圆锥形件拉深成形应力应变的直接积分解法

针对圆锥形件的拉深成形,在平面应力和比例加载条件下,采用参数方程的方法分析得到了变形区应变的微分方程。可在圆锥形件的凸缘区、凹模圆角区及锥壁区分别根据应变微分方程,代入相应的边界条件,采用直接积分得到应力、应变解,将应用于轴对称平面内的积分解法推广至分析圆锥形件的拉深成形问题。在凸缘区,锥角等于0;在锥壁区,锥角等于一定值;在凹模圆角区,将圆角部分的弧段分成若干个微锥段,每一微锥段都可分别作为一个小的等锥角的锥环处理。采用该方法,不仅可以计算锥形件的拉深成形问题,而且可以计算曲面形状已知的一般轴对称曲面零件的成形问题。用直接积分法替代迭代法求解非线性方程,使求解过程大大简化。 选取厚0.87mm 的ST16板材进行了拉深成形实验,以板坯内层为测量面,测量了凸缘区、凹模圆角区和锥壁区的应变分布,理论计算结果与实验结果一致。     

平面应力条件下轴对称拉深成形法兰区起皱和破裂分析

分别采用平面应力和平面应变假设条件,对轴对称拉深成形法兰区的应力分布进行了分析比较,两种情况下的径向应力计算值相差较小,但周向应力计算值相差较大。有限元模拟表明,平面应力条件下得到的解析结果与模拟值非常接近,表明平面应力假设条件比平面应变假设条件更接近于实际情况。在平面应力条件下,建立了轴对称成形法兰区起皱失稳条件和圆筒形件破裂失稳条件,导出了临界压边力的计算式。对于某一具体的拉深成形问题,计算得到了临界压边力与拉深位置的关系曲线。分析结果有助于进一步认识拉深成形各变形区的变形特点,建立更符合实际的起皱、破裂准则,预测成形缺陷及临界压边力。     

轴对称拉深成形中法兰变形区的解析方法

轴对称拉深成形中法兰变形区的应力、应变分析是研究板材拉深成形中失稳起皱和成形极限的基础。以轴对称拉深法兰变形区为研究对象,分别建立法兰变形区应力、应变两种解析方法,即以主应力法为基础的主应力解,以广义胡克定律和变形协调方程为基础的广义胡克定律解。分别通过试验和数值模拟对两种解析方法的计算结果进行比较,结果表明:主应力解在求解过程中忽略了法兰厚度的变化,使得径向应变的计算值较试验和模拟值偏差较大;采用以切向应变表示的平均硬化模型,使得切向应力的计算结果偏差较大,径向应力的计算结果与模拟相差不大,可以满足工程中对拉深成形力的估算。广义胡克定律解以广义胡克定律和变形协调方程为基础,避免了主应力解的缺陷,应力、应变的理论计算值与试验值、模拟值基本吻合,且相对偏差不大于5%,是一种相对精确的理论分析方法。     

盘形件增量拉深成形过程的数值模拟

增量拉深成形由于旋转的模具与坯料接触区域的不断变化而一直是数值模拟的难点,为此用Deform-3D有限元软件对为A1100铝合金的盘形件增量拉深过程进行了数值模拟.结果表明:增量拉深成形凸模的受力与传统拉深工艺相比大大降低,据此得到了凸模受力图和板料应变云图,每一步凸模受力峰值和坯料等效应变值与已有的盘形件工艺试验研究结果一致.     

轴对称拉深成形凸缘变形区应力的解析求解

在一定的假设条件下,对轴对称拉深成形凸缘变形区的应力进行解析分析,得到以积分形式表示的应力表达式.进行恰当的变量代换后,根据积分函数符合线性变化的规律,分别利用积分中值定理和泰勒级数展开公式,简化得到径向应力的解析表达式.根据简化公式可直接计算得到任一变形瞬间凸缘变形区的应力分布,以及不同变形瞬间的凹模入口处的径向应力.采用两种简化方法计算与以积分计算得到的结果非常接近,给出的算例表明,在拉深过程中,凹模入口处的径向应力最大相对误差小于0.6％,最大应力相对误差小于0.15％.以圆筒形件的拉深成形为例,在考虑板坯在凸缘区和凹模圆角区的摩擦、及板坯在凹模圆角区的弯曲等条件下,采用简化解析公式,计算极限拉深系数,计算结果与试验值吻合较好.     

