考虑可靠度的成形极限曲线建立方法

实验获得板材成形极限的方法是通过对不同加载路径下获得的极限应变点进行拟合,从而得到成形极限曲线。将百分回归分析理论应用到成形极限实验数据点的曲线拟合方法中,利用该方法可以对成形极限曲线的百分位值进行分析和预测,可以在给定的实验可靠度和置信度下,根据实际需要调节曲线的位置,同时为给定极限应变点分布带的上下限的确定提供理论依据。     

Prediction of sheet forming limits with Marciniak and Kuczynski analysis using combined isotropic-nonlinear kinematic hardening

The forming limit curve (FLC), a plot of the limiting principal surface strains that can be sustained by sheet metals prior to the onset of localized necking, is useful for characterizing the formability of sheet metal and assessing the forming severity of a drawing or stamping process. Both experimental and theoretical work reported in the literature has shown that the FLC is significantly strain-path dependent. In this paper, a modified Marciniak and Kuczynski (MK) approach was used to compute the FLC in conjunction with two different work-hardening models: an isotropic hardening model and a mixed isotropic-nonlinear kinematic hardening model, which is capable of describing the Bauschinger effect. Predictions of the FLC using the MK analysis have been shown to be dependent on the shape of the initial yield locus and on its evolution during work hardening; therefore the hardening model has an influence on the predicted FLC. In this investigation, published experimental FLCs of AISI-1012 low carbon steel and 2008-T4 aluminum alloy sheets that were subjected to various nonlinear loading paths were compared to predictions using both hardening models. The predicted FLCs were found to correlate quite well with experimental data and the effects of strain path changes and of the hardening model on predicted FLCs are discussed.     

Study on experimental approaches of forming limit curve for tube hydroforming

This paper proposes a set of experimental approaches to establish the forming limit curve (FLC) in different forming modes for tube hydroforming. In tension–compression strain state, analytical models are constructed to determine the linear strain paths at the pole of the hydroformed tube, and a self-designed free hydroforming apparatus with axial feeding and internal pressure are used to carry out the bulge tests. In plane strain state, the difference is that both ends of the tube are fixed with different punches. In tension–tension strain state, a novel hydroforming apparatus are designed. The novel device requires the simultaneous application of lateral compression force and internal pressure to control the material flow under tension–tension strain states. The linear strain paths for the right hand side of FLC by finite element method simulation are calculated. The linear strain paths in different strain states are verified and the FLC of roll-formed QSTE340 seamed tube is constructed through the proposed experimental approaches. Comparison between simulation and experimental results for hydroforming process of front crossmember shows that the experimental FLC is accurate and valid for tube hydroforming.     

A FE technique to improve the accuracy of drawbead models and verification with channel drawing experiments of a high-strength steel

A drawbead modeling technique is presented to improve the accuracy of finite element simulations in terms of part draw-in and thickness predictions and validated with channel drawing experiments of a high-strength low-alloy steel. The drawing characteristics of 1.5-mm thickness blanks are obtained with strip drawing tests with a round drawbead, and drawbead model parameters are computed for three bead settings. The consequences of bending deformation cycles are determined experimentally on strip draw-in and thickness values, and model limitations of equivalent drawbead elements are also assessed for test conditions in which the drawbead restraint force is lower than the sectional yield limit. The influence of omitted drawbead geometry and overestimated drawbead-exit thickness are described using an analytical model, and a closed form expression is obtained to correct draw-in model error under sectional deformation conditions. Blank thickness and equivalent strain at the drawbead exit are additional drawbead model parameters of the proposed technique. Then, drawing simulations of a variable section, open-ended channel part are performed. The drawbead design, bead settings and tool-blank interface conditions are identical to those in strip drawing tests. Computed draw-in and thickness distributions were compared with measurements on produced channels using an experimental channel draw die. It is concluded that simulation models, based on drawbead force parameters only, overestimate blank thickness at the die entry and bring about relatively high draw-in values along part border lines. The thickness distribution predicted with proposed technique shows an enhanced correlation with on-part thickness measurements, and bead penetration effects on channel border lines are also simulated acceptably.     

