Rectangular Cup Drawing Research Articles

The Effect of Die Geometry on Cup Damages in Cold Deep Drawing of Rectangular Cups

Derin çekme, zımba kuvveti uygulanarak sac malzemenin kalıp boşluğuna akışıdır. Derin çekmede, düz ince tabakalar arasında sacı istenen şekle getirmek için zımba kullanılarak sacı merkez kısmından kalıp boşluğuna iterek kaplar üretilmektedir. Derin çekilmiş kaplarda kabın köşe yarıçaplarında boyun oluşumu veya çatlamaların oluşması nedeniyle daha yüksek çekme oranları elde edilememektedir. Bunun için derin çekme işleminin başarılı olmasında uygun işlem parametrelerinin doğru seçilmesi önemlidir. Bu makalede, dikdörtgen geometriye sahip kapların derin çekilmesinde matris üst yüzeyine ve pot çemberinin alt yüzeyine açılar verilerek matris geometrisinin, kap kesit incelmeleri ve hasarları üzerinde olan etkileri tespit edilmiştir. Bunun için matris üst yüzeyine/pot çemberi alt yüzeyine 0°, 3°, 6° ve 9°’lik açılar verilmiştir. Pot çemberi kuvveti sabit 1800 daN ve stampa hızı da sabit 4 mm/s olarak uygulanmıştır. Derin çekme işlemlerinde, matris/stampa arası boşluk 1.2 mm, stampa uç ve kenar radyüsleri ile matris ağız yarıçapları 6 mm alınmıştır. Çalışmada kalınlığı 1 mm olan St37 çeliği kullanılmıştır. Cidar kalınlıkları Mitutoyo LH-600E hassas lineer ölçüm cihazında 0.001 hassasiyetinde nokta temaslı olarak ölçülmüştür. Kap yükseklikleri artıkça kaplardaki cidar incelmelerinin arttığı, maksimum incelmenin kabın alt kısımlarındaki köşelerde meydana geldiği ve bu değerin 0,373 mm olduğu tespit edilmiştir. Plastik deformasyonun en çok etkilediği bölge kap alt bölgesidir. Bu bölgede deformasyon sertleşmesi nedeniyle maksimum basma ve çekme kuvvetleri oluşmakta ve dolayısıyla maksimum gerilme ve sertlik bu kısımda meydana gelmiştir. Maksimum sertlik kabın tabanının olduğu bölgede ve 61.4 HRC olarak ölçülmüştür. Minimum sertlik kap üst bölgesinde ölçülmüştür. Kabın üst ağız kısımlarına doğru sertliğin daha da düştüğü ve 43.8 HRC olduğu görülmüştür. Ortalama sertlik değeri ise 53.1 HRC olarak tespit edilmiştir. Sonuç olarak, dikdörtgen geometriye sahip kapların soğuk derin çekilmesinde, matris üst yüzeyine ve pot çemberinin alt yüzeyine açılar verilerek kalıp geometrisinin, kap cidar kalınlık değişimleri ve kap hasarları üzerinde önemli bir etkisinin olduğu tespit edilmiştir.

Wrinkling limit curves with consideration of anisotropic behaviour for the deep drawing of aluminium sheet alloys

In this work, a combined experimental and finite-element (FE)-based approach was introduced for determining the wrinkling limit curves (WLCs) of sheet metals during forming processes. Aluminium sheets of grade AA5052-O and AA5052-H32 with different formabilities and anisotropic behaviours were investigated. Modified Yoshida buckling tests were carried out for aluminium sheets in both the rolling (RD) and transverse direction (TD). In parallel, FE simulations of the buckling tests were conducted, in which the Hill’48 (both r- and stress-based) yield criteria and Swift strain hardening law were incorporated. Local principal strain histories of observed wrinkle areas on both surfaces of samples were gathered from the simulations and the state of wrinkling initiation was then identified at the inclination of these strain paths. The calculated strain values were verified with developed compressive stresses as well as corresponding strains measured by a digital image correlation technique. The influences of material anisotropies and used yield functions on the determined WLCs were discussed. Subsequently, the determined WLCs were applied for evaluating non-flange wrinkling formation during a rectangular cup drawing test. The forming tests were experimentally and numerically performed for the examined aluminium sheets in both RD and TD. It was found that strain distributions of critical side wall areas at predicted wrinkling onset and severe wrinkle states were well correlated with the WLCs. Thus, WLCs based on the r-based criterion could more accurately describe the non-flange wrinkling incidents of the cup-drawn samples than those of the stress-based model.

