An investigation of springback scatter in forming ultra-thin metal-sheet channel parts using crystal plasticity FE analysis

Springback is a difficult problem to solve in sheet-metal forming. It is more difficult in the forming of ultra-thin metal sheet (UTMS) parts. This is not only due to the lesser plastic deformation in the pure bending of UTMS but also due to their variations in microstructure. This research concentrates mainly on the understanding of the effects of grains, their sizes, and distributions on the amount of springback and to identify at which conditions the crystal plasticity finite element (CPFE) modeling technique has to be used for the process simulation. A simplified 2D FE analysis coupled with a crystal viscoplasticity model has been used in this study. Grains, their distributions, and their orientations are generated automatically based on probability theories using the developed VGRAIN system. For the same control parameters, average, maximum, minimum grain sizes, and distribution patterns were in either regular or non-regular distribution. Four microstructures of the UTMS are generated based on the gamma distribution. Up to six grain orientations are assigned randomly to each grain structure. Thus, a large number of FE analyses have been carried out based on the variation of grain structures and orientations. These are used to investigate the effect of grain size and orientation on the scatter of springback values in the forming of UTMS channel parts.     

Development of a VGRAIN system for CPFE analysis in micro-forming applications

To aid crystal-plasticity finite-element (CPFE) simulation for the forming of micro-components, a VGRAIN system has been developed to generate the microstructure of materials. Based on Voronoi tessellation and probability theory, grains and grain boundaries for micro-materials can be generated. A gamma-distribution function with three physical parameters of a material, which are the average, minimum, and maximum grain sizes, is used to describe the grain-size distribution of the material and a numerical method has been developed to link the gamma-distribution variables and the physical parameters of the material. The distribution of generated virtual gains using the developed VGRAIN system is compared with that of microstructural-examination data for a number of engineering materials, close agreements being obtained for the cases studied. Grain orientations, which are defined using two angles, related to the global coordinate system, have been assigned in the VGRAIN system according to probability theory. The crystal orientations for the virgin and deformed materials are represented using pole figures, so that the grain orientation before and after deformation can be compared and analyzed. The generated virtual microstructure, with grain-orientation information, is then input the commercial FE solver, ABAQUS/CAE, for further pre-processing for CPFE micro-forming simulation. A crystal-viscoplasticity material model for face-centered cubic metals is implemented in the FE code through the used-defined sub-routine, VUMAT/UMAT. CPFE analyses have been carried out to investigate the grain-size and orientation effects on the distortion of formed micro-pins.     

Experimental study and finite element analysis of simple X- and T-branch tube hydroforming processes

The tube hydroforming process is a relatively complex manufacturing process; the performance of this process depends on various factors and requires proper combination of part design, material selection and boundary conditions. Due to the complex nature of the process, the best method to study the behaviour of the process is by using numerical techniques and advanced explicit finite element (FE) codes. In this work, X- and T-branch components were formed using a tube hydroforming machine and experimental load paths (forming pressure and axial feed) were obtained for the processes via a data acquisition system integrated with the machine. Subsequently, the processes were simulated using LS-DYNA3D explicit FE code using the same experimental boundary, loading conditions and the simulation results were compared with the experimental results. It was found that the developed branch height and the wall thickness distribution along different planes were in good agreement with the experimental results.     

Effects of forming media on hydrodynamic deep drawing

Apart from the punch and the die, a pressurized fluid (water or oil) is used in hydroforming. The presence of such pressure media is the main difference between hydroforming and conventional deep drawing. No comprehensive study has yet been conducted on the effect of forming media on the formation of cylindrical cups via hydrodynamic deep drawing assisted by radial pressure. This study investigated the formation of such cups through Finite element (FE) simulation and experiments. First, the process was modeled numerically using ABAQUS FE software. After simulation, copper and St14 sheets were formed with water and oil as the forming media. The effect of these forming media on thickness distribution and maximum punch force was investigated. By examining the thickness distribution curve of the hydroformed cup, a close agreement was found between experimental and numerical results. Using oil as the forming media reduced thinning at the corner radius zone of the punch and increased the maximum punch force. Changing the forming media does not significantly influence the maximum thickening at the cup wall region.

     

Analytical model for planar tube hydroforming: Prediction of formed shape, corner fill, wall thinning, and forming pressure

An analytical model for planar tube hydroforming based on deformation theory has been developed. This analytical model can be used to predict hydroformed shape, corner fill, wall thinning, and forming pressure. As the model is based on a mechanistic approach with bending effects included, local strain and stress distribution across the wall thickness can be determined. This includes strain and stress distributions for the outer layer, inside layer, and middle layer. The model is validated using finite element analysis and tube hydroforming experiments on irregular triangular, irregular quadrilateral, and pentagonal hydroformed shapes.     

