Thickness Strain Distribution Research Articles

Redrawing analysis of aluminum–stainless-steel laminated sheet using FEM simulations and experiments

The behavior of two-layer aluminum–stainless-steel (AL-SUS) laminated sheets during deep drawing, direct and reverse redrawing processes (first and second drawing stages), have been examined by simulations and laboratory experiments. For the simulation a rigid-plastic finite element program has been used. The results of simulations are presented as the variation of drawing ratios with respect to various thickness ratios and setting conditions. They show that to achieve the highest drawing ratios in direct and reverse redrawing, the thickness ratio should be about 1 3 (one-layer aluminum and three-layer stainless-steel) and the setting conditions are opposite to each other. Considering the FEM results, laminated sheets with a thickness ratio of 71.3% aluminum and 28.7% stainless-steel were used to prepare deep drawing and redrawing experiments. The results of experiments are presented as the variation of thickness strain distribution in the drawn cup and punch load–stroke curves with respect to the setting condition. Results show that while in direct redrawing, contact of stainless-steel with the punch leads to the maximum drawing ratio, in reverse redrawing, aluminum should contact the punch in order to achieve the highest drawing ratio. An explanation for this finding is offered based on the thickness strain distribution, and punch load–stroke curves.

Finite element inverse analysis for the design of intermediate dies in multi-stage deep-drawing processes with large aspect ratio

An inverse finite element approach for multi-stage deep-drawing processes is introduced for robust capability to determine the optimum blank shape from the desired final shape and to obtain the thickness strain distribution in the final shape with a small amount of computing time and effort. A direct numerical analysis of multi-stage deep-drawing processes is extremely difficult to carry out because of its complexities and convergence problems as well as tremendous computing time. The analysis of elliptical or rectangular cup drawing with large aspect ratio is likewise very difficult with respect to the design process parameters including the intermediate die profiles. In order to overcome the difficulties, an inverse scheme is proposed in the present analysis and design. The multi-stage inverse analysis deals with the convergence among intermediate shapes and the corresponding sliding constraint surfaces. In this paper, finite element inverse analysis is applied to multi-stage deep-drawing processes in order to calculate the thickness strain distribution in each intermediate shape and to design the intermediate die shapes. The original design has been modified to enhance the discrepancy in the thickness strain distribution for each intermediate shape.

The effect of the drawbead dimensions on the weld-line movements in the deep drawing of tailor-welded blanks

Tailor-welded blanks made by the laser welding process with different thickness combinations were applied in the deep drawing process without drawbeads to investigate their forming behavior. The purpose of this study is to investigate quantitatively the effects of the drawbead dimensions on the weld-line movements in the deep drawing of the tailor-welded blanks. Square blanks have been used and five different circular drawbeads of 0.0, 1.5, 2.0, 3.0, 4.0, 5.0 mm radius and also no drawbead were installed in the blank holder in the experimental apparatus. The differences in the weld-line movements and the tendencies of the thickness strain distributions were investigated by experimental and numerical methods. The results of the weld-line movement show that the smaller the radius of the drawbead installed, the larger are the values of the movements. Also it is shown that for thickness strain along the central and diagonal direction that the larger is the dimension of the drawbead, the larger are the values of maximum thickness strain. The drawbead adds additional restraining forces to the blank, hence the movement of the weld line could be controlled by adequate drawbead installation.

Characteristics of weld line movements for the deep drawing with drawbeads of tailor-welded blanks

The purpose of this study is to investigate the weld line movements of laser welded tailored sheets during the deep drawing process with and without round drawbeads. Square blanks have been used and they have three different weld line locations. The differences of the weld line movements and the tendencies of the thickness strain distributions were investigated by experimental and analytical methods. With consideration for the amount of movement and for the thickness strain in the central and diagonal direction, the larger are the values, the longer are the distances from the center line to the initial weld lines. The drawbead adds additional restraining forces to the blank, so that the movement of the weld line is reduced and the thickness strain distribution is changed.