Deep drawing of a rectangular cup with a small radius at the bottom circular arc by employing a locally-thickened plate

A rectangular cup with a small radius at the bottom circular arc is a common sheet metal structure in aerospace components. However, when aluminum alloy plates are used for deep drawing of this type of rectangular cups, the wall thickness around the bottom circular arc is severely decreased. Hence, in this paper, locally-thickened plates were adopted for deep drawing of aluminum alloy rectangular cups with a relatively small radius at the bottom circular arc. The effect of thickening parameters of a locally-thickened plate on the radius at the bottom circular arc and the forming load was investigated by employing finite element simulations and deep drawing experiments. The results indicate that a smaller radius at the bottom circular arc is obtained by increasing the angle or reducing the thickness of the thickened convex rib of a plate. Moreover, the aforementioned is achieved when the side length of the thickened convex rib is equal to the punch width. The forming load is closely related to the thickening parameters of a locally-thickened plate. A small radius of 5 mm at the bottom circular arc was successfully obtained by optimizing the thickening parameters. Furthermore, the forming load during the deep drawing was significantly reduced.

Analysis of rectangular cup drawing considering anisotropic hardening and cyclic effect for orthogonal anisotropic materials

An anisotropic plasticity model is developed based on the non-associated flow rule with anisotropic hardening. The model combines non-quadratic yield function and quadratic plastic potential function for orthogonal anisotropic sheet metals. The model is also expanded to properly reproduce the cyclic effect during forming processes. The simple formulations can contribute to cost saving in the parameter acquisition process and implementation. The developed model was implemented into the finite element code ABAQUS as a user material subroutine under a general three-dimensional condition. To evaluate the capability of the plasticity model, different loading conditions and prediction of the yield surface were considered. A multi-step rectangular cup drawing process with the AA5182-O and DP600 sheets including draw/re-draw effects was applied to evaluate the performance of capturing complex plastic behavior by finite element simulation. The results show that the anisotropic plasticity model is capable of describing the anisotropic behaviors including anisotropic hardening and cyclic hardening with high accuracy and efficiency.

Experimental and numerical analysis on deep drawing rectangular cups made of different anisotropic materials

Deep drawing process is a significant metal forming process used in the sheet metal forming industries. From these process most complex shapes is manufactured with less defects. Deep drawing process has many effectible process parameters from which optimum parameters must be identified so that an efficient final product will be obtained. In which effects of different sheets on deep drawing process observed for sheet metal of 0.8mm of SS304, Brass and 0.9 mm of Al. The experiments are performed by designing the deep drawing tools such as die, blank holder, and punch. Also the numerical simulations are performed for deep drawing of rectangular cups using two levels of aforesaid parameters like lubricating condition and blank material. The experiments are conducted by attaching the deep drawing tools to the Universal Testing Machine. For numerical simulation a commercial FEM code is used in which Hollomon’s power law and krupowski power law along with Hill’s 1948 yield criterions are implemented. The deep drawing setup used in the FEM code is modelled using a CAD tool by considering the modelling requirements from the literature. Strain path of 55x55mm are simulated. Punch forces and dome heights are evaluated for all the conditions. From this work the formability for different metal sheets is observed for different blank materials

Stress and strain based fracture forming limit curves for advanced high strength steel sheet

In this work, strain based fracture forming limit curve (FFLC) of advanced high strength (AHS) steel grade 980 was determined by means of experimental Nakajima stretch-forming test and tensile tests of samples under shear deformation. During the tests, a digital image correlation (DIC) technique was applied to capture the developed strain histories of deformed samples up to failure. The gathered fracture strains from different stress states were used to construct the FFLC. Subsequently, the FFLC in the strain space was transformed to a principal stress space by using plasticity theories. As a result, the fracture forming limit stress curve (FFLSC) of examined steel was obtained. Furthermore, fracture locus (FL) as a relationship between stress triaxialities and critical plastic strains was determined. Hereby, two anisotropic yield functions, namely, the Hill’48 and Yld89 model were taken into account and their effects on the calculated curves were investigated. To verify the applicability of the obtained limit curves, rectangular cup drawing test and forming tests of so-called Diabolo and mini-tunnel samples were performed. Obviously, the FFLSCs and FLs more accurately described the failure occurrences of 980 steel sheets than the FFLCs. In addition, it was found that the drawing depths predicted by the FLs and the Yld89 yield criterion slightly better agreed with the experimental results than those from the FFLSCs and the Hill’48 model, respectively.

