Effect of strain gradient and curvature on forming limit diagrams for anisotropic sheets

Recent work on sheet metal formability had shown that the position of forming limit diagrams (FLDs) in punch stretching is higher than that in in-plane stretching because of a strain gradient effect resulting from bending a flat sheet into a curved sheet by punch stretching. To our knowledge, none of the developed theoretical models in the study of localized necking can be used to predict this phenomenon accurately so far. In this study, a new model, using Barlat and Lian’s new nonquadratic anisotropic yield criterion, is proposed by introducing a strain gradient term in the constitutive equation to consider the effect of the first order strain gradient (curvature), in the thickness direction resulting from bending, on the localized necking in anisotropic sheets. The developed model is used to study the effects of curvature on FLDs and to predict FLDs in punch stretching and inplane stretching for various materials. It is found that the theoretical predicted results are in good agreement with experimental data.     

板料自由弯曲成形及回弹理论解析

对宽板自由弯曲成形及弹复过程进行理论分析,将弯曲过程分为板料未包覆凸模和已包覆凸模两个成形阶段,在每个成形阶段将弯曲板料分为弹性和弹塑性变形区。基于单向应力和小变形假设,分别建立了两个成形阶段的回弹计算模型,导出了任一成形阶段中性层上任一质点卸载前后的转角和弯曲半径数学表达式。基于VC++软件平台,对回弹计算模型进行编程计算,并进行了实验验证,计算结果与实验结果吻合较好,最大误差为0.58°。     

Prediction of spring-back and side-wall curl in 2-D draw bending

Accurate prediction of spring-back is essential for the design of tools used in automotive sheet-stamping operations. The 2-D draw bending operation presents a complex form of spring-back occurring in sheet-metal forming since the sheet undergoes stretching, bending and unbending deformations. These three sets of deformation can create complex stress-strain states in the sheet which result in the formation of side-wall curls after the sheet is allowed to unload. Accurate prediction of the side-wall curl requires using finite-element shell models which can account for curvature and stress variation through the thickness caused by bending and unbending of sheet. Since such models are generally computationally intense, an alternative and efficient method of predicting side-wall curls is desirable. This paper describes a novel and robust method for predicting spring-back and side-wall curls in 2-D draw bending operations, using moment-curvature relationships derived for sheets undergoing plane-strain stretching, bending and unbending deformations. This model makes use of the membrane finite-element solution to calculate spring-back. The accuracy of the model is verified by comparison with finite element (ABAQUS) and experimental results.     

宽板V型自由弯曲智能化控制过程的解析定量描述

板料在弯曲卸载过程中,由于弹性变形回复,从而产生回弹。回弹的结果使弯曲件的精度降低。影响回弹的因素很多,也很复杂。根据弹塑性弯曲理论,在平面变形假设的前提下,考虑了材料的硬化、各向异性及弹性变形,对宽板V型自由弯曲应力应变进行了分析,得到了弹塑性交界处曲率半径,推导出了弯曲力及目标弯曲角随弯曲行程变化的关系式。理论计算与实验及数值模拟结果进行了比较,为宽板V型自由弯曲智能化控制中参数识别及预测模型输入层和输出层变量的确定提供了理论依据。     

Computer aided engineering of the sheet bending process

The effects of the punch nose radius and sheet thickness on the elastic springback and residual stresses in the 90° V-punch and U-die bending process of AA 5083 aluminium alloy have been extensively studied by numerical simulations based on the finite element method. The results show that, irrespective of the sheet thickness and punch stroke, the springback ratio is not affected by the punch nose radius. Such results are in excellent agreement with the experimental ones obtained in similar conditions. As far as punch nose radius effects on the residual stresses are considered, significant differences were observed between residual stresses predicted with different nose radii. In particular, the shifting of the neutral layer and increase in the magnitude of the residual stresses predicted by the FEM code were found with decreasing punch nose radius.     

U型钢压弯的有限元分析与回弹预测

采用压弯法对U型钢进行逐步冷弯成形分析。通过有限元和试验相结合的方式,得出较准确的回弹结果。经过数值模拟,发现变形过程产生的缺陷,在模具制造前修正了模具结构。在分析现有数据,参照板料成形设计公式的基础上,根据模拟结果,对板料成形的设计公式进行修正,在型材的弯曲凸模设计中引入相对弯曲半径系数K,设计出适合U型钢压弯的模具,在现场试验中取得了良好效果,生产出符合设计要求的工件。     

An elasto-plastic finite-element analysis of sheet metal camber process

This study aims to clarify the process conditions of the V-die bending of a sheet metal of steel. It provides a model that predicts not only the correct punch load for bending, but also the precise final shape of products after unloading, based on the tensile properties of the material and the geometry of the tools used. An elasto-plastic incremental finite-element computer code, based on an updated Lagrangian formulation (ULF), was developed to simulate the V-die bending of sheet metal. In particular, selective reduced integration (SRI) was adopted to formulate the stiffness matrix. The extended r-minimum technique was used to deal with the elasto-plastic state and contact problems at the tool–metal interface. A series of experiments were performed to validate the formulation in the theory, leading to the development of the computer codes. The predicted value of the punch load in the finite-element model agrees closely with the results of the experiments. The whole deformation history and the distribution of stress and strain during the forming process were obtained by carefully considering the moving boundary condition in the finite-element method.