参数求解方法对屈服准则的各向异性行为描述能力的影响

详细分析基于应力各向异性和变形各向异性两种求解Hill48屈服准则参数的方法。在给出两种各向异性参数求解表达式的基础上,具体分析Hill48屈服准则本身的局限性。以5754O铝合金板为研究对象,进行不同方向的单向拉伸试验。采用两种各向异性参数求解方法,基于Hill48屈服准则推导不同方向拉伸过程中的理论应力-应变曲线和拉伸过程中的变形规律。通过对比理论与试验结果具体分析参数求解方法对屈服准则精度的影响。基于两种参数求解方法,进行5754O铝合金板拉深试验的有限元模拟,讨论不同求解方法对凸耳现象的描述精度。得出结论：当对应力各向异性为主的问题进行分析时,应采用应力各向异性法求解;当对变形各向异性为主的问题进行分析时,则应采用变形各向异性法求解。研究结果对屈服准则在板料成形方面的合理应用具有重要的参考价值。     

Drawability assessment of BCC steel sheet by using elastic/crystalline viscoplastic finite element analyses

Elastic/crystalline viscoplastic finite element (FE) analyses were carried out to asses the drawability of three kinds of BCC steel sheets, such as mild steel, dual-phase steel and high-strength steel, in the cylindrical cup deep drawing processes. In this study, the crystal orientations were obtained by X-ray diffraction and orientation distribution function (ODF) analyses. The measured ODF results have revealed clearly different textures of sheets, featured by orientation fibers, skeleton lines and selected orientations in Euler angle coordinate space, which can be related to the plastic anisotropy. An orientation probability assignment method, which can be categorized as an inhomogenized material modeling, was used in this FE modeling. The orientations were determined from the measured ODF and assigned to FE integration points one by one. Numbers of integration points, which represent crystallites and can rotate individually, are employed to represent textures of the sheet metals for taking account of the initial and evolutional plastic anisotropy without introducing Taylor or Sachs homogenization assumption. The FE analyses showed how the fiber textures affect the strain localization and earing in the deep drawing operation. It was confirmed by comparison with experimental results that this FE code could predict the extreme strain localization and earing with good accuracy and assess the sheet drawability.     

Minimization of sheet thickness variation and other defects of mini drawn parts using a blank holder plate made from concentric rings

Thickness variation is a major defect of the drawn parts made from sheet metals, which influences the intensity of part defects and may cause part failure. In the case of mini deep drawing, sheet thickness variation along part's profile has the following effects on the drawn part geometry: increased non-uniformity of diameter variation, variation of springback parameters (part edge radius deviations and angle of wall inclination), different wrinkling intensities, and part cracking and fracture. The present paper analyses the experimental results of the investigations concerning the sheet thickness variation in the case of mini cylindrical drawn parts made from a copper alloy. Some constructive solutions of tool components that allow the control and minimization of sheet thickness variation by controlling the blank holder force, contact and friction forces (especially in the part flange zone) are also proposed and tested by simulation and experiment. The constructive solutions of the new tools were obtained by constructing the blank holder plate from two concentric rings made from different materials with equal or unequal widths.     

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%。     

An analysis of localized necking in aluminium alloy tubes during hydroforming using a continuum damage model

In this work, localized necking in aluminium alloy tubes subjected to free hydroforming is analyzed. The main objective is to study the influence of loading conditions, such as prescribed fluid pressure or volume flow rate in conjunction with axial end feed, on the nature of the forming limit curve (FLC). To this end, the strain histories experienced at the tube mid-length, which were computed in an earlier investigation [14] [Varma NSP, Narasimhan R. A numerical study of the effect of loading conditions on tubular hydroforming, Journal of Materials Processing Technology 2005; [Submitted for publication]], are analyzed using the Marciniak–Kuczynski (M–K) method along with an anisotropic version of the Gurson model. The Gurson constitutive parameters are determined following an inverse approach using the sheet FLC for the chosen alloy. The predicted FLC for combined pressure and axial contraction corroborates well with the experimental data obtained in [12] [Kulkarni A, Biswas P, Narasimhan R, Luo A, Stoughton T, Mishra R, Sachdev AK. An experimental and numerical study of necking initiation in aluminium alloy tubes during hydroforming. International Journal of Mechanical Sciences 46:2004;1727–46] and is almost flat, whereas it is akin to the sheet FLC and increases with negative minor strain when fluid volume is specified. The forming limit strains for loading with specified fluid volume are in general higher when compared to those with prescribed fluid pressure. Finally, it is demonstrated that a transition from axial to circumferential necking occurs when high ratios of axial extension to volume flow rate are applied to the tube.     

Strain localisation in biaxially stretched sheets containing compact defects—II: Analysis using a finite element model

The development of strain localisation in a biaxially stretched sheet of work hardening material which contains a regular array of axisymmetric defects has been analysed by the finite element method. The defects were circular regions of reduced initial thickness and their spacing was close enough to permit interaction of the individual fields of strain concentration, leading to the formation of coherent regions of strain localisation across the sheet. Numerical results for the effects of defect severity on limit strains given by the new model are compared with those given by Marciniak and Kuczynski's long groove model. When failure is assumed to coincide with completed localisation, the forms of the relationships between limit strains and the applied strain state predicted by the two models are closely similar but, in order to give similar magnitudes of the limit strains, the defect severities and the defect strains required in the axisymmetric defect model are much larger than those in the long groove model. For this reason, when defect strains are limited by fracture, the strain state dependencies predicted by the two models can be distinctly different. For the case of a typical drawing quality low-carbon steel, the predictions of the axisymmetric defect model are in much closer accord with experimental values than are those of the long groove model.     