Pulse current assisted drawability of AZ31B magnesium alloy sheets

The thermal effect and athermal effect such as electro-plastic effect of metallic materials induced by high density current can dramatically reduce the flow stress, which is beneficial to the forming process of less formable metal. In this paper, pulse current-assisted deep drawing of the magnesium alloy is proposed due to lower energy consumption and higher efficiency. In this process, the metal sheet is designed in series in a pulse current circuit and heated directly by the pulse current. In addition, the insulated mould is employed to avoid the current leaking. Experiments were conducted to demonstrate the feasibility and advantages of the proposed process. An experimental process system was established and the electrical-assisted Erichsen cupping tests and rectangular cup drawing tests were performed. The experiments showed that the forming load was reduced and the cupping height and associated principal strains were increased in the Erichsen cupping and deep drawing process assisted by high-density electric current.

Forming limit diagrams of tailor rolled blank in hot stamping and its verification

The purpose of this study is to predict the rolling-orientation and temperature dependent forming limit diagrams (FLDs) of tailor rolled blank (TRB) in hot stamping process. The rolling orientation is defined by the angle of major loading direction and rolling direction and influences to hot formability of TRB. When forming take places at elevated temperature, the formability of TRB is greatly affected not only by the rolling orientation but also by inhomogeneous forming temperature. In this study, TRB of thickness ratio 1.43(1.5/1.05 mm) was employed to evaluate the formability at elevated temperature using stretch forming test which was performed according to various deformation modes. The experimental FLDs were determined by the second derivative Bragard method which was based on the analysis of strain distribution near failure. In order to obtain the rolling-orientation and temperature dependent FLDs, the experimental FLDs were used to establish interpolating equation using major loading direction, rolling direction and forming temperature. The determined equation was applied to predict failure by comparison of calculated major strain with the value of FE-simulation. The rolling-orientation and temperature dependent FLDs were also applied to FE-simulation for hot stamping of rectangular cup drawing to predict limit drawing height (LDH). The predicted LDH was verified by comparison with experimentally measured one. As a result, hot formability of TRB can be precisely predicted by the suggested FLDs compared to conventional FLDs considering thickness of TRB.

Continuous Dry Cylindrical and Rectangular Deep Drawing by Electroconductive Ceramic Dies

Two types of electroconductive ceramic tools are employed in this study to describe the dry deep drawing behavior of cold rolled steel sheets into cylindrical and rectangular cups. Each of electroconductive ceramic tools is machined by die sinking electric discharge. Four experimental setups are also prepared to investigate the effect of the surface roughness on the quality of dry deep drawing: the unlapped and the lapped electroconductive ceramic dies in dry condition and the unlubricated and the lubricated SKD11 die. Even without lubricating oils, cylindrical and rectangular cups are successfully deep drawn over 10,000 by the present tooling. Furthermore, compared to the lubricated SKD11 tooling, surface roughness of deep drawn cups is reduced by the present ceramic tooling. Fine finishing in ceramic tooling never leads to low surface roughness in the deep drawn cups since the work materials make unconstrained plastic flow in the direction of thickness. Hence, the unlapped electroconductive ceramic tooling is favored for practical ceramic tooling to preserve well-defined contact interface between metallic work sheets and ceramic tools in dry deep drawing. In addition, the rectangular cup drawing is evaluated by more severe conditions than the cylindrical cup drawing because the stress concentrates on the corner parts. Through this test, it is demonstrated that the electroconductive ceramic tooling has a potential of practical dry deep drawing.

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.

Application of Drucker–Prager plasticity to predict fracture in rectangular cup drawing of AZ31 alloy sheet

Abstract The formability in three-dimensional rectangular cup drawing of AZ31 magnesium alloy sheet is successfully predicted by the Drucker–Prager plasticity (DP model). Numerical results show that the punch corner shoulder is under the condition of high tension bending and the die corner shoulder is on pure bending regardless of constitutive models. The failure is attributed to the competition between the biaxial tension bending induced fracture on the punch corner shoulder and the through-thickness shear induced fracture on other shoulders in the sheet forming. Taking the yield surface asymmetry into consideration, in a way of the friction angle in the coordinate of compressive and tensile strengths in the DP model, the accuracy of plastic strain is improved remarkably. The fracture locates on the punch corner shoulder where the strain reaches its fracture limit earlier than the die corner shoulder's. The predictions of forming limit and fracture locus in the DP model simulation are in good agreement with the experimental results.

