An elasto‐plastic analysis of hydrostatic bulging of a circular sheet

Abstract

An incremental finite element method for large elasto‐plastic deformation of metal has been developed. The method takes account of mixed boundary data using the updated Lagrangian formulation variational procedure. The code developed is applicable to the process of hydrostatic bulging of a circular sheet clamped at its periphery. The computation algorithm is based on a convenient explicit form of the hydrostatic pressure load correction stiffness matrix for isoparametric elements. Computer programs are able to determine stress, strain, residual stress, surface profile and spring back. Most predictions agree favorably with experimental results.     

Numerical study on the deformation behaviors of the flexible die forming by using viscoplastic pressure-carrying medium

The flexible die forming (FDF) of sheet metal with the aid of viscoplastic pressure-carrying medium (VPCM) is one of the advanced forming technologies for forming complex sheet metal components with large plastic deformation. The technology has been used in industries by employing different VPCMs, the epistemological understanding of the deformation and process behaviors of this process, however, has not yet been fully addressed. In this paper, numerical study is conducted to look into the deformation behaviors of this process by explicit 3D-FE simulation under the ABAQUS platform, in which the counter pressure variations of VPCM is applied via user subroutine VDLOAD and the ductile fracture criterion is implemented by using VUMAT. Three case study parts, viz., barrel, conic and parabolic parts with large Limit Drawing Ratio (LDR) are studied. The comparison between the conventional deep drawing (CDD) and VPCM-based FDF is conducted in terms of wall-thickness reduction, hydrostatic pressure, principal stress distribution and damage factor. The uniqueness and the deformation behaviors of the VPCM-based FDF are then highlighted. The simulation results show that the higher VPCM pressure could result in the higher hydrostatic pressure throughout the process and further resist wall thinning and prevent fracture of the sheet metal. The formability is thus increased significantly.     

Cracks emanating from a circular hole under biaxial load

The principle of linear superposition has been employed in studying cracks emanating from a circular hole in a finite sheet under biaxial loading. The series type analytical solution around the crack tip has been combined with numerical analysis for the purpose of this investigation. The method presented here makes it possible to demonstrate both analytically and numerically, the effects of applied load biaxiality on the stress intensity factor. The ratio of the hole-radius-to-crack-length (R/c) is shown to determine the effect of the applied load biaxiality on the crack emanating from a circular hole in a finite sheet.     

Finite Element Modelling and the Experimental Verification of Superplastic Forming

FEM analysis has proved to be a powerful investigative tool capable of encompassing all the aspects that characterise an SPF process. However, despite the high potential of FEM programs they do not allow one to directly and suitably obtain the thickness of a sheet product for high deformation values, as commonly occurs in SPF processes. Many papers have been published on finite element analysis of S.P.F. process but the question of calculus accuracy in thicknesses of a sheet product has not been directly investigated. This problem has been already considered by the authors in a previous study which proposed an algorithm to determine thicknesses for a specific application. The software set up starts out with the results of the FEM modelling, keeps track of the deformation undergone by each element of the mesh and calculates to a good approximation the thicknesses at the end of the forming. Although the original version of the algorithm could only be used for the application studied an updated version is introduced in this study that can be used for any case. In other words, the software generates the thickness profile at the end of the analysis independently of technological set up, item shape and type of simulation (3D and 2D). The proposed algorithm was tested with reference to the superplastic forming of an item of simple geometry beginning with a thin circular plate blocked at the edges and put under constant hydrostatic pressure on one side. The test material, made superplastic by means of a series of repeated laminations, was characterised using an alternative method to the traditional tension test. The results of the experiments are in good accordance with the numerical predictions both in terms of thickness distribution and forming times.     