A practical method to evaluate the forming severity of tubular hydroformed parts

In view of the prevalence of non-linear strain paths that develop in parts that are formed in multiple stages, such as bent and hydroformed structural components, the conventional forming limit curve (FLC) cannot be used to assess the forming severity of this manufacturing process. A path-independent stress-based forming limit criterion has been shown to be far more suitable to evaluate such parts, and this paper shows how this failure criterion can be effectively used to evaluate tubular hydroformed parts “on the shop floor”. Knowing the strain history in a given location of a part, a shifted FLC can be computed from the stress-FLC and used to determine the safety margin at this location. This methodology was used to evaluate the forming severity of an automotive instrument panel beam. It was found that this approach is user-friendly and provides a significant improvement in the ability to assess process robustness and product quality compared to the conventional method. The FLCs obtained using the proposed method were found to be in good agreement with those predicted with an MK-based calculation code. Finally, it is shown that a numerical simulation of the entire forming process is recommended to confirm the estimated strain path in critical locations and improve the accuracy of the method.     

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.     

Statistical evaluation of forming limit in hydroforming process using plastic instability combined with FORM

Deviation of raw material parameters, such as work hardening, anisotropy, yield stress, etc., leads to an uncertainty to the position of the forming limit curve (FLC). This paper presents a novel approach to statistically evaluate the forming limit in hydroforming processes when taking into account the variations in the material parameters. First, plastic instability based on the Hill’s quadratic plastic potential is employed to construct the deterministic FLC. Then, with using the assumption that all material parameters are normally distributed random variables, stochastic modeling of the FLC with a confidence level is carried out, and statistical evaluation of the FLC is performed. In this work, a first-order reliability method is adopted for the reliability assessment of the FLC, and this is verified with the Monte-Carlo simulation method.     

Experimental evaluation of coating delamination in vinyl-coated metal forming

In this paper, a new evaluation and prediction method for coating delamination during sheet metal forming is presented. On the basis of the forming limit diagram (FLD), the current study evaluates the delamination of PET coating by using a cross-cut specimen, dome test, and rectangular-cup drawing test. Dome test specimens were subjected to biaxial, plane strain, and uniaxial deformation modes. Rectangular cup-drawing test specimens were subjected to the deep-drawing deformation mode, and compression deformation mode. A vinyl-coated metal (VCM) sheet consists of three layers of polymer on the sheet metals: a protective film, a PET layer and a PVC layer. The areas with coating delamination were identified, and the results of the evaluation were plotted according to major and minor strain values, depicting coating delamination. The constructed delamination limit diagram (DLD) can be used to determine the forming limit of VCM during the complex press-forming process. ARGUS (GOM) was employed to identify the strain value and deformation mode of the delaminated surface after the press forming. After identifying the areas of delamination, the DLD of the PET coating can be constructed in a format similar to that of the FLD. The forming limit of the VCM sheet can be evaluated using the superimposition of the delamination limit strain of the coating onto the FLD of VCM sheet. The experimental results showed that the proposed test method will support the sheet metal forming process design for VCM sheets. The assessment method presented in this study can be used to determine the delamination limit strain under plastic deformation of other polymer coated metals. The experimental results suggested that the proposed testing method is effective in evaluating delamination for specific applications.     

利用激光局部硬化效应提高2B06铝合金板材拉深成形性研究

针对2B06铝合金复杂零件成形困难问题,提出了利用激光热处理局部硬化提高板材成形性的思路。在通过激光热处理试验研究了铝合金板的激光硬化效应的基础上,采用数值模拟计算了铝合金板激光热处理过程中激光光斑路径和其周边热影响区域的峰值温度场,并通过实际测温验证了其准确性。提出并构建了耦合性能梯度的差性坯料模型,对激光局部硬化的杯形件拉深成形性进行了模拟和试验研究。结果表明,激光扫描方式可以形成稳定的梯度温度场并对周边非加热区影响较小,且可以通过多道次扫描方式设计不同宽度范围的大梯度差性板材坯料。力学性能试验表明激光热处理可以有效地提高铝合金的局部加工硬化能力,这种效应可以有效抑制杯形件拉深时圆角大变形区的减薄,从而提升了板材的拉深性能。在上述基础上,将激光局部热处理用于2B06铝合金航空复杂口框零件的成形,通过设计激光处理路径和参数,获得合理的局部硬化区域,可有效地避免在加强筋处出现过度减薄导致的破裂,大大提高复杂零件的成形性。     