复杂形状拉深件快速展开与成形模拟

基于UG的CAD技术 ,从UG中导出了零件几何信息数据 ,用文献 [1]提出的方法得到拉深件毛坯猜测值 ;采用大变形理论和理想变形假设 ,给出了用于复杂形状拉深件成形分析的一步法数学公式和有限元表达。在此基础上 ,对拉深件毛坯初始形状进行了优化 ,并就成形中拉深件厚向应变分布进行了分析 ,得到满意结果     

AA7075-T6圆筒形零件热态颗粒介质压力成形过程的力学分析

基于颗粒介质传压性能试验和AA7075-T6板材材料性能试验,对采用热态颗粒介质压力成形(HGMF)工艺拉深成形圆筒形件的法兰区、传力区和自由变形区进行了塑性力学分析,求解得到内压非均匀分布条件下成形压力的函数关系式,并与实测数据进行比对。分析结果表明,在成形中后期产生较大的偏差,理论求解最大成形力低于实测值24.6%。工艺试验研究表明,在成形温度为250℃条件下,采用HGMF工艺可一道次成形AA7075-T6圆筒形零件(底部为自由变形区)的极限拉伸比(LDR)为1.71。HGMF工艺操作便捷,装置简单,可在通用压力设备上实现轻合金板材件热成形,适用于航空、航天和军工等领域中小批量产品。     

变温情形下单晶体热-粘塑性有限变形的分析方法

提出一种对单晶体热-粘塑性力学行为的分析方法.该方法跟随加载路径对考虑变温过程的单晶体粘塑性构形演化进行增量计算,而用Hencky对数弹性应变在卸载构形的基础上来计算总量的应力;在对滑移系增量分切应力、分切应变及硬化函数的增量非线性本构关系的计算过程中采用泰勒展开得到了便于求解的线性方程组,同时得到了用于计算有限元刚度矩阵的本构矩阵,该格式在本构计算时不需进行迭代因而有较高的计算效率.     

方盒形件拉深变压边力加载研究

选择方盒形轴对称件为模拟研究对象,利用专业CAE分析软件Dynaform研究分析了方盒形件在恒定加载模式、直线递增模式、直线递减模式、V型模式和Λ型模式等典型压边力加载模式下的拉深成形性能。研究结果表明,通过对比分析方盒形件壁厚分布和成形极限图,采用V型变压边力控制曲线,可以有效合理地控制材料的流动,降低板料拉深成形的难度,减小拉深力,特别是能够有效地避免工件拉深过程当中出现的的起皱和破裂两大主要成形缺陷,最终可以显著改善成形件的拉深成形性能。     

全膜润滑金属成形工艺的有限元分析

针对求解润滑模型的方法只适用于轴对称和平面应变情况，提出了全润滑膜润滑和金属成形有限元法相结合的统一方法，既适用于稳态和非稳态的三维成形工艺，也适用于轴对称和平面应变情况。采用轴对称拉深成形实验，证明这种方法是正确的。该法大幅度增加了仿真的精度，且理论计算的润滑膜厚与实测值相一致。     

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.     