电磁成形放电频率对板料变形的影响

目的研究电磁成形放电频率对板料变形的影响规律。方法以商用有限元软件ANSYS为平台,建立板料电磁成形有限元模型。通过数值模拟方法,研究不同厚度的1040铝合金板在不同放电频率下的变形过程,得到不同板厚对应的最优放电频率。对比板料自由胀形试验结果,验证数值模拟的可靠性。结果放电频率对线圈放电电流、板料内电流分布、磁场力分布以及变形影响较大,并且存在最优放电频率使得板料的变形量最大。结论最优相对放电频率随着板厚的增加而减小,其变化规律呈幂指数函数变化。     

板厚对08Al薄板单点渐进成形中成形极限的影响

目的 针对渐进成形中成形极限测量难的问题,提出一种新的评定成形极限方法.方法 选用08Al为实验材料,通过模拟和实验相结合的方法,研究不同板厚下成形极限角和减薄率的关系,提出利用成形极限角和最大减薄率2个参数组合的方法判断薄板的成形极限,并通过数控实验验证提出方法的准确性,分析板厚对单点渐进成形工艺成形极限的影响.结果...     

Quantitative Evaluation for Drawability of Sheet Metal

1.IntroductionDeep-drawing is one of common forming methods ofsheet metal.The drawability is the maximum formablecapability of drawn materials under special condition.For deep-drawing without blankholder,the drawabil-ity is restricted by the wrinkling of sheet or shell.Researchers[1~6]made much effort for this.Otherwise,it is restricted by cracking of cup's wall.Rolled sheetmetal possesses anisotropy in varying degrees.It hasbeen proved that the drawability is in close relationshipwith the n…     

水下爆炸作用下固支多层片组结构的塑性毁伤研究

为研究固支多层片组结构在水下爆炸作用下的毁伤行为,以能量法为基础,建立了典型多层片组结构在水下爆炸冲击波作用下的塑性响应模型,给出了一定爆炸载荷迎面作用下固支多层片组结构的塑性变形以及剪切断裂毁伤计算方法。利用AUTODYN仿真软件,对不同工况下固支多层片组结构的毁伤进行了仿真研究,并开展了水下爆炸毁伤试验,测试了水下爆炸冲击波参数和多层片组结构的毁伤情况。结合数值模拟和试验结果可知,该理论模型可以很好的预测多层片组结构的毁伤破坏情况,包括其塑性变形层数、剪切破坏层数和最大破坏深度,为水下多层防护结构抗冲击设计提供了一定的依据。     

数值模拟技术在微成形研究中的应用

微成形技术具备高生产效率、高材料利用率和优异的成形质量,是一种极具发展前景的高精度加工技术。数值模拟技术作为一种先进的研究手段,可以在塑性加工中对材料的变形和工艺可行性等进行评估和预测,达到节约生产成本、缩短研发周期的作用。主要综述了数值模拟技术在微成形研究中的典型应用。介绍了数值模拟技术在研究材料性质和材料变形方面的应用,包括利用Voronoi方法和晶体塑性方法建立金属多晶体模型,研究了微成形过程中材料的变形机制和尺寸效应,建立了材料摩擦函数、构建了零件粗糙表面,研究了微成形过程中的摩擦行为;将晶粒大小、晶体取向与板料模型相关联,研究了微成形过程中薄板的回弹行为和成形极限。除此之外,也介绍了近年来微成形领域的许多新成形技术,如激光辅助微成形、水射流增量微成形、超声辅助微成形,以及数值模拟方法在这些新微成形技术方面的应用。最后,总结了数值模拟技术在微成形研究中所起的作用,并展望了该领域的未来发展趋势。     

Soft-punch Hydro-forming of 304 Stainless Steel Sheet

The process of soft-punch hydro-forming was used to form some workpieces. However, it has not been completely understood until now. In this paper, based on some primary experiments, in which cups have been tried under different working conditions with the soft-punch hydro-forming process, systematical know-how about why the LDR of a metal sheet is different, how working conditions influence qualities of a work-piece, and how the deformation takes place has been achieved when simulations are employed. All these results claim that the cup depth heavily weighs on the cup wall thinning rate, and a satisfied complex part can be achieved when the contacting time between the sheet and the female die is under our control well by a movable slider, which is fixed as the bottom of the female die.     

