On the prediction of side-wall wrinkling in sheet metal forming processes

Prediction and prevention of side-wall wrinkling are extremely important in the design of tooling and process parameters in sheet metal forming processes. The prediction methods can be broadly divided into two categories: an analytical approach and a numerical simulation using finite element method (FEM). In this paper, a modified energy approach utilizing energy equality and the effective dimensions of the region undergoing circumferential compression is proposed based on simplified flat or curved sheet models with approximate boundary conditions. The analytical model calculates the critical buckling stress as a function of material properties, geometry parameters and current in-plane stress ratio. Meanwhile, the sensitivities of various input parameters and integration methods of FEM models on the prediction of wrinkling phenomena are investigated. To validate our proposed method and to illustrate the sensitivity issue in the FEM simulation, comparisons with experimental results of the Yoshida buckling test, aluminum square cup forming and aluminum conical cup forming are presented. The results demonstrate excellent agreements between the proposed method and experiments. Our model provides a reliable and effective predictor for the onset of side-wall wrinkling in sheet metal forming processes.     

Effects of plastic anisotropy and yield criteria on prediction of forming limit curves

The effects of yield criteria on predictions of the right-hand side of forming limit diagrams (FLDs) are investigated. Predictions of limit strains are determined from an initial imperfection model based on the early work of Marciniak and Kuczynski (1967). Particular attention is placed on the effect of normal plastic anisotropy on limit strains during biaxial sheet stretching. The anisotropic yield criteria investigated in this paper include Hill’s (1948) quadratic criterion, Hosford’s (1979) higher-order criterion, and case 4 of Hill’s (1979) non-quadratic criterion. Several important characteristics of the yield surface shape are discussed and a new parameter that quantifies some of these aspects is introduced. Similar to the work of Barlat (1987), this parameter is based on the relative position of plane strain on the yield surface and can be used to predict the various effects of yield criteria on limit strains. Results indicate that predictions of FLD are very sensitive to selection of yield criteria.     

A general forming limit criterion for sheet metal forming

The forming limit of sheet metal is defined to be the state at which a localized thinning of the sheet initiates during forming, ultimately leading to a split in the sheet. The forming limit is conventionally described as a curve in a plot of major strain vs. minor strain. This curve was originally proposed to characterize the general forming limit of sheet metal, but it has been subsequently observed that this criterion is valid only for the case of proportional loading. Nevertheless, due to the convenience of measuring strain and the lack of a better criterion, the strain- based forming limit curve continues to play a primary role in judging forming severity. In this paper it is shown that the forming limit for both proportional loading and non-proportional loading can be explained from a single criterion which is based on the state of stress rather than the state of strain. This proposed criteria is validated using data from several non-proportional loading paths previously reported in the literature for both aluminum and steel alloys. In addition to significantly improving the gauging of forming severity, the new stress-based criterion is as easy to use as the strain-based criterion in the validation of die designs by the finite element method. However, it presents a challenge to the experimentalist and the stamping plant because the state of stress cannot be directly measured. This paper will also discuss several methods to deal with this challenge so that the more general measure of forming severity, as determined by the state of stress, can be determined in the stamping plant.     

A new cyclic anisotropic model for plane strain sheet metal forming

A finite difference model was developed for sheet metal subjected to plane strain cyclic bending under tension. The model was used to describe the effects on the mechanics of the deformation of the sheet due to mixed isotropic-kinematic cyclic hardening curves. The analytical results were compared with experimental results obtained under testing conditions closely representative of the analytical model. Two tests were used: a pure bending moment device and a bending/unbending under tension device consisting of three cylindrical pins. The model was used to determine a constitutive curve that best characterize the cyclic behavior of the material tested, as compared with the experimental results. The significance of these results were discussed in relation to the prediction of the restraining forces in the sheet as it is drawn through the blank holder drawbeads.     