A special feature of this V-die bending process is the camber after unloading. The computer program successfully simulates this camber. The simulation was performed to evaluate the effects of the size of the blank and the bending angle on camber process. The effects of all process variables on the final bending angle of the bent parts of the sheet after unloading were also evaluated. Results in this study clearly demonstrated that the code for simulating the V-die bending process was efficient.     

Experimental Investigations of Bend Force in Air Bending of Electrogalvanized Steel Sheets

This article deals with bend force behavior of electro-galvanized (EG) steel sheets in air bending process. A detailed experimental study was carried out on EG steel sheets of various coating thicknesses to investigate the influence of parameters such as coating thickness, orientation of the sheet, punch radius, die opening, die radius, and punch velocity on bend force behavior. From the results, it is found that zinc coating reduces the bend force and the increase in coating thickness reduces the bend force significantly. It is observed that the bend force is larger for larger punch radius, smaller die opening, and smaller die radius. It is also observed that the bend force is larger for 0° orientation than for 90° orientation. The bend force decreases with increase in punch velocity, and this influence is more prevailing in EG sheets than in plain sheets.     

Air bending and springback of stainless steel clad aluminum sheet

This paper deals with bending and springback phenomena of a stainless-steel clad aluminum sheet in V-shaped air bending. The aim of this study is to investigate the bending characteristics such as sheet thickness change and the bending angles of the sheet before/after springback. The first part of this paper is on the experimental observations. V-bending experiments were performed for both the cases of Al_in/SS_out (i.e., aluminum layer is located inside the bent clad) and SS_in/Al_out (i.e., stainless-steel layer is located inside the bent clad). From these results, it was found that the sheet-set condition (either Al_in/SS_out or SS_in/Al_out) has a great influence on the bending phenomena. In the second part, the accurate prediction of springback by FE analysis, especially the role of elasto-plasticity models, is discussed. When using Yoshida–Uemori kinematic hardening model (F. Yoshida, T. Uemori, Int. J. Plasticity 18, 2002; Int. J. Mech. Sci., 45, 2003), which well describes the Bauschinger effect of materials, the springback of the clad sheet is accurately calculated, whereas the classical isotropic hardening model underestimates the springback.     

Improvement of shearing tool life by bevelled punches with high slenderness ratio

In the present investigation the cutting edge of a slender punch was bevelled in an attempt to prevent bending or breakage in use. Tests with Kovar sheet showed that use of a bevelled punch significantly reduces the risk of bending or breakage, a particular problem when clearance on both sides of the punch is unbalanced. This is because the punch guides itself in the later stage of the stroke. Tool life tests shearing Kovar sheet with the bevelled punch produced a smaller burr on the product than with the conventional punch. The application of such punches is found to be most suitable for thin materials such as are used in the manufacture of IC and LSI parts.     

Prediction of damage in small curvature bending processes of high strength steels using continuum damage mechanics model in 3D simulation

Sheet metal bending of modern lightweight materials like high-strength low-alloyed steels (HSLA) is one major challenge in metal forming, because conventional methods of predicting failure in numerical simulation, like the forming limit diagram (FLD), can generally not be applied to bending processes. Furthermore, the damage and failure behaviour of HSLA steels are changing as the fracture mechanisms are mainly depending on the microstructure, which is very fine-grained in HSLA steels composed with different alloying elements compared to established mild steels. Especially for high gradients of strain and stress over the sheet thickness, as they occur in small curvature bending processes, other damage models than the FLD have to be utilised. Within this paper a finite element (FE) 3D model of small curvature bending processes is created. The model includes continuum damage mechanics model in order to predict and study occurring failure by means of ductile coherence loss of the material and crack formation with respect to influencing process parameters. Damage parameters are determined by inverse numerical identification method. The FE-model is strain based validated considering the deformation field at the outer bending edge of the specimen by using an optical strain measurement system. The Lemaitre based damage model is calibrated against the experimental results within metallographic analysis adapting the identified damage parameters to the bending process und thus adjusting the crack occurrence in experiment and simulation. Using this model the bendability of common HSLA steel, used for structural components, is evaluated with respect to occurring damage and failure by numerical analysis.     

Determination of hammering sequence in incremental sheet metal forming using a genetic algorithm

A method for determining hammering sequences in incremental forming of sheets is proposed on the basis of the genetic algorithm. The determination of the sequences for hammering the sheet to a desired distribution of curvature in incremental forming is treated as a combinatorial optimisation problem. The sheet is modelled to have many numbered points worked with a hammer and is deformed under a constant load. In the genetic algorithm, a group of individuals having a combination of the hammering points is set, and the combinations are optimised by using selection, crossover and mutation operations in order to minimise the difference from the desired curvature distribution. The hammering sequences in incremental forming of aluminium square sheets with a hemispherical punch and a flat die are chosen as an example.     

