Deformation Of Sheet Metal Research Articles

Analytical modeling and experimental validation of the forming force in several typical incremental sheet forming processes

Abstract Incremental sheet forming (ISF) is recognized as an advanced forming process which is highly flexible in cost-effectively producing small batched sheet metal parts. The forming force is dramatically reduced due to the local deformation and successive forming characteristics compared with traditional stamping process, and has vital impact on forming quality. It may however, be noted, that the forming force prediction models widely used are empirical ones, which needs further improvement for wider applicability. Besides, the force fluctuation in ISF has impact on the geometric accuracy, which has been less studied so far. In the present work, the analytical models for predicting the forming force for single-pass single point incremental forming (SPIF), multi-pass incremental forming (MPIF) and incremental hole flanging (IHF) processes are developed based on the new analytical models used to calculate the contact area and the through-thickness stress. A series of experiments of typical sheet metal parts in different geometries for different materials with varied process parameters including wall angle, step depth, tool radius and sheet metal thickness are used to validate the proposed analytical models. The new prediction models are proved to calculate the forming force and force components along the axial, tangential and radial directions with high accuracy for SPIF, MPISF and IHF processes. Moreover, the mechanism of force fluctuation is also investigated, and it's proved that the force fluctuation is caused by varied elastic deflection of the deforming sheet metal.

A three-hinge-line method for calculating the deformation process of thin plates under quasi-static axial loading

This paper presents a modified calculation method for the crushing deformation of sheet metals, which is called the three-hinge-line method (THLM). Through developing the folding mechanism of a thin-walled square tube, the effect of the buckling curvature on thin plates is approximately considered by improving the original single hinge to three hinges, and a method for calculating the distance between the hinges is given. A program is designed for the solution of this problem. In addition to solving for the average force and energy, the deformation process and force-displacement curves are also included. The accuracy of the THLM can be checked by the finite element method (FEM). The good agreement between the methods shows that the compressive forces are predicted satisfactorily from the results of the proposed uniaxial crushing.

The mechanical analysis of flexible die drawing for spherical parts based on weight function

With the development of sheet metal forming technology and the increase in the application of spherical shell parts, flexible male die drawing technology has become one of the research hotspots because of its merits on strong applicability and ability to significantly increase the forming limit of the sheet. As a new type of flexible male die drawing process, solid granule medium forming (SGMF) has been rapidly developed in recent years. During the granule medium drawing process, there is a significant reduction in the thickness of the sheet metal in the female die in addition to the flange deformation. Thus, the stress state and the required forming force during the sheet metal forming process are very different from those during the conventional drawing. Taking the deformation process of the spherical shell parts as research object, the stress state of the spherical shell and the pressure of the granule medium were studied between the single drawing deformation and the single bulging deformation. On this basis, the stress model, pressure model, and required forming force model of the spherical shell parts in the granule medium drawing process were established with the drawing weight and bulging weight. Theoretical analysis, experiments, and FEM-DEM numerical simulations were employed to study the deformation of the spherical shell parts. The results show that the mechanical model based on the weight function theory can accurately reflect the stress state of the spherical shell parts during SGMF and can fully reveal the sheet metal deformation mechanism during SGMF. In addition, the theoretical analysis model established in this paper provides necessary theoretical support for the selection of equipment for SGMF process in practical application.

Parameters for the FEA simulations of single point incremental forming

ABSTRACTSingle point incremental forming has shown immense potential in the manufacture of prototypes. The sheet metal deformation in this technique is carried out by a small hemispherical or flat tool that moves from the sheet periphery to the sheet center while also pushing the sheet down. Simulations of single point incremental forming can be a tedious task since the area required to be formed is large and the two sheet contact area is fairly small. The effect of tool however, affects the entire geometry by causing deflections and radial strains. Hence, it becomes essential to understand the effect of certain parameters that influence the simulation results for this forming process. The paper aims to study factors influencing the simulation of single point incremental forming process. It gives a description of techniques employed to simulate non-linear behavior of sheet metal forming along with the implicit and explicit methodology. Information on the selection of element type including Reduced Enhanced Solid-Shell element is presented. Techniques employed to avoid locking are also discussed.