Lubricant test methods for sheet metal forming

Sheet metal forming of tribologically difficult materials such as stainless steel, Al-alloys and Ti-alloys or forming in tribologically difficult operations like ironing, punching or deep drawing of thick plate requires often use of environmentally hazardous lubricants such as chlorinated paraffin oils in order to avoid galling. The present paper describes a systematic research in the development of new, environmentally harmless lubricants focusing on the lubricant testing aspects. A system of laboratory tests has been developed to study the lubricant performance under the very varied conditions appearing in different sheet forming operations such as stretch forming, deep drawing, ironing and punching. The laboratory tests have been especially designed to model the conditions in industrial production. Application of the tests for evaluating new lubricants before introducing them in production has proven successful and has in a number of examples assisted the substitution of environmentally hazardous lubricants by more friendly ones in industrial production.     

Electromagnetic blank restrainer in sheet metal forming processes

Electromagnetic blank restrainer (EMBR) is a new technology that was recently developed to control material movement in sheet metal forming processes. Magnetic attraction on the ferrous sheet metal is the intrinsic property of EMBR. Such magnetic force is quantified using Maxwell's stress tensor to assess the feasibility of EMBR in the sheet metal forming process. The 3D finite element analysis (FEA) of an electromagnetic system is conducted to determine the distribution of magnetic flux density on contacting surfaces of the sheet metal. The distribution is then used to estimate the magnetic force. Experiments have been conducted to measure the magnetic force and compare with results from the FEA. Biaxial-loading apparatus has been built to measure restraining forces on the sheet metal with blankholder, drawbead, and EMBR. All the restraining forces are put together in a chart to see where each method stands with respect to one another. In order to evaluate the quality of forming with each method, an experimental die has been built. The die forms a channel in a single stroke and provides a direct indication of how each restraining method controls blank movement in the die. The real advantage of EMBR lies in the effectiveness of force control and its flexible location in a sheet metal forming die. To prove this, a prototype has been built in a tryout die where house appliance panel is formed with blankholder and EMBR. EMBRs are locally installed in the die and actively controlled during the forming process. The part formed with EMBR shows a significant improvement in the forming quality. At the end of this paper, two immediate impacts that EMBR can bring to the sheet metal forming industry are also discussed.     

Sectional finite element analysis of forming processes for aluminum-alloy sheet metals

The sectional finite element analysis of the forming processes for the aluminum-alloy sheet metal known to be planar anisotropic was performed. The two-dimensional rigid-viscoplastic FEM formulation based on the bending augmented membrane theory as well as the anisotropic yield criteria was introduced. For modeling the anomalous behavior of aluminum-alloy sheet metals, Barlat's strain rate potential and Hill's (Journal of the Mechanics and Physics of Solids 1990;38:405–17) non-quadratic yield theory with an isotropic hardening rule were employed. Furthermore, a new method to determine anisotropic coefficients of Barlat's strain rate potential was proposed. For evaluating bending effects in the forming process of aluminum-alloy sheet metals, the bending equivalent forces were calculated in terms of the changes in the interior angle at a node between two linear finite elements and were augmented to the membrane stretch forces. In order to verify the validity of sectional finite element formulation based on the bending augmented membrane theory, the plane strain stretch/draw forming processes of a square cup test were simulated and simulation results are compared with experimental measurements. Friction coefficient was obtained from drawbead friction test. The properties of selected material were obtained from uniaxial tensile tests. Simulation shows good agreement with measurements. For the application of the sectional finite element formulation introduced in this research, the drawing process of a rear seat back upper bracket of passenger cars is simulated assuming plane strain condition. The thinning distribution of the simulation agreed well with that of the measurement, so that the sectional analysis is acceptable in the design and analysis of aluminum-alloy sheet stamping dies.     

金属薄板激光弯曲成形的工艺参数研究

以不锈钢薄板的激光弯曲成形为研究对象,研究其成形的工艺过程及影响因素;介绍实验设备和激光调焦方法。通过实验研究了激光能量因素、扫描速度因素、激光光斑大小和扫描次数等因素对弯曲成形角度的影响。     

On the prediction of the effect of process parameters upon forming limit strains in sheet metals

Plasticity analysis of sheet metal forming requires a detailed knowledge of the influence of process parameters on the stress–strain relationships from yielding up to localized necking, for accurate prediction of forming limits. Achievable strain and stress–strain relationships are sensitive to modulations in process parameters, chiefly temperature and strain rate. However, the effects of changes in strain rate and temperature are often complex as they also depend on the levels of strain, strain rate and the temperature employed. Such variations could be either triggered by the process dynamics of the forming operation or imposed for optimal exploitation of the material ductility. In this study, the influence of such process parameter modulations upon formability has been theoretically modelled, following the Sing–Rao prediction approach. The limit strains thus predicted compare favourably with experimental results for a drawing steel, thus validating the present formalism. This approach can also be adopted to accommodate non-linear straining conditions. Thus, theoretical modelling of strain-path-dependent forming limits, which has not been explored adequately so far, now becomes feasible.     