Numerical simulation for the multi-point stretch forming process of sheet metal

Multi-point stretch forming (MPSF) is a flexible manufacturing technique to form large sheet panels of mild curvature. The traditional fixed shape-stretching die is replaced by a matrix of punch elements, and the sheet metal are stretch-formed over the multi-point stretching die (MPSD) generated by the punch element matrix. In this paper, extensive numerical simulations of the processes for stretching parabolic cylinder, toroidal saddle and sphere parts were carried out by dynamic explicit finite element analysis. The forming results using multi-point die were compared with those of using traditional die. The use of an elastic cushion to suppress dimpling of the part caused by the discrete punch elements was investigated along with a discussion of its influence on part shape accuracy. The effect of the size of punch element and the shape of MPSD on the shape accuracy of formed parts were analyzed. The results may provide useful guidance on determining MPSF parameters and optimizing MPSF manufacture processes.     

中厚板轿车摇臂件拉深成形有限元模拟分析

将厚向异性屈服函数、单元级双面接触算法的能够反映强烈弯曲效应的Mindlin曲壳单元模型引入动力显式中心差分格式的有限元算法,建立对复杂形状的中厚板件拉深成形有限元模拟分析算法;在此基础上,以轿车摇臂厚板金件为例,分析了材料厚向异性参数r值、凹模圆角以及压边力大小对此类成形件成形性的影响。通过数值模拟与实际拉深成形实验的对比,验证了本文方法的有效性;同时,结合实验研究了此类单元对工具弯曲圆角大小的适应性。     

The Effect of the Imposed Boundary Rate on the Formability of Strain Rate Sensitive Sheets Using the M-K Method

In spite of the fact that the experimental results indicate the significant effect of strain rate on forming limits of sheets, this effect is neglected in all theoretical methods of prediction of Forming Limit Diagrams (FLDs). The purpose of this paper is to modify the most renowned theoretical method of determination of FLDs (e.g., M-K model) so as to enable it to take into account the effect of strain rate. To achieve this aim, the traditional assumption of preexistence of an initial geometrical inhomogeneity in the sheet has been replaced with the assumption of a preexisting “material” inhomogeneity. It has been shown that using this assumption, the strain rate would not be omitted from equations; thus, it is possible to demonstrate its effect on FLDs. To validate the results, they are compared with some published experimental data. The good agreement between the theoretical and experimental results shows capabilities of the proposed method in predicting the effect of the imposed rate at the boundary (which is physically the effect of the punch speed difference in sheet forming) on FLDs.     

Gradually contacting punch for improving stretch flangeability of ultra-high strength steel sheets

A gradually contacting punch for improving stretch flangeability of ultra-high strength steel sheets having small ductility was developed. In the gradually contacting punch, tensile stress around the corner edge of the sheet in stretch flanging is decreased by gradually pressing the edge of the sheet with the inclined bottom of the punch. The critical flange heights of bent 980 and 1180 MPa ultra-high strength steel sheets without fracture with the gradually contacting punch increased by 32% and 31%, respectively. In addition, the stroke limit of the press was avoided by 2-stage flanging consisting of peripheral bending and corner bending.     

金属板弹塑性非圆弧弯曲回弹的计算

本文提出了计算金属板弹塑性非圆弧弯曲回弹的结构离散方法，建立了计算回弹后零件形状及回弹前模具形状的解析一数值混合计算模型，实验验证表明此套计算模型的计算精度良好。     

钛合金板料激光曲线弯曲及热辐射对其组织性能的影响

研究了激光能量密度、路径曲率和扫描次数对TC4（Ti－6Al-4V）板料弯曲变形的影响规律,同时,分析了热辐射对板料显微组织和表面硬度的影响。结果表明：（1）存在一个最的能量密度值使板料一次弯曲所获得的的弯曲角度达到峰值;（2）随路径曲率的增加,弯曲角度减小;（3）第一次扫描以后的扫描次数与弯曲角度呈准线性关系。（4）合适的工艺参数不会导致材料显微组织变化,且激光热辐射对材料表面有淬火效应,使加热区材料表面硬度均有所提高。     

A new incremental in-plane bending of thin sheet metals for micro machine components by using a tiltable punch

This paper proposes an innovative incremental in-plane bending of thin metal sheets for manufacturing microscopic machine components. The unique feature of the process is that a tiltable punch having a beating face with trapezoidal profile is used. The beating face enables the punch to bend thin metal sheets in in-plane manner. Working conditions, including indentation and feeding pitch, can easily and flexibly control the bending radius and even the bending direction. The in-plane bent thin sheet products are expected to be used as springs, conical cylinders, bushes and other components of micro machines such as medical instruments.     

板金弯曲成形回弹问题的理论研究

分析了板金弯曲成形过程的回弹过程 ,利用成形过程中弯曲区域的平面应变和恒定厚度假设 ,根据VonMises屈服准则 ,建立了弹塑性材料线性硬化条件下板金弯曲成形的回弹计算模型 ,导出了纯弯曲条件下板金件的最小弯曲半径计算公式 ,并讨论了弯曲成形一般不等角平面弯曲问题的数值解法