Warm Forming Simulation of Dual-Phase Steel Tailor-Welded Blanks Based on Thermo-Mechanical Coupled Method

A thermo-mechanical coupled finite element model for warm forming of dual-phase steel (DP) laser tailor-welded blanks (TWBs) was established based on ABAQUS software. The isothermal deep drawing of rectangular cups at elevated temperatures and the non-isothermal deep drawing at the temperature of 400°C were simulated. The distributions of temperature and differences between the isothermal and non-isothermal conditions were discussed. The results show that the temperature has great effect on the warm forming of DP-TWBs, and it achieves the best formability at the forming temperature of 400°C, and the non-isothermal deep drawing can further improve the warm formability.

Investigation of anisotropy problems in sheet metal forming using finite element method

This paper discusses the results of the numerical study of rectangular cup drawing of steel sheets using finite element methods. To be able to verify the results of the numerical solutions, an experimental study was done where the material behavior under deformation was analyzed. A 3D parametric finite element (FE) model was built using the commercial FE-package ABAQUS/Standard. ABAQUS allows analyzing physical models of real processes putting special emphasis on geometrical non-linearities caused by large deformations, material non-linearities and complex friction conditions. Friction properties of the deep drawing quality steel sheet were determined by using the pin-on-disc tribometer. The results show that the friction coefficient depends on the measured angle from the rolling direction and corresponds to the surface topography. A quadratic Hill anisotropic yield criterion was compared with von Mises yield criterion having isotropic hardening. The sensitivity of constitutive laws to the initial data characterizing material behavior is also presented. It is found out that plastic anisotropy of the matrix in ductile sheet metal has influence on deformation behavior of the material. When the material and friction anisotropy are taken into account in the finite element analysis, this approach gives better approximate numerical results for real processes.

3D elasto-plastic FEM analysis of the sheet drawing of anisotropic steel sheet

The article presents the experimental and numerical results of rectangular cup drawing of DC03 cold-rolled steel sheet. The aim of the experimental study was to analyse material behaviour under deformation. The received numerical results were further verified by experimental results. A 3D parametric finite element model was built using the commercial package ABAQUS. If the material and friction anisotropy are taken into account in the numerical model, this approach undoubtedly gives the most approximate numerical results to real processes.

Warm deep drawing of magnesium alloy sheets — formability and process conditions

The influence of deformation conditions on the formability of magnesium alloy was systematically investigated using the experimental method and finite element analysis. The research activity aimed to gain further insight into the formability of magnesium alloy AZ31 (aluminium 3 wt per cent, zinc 1 wt per cent) and to have first-hand knowledge of the correlations between the material's properties and the processing parameters. In this work, the mechanical properties of magnesium alloy AZ31 sheet were analysed according to the results of tensile tests. A set of experimental equipment with temperature control was employed to perform warm deep drawing of magnesium alloy AZ31 sheets under various forming conditions. The most important process parameters, including the punch speed, the forming temperature, and the geometrical shape of the blank, were taken into account and optimal values were proposed. Finite element analyses were also performed to evaluate the effects of the process parameters on the formability of rectangular cup drawing and to predict the process defects during the process.

Stress analysis of rectangular cup drawing

Experimental test and numerical simulation of rectangular cup drawing have greatly enhanced the engineering knowledge on its deformation characteristics. To facilitate theoretical analysis, a “three-segment-approach” was adapted by the authors on the rectangular cup drawing. Due to a twofold symmetry, only a quarter of the drawings were analyzed. Sheet material on areas corresponding to the two straight flange areas and one corner flange area were treated as three independent deformation zones. For the blank material located in the corner flange area, a concept of “equivalent circle” was put forward to simplify the stress analysis. Theoretical stress distributions on the straight flange areas and corner flange area were obtained separately from the analysis. Comparison of predicted results from the theoretical model with experimental and FEM simulation results showed a good agreement. It was found that the maximum radial stress along the punch opening is always located at the cup corners. The location with the predicted leading radial stress during the drawing was found always at the upper tangential point of the punch shoulder, where the sheet material disengaged from the punch. It was therefore justified as the most split-critical location of deep drawing of a rectangular cup. For the straight cup side, both the experimental and the FEM simulation results showed that the higher radial stress was at the upper tangential point of the punch. Since there is no complete theory available for the rectangular cup drawing problem, current three-segment-approach can be considered as a practical engineering method. Combining with results obtained from experiment and FEA simulation, this theoretical analysis can help the optimization of control scheme for stamping panels by using an advanced variable blank holder force rather than using a constant binder force.