Investigations of weld-line movements for the deep drawing process of tailor welded blanks

The purpose of this study is to investigate the weld-line movement of the laser welded sheets during deep drawing process. Two kinds of blank shape, namely square and circular, have the three different initial weld-line locations, respectively. During the deep drawing process of these specimens, the differences of weld-line movement and thickness strain distribution are investigated by experiment and analysis

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.

Deep drawing of pressure vessel end closures: finite element simulation and validation

The development of tooling for the deep drawing of pressure vessel end closures (PVECs) can be a time-consuming and expensive process. Finite element (FE) modeling of this process has the potential to reduce these costs. Accordingly, a parametric model of the forming of PVECs on a 500 t hydraulic press at C.E. MacPherson (a division of Conrex Steel) of Kingston, Ontario has been developed using the commercial FE software, MARC. The tooling is modeled as rigid surfaces. The workpiece is modeled as a deformable body using a quadrilateral axisymmetric element. The plastic stress–strain characteristics are based on tensile-test data fitted to the Ludwik–Hollomon hardening law. Isotropic material, isotropic hardening and the Prandtl–Reuss flow rule are assumed. A mesh-refinement study is conducted to determine the optimal FE mesh. Sensitivity studies of the effects of the Coulomb friction coefficient and the blank-holder gap are also conducted. The FE results for two sizes of PVECs are validated by comparison with in-process parameters (punch displacement, punch force, and blank-holder force) and post-process (part profile, thickness-strain distribution, and surface-strain distribution) forming data.

Improvement of formability for the incremental sheet metal forming process

In order to obtain competitiveness in the field of industrial manufacture, a reduction in the development period for the small batch manufacture of products is required. In order to meet these requirements, an incremental sheet metal forming process has been developed. In this process, a small local region of a sheet blank deforms incrementally by moving a hemispherical head tool over an arbitrary surface. In this work, an incremental sheet metal forming process controlled three dimensionally by a computer has been accomplished. It has been shown by the experiments that a sheet blank is mainly subject to shear-dominant deformation. Therefore, the final thickness strain can be predicted. The uniformity of thickness throughout the deformed region is one of the key factors to improve the formability in the sheet metal forming processes. Using the predicted thickness strain distribution, the intermediate geometry is decided in the manner that a shear deformation is restrained in the highly shear-deformed region and vice versa. This double-pass forming method is found to be very effective so that the thickness strain distribution of a final shape can be made more uniform.

Optimum blank design of an automobile sub-frame

A roll-back method is proposed to predict the optimum initial blank shape in the sheet metal forming process. The method takes the difference between the final deformed shape and the target contour shape into account. Based on the method, a computer program composed of a blank design module, an FE-analysis program and a mesh generation module is developed. The roll-back method is applied to the drawing of a square cup with the flange of uniform size around its periphery, to confirm its validity. Good agreement is recognized between the numerical results and the published results for initial blank shape and thickness strain distribution. The optimum blank shapes for two parts of an automobile sub-frame are designed. Both the thickness distribution and the level of punch load are improved with the designed blank. Also, the method is applied to design the weld line in a tailor-welded blank. It is concluded that the roll-back method is an effective and convenient method for an optimum blank shape design.

Evaluation of the forming limit of aluminum square cups

Abstract Combined effects of process variables (blank shapes, tool shapes, blank materials and punch lubrication) on the deep-drawability of square cups were studied. Characteristic force lines to estimate the deep-drawability were introduced. The combined effects of the process variables were explained based on the force lines, the types of fractured cups and the thickness strain distribution. Moreover, the limiting drawing ratio could be easily evaluated from the force lines. The constant fracture force and the transitional fracture force were defined. These forces were used as the target values for the improvement in the deep-drawability. The extent of the improvement in the deep-drawability was evaluated using the fracture forces.