A study on high ratio cup drawing by Maslennikov’s process

Deep drawing of sheet metals using Maslennikov’s technique has been analyzed by analytical and finite element simulation approaches. A new friction model based on local contact conditions has been used in the finite element (FE) simulations of the process. Compared to traditional Coulomb friction model, the results of FE simulations with the new friction model show good correlation with analytical calculations. The effects of key process parameters such as rubber ring thickness, ring inner diameter, die hole diameter, and die profile radius on the results have been investigated. The results showed that very deep cups without thinning in the side wall portion can be achieved with this process. Based on the results of FE analysis, it was found that the maximum drawing ratio can be achieved by adopting a combination of process parameters which correspond to points nearest to the fracture limit.     

Evolution of matt surface topography in aluminium pack rolling. Part I: model development

Roughening of the matt surface of pack rolled aluminium foil has been modelled. The model is based on the finite element method using isotropic plasticity. A distribution in material properties has been used to simulate the distribution of grain orientations through the material. It is found that the formation of shear bands causes roughening of the matt surface. The length of these shear bands allows individual grains or the hard roll to influence the roughness a significant distance away. Results show the effect of the ratio of the grain size to the strip thickness on the predicted roughness generated. The predictions show good qualitative agreement with the reported experiments. It is concluded that the model is able to simulate efficiently the effect of the granular behaviour of polycrystals on the matt surface roughness.     

Integration of artificial neural network and simulated annealing algorithm to optimize deep drawing process

Deep drawing is characterized by very complicated deformation affected by the process parameter values including die geometry, blank holder force, material properties, and frictional conditions. The aim of this study is to model and optimize the deep drawing process for stainless steel 304 (SUS304). To achieve the purpose, die radius, punch radius, blank holder force, and frictional conditions are designated as input parameters. Thinning, as one of the major failure modes in deep drawn parts, is considered as the process output parameter. Based on the results of finite element (FE) analysis, an artificial neural network (ANN) has been developed, as a predictor, to relate important process parameters to process output characteristics. The proposed feed forward back propagation ANN is trained and tested with pairs of input/output data obtained from FE analysis. To verify the FE model, the results obtained from the FE model were compared with those of several experimental tests. Afterward, the ANN is integrated into a simulated annealing algorithm to optimize the process parameters. Optimization results indicate that by selecting the proper process parameter settings, uniform wall thickness with minimum thinning can be achieved.     

Analysis and finite element simulation of the tube bulge hydroforming process

To investigate the effect of the loading path on the forming result and get the reasonable range of the loading path in tube bulge hydroforming process, a mathematical model considering the forming tube as an ellipsoidal surface is proposed to examine the plastic deformation behavior of a thin-walled tube during the tube bulge hydroforming process in an open die, and thus different loading paths are gained based on this model. The finite element code Ls-Dyna is also used for simulating the tube bulge hydroforming process. The effect of the loading paths on the bulged shape and the wall thickness distribution of the tube are discussed, and then the reasonable range of the loading path for the tube bulge hydroforming process is determined.     

高盒形件多道次变薄拉深工艺机理研究及数值模拟模型确立

盒形件有限元模拟通常采用壳单元进行建模,由于薄壳单元在计算中忽略了厚向应力,因此在多道次拉深成形及变薄拉深成形工况下的适用性存在质疑。以3003H14高盒形件多道次变薄拉深为研究对象,利用Dynaform并结合LS-DYNA有限元软件进行数值模拟,对比壳体单元与实体单元的模拟计算数据,通过分析外观模拟结果和Levy-Mises增量理论中瞬时本构关系系数的模拟数据,得到单元类型对薄板多道次变薄拉深成形模拟计算精度的影响规律。利用实际工程中的毛坯尺寸样本数据对建立的盒形件拉深毛坯尺寸计算程序进行训练,从而实现了盒形件拉深工艺毛坯尺寸预测软件的开发。此外,在明确建模方法后,结合实体单元有限元模拟结果研究板料在变薄拉深过程中材料的减薄与增厚的机理,揭示了材料流动规律。研究表明:实体单元模拟计算结果与实际更接近。若以坯料单元在工序前后的理论变形厚度的百分比差值作为变形程度衡量指标,当变形程度为0~11.1%时,两种单元计算差异为0.5%~27.8%;当变形程度为24.2%~34.9%时,两者计算差异为44.4%~79.3%。经多道次变薄拉深后,金属材料增厚区域多发生在凸缘及长边与短边交界处的圆角上;在模具的限制作用下,减薄区域多发生在底部圆角,长边与短边区域都有一定减薄;除工序1外,其他各个工序长边侧直壁平均厚度比工艺设计的理想值大1.00%~2.02%,短边侧直壁平均厚度比工艺设计的理想值小0.86%~12.90%。     