Influence of a multi-step process on the thickness reduction error of sheet metal in a flexible rolling process

Flexible rolling is a forming process based on thickness reduction, and the precision of thickness reduction is the key factor affecting bending deformation. The major purpose of the present work is to solve the problem of bending deformation error caused by insufficient thickness reduction. Under the condition of different rolling reductions with the same sheet thickness and the same thickness reduction with different sheet thicknesses, the thickness reduction error of sheet metal is analyzed. In addition, the bending deformation of sheet metal under the same conditions is discussed and the influence of the multi-step forming process on the thickness reduction error is studied. The results show that, under the condition of the same sheet thickness, the thickness reduction error increases with increasing rolling reduction because of an increase in work hardening. As rolling reduction increases, the longitudinal bending deformation decreases because of the decrease of the maximum thickness difference. Under the condition with the same thickness reduction, the thickness reduction error increases because of the decrease of the rolling force with increasing sheet thickness. As the sheet thickness increases, the longitudinal bending deformation increases because of the increase in the maximum thickness difference. A larger bending deformation is divided into a number of small bending deformations in a multi-step forming process, avoiding a sharp increase in the degree of work hardening; the thickness reduction error is effectively reduced in the multi-step forming process. Numerical simulation results agree with the results of the forming experiments.

Forming of hemispherical and hemi-ellipsoidal parts of low carbon steel sheet by mandrel free metal spinning process

Metal spinning (MS) is an efficient and economical alternative method for low-volume functional sheet metal products. It has higher potential to shape three dimensional parts without employing matching die. The focus in advancement of shape forming shall bring an effective approach to produce defect free shapes and economically viable products. This paper is going to discuss about the modification in the MS process, without using matching dies or mandrel to produce a hemispherical and hemi-ellipsoidal profile product. The forming occurs by the deformation of sheet metal when the roller feed is against the rotating metal blank. Low carbon extra deep drawing Al killed steel sheets of thickness 1.6 mm were exploited as forming material. Further the paper illustrates on thickness variation, hardness, micro-structure, surface roughness and forming limit diagram (FLD) of the various zone of the formed part. It is examined that as the depth varies, the changes in thickness of formed part also varies. Also, the surface roughness was proportionally increased with increasing in percentage of reduction in thickness. In all zone of the formed steel part are in tension- tension strain conditions, there is no tension compression and plane strain condition occurred in the forming process. Due to this reason wrinkles failure is eliminated in die less MS process.

Experimental and numerical study of DC04 sheet metal behaviour—plastic anisotropy identification and application to deep drawing

This paper deals with the identification and modelling of the deformation behaviour of DC04 sheet metal. An application of the identified behaviour model in the framework of finite element (FE) simulation of deep drawing is performed. Uniaxial tensile tests in three directions are performed to reveal the in-plane plastic anisotropy of the DC04 sheet. The Hill48 quadratic criterion is introduced to represent the initial plastic anisotropy, while the work hardening is represented by power and exponential type laws. Parameters of the established behaviour model are identified using two methods based on Hill48 criterion. FE simulations of uniaxial tensile tests are carried out to validate the identified parameters and thus retain the identification method giving best fitting of performed tests. The identified plastic behaviour model, including initial plastic anisotropy and hardening, is then introduced in FE simulation of deep drawing of waterproof case for a truck, in which the effect of blank-holder force on the drawpiece quality is analysed in order to determine the optimum thickness. Then, the effect of combination between plastic anisotropy and friction anisotropy on the sheet thickness distribution is investigated. The performed analysis shows that the plastic and friction anisotropies have an effect on the DC04 sheet metal deformation.