Application of Blank Optimization Method in Deep Drawing of Rectangular Magnesium Alloy Cups under Non-Isothermal Condition

Using the optimum blank in sheet metal forming process not only can decrease the material wasting but also avoid possible defects such as local severe thinning, wrinkling and fracture. Since it is practical technology for industrial production, many blank optimization methods have been proposed and their validity was verified by some forming tests of typical or complicated components. However, all the forming tests were carried out at room temperature or under isothermal condition. In present work, a blank optimization method was employed to evaluate its efficiency in deep drawing of rectangular magnesium alloy cups under non-isothermal condition. It is proved by experiment that the employed blank optimization method can predict successfully the optimum initial blank shape for the component with specified shape and dimension.

One-step FEM based control of weld line movement for tailor-welded blanks forming

One-step finite element method (also called inverse approach) is widely used recently in the automobile industry. In order to speed up and ensure the convergence of Newton–Raphson iterations, energy based 3D mesh mapping algorithm is used to obtain the initial solution. The action of punch and die, effect of restraining forces under the blankholder due to drawbeads and blankholder pressure with friction are considered as well. Hydraulic controlled pads used to clamp the weld line during deep drawing process are simplified as static external force to reduce the movement of weld line. The above-mentioned methods have been implemented in authors’ in-house one-step code InverStamp. The initial weld line can be well predicted by one-step finite element analysis from the desired weld line in a formed workpiece which is demonstrated by a rectangular cup drawing study.

One-step FEM-based evaluation of weld line movement and development of blank in sheet metal stamping with tailor-welded blanks

Currently, more and more tailor-welded blanks (TWBs) are used in the automobile industry. It is very important to locate the weld line and predict its movement during the forming process. The initial weld line can be predicted by one-step finite-element analysis according to the desired weld line in the final workpiece. Meanwhile, weld line movement during the deformation process can be evaluated in advance. In this paper, the procedures of finite-element analysis of one-step FEM with TWBs are established. The contact between tool and blank and the effect of restraining forces under the blankholder due to drawbead and blankholder pressure are considered as well. Forming limit diagram (FLD) is used to show not only the tendency of reduction in thickness and fracture but also of increase in thickness and wrinkle. Hydraulic controlled pads used to clamp the weld line during the deep drawing process are simplified as static external force to eliminate the movement of the weld line. In order to speed up and ensure the convergence of Newton-Raphson iterations, energy-based 3D mesh mapping algorithm is introduced to obtain the initial solution. The above-mentioned methods have been implemented in the authors’ in-house one-step FEM code InverStamp. A rectangular cup drawing case demonstrates that this approach can be easily implemented to evaluate weld line movement and develop initial blank in sheet metal stamping with tailor-welded blanks.

A formability index for the deep drawing of stainless steel rectangular cups

The effects of process parameters on the formability of the deep drawing of rectangular cups made of SUS304 stainless steel were investigated by both the finite element analysis method and the experimental approach. A statistical analysis was employed to construct an orthogonal chart which reflects the effects of the process parameters and their interactions on the formability of rectangular cup drawing. The material properties and the forming limit diagram (FLD) of SUS304 stainless steel were obtained from the experiments conducted in the present study and were employed by the finite element simulations. In the finite element analysis, the strain path that led to fracture in the drawing process was examined and the failure modes caused by different process parameters were also identified. With the help of statistical analysis, a formability index for the deep drawing of SUS304 stainless steel rectangular cups was constructed and the critical value of the formability index was determined from the finite element simulation results. The actual drawing processes of rectangular cups were also performed in the present study. The validity of the finite element simulations and the formability index were confirmed by the good agreement between the simulation results and the experimental data. The formability index proposed in the present study provides a convenient design rule for the deep drawing of SUS304 stainless steel rectangular cups.