等效拉延筋模型及其在板料成形数值模拟中的应用

讨论等效拉延筋的建模方法、常用模型及其在板料成形数值模拟中的应用情况,并指出研究中仍存在的问题及今后的发展方向。     

Fracture limit prediction using ductile fracture criteria for forming of an automotive aluminum sheet

Forming limit curves at neck and at fracture have been experimentally determined, and surfaces of fractured dome specimens have been observed optically and in the SEM, for an automotive AA6111-T4 sheet material. Various continuum ductile fracture criteria from the literature along with the assumptions of power law hardening, Hill’s quadratic yield criterion, and proportionality of stress and strain paths have been utilized for prediction of forming limit curve at fracture and compared with the experimental curve to assess the applicability of the different fracture criteria. The maximum shear stress criterion by Tresca predicts reasonably well the fracture limits of AA6111-T4 sheet material for a range of strain ratios, and is consistent with the microstructural observations. The criterion can be used to predict fracture limit curves from uniaxial tensile data and plane strain limit at fracture. A methodology for incorporating such a ductile fracture criterion into FE simulations of sheet stampings for prediction of fracture is discussed.     

Characterisation of a measurement system for reproducible friction testing on sheet metal under plane strain

The testing equipment can compromise the quantification of the friction on sheet metal. This paper focuses on a systematic analysis of the testing equipment as a measurement system of the friction phenomena. It is shown that the mechanical response of the system may be responsible for significant variations on the quantification of frictional effects. Historical and inter-laboratory testing data show that, upon proper design of the measurement system, friction can be quantified, reproduced, and replicated with a significant degree of accuracy. This paper discusses the requirements and the controls of the test needed to maintain the uncertainty at its minimum level. The results show the feasibility of characterising friction in order to study the effects of the sheet, lubricant, and forming tools. This study is based on tests where cyclic bending under tension resulted in significant stretching and thinning of the sheet, but with the width remaining approximately constant. Friction research under other sheet forming modes may, however, benefit from the significance of the findings presented here.     

Characterising material and process variation effects on springback robustness for a semi-cylindrical sheet metal forming process

Variation in the incoming sheet material and fluctuations in the press setup is unavoidable in many stamping plants. The effect of these variations can have a large influence on the quality of the final stamping, in particular, unpredictable springback of the sheet when the tooling is removed. While stochastic simulation techniques have been developed to simulate this problem, there has been little research that connects the influence of the noise sources to springback. This paper characterises the effect of material and process variation on the robustness of springback for a semi-cylindrical channel forming operation, which shares a similar cross-section profile as many automotive structural components. The study was conducted using the specialised sheet metal forming package AutoForm™ Sigma, for which a series of stochastic simulations were performed with each of the noise sources incrementally introduced. The effective stress and effective strain scatter in a critical location of the part was examined and a response window, which indicates the respective process robustness, was defined. The incremental introduction of the noise sources allows the change in size of the stress–strain response window to be tracked. The results showed that changes to process variation parameters, such as BHP and friction coefficient, directly affect the strain component of the stress–strain response window by altering the magnitude of external work applied to forming system. Material variation, on the other hand, directly affected the stress component of the response window. A relationship between the effective stress–strain response window and the variation in springback was also established.     