Analysis and finite element simulation of the tube bulge hydroforming process

To investigate the effect of the loading path on the forming result and get the reasonable range of the loading path in tube bulge hydroforming process, a mathematical model considering the forming tube as an ellipsoidal surface is proposed to examine the plastic deformation behavior of a thin-walled tube during the tube bulge hydroforming process in an open die, and thus different loading paths are gained based on this model. The finite element code Ls-Dyna is also used for simulating the tube bulge hydroforming process. The effect of the loading paths on the bulged shape and the wall thickness distribution of the tube are discussed, and then the reasonable range of the loading path for the tube bulge hydroforming process is determined.     

Bursting failure prediction in tube hydroforming processes by using rigid–plastic FEM combined with ductile fracture criterion

The most common failure in tube hydroforming is the bursting failure due to excessive thinning of large deformation. To evaluate the forming limit of hydroforming processes, the Oyane's ductile fracture integral I was introduced and calculated from the histories of stress and strain according to every element by using the rigid–plastic finite element method. The region of fracture initiation and the forming limit for three hydroforming processes, such as a tee extrusion, an automobile rear axle housing, and a lower arm under different forming conditions are predicted in this study. Also it is shown that the material parameters used in the ductile failure can be obtained from the experimental forming limit diagram. From the results, the prediction of the bursting failure and the plastic deformation for the three hydroforming examples demonstrates to be reasonable so that this approach can be extended to a wide range of practical tube hydroforming processes.     

Analysis of thin composite structures using an efficient hex-shell finite element

In this paper a general methodology for the modeling of material composite multilayered shell structures is proposed using a Hex-shell finite element modeling. The first part of the paper is devoted to the general FE formulation of the present composite 8-node Hex-shell element called SCH8, based only on displacement degrees of freedom. A particular attention is given to alleviate shear, trapezoidal and thickness locking, without resorting to the classical plane-stress assumption. The anisotropic material behavior of layered shells is modeled using a fully three dimensional elastic orthotropic material law in each layer, including the thickness stress component. Applications to laminate thick shell structures are studied to validate the methodology, and good results have been obtained in comparison with ABAQUS© commercial code.     

Development of a hydroforming setup for deep drawing of square cups with variable blank holding force technique

Sheet hydroforming is a process that uses fluid pressure for deformation of a blank into a die cavity of desired shape. This process has high potential to manufacture complex auto body and other sheet metal parts. Successful production of parts using hydroforming mainly depends on design aspects of tooling as well as control of important process parameters such as closing force or blank holding force (BHF) and variation of fluid pressure with time. An experimental setup has been designed and developed for hydroforming of square cups from thin sheet materials. Square cups have been deep drawn using constant and variable BHF techniques. A methodology has been established to determine the variable BHF path for successful hydroforming of the cups with the assistance of programmable logic controller and data acquisition system. Finite element (FE) simulations have also been carried out to predict formability with both of these techniques. It has been found that it is possible to achieve better formability in terms of minimum corner radius and thinning in the case of variable BHF technique than in the case of constant BHF technique (constant force during forming and calibration). The results of FE analysis have been found to be in good agreement with experimental data.     

Analysis of deep drawing of sheet metal using the Marform process

This paper deals with the deep drawing of metal cups using the Marform process. Using this technique, higher limiting drawing ratios can be obtained compared with the conventional deep drawing process. The analytical model of the process is presented initially, followed by the finite element simulations using ABAQUS software. A new friction model based on local contact conditions is presented and used in the finite element (FE) simulations of the process. Compared with traditional Coulomb friction model, the results of the FE simulations with the new friction model showed good correlation with experimental results. The results showed that the maximum thinning occurs at the punch profile portion, and by increasing the forming pressure, thinning of the sheet metal propagates from the punch profile portion to the side wall. At low forming pressures, wrinkles appear in the flange, whilst at higher pressures, fracture is the main defect of the Marform process.     