Temperature dependent micromechanics-based friction model for cold stamping processes

Temperature rise in cold stamping processes due to frictional heating and plastic deformation of sheet metal alters the tool-sheet metal tribosystem. This is more prominent in forming advanced high strength steels and multi-stage forming operations where the temperature on the tool surface can rise significantly. The rise in temperature directly affects the friction due to break down of lubricant, change in physical properties of tribolayers and material behavior. This can result in formability issues such as workpiece-splitting, etc. Therefore, it is important to account for temperature effects on friction in sheet metal forming analyses. In this study, the temperature effect was included in a micromechanics-based friction model which allows calculation of local friction coefficients as a function of contact pressure, bulk strain and relative sliding velocity. The temperature influence on friction was introduced through material behavior of sheet metal, viscosity of lubricant and shear strength of boundary layer in the micromechanics-based model. The model validation has been done by comparing the calculated fractional real contact area with the experimental results. The model can be used in formability analyses and to predict optimum stamping press parameters such as the blank holder force and the press speed.

An Analytical Model for Nonhydrostatic Sheet Metal Bulging Process by Means of Polymer Melt Pressure

In this paper, a theoretical approach to model free deformation of sheet metal via polymer injection pressure is presented. It is a general methodology that can be applied for any situation where a nonuniform pressure distribution is responsible for free deformation of sheet metal within a circular cavity. This approach is composed of two iterative approximation loops. In the outer loop, the radius of curvature at the tip of dome shape was optimized based on the boundary condition at the edge of clamped area while in the inner successive loop, principal stresses determined from plasticity theories were used to satisfy the equilibrium equations. While forming sheet metal via polymer injection is a revolutionary yet complex process, its modeling is challenging. Hence, before implementing this general approach to this process, the modeling methodology as such necessitates a simplified solution for melt flow analysis to obtain a pressure distribution encompassing the entire cavity. To evaluate the proposed model, a customized experimental setup was designed and fabricated, which allows sheet metal bulging with the plastic injection. The deformation of the AA1100-O sheet was investigated during the injection of the polypropylene–olefin compound. The comparison of the theoretical and experimental results shows that the general approach formulated here can be successfully applied to predict the surface strains and thickness distributions with maximum error of 6% while the deformed geometry remains within ±0.35 mm deviation in the final deformation stage.

Multi-scale investigation of highly anisotropic zinc alloys using crystal plasticity and inverse analysis

Zinc and its alloys are important industrial materials due to their high corrosion resistance, low cost and good ductility. However, the characterization of these materials remains a difficult task due to their highly anisotropic behavior, the latter being due to the influence of microstructural effects, i.e. loading orientation-dependent activation of different families of slip systems and subsequent texture evolution, rendering the development of a reliable material model considerably difficult. A micro-mechanical approach based on polycrystal plasticity would better describe the physical mechanisms underlying the macroscopic behavior. This improved model should ostensibly improve the comprehension of the mechanical behavior, compared to the macroscopic approach using solely phenomenological anisotropy models along with a prohibitively large number of experiments required to identify the material parameters. In this paper, a multi-scale Visco-Plastic Self-Consistent (VPSC) approach is used. It is based on a micro-scale model calibrated by microstructural and deformation mechanism information based on Electron Back-Scattered Diffraction (EBSD) to describe the macroscopic anisotropic mechanical response during sheet metal deformation. The critical resolved shear stress (CRSS) as well as the micro-scale crystal parameters are obtained by an inverse analysis comparing the simulated and experimental results in terms of obtained tensile curves along three different directions. In order to obtain a global solution for the identification, we then use the Covariance Matrix Adaptation-Evolution Strategy (CMA-ES) genetic algorithm to the inverse problem. We validate our approach by comparing the simulated and experimental textures and activated slip systems. Finally, the identified mechanical parameters are used to investigate the anisotropy of the alloy and predict its formability by determining the corresponding R-values and Hill yield coefficients.