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。     

Finite element simulations of sheet metal forming under complex strain paths

Fracture is a common defect in sheet metal forming and it is essentially caused by tensile instability. This paper analyzes some experiments and theories for building forming limit diagrams of sheet metal and points out the advantages and disadvantages of current experiments and theories. According to this, a method that integrates the finite element simulation and experiment was used to research the forming limit diagrams of the sheet metal under complex strain paths. Taking the rear hanger that undergoes twice stamping as an example, the strain paths of the dangerous point of the rear hanger is investigated. Finally, the forming method of the rear hanger is confirmed. Results indicate that finite element method (FEM) can achieve the complex strain paths and different strain paths will have great impacts on the result of the sheet metal forming. __________ Translated from Journal of Jiangsu University (Natural Science Edition), 2005, 26(4): 289–293 [译自: 江苏大学学报 (自然科学版)]     

Modified membrane finite element formulation for sheet metal forming analysis of planar anisotropic materials

A finite element formulation is derived for sheet metal forming analysis of planar anisotropic materials. The formulation incorporates membrane elements whereas it takes the bending effect into account explicitly. The strain energy term in the formulation is decomposed into the membrane energy term for mean stretching and the bending energy term for pure bending. This procedure needs careful evaluation for the orientation of the anisotropic axes. The formulation is then combined with an effective algorithm to calculate distribution of the blank holding force in each step according to the thickness in the flange region. The calculation employs a special relation between the thickness and the blank holding force. The simulation examples demonstrate the validity and versatility of the developed computer code by showing that the thickness variation in the flange region redistributes the blank holding force during the deformation. The present algorithm can predict accurate deformed shapes and thickness strain distribution with the anisotropy of materials and the variable blank holding force.     

Springback prediction for sheet metal forming process using a 3D hybrid membrane/shell method

To reduce the computational time of finite element analyses for sheet forming, a 3D hybrid membrane/shell method has been developed and applied to study the springback of anisotropic sheet metals. In the hybrid method, the bending strains and stresses were calculated as post-processing, considering the incremental change of the sheet geometry obtained from the membrane finite element analysis beforehand. To calculate the springback, a shell finite element model was used to unload the sheet. For verification purposes, the hybrid method was applied for a 2036-T4 aluminum alloy square blank formed into a cylindrical cup, in which stretching is dominant. Also, as a bending-dominant problem, unconstraint cylindrical bending of a 6111-T4 aluminum alloy sheet was considered. The predicted springback showed good agreement with experiments for both cases.     

Modeling of springback, strain rate and Bauschinger effects for two-dimensional steady state cyclic flow of sheet metal subjected to bending under tension

An elastic-plastic mathematical model is presented for plane strain flow of sheet metal subjected to strain rate effects during cyclic bending under tension. The model calculates the stress, strain, strain rate, flow profile geometry, springback and residual stresses for steady state flow of sheet metal under plane strain along the width. Stress reversals were experimentally quantified using a pure bending moment test and were included in the model through Bauschinger factors. Modeling results for two materials, mild steel and aluminum alloy, were in good agreement with experimental results from bending under tension test devices. The iterative nature of the model, associated with a representative experimental framework proved a valuable approach to improving the modeling of sheet metal forming and springback control.     

An analytical model for plate wrinkling under tri-axial loading and its application

The prediction and prevention of wrinkling have been challenging issues in sheet metal forming processes. In an effort to provide the design and process engineers a reliable and efficient tool in assessing the onset of flange wrinkling, an analytical model, based on the wrinkling criterion proposed by Cao and Boyce [1], is presented here. The critical buckling stress and wavelength as functions of normal pressure are calculated using a combination of energy conservation and plastic bending theory. The present results are in excellent agreement with those obtained from Cao and Boyce’s numerical approach which has demonstrated its excellent predictive capability by comparing the experimental study of a conical cup [1] and a square cup forming [2]. Additionally, the effects of the tension in the plane of sheet and material properties on the initiation of flange wrinkling are investigated.     

Finite element analysis of the effects of martensitic phase transformation in TRIP steel sheet forming

This paper aims at investigating the effects of the martensitic phase transformation on the formability of unstable austenitic steel sheets. To this end, the constitutive model developed by Iwamoto and Tsuta (International Journal of Plasticity 2002;18:1583–606) has been implemented in the user's material subroutine of the finite element code Abaqus/Explicit. The different contributions of the martensitic transformation to the overall plastic behaviour are analysed with the aim of assessing their influence in sheet-metal forming. The effects of transformation strains, and of the stress-state dependence of the kinetics of phase transformation are critically discussed in the case of the cup drawing test. The simulation results are also compared with experimental cup tests from the literature.