Finite element method for sheet forming based on an anisotropic strain-rate potential and the convected coordinate system

A variational formulation and the associated finite element (FE) equations have been derived for general three-dimensional deformation of a planar anisotropic rigid-plastic sheet metal which obeys the strain-rate potential proposed by [11.]. By using the natural convected coordinate system, the effect of geometric change and the rotation of planar anisotropic axes were efficiently considered. In order to check the validity of the present formulation, a cylindrical cup deep drawing test was modeled for a 2008-T4 aluminum alloy sheet sample. Eating simulations were performed and planar anisotropic material properties were experimentally determined. Even though quantitative agreement was not fully achieved, reasonably good agreement was found between the FE simulation and the experiment in thickness strain distribution and caring. No numerical difficulty due to planar anisotropy was encountered, and the computational procedure was found to be very stable, requiring only moderate computational time. The results have shown that the present formulation for planar anisotropic deformation can provide a good basis for the analysis of sheet metal forming processes for planar anisotropic materials, especially for aluminum alloy sheets.     

Blank optimization for sheet metal forming using multi-step finite element simulations

The present study aims to determine the optimum blank shape design for deep drawing of arbitrary shaped cups with a uniform trim allowance at the flange, i.e., cups without ears. The earing, or non-uniform flange, is caused by non-uniform material flow and planar anisotropy in the sheet. In this research, a new method for optimum blank shape design using finite element analysis is proposed. The deformation process is first divided into multiple steps. A shape error metric is defined to measure the amount of earing and to compare the deformed shape and target shape set for each stage of the analysis. This error metric is then used to decide whether the blank needs to be modified. The blank geometry change is based on material flow. The cycle is repeated until the converged results are achieved. This iterative design process leads to optimal blank shape. To test the proposed method, three examples of cup drawing are presented. In every case converged results are achieved after a few iterations. The proposed systematic method for optimal blank design is found to be very effective in the deep drawing process and can be further applied to other sheet metal forming applications such as stamping processes.     

Experimental research on micro-deep drawing processes of pure gold thin sheet using DLC-coated female die

Micro-forming has been considered as an alternative for micro-fabrication method of micro-parts for its massive production characters. With pure gold thin sheet, the manufacture of micro-parts, e.g., micro-cup is still a delicate and challenging task and has received less attention. Since there are size effects of friction when a liquid lubricant is applied, the forming process becomes sensitive to the friction for the small strength of pure gold shin sheet, and the traditional deep drawing process cannot easily adapt to these kinds of micro-parts. This study presents the results of research conducted on micro-cup deep drawing process with pure gold thin sheet using diamond-like carbon film and polyethylene film to reduce the friction. In particular, the effect of lubrication condition on punch load, surface profile, reduction of thickness, and accuracy of inner diameter are investigated and discussed. Experimental results show that the diamond-like carbon-coated female die leads to lower punch load, high surface quality, uniform thickness of sheet, and high diameter accuracy. The diamond-like carbon film presents excellent wear-resistance properties under high contact pressure and large plastic deformation of thin sheet. The results indicate that micro-forming using diamond-like carbon-coated female die shows potentiality to be feasible alternative to micro-parts of pure gold thin sheet.     

A method for visualization of surface texture anisotropy in different scales of observation

Anisotropy of functional surfaces can in many practical cases significantly influence the surface function. Tribological contacts in sheet forming and engine applications are good examples. This article introduces and exemplifies a method for visualization of anisotropy. In a single graph, surface texture properties related to the anisotropy as a function of scale are plotted. The anisotropy graph can be used to explain anisotropy properties of a studied surface such as texture direction and texture strength at different scales of observation. Examples of milled steel surfaces and a textured steel sheet surface are presented to support the proposed methodology. Different aspects of the studied surfaces could clearly be seen at different scales. Future steps to improve filtering techniques and an introduction of length-scale analysis are discussed.     

Necking in sheet metal forming. Influence of macroscopic and microscopic properties of materials

The necking of sheet metal is a main problem in forming processes that causes unacceptable thickness decreasing and leads to stop the process. There is a large amount of literature and research papers in this field. But the remaining problems to solve are the applicability and the accuracy of the methods for determining forming limits for various strain paths encountered in industrial processes. In the paper, we demonstrate that the linear stability analysis can provide accurate results considering various constitutive relationships and also considering that now the finite element analyses provide accurate results concerning the main field variables. The method is first presented, and then developments are done in the rigid-plastic case or in the rigid-plastic one accounting for damage by void growth. It is then demonstrated that the proposed method gives accurate results and then can be substituted to classical forming limit analyses.