Anisotropic fracture of advanced high strength steel sheets: Experiment and theory

Sheet metals such as advanced high strength steels often exhibit varying degrees of anisotropy due to the existence of preferred orientation of their grain structures from the rolling process. While extensive research has been devoted to characterize and model anisotropic plasticity behavior over the past decades, only recently people began to tackle their anisotropic fracture behavior. The focus of these studies is almost always on the in-plane anisotropy, and ignores out-of-plane fracture behavior. The reasons are two-folds: (1). Sheet metal deformation during a stamping or crash application is mostly thought as in a plane stress state and modeled as such, so there is no need to consider out-of-plane fracture behavior; and (2). It is very challenging to develop experimental techniques to reliably measure out-of-plane fracture strengths for sheet metals with a thickness only about 1 mm. In this paper, we theorize, based on strong empirical evidence, that the fracture strength of a thin sheet metal in out-of-plane shear is inherently weaker than that under in-plane shear, analogous to the interlaminar properties of composite laminates. This weakness is responsible for the so-called “shear fracture” behavior, often observed during the stamping operations of advanced high strength steels when the sheet metal flows around a tight radius. A new double-notched shear specimen with shear plane perpendicular to the thickness direction is carefully designed and tested to accurately measure the out-of-plane shear fracture strength. Simulations are executed to validate the rationality of the out-of-plane shear specimen design. Test results of a DP980 sheet show that the out-of-plane shear fracture strength is indeed about 15% lower than that measured under the in-plane shear condition. A new anisotropic ductile fracture model based on linear transformation of stresses is proposed to account for the out-of-plane fracture strength for AHSS sheets. The model is calibrated with experimental data, and the fracture surface is compared to the isotropic Mohr-Coulomb (M-C) fracture model to illustrate its effectiveness.

Experimental Investigation on Forming Limit Diagram of Mild Carbon Steel Sheet

The sheet metal forming process is the process of deforming the sheet metal into a desired shape without fracture or excessive localized necking. Variables in sheet metal forming process can be discussed together with formability and test methods. There are many defects occurring during sheet metal forming processes, such as cracking, wrinkling, local necking, buckling etc. The strain measurement in a deformed sheet metal is necessary for measurement comparison. As the thickness of sheet metal is very small as compare to other dimensions of the sheet metal, the sheet metal operation is usually considered as a plane stress problem. The Forming Limit Diagram (FLD) was also determined from surface strain measurement. The FLD is the graph between major strain (℮1) and minor strain (℮2). The Forming Limit Curve (FLC) or the Forming Limit Diagram (FLD) is useful concept for characterizing the formability of sheet metal, which reflects the maximum principal strains that can be sustained by sheet materials prior to the onset of localized necking. Generally there are three methods to establish FLD i.e. theoretical, numerical and experimental. In this paper experimental method is used to develop FLD. For experimental determination of FLD of Mild Carbon steel sheet Limit Dome Height testing is used according to the American Society of Testing Material (ASTM) as published in ASTM E 2218-02. In this paper the procedure of grid marking, punch stretching and strain measurement is used. For punch stretching operation the set up of spherical die and punch has developed on the hydraulic Universal Testing Machine (UTM). The material used for the die and punch is High Carbon High Chromium Steel (HCHCr). For printing the grids on sheet material chemical etching method is used. In this grid making process grids of 5 mm diameter circles printed. For trial experiment the sheet metal sample is stretched at the force of 23 KN. The deformed circles were converted into ellipse and from that deformed ellipse major and minor strains are to be calculated. After that the FLD will give the two different regions of safe and failure zone.

Cyclic stress and strain responses of AZ31 magnesium alloy sheet metal at elevated temperatures

Lightweight materials have been widely and increasingly utilized for the automotive industry to reduce the carbon dioxide (CO2) emissions. To replace the existing ordinary steels, the automotive companies have been investigated the other materials to satisfy the specific strength, stiffness and recyclability. Under these circumstances, some researchers have been paying attention to the magnesium alloy sheets. Although the material have low ductility at room temperature due to small number of slip systems, it is the well-known fact that the formability at the elevated temperatures around 200 ºC is drastically improved. In these days, the local heating techniques have been applied to the press forming systems in order to realize the power saving manufacturing systems in spite of the existing systems. Although the warm stamping has some great advantages to improve the formability, the prediction of the deformed sheet metal is not always enough accurate. In order to investigate the stress strain responses for the material at the elevated temperatures, a testing device which can observe the cyclic stress strain responses was developed in the present research. The magnesium alloy sheets were warmed at around 200 ºC to reduce the critical resolved shear stress of slip systems and improved its deformability. The corresponding stress strain responses by finite element method based on the crystal plasticity were calculated. It was found that the calculations could capture the above-mentioned features very well.