铝板数控单点渐进成形的成形极限曲线研究

对薄壁复杂构件进行数控单点渐进成形时，板料易发生破裂、起皱等缺陷，且材料变形机制演化复杂，对加载条件极为敏感，使得板料在数控单点渐进成形时的破裂预测和控制变得极难。为此，选取1060铝板作为研究材料，通过试验研究了数控单点渐进成形技术中板料的成形性能，以实现对破裂的预测和控制。利用拓印法将制件的空间变形问题转化为平面变形问题，采用数码显微镜对拓印的制件网格数据进行测量和提取，选用插值法和多项式拟合法对数据进行拟合处理，最终得到了1060铝板料在数控单点渐进成形技术下的成形极限曲线（FLC）。通过对FLC进行分析研究，得到了制件破裂区和安全区域的应变分布，实现了制件破裂的预测和控制。为进一步提高1060铝板的成形极限，将超声振动引入到单点渐进成形中，通过试验对比研究了超声振动辅助渐进成形的FLC和传统渐进成形的FLC，试验结果表明：当振动功率为120 W、振动频率为25 kHz时，1060铝板料的成形极限提高了11%。     

Finite Element Method on Shape Memory Alloy Structure and Its Applications

It is significant to numerically investigate thermo-mechanical behaviors of shape memory alloy(SMA) structures undergoing large and uneven deformation for they are used in many engineering fields to meet special requirements To solve the problems of convergence in the numerical simulation on thermo-mechanical behaviors of SMA structures by universal finite element software.This work suppose a finite element method to simulate the super-elasticity and shape memory effect in the SMA structure undergoing large and uneven deformation.Two scalars,named by phase-transition modulus and equivalent stiffness,are defined to make it easy to establish and implement the finite element method for a SMA structure.An incremental constitutive equation is developed to formulate the relationship of stress,strain and temperature in a SMA material based on phase-transition modulus and equivalent stiffness.A phase-transition modulus equation is derived to describe the relationship of phase-transition modulus,stress and temperature in a SMA material during the processes of martensitic phase transition and martensitic inverse phase transition.A finite element equation is established to express the incremental relationship of nodal displacement,external force and temperature change in a finite element discrete structure of SMA.The incremental constitutive equation,phase-transition modulus equation and finite element equation compose the supposed finite element method which simulate the thermo-mechanical behaviors of a SMA structure.Two SMA structures,which undergo large and uneven deformation,are numerically simulated by the supposed finite element method.Results of numerical simulation show that the supposed finite element method can effectively simulate the super-elasticity and shape memory effect of a SMA structure undergoing large and uneven deformation,and is suitable to act as an effective computational tool for the wide applications based on the SMA materials.     

The effects of proportional loading, plane stress, and constant thickness assumptions on hydro-mechanical deep drawing process

The goal of this study is to evaluate the effects of proportional loading, plane stress, and constant thickness assumptions on hydro-mechanical deep drawing (HDD) by developing analytical models. The main model includes no simplifying assumption, and then each of the mentioned assumptions is considered in a specific model. The interrelationships between geometrical and mechanical variables are obtained in the finite difference form based on the incremental strain theory, thereby being solved by Broyden algorithm. Published experimental and FE results are used for evaluation of the results obtained in the present work. The results of models under proportional loading, plane stress, and constant thickness conditions show more differences with the experimental data in strain distributions than the results of the main model. Thus, the analyses will be more accurate and the results more reliable without considering such assumptions.     

塑性状态下轴对称平面应力问题的位移解法

由于数学手段上的限制,解析求解一直是固体力学中一条难以逾越的鸿沟.从轴对称问题的应力平衡微分方程、几何方程与Levy-Mises增量理论出发,采用位移法分析轴对称平面应力问题,以位移增量的形式给出塑性状态下轴对称平面应力问题位移解的通解.研究结果表明,塑性状态下轴对称平面应力问题中,位移解的结果与材料属性无关.按照研究结果,利用位移和应力混合边界条件,分析发电机护环液压胀形过程中坯料高度及外径的变化规律,建立以增量形式表述的计算护环内径、外径及高度变化的递推公式.所得结果与相关文献的试验数据相比具有较高的精度:外径相对误差为0.09％,高度相对误差为1.178％,完全能够满足实际工程的需要.     