VPF用粘性介质粘弹塑性本构模型及参数确定

为确定粘性介质压力成形所采用的粘性传力介质的材料模型及其参数,对粘性介质剪切蠕变-回复实验结果进行分析,提出采用粘弹塑性材料模型描述粘性介质变形行为.将粘性介质的总变形分解为弹性分量、粘弹性分量和粘塑性分量,对实验结果进行拟合分析,分别确定了粘性介质变形的各个应变分量与应力之间的关系,最终建立了所选用的粘性介质粘弹塑性模型,为数值模拟粘性介质变形行为提供了依据.     

Investigation of Surface Damage in Forming of High Strength and Galvanized Steel Sheets

Powdering/exfoliating of coatings and scratching are the main forms of surface damage in the forming of galvanized steels and high strength steels (HSS), which result in increased die maintenance cost and scrap rate.In this study, a special rectangular box was developed to investigate the behavior and characteristics of surface damage in sheet metal forming (SMF) processes.U-channel forming tests were conducted to study the effect of tool hardness on surface damage in the forming of high strength steels and galvanized steels (hot-dip galvanized and galvannealed steels).Experimental results indicate that sheet deformation mode influences the severity of surface damage in SMF and surface damage occurs easily at the regions where sheet specimen deforms under the action of compressive stress.Die corner is the position where surface damage initiates.For HSS sheet, surface damage is of major interest due to high forming pressure.The HSS and hot-dip galvanized steels show improved ability of damage-resistance with increased hardness of the forming tool.However, for galvannealed steel it is not the forming tool with the highest hardness value that performs best.     

A new approach to evaluate bending forces for deep-drawing operations of a TRIP700 +EBT steel sheet

In this work, a new approach was developed to determine the bending, unbending and friction forces involved in deep-drawing processes of metallic sheets based on a sheet drawing-bending test. The procedure used both the experimental and deduced behavior of sheets in bending and unbending processes under tension. To obtain experimental data, a new apparatus was built to measure the reactions forces in the bending tool. These tests were applied to a TRIP700 +EBT steel sheet in diverse pure shear deformation states, with two different lubricants. The effect of the back tension and the state of the material were also studied by bending and unbending processes using tensile tests under diverse pure-shear conditions. Deduced forces, like bending and unbending forces, were determined by introducing these experimental data into an expressly created numerical method. The obtained results allowed us to state that the TRIP700 +EBT steels sheet displayed evolutional mechanical behavior since the induced martensite phase transformation effect depended on the deformation mode and intensity, had good formability and a low friction coefficient with steel tools, which was almost constant and independent of the pressure in the bending tool.     

堆载-电渗联合作用下的一维非线性大变形固结理论

堆载-电渗联合作用下的软土地基加固属于大变形固结问题。该文在Esrig电渗固结理论的基础上,建立了拉格朗日坐标下以超静孔压作为变量的一维非线性大变形固结理论方程,推导出相应的超静孔压、沉降、平均固结度和孔隙比的解析公式,且通过了模型试验的验证。之后,采用该解分析了土体在堆载-电渗联合作用下的地基大变形固结特性,且与Esrig小变形固结解析解进行对比。结果表明:堆载-电渗联合作用下,考虑大变形的计算结果更符合工程实际,且此解可用于对大变形固结问题数值解法的验证。     

气辅注射成型中气体穿透下的聚合物熔体壁厚的形成

针对气辅注射成型模壁表层熔体形成的复杂过程，对薄壁气辅注塑件在气体沿圆形截面气道进行气体穿透推进的充模过程进行了研究分析，通过引入合理的简化和假设，建立了描述气体穿透下模壁表层熔体厚度比β计算的数学模型和近似计算公式。在此基础上，进一步提出了三维薄壁气辅注塑件在气辅注射成型中气体穿透并推动熔体向前充模流动发展变化的熔体／气体前沿处理的程序算法，并用实例进行了数值模拟。研究结果表明，当气体前沿与熔体前沿的压力梯度之比值m在1．0—1．3范围内时，其β的计算结果为0．20—0．43，接近国外学者的实验到定值0．23—0．40，也比较符合实际的气辅注射成型工艺结果。     