Clamping-sequence optimisation based on heuristic algorithm for sheet-metal components

The traditional clamping-sequence optimisation of sheet-metal parts requires many complicated finite element analyses, and clamping-sequence planning does not account for the springback from clamp-release. Therefore, this paper proposes a new optimisation method based on a heuristic algorithm. We first propose a new contact model of parts, clamps and supporting locators to analyse assembly deformation. Then, we use the distance between the actual and nominal positions to evaluate the clamp layout. Finally, we apply the heuristic algorithm to optimise the clamping sequence. We illustrate the proposed method with a case study of a taillight bracket, whose results show that the method of clamping-sequence optimisation can effectively decrease the deformation of sheet metal from clamping.

A new specimen for out-of-plane shear strength of advanced high strength steel sheets

Compared with the conventional steels, “shear fracture” is one of the main issues for advanced high strength steels (AHSS). Due to rolling, anisotropy is an intrinsic property for sheet metals. Not only the plastic responses of sheet metals but also the fracture strengths are orientation dependent. In the small radius forming process, for example, the stretch-bending deformation of sheet metals under small radius condition, the normal stress cannot be neglected. Three-dimensional loading condition constructs complex shear stress states of sheet metals especially the out-of-plane shear stress. The out-of-plane performance must be considered in order to better understand the “shear fracture” phenomenon of AHSS. Compared to in-plane shear test, the out-of-plane shear test is more difficult to carry out due to the severe restriction of the dimensions in the thickness direction. In this paper, a new specimen is presented for out-of-plane shear test. Failure of the specimen occurs in shear between two centrally located notches machined halfway through its thickness from opposing sides. Meanwhile, the finite element (FE) model and possible failure modes of this specimen are investigated in detail. At last, brief experimental results between out-of-plane shear fracture strength and the in-plane shear fracture strength are compared for DP980 sheets.

Investigation of deformation in stretch forming based on distributed displacement loading

Stretch forming based on distributed displacement loading is a new stretch forming process, in which distributed displacements are applied at a series of discrete points, therefore, the deformation in different positions of sheet metal can be individually controlled. To investigate the deformation of sheet metal in stretch forming, the rational loading trajectory is designed, and it is determined by the respective length of longitudinal cross-section curve. The numerical simulation results show that, the loading trajectory is valid to form three-dimensional surface parts, and the relatively small shape errors between the simulated results and target results make it possible to form qualified parts. Meanwhile, the longitudinal strains are uniformly distributed along the longitudinal material lines, and longitudinal strains increase evenly with the process of stretch forming. Finally, experimental tests proved the effectiveness and feasibility of the stretch forming based on distributed displacement loading.

Investigating Bauschinger Effect and Plastic Hardening Characteristics of Sheet Metal under Cyclic Loading

To improve sheet metal forming process simulation using finite element method, there is a need to incorporate an appropriate constitutive equation capable of describing the Bauschinger effect and the so-called cyclic transient, derived from a near to actual sheet metal forming process testing tool. A cyclic loading tool has been developed to test and record the characteristics of sheet metal deformation by investigating the Bauschinger effect factors (BEF) and cyclic hardening behaviour. Experimental investigation conducted on low carbon steel and stainless steel demonstrates that the tool is able to record sheet metal behaviour under cyclic loading. The results are analysed for signs of the Bauschinger effect and cyclic hardening effect. It was found that the Bauschinger effect does occur