性能实验方面的可行性,利用标准材料试验机和自主研制的图像采集装置设计了钢试件的标准拉伸实验,并采用Q235板材件进行了焊接变形测量实验.实验表明:本文方法的应变测量精度为0.5％,与引伸计的测量结果基本相当;与传统的测量方法相比,提出的方法可以更全面、更直观地测量金属薄板在整个焊接过程中的三维移和应变场,并且测得的3个方向的位移变化曲线过渡自然、数据合理,是研究焊接变形规律的有效手段.     

A theoretical and experimental investigation of limit strains in sheet metal forming

The paper deals with an analytical technique for predicting FLDs based on linear, bilinear and trilinear straining paths—although any general curvilinear strain path can be handled by the method. The analytical procedure was based on the work of Marciniak and Kuczynski (known as the M-K model). The influence of material properties, such as anisotropy, strain hardening and strain rate sensitivity, as well as the effect of strain path, on the shape and level of the FLD were investigated. Material property data were determined from tests on Interstitial Free (IF) steel sheet.An experimental FLD was constructed for the IF steel sheet in the as-received condition. Additional FLDs were also produced following pre-straining of the as-received sheet. Comparison between the experimentally determined FLDs and those predicted from the theoretical model was favourable.Conventional FLDs are constructed in strain space with the principal surface strains as coordinate axes. However, they can be plotted in principal stress space, and some investigators have claimed this is a better representation. By knowing the strain path the stress state at the limit strain can be determined, and these limit stresses were plotted in principal stress space in order to construct a Forming Limit Stress Diagram (FLSD). It turned out that regardless of the shape of the FLD and the type of pre-strain imposed, all the FLSDs were almost identical. In contrast when plotted in strain space the FLD was very sensitive to the type of straining path.     

An internal state variable plasticity-based approach to determine dynamic loading history effects on material property in manufacturing processes

Worked materials in large deformation processes such as forming and machining experience a broad range of strain, strain rate, and temperatures, which in turn affect the flow stress. However, the flow stress also highly depends on many other factors such as strain path, strain rate and temperature history. Only a model that includes all of these pertinent factors is capable of predicting complex stress state in material deformation. In this paper, the commonly used phenomenological plasticity models (Johnson–Cook, Usui, etc.) to characterize material behavior in forming and machining were critically reviewed. Although these models are easy to apply and can describe the general response of material deformation, these models lack the mechanisms to reflect static and dynamic recovery and the effects of load path and strain rate history in large deformation processes. These effects are essential to understand process mechanisms, especially surface integrity (residual stress, microhardness, and microstructure) of the manufactured products.As such a dislocation-based internal state variable (ISV) plasticity model was used, in which the evolution equations enable the prediction of strain rate history and temperature history effects. These effects can be quite large and cannot be modeled by the equation-of-state models that assume that stress is a unique function of the total strain, strain rate, and temperature, independent of the loading path. The temperature dependence of the hardening and recovery functions results in the prediction of thermal softening during adiabatic temperatures rises, which are common in metal forming and machining.The dynamic mechanical behaviors of three different benchmark work materials, titanium Ti-6Al-4V, AISI 52100 steel (62 HRc), and aluminum 6061-T6, were modeled using the ISV approach. The material constants were obtained by using a nonlinear regression-fitting algorithm in which the stress–strain curves from the model were correlated to the experiments at different (extreme) temperatures. Then the capabilities of the determined material constants were examined by comparing the predicted material flow stress with the test data at different temperatures, strains, and strain rate history. The comparison demonstrates that the internal state variable plasticity model can successfully recover dynamic material behavior at various deformation states including the loading path effect. In addition, thermal softening due to adiabatic deformation was also captured by this approach.     

金属带材少无毛刺精密分切加工新工艺分析

在分析金属带材分切加工过程及其主要缺陷和分切毛刺去除技术的基础上,提出将上下成对圆盘刀设置为轴向负间隙、径向正间隙,在分切过程中,金属板材表面形成剪切缺口但不分开,随后增设压力分断辊使残留材料层延性断裂分离,亦即"塑性剪切压迫分离"。通过设置上下圆盘刀间隙,使刃口作用区材料处于压应力状态而塑性剪切变形形成切口,再经分断辊压力作用,产生二次变形分离,实现少无毛刺精密分切加工。     

Consideration of geometric nonlinearity in rigid-plastic finite element formulation of continuum elements for large deformation

A rigid—plastic finite element formulation for the continuum elements employing the geometric nonlinearity during an incremental time step is presented. In sheet metal deformation, the displacement for each step is considerably large even though the effective strain increment is very small. For such large displacement problems, geometric nonlinearity must be considered. In the elastic—plastic finite element using continuum elements, general incremental formulations to include the geometric nonlinearity are available. However, in the conventional rigid—plastic finite element analysis using continuum, elements, the geometric nonlinearity has not been considered properly during an incremental time step. In this paper, in order to incorporate geometric nonlinearity to rigid—plastic continuum elements during a step, the convected coordinate system is introduced. To show the stability of strain distributions by the effect of geometric nonlinearity according to incremental step size, two sheet metal forming processes, stretching and deep drawing process, are analysed with various step sizes. Then the computed results using the derived equation are compared with those obtained without considering geometric nonlinearity.     

基于HALCON的板料成形网格应变的测量

计算机视觉在网格应变测量领域的应用已成为研究热点,本实验是基于先进的图像处理软件HALCON,利用双目立体视觉原理,对印制有圆形网格的板料应变测量.首先采用印制有圆形标志点的平面标准标定板,对摄像机进行标定,获得摄像机的内外参数.采用基于NCC的匹配方法对左右图像特征点进行匹配,利用视差原理获得匹配点的三维坐标,对印制有圆形网格的板料进行三维重建.然后根据圆形网格变形后的椭圆长短轴的长度变化,计算得到真实应变,用OpenGL语言将应变可视化.     

非回转对称拉深成形中压料面上摩擦的研究

在大量拉深试验的基础上,结合法兰、矩形盒底部产生的应力应变状态以及载荷的变化情况,分析了相对凸模半径较大的薄板非回转对称成形过程中,压料力对拉深载荷以致断裂载荷所产生的复杂影响。指出法兰曲边部的滑动摩擦因数对于成形过程中的压料力相当敏感,并且对法兰部和断裂危险部材料的应力应变状态产生直接影响。特别是在面压较高的成形后期,由于法兰部润滑效果恶化,导致拉深载荷增大、成形极限降低。