Development and experimental validation of a three-dimensional finite element model of the human scapula

A new modelling approach, using a combination of shell and solid elements, has been adopted to develop a realistic three-dimensional finite element (FE) model of the human scapula. Shell elements were used to represent a part of the compact bone layer (i.e. the outer cortical layer) and the very thin and rather flat part of the scapula--infraspinous fossa and supraspinous fossa respectively. Solid elements were used to model the remaining part of the compact bone and the trabecular bone. The FE model results in proper element shapes without distortion. The geometry, material properties and thickness were taken from quantitative computed tomography (CT) data. A thorough experimental set-up for strain gauge measurement on a fresh bone serves as a reference to assess the accuracy of FE predictions. A fresh cadaveric scapula with 18 strain gauges fixed at various locations and orientations was loaded in a mechanical testing machine and supported at three locations by linkage mechanisms interconnected by ball joints. This new experimental set-up was developed to impose bending and deflection of the scapula in all directions unambiguously, in response to applied loads at various locations. The measured strains (experimental) were compared to numerical (FE) strains, corresponding to several load cases, to validate the proposed FE modelling approach. Linear regression analysis was used to assess the accuracy of the results. The percentage error in the regression slope varies between 9 and 23 per cent. It appears, as a whole, that the two variables (measured and calculated strains) strongly depend on each other with a confidence level of more than 95 per cent. Considering the complicated testing procedure on a fresh sample of scapula, the high correlation coefficients (0.89-0.97), the low standard errors (29-105 micro epsilon) and percentage errors in the regression slope, as compared to other studies, strongly suggest that the strains calculated by the FE model can be used as a valid predictor of the actual measured strain. The model is therefore an alternative to a rigorous three-dimensional model based on solid elements only, which might often be too expensive in terms of computing time.     

Forming characteristics of austenitic stainless steel sheet alloys under warm hydroforming conditions

Stainless steel sheet alloys have been increasingly used in heating, ventilating, and air conditioning; appliance; sanitary and medical devices; as well as several structural and transportation applications, due to their high strength-to-weight ratio, corrosion resistance, biomedical compatibility, and esthetic appearance. Among various stainless steel alloys, austenitic stainless steels are the most commonly used type. Due to the forming limitations into complex shapes at room temperature conditions and stress-corrosion cracking issues, forming at elevated temperature has been considered as an enabling technique. Formability of stainless steels is affected by strain rate and temperature due to martensitic transformation of meta-stable austenite microstructure. In this study, deformation characteristics of three common austenitic stainless steels (AISI 201, 301, and 304) were investigated using closed-die hydroforming under different process conditions. Specifically, effects of pressure, temperature, and die/part geometry on the material forming characteristics quantified using cavity filling ratio and thinning distribution were investigated. Results suggested that, in terms of cavity filling, pressure and material grade are significant factors while temperature is not in the case of axisymmetric part. For the non-axisymmetric case, all parameters were found to be significant. In addition, finite element (FE) modeling was performed to simulate several forming cases that were experimentally conducted in this study. The FE model was simulated based on material flow curves obtained from previous studies under similar conditions (strain rate and temperature) by the authors. FEA results were shown to be in good agreement with experimental findings, particularly for cavity filling and part profile predictions. Hence, the FE model and the material models can be used for further predictions of complex and different parts with confidence.     

Multi-objective optimization of forming parameters for tube hydroforming process based on the Taguchi method

Tube hydroforming is an attractive manufacturing technology which is now widely used in many industries, especially the automobile industry. The purpose of this study is to develop a method to analyze the effects of the forming parameters on the quality of part formability and determine the optimal combination of the forming parameters for the process. The effects of the forming parameters on the tube hydroforming process are studied by finite element analysis and the Taguchi method. The Taguchi method is applied to design an orthogonal experimental array, and the virtual experiments are analyzed by the use of the finite element method (FEM). The predicted results are then analyzed by the use of the Taguchi method from which the effect of each parameter on the hydroformed tube is given. In this work, a free bulging tube hydroforming process is employed to find the optimal forming parameters combination for the highest bulge ratio and the lowest thinning ratio. A multi-objective optimization approach is proposed by simultaneously maximizing the bulge ratio and minimizing the thinning ratio. The optimization problem is solved by using a goal attainment method. An example is given to illustrate the practicality of this approach and ease of use by the designers and process engineers.     

机油盘冲压过程截面的有限元模拟与实验验证

板料冲压过程的模具设计是一个费时费力的过程。采用有限元可以降低设计费用 ,缩短设计周期。本文采用有限元软件 MARC基于拉格朗日的弹塑性本构方程建立了一个有限元模型来分析机油盘的成形过程。模拟中考虑板料的厚向异性 ,接触面间的摩擦约束采用库仑摩擦模型。模具看作刚体 ,板料作为变形体。模拟和实验结果的比较表明模拟的壁厚变薄分布与测量结果吻合得很好 ,因而理论模拟的结果可用于真实情况的预测