一种新型的数字积分圆弧插补方法的研究

传统的数字积分法(DDA法)在圆弧插补时存在插补误差≥1个脉冲当量,沿各轴脉冲输出不均匀,且插补速度较低.为克服这一问题,基于DDA法插补原理,采用一种非对称式的加载方法把积分累加器中的数值增大.即将圆弧起始点所在轴方向进给的积分累加器赋初值为≥该方向最大增量值的2/3的最小整数,而在另外一根轴方向进给的积分累加器赋初值为≤该方向最大增量值的1/2的最大整数.结果表明,在x轴、y轴采用非对称式加载后,x轴、y轴的插补误差由半加载时的超过0.88个脉冲当量,减为小于0.7个脉冲当量,且使x轴、y轴脉冲分配较均匀.插补算法难度没有提高,但插补次数明显减少,插补速度提高.     

Strain gradient plasticity based finite element analysis of ultra-fine wire drawing process

Steady-state rigid-plastic finite element analysis coupled with strain gradient plasticity theory has been performed to examine the size effect of material on its plastic deformation behavior and find an optimal semi-cone angle of die which minimizes the drawing energy in the ultra-fine wire drawing process. A stream-line tracing method was adopted to calculate strain component at each element and a strain surface function was introduced to compute the equivalent strain gradient of each element. Introduction of this function enables us to use an established FE code without renewal of its main structure. Hence, the constitutive equation in FE formulation is changed to couple the strain gradient plasticity. A series of FE simulation reveals that significant differences in drawing stress are observed when material size approaches its intrinsic material length. When the strain gradient plasticity theory is reflected on the steady-state FE analysis, the optimal semi-cone angle of the die is reduced by 30%. The variation of optimal semi-cone angle is attributable to considerable increment of homogeneous deformation when the material size reaches its intrinsic material length.     

An investigation of contact problem between strip and work roll with a smooth straight surface during cold rolling

Under the assumption of elastic roller, and the neglect of heat transfer problem, this paper explores the distribution of elastic deformation of the work roll with initially smooth straight surface in the rolling area during the rolling process, and analyzes the effect of this deformation distribution on the strip shape after rolling.

Based on the large deformation—large strain theory, the update Lagrangian formulation (ULF) and the incremental principle were used to develop 3D elastic-plastic analytical model of aluminum strip rolling. The flow stress was considered the function of strain and strain rate to infer the governing equation containing the effect of strain rate.

Besides, in this article, we propose an iteration procedure to calculate the contact force between strip and work roll, and the contact deformation of the work roll. In the treatment of the contact problem, the work roll was regarded as a rigid body at the beginning of each step. The incremental displacement and contact force of strip nodes were first calculated, and then entered into the first iteration loop. The contact forces of strip nodes were allocated to the work roll to calculate work-roll elastic deformation. The elastic deformation of work-roll nodes would be compensated to the incremental displacement of the strip nodes (the work-roll deformation increment was added on the incremental displacement of strip node). Then the new contact nodal forces were derived from the finite element program of strip. The above procedures were repeated to incorporate the new contact nodal forces into the first iteration loop to obtain the new strip node incremental displacement. An error range was also designated as the comparison standard to compare the displacement increments of the strip from two iterations to determine whether the iteration was completed.

This paper considers the initial shape of work roll is straight and smooth. The elastic deformation distribution on the work roll surface in the rolling area is analyzed to serve as the basis for work-roll radius compensation. Finally, deformation of strip shape is also discussed.     

金属构件双变量疲劳损伤模型的研究

引入描述双变量损伤条件下的本构关系,进而以热力学原理为基础,引入损伤驱动力,建立损伤演化准则。构建一般情况下的时间型损伤演化方程和循环型损伤演化方程。利用分离变量方法再对损伤演化方程积分,得到光滑试件在恒幅应变交变载荷作用下寿命预估方法。根据损伤力学守恒积分原理,得到有缺口试件在恒幅应变交变载荷作用下寿命预估方法。利用上述寿命预估方法,由KT=1与KT=3的标准试件中值疲劳试验数据确定损伤演化方程中的材质参数。在此基础上给出不同KT下的理论中值疲劳曲线,为采用损伤力学方法来描述构件的疲劳寿命提供一种可行的方法。