铝合金板材热塑性变形行为研究

为了研究铝合金板材的热塑性变形行为,进行了热态胀形试验,获取了不同温度及压力率下的胀形压力-高度曲线,分析了压力率对胀形高度的影响规律.基于同一压力率、不同温度下胀形压力与等效应变之间的关系,提出胀形压力关于等效应变及压力率的拟合方程,同时获得压力率和应变率之间的函数关系.试验结果表明,板材充液热成形工艺过程中,压力率对金属材料的变形行为影响显著,同时压力率能够表征材料成形过程中的变形快慢.     

Roll forming continuous fibre-reinforced thermoplastic sheets: experimental analysis

This paper describes the results of an experimental roll forming study performed on sheets of continuous fibre-reinforced thermoplastic (CFRT) material. The deformation length, or transitional region over which the material deforms under each roll station, is studied for various temperatures, laminate configurations, and roll settings using still photography and surface grid strain techniques. The severity of the deformation through the first forming pass has been found to be related to the fibre architecture as well as the forming temperature. The kinematic constraints imposed by the fibres are found to result in a trellising effect that is observed clearly using surface grid strain techniques. Finally, as a first step in the theoretical analysis of the process, kinematic relations are developed, which describe the rate of change of strain in a sheet through the deformation zone.     

A contact algorithm for 3D discrete and finite element contact problems based on penalty function method

A contact algorithm in the context of the combined discrete element (DE) and finite element (FE) method is proposed. The algorithm, which is based on the node-to-surface method used in finite element method, treats each spherical discrete element as a slave node and the surfaces of the finite element domain as the master surfaces. The contact force on the contact interface is processed by using a penalty function method. Afterward, a modification of the combined DE/FE method is proposed. Following that, the corresponding numerical code is implemented into the in-house developed code. To test the accuracy of the proposed algorithm, the impact between two identical bars and the vibration process of a laminated glass plate under impact of elastic sphere are simulated in elastic range. By comparing the results with the analytical solution and/or that calculated by using LS-DYNA, it is found that they agree with each other very well. The accuracy of the algorithm proposed in this paper is proved.     

Elastic-plastic analysis of a finite sheet with a cold-worked hole

An exact elastic-plastic solution has been obtained for the residual stress and strain field in a finite circular sheet having a cold-worked or interference fitted hole on the basis of J₂ deformation theory together with a modified Ramberg-Osgood law. Many factors influencing the residual stresses are analysed. Comparison with finite element results and experimental data for rectangular sheets containing cold-worked holes is made. It is shown that the solution of a finite circular sheet can be used to predict the residual stresses on the minimum cross section in a rectangular sheet with a cold-worked hole fast and effectively, so long as the diameter of the circular sheet is equal to the width of the sheet.     

空化水射流冲击微成形数值模拟与实验研究

利用空化水射流中空泡溃灭产生的高压冲击波使TA2箔材产生微塑性变形,分析水射流主要工艺参数对微成形质量的影响规律。采用ANSYS/LS-DYNA数值模拟和实验研究对比的方法,通过不同冲击压力和持续时间对成形深度、成形件厚度减薄率影响的数值模拟,并进行成形工件形貌的实验验证。结果显示,对于不同冲击压力峰值和冲击压力持续时间下的板料成形,随冲击压力峰值和持续时间的增加,其成形深度、成形件厚度减薄率呈正比增加;当数值模拟冲击压力峰值Pmax=2.2 GPa、冲击压力持续时间t=40 ns时,与实验入射压力P=20 MPa、冲击时间t=1 min时的试样截面轮廓成形曲线和截面厚度减薄结果比较一致。TA2箔材微成形件圆孔阵列特征在空化冲击区内表面质量良好,具有较大的成形深度及其较好的成形深度一致性。