Characteristic behavior of aluminum-stainless laminated sheet in redrawing

Using a rigid-plastic finite element program deep drawing, direct and reverse redrawing of two layer aluminum-austenitic stainless steel (AL-ASS) laminated sheets have been simulated. The results of simulations as the variation of drawing ratios with thickness ratio and setting condition are presented. They show that to access the highest drawing ratios in direct and reverse redrawing, thickness ratio should be about 1/3 (one layer aluminum and three layer stainless steel) and the setting conditions are opposite to each other. In another word, while in direct redrawing contact of austenitic stainless steel with punch leads to the maximum drawing ratio, in reverse redrawing, aluminum should contact the punch in order to access highest drawing ratio. An explanation for this finding is offered through the thickness strain distribution.

DMSO inhibits the aggregation of the prion proteins (PRP SC) into amyloid rods

In order to obtain competitiveness in the field of industrial manufacture, a reduction in the development period for the small batch manufacture of products is required. In order to meet these requirements, an incremental sheet metal forming process has been developed. In this process, a small local region of a sheet blank deforms incrementally by moving a hemispherical head tool over an arbitrary surface. In this work, an incremental sheet metal forming process controlled three dimensionally by a computer has been accomplished. It has been shown by the experiments that a sheet blank is mainly subject to shear-dominant deformation. Therefore, the final thickness strain can be predicted. The uniformity of thickness throughout the deformed region is one of the key factors to improve the formability in the sheet metal forming processes. Using the predicted thickness strain distribution, the intermediate geometry is decided in the manner that a shear deformation is restrained in the highly shear-deformed region and vice versa. This double-pass forming method is found to be very effective so that the thickness strain distribution of a final shape can be made more uniform.

Elastic-Plastic Finite Element Analysis of Deep Drawing Processes by Membrane and Shell Elements

Both cylindrical cup drawing and square cup drawing are analyzed using both membrane analysis and shell analysis by the elastic-plastic finite element method. An incremental formulation incorporating the effect of large deformation and anisotropy is used for the analysis of elastic-plastic non-steady deformation. The corresponding experiments are carried out to show the validity of the analysis. Comparisons are made in punch load and distribution of thickness strain between the membrane analysis and the shell analysis for both cylindrical and square cup drawing processes. In punch load, both methods of analysis show very little difference and also show generally good agreement with the experiment. For the cylindrical cup deep drawing, the computed thickness strain of a membrane analysis, however, shows a wide difference with the experiment. In the shell analysis, the thickness strain shows good agreement with the experiment. For the square cup deep drawing, both membrane and shell analysis show a wide difference with experiment, this may be attributable to the ignorance of the shear deformation. Concludingly, it has been shown that the membrane approach shows a limitation for the deep drawing process in which the effect of bending is not negligible and more exact information on the thickness strain distribution is required.

Flexible and Incremental Sheet Metal Bulging using a Path-Controlled Spherical Roller. 2nd Report. Vertical Wall Surface Forming of Rectangular Shell Using Multistage Incremental Forming with Spherical and Cylindrical Rollers.

A multistage incremental sheet metal bulging machine using spherical and cylindrical rollers has been developed for vertical wall surface forming of rectangular shallow shells. Multistage incremental forming comprises three operations : bulging with a spherical roller, right-angle forming and flattening with cylindrical rollers. The hand-operated bulging machine formed a vertical wall surface which is highly precise and preferred by designers. A method of calculating for the approximate distribution of thickness strain and the maximum bulging height of the rectangular panel was proposed using the fracture limit obtained from the incremental bulging test with a ball roller and a geometrical plane-strain deformation model with a constant strain gradient. The predictions for the rectangular shell were in reasonably good agreement with experimental values for the annealed aluminum sheet.

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 Barlat et al. [Int. J. Plasticity 9, 1(1993)] . 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.

Analysis of three-dimensional deep drawing by the energy method

A systematic approach of the energy method is proposed for analysis of three-dimensional sheet metal forming of noncircular cups with complicated shape. In the proposed method, the whole deforming region is divided into several zones by considering the geometric characteristics and contact boundary condition. The geometric shape is expressed by sweeping the section curves defined on the boundary of each zone. Velocity fields are expressed in a similar manner by sweeping the boundary velocity functions. The solution is found through optimization of the total energy dissipation with respect to some parameters assumed in the kinematically admissible velocity field defined over each zone. In order to check the effectiveness of the present method, three-dimensional deep drawing by the elliptic punch and the clover-type punch are analysed and compared with the corresponding experiments. In analysing the deep drawing process by the elliptic and clover-type punches, the total deforming region has been divided into five zones. The computed results are shown to be in good agreement with the experiment in punch load, deformed edge contour and distribution of thickness strain.

Deep Drawing of Square-Shaped Sheet Metal Parts, Part 2: Experimental Study

The deep drawing process of square and rectangular shells were investigated under different process conditions, and using two different drawing quality steels. The main objective was to identify the significance of some of the process parameters on the outcome of the drawing operation. The process parameters examined were shape and size of blank, the blank-holder force and frictional condition between blank and tooling. The results of this investigation were presented in terms of punch load, through thickness and in-plane strain distributions, formations of flange wrinkles and fracture, and the largest possible blank size that can be drawn successfully. Some of these experimental results were used to verify the validity of a simplified analytical model which was described in the first part of this paper.

Flexible and Inclemental Sheet Metal Bulging Using a Few Spherical Rollers.

A flexible and incremental sheet metal bulging machine using a few spherical rollers has been developed for the small-batch manufacture of nonsymmetrical shallow shells, and for eliminating the necessity of the forming die and punch. The hand-operated bulging machine performed a wide range of sheet metal shaping of complex shapes, for example, pyramidal shells, shells of the frustum of a pyramid, shallow pans and embossed panels. An approximate calculation method for the distribution of thickness strain and the maximum bulging height of the shell was proposed using the fracture limit from the incremental bulging test with a ball punch and a geometrical plane-strain deformation model. The predictions for the shell of the frustum of a quadrangular pyramid and the shell of the frustum of a right circular cone were in reasonably good agreement with experimental values for the annealed aluminum sheet.

Comparative investigation of sheet metal forming processes by the elastic‐plastic finite element method with emphasis on the effect of bending

The effect of bending is investigated through the comparison of the membrane analysis and the shell analysis for stretching and deep drawing. An incremental formulation incorporating the effect of shape change and anisotropy is used for the analysis of elastic‐plastic non‐steady large deformation. The deformation during a step is considered using the natural convected coordinate system. Stretching of a square blank with a hemispherical punch and deep drawing of a cyclindrical cup is analysed and the corresponding experiments are carried out. The computational results are compared with the experiments. In stretching, the comparison has shown that both the membrane analysis and the shell analysis are in good agreement with the experiment for punch load and strain distribution. In deep drawing, the computed loads of both the membrane analysis and the shell analysis are generally in good agreement with the experiment. The computed thickness strain of the membrane analysis, however, shows a wide difference with the experiment. In the shell analysis, the thickness strain shows good agreement with the experiment. It has been shown that the membrane approach shows a limitation for the deep drawing process in which the effect of bending is not negligible and more exact informations on the thickness strain distribution are required.

Incorporation of the strain-rate-sensitive constitutive relations in the analysis of sheet metal forming

Two forms of rate-sensitive constitutive equations, additive and multiplicative, are examined in the analysis of sheet metal forming using the finite element method. Results are obtained for hemispherical punch stretching of an AK steel sheet material with various punch speeds. The computed results in thickness strain distributions and load-displacement curves are almost identical for the two constitutive laws at a low punch speed. However, the additive law provides better agreement in the thickness strain distributions with the experimental trends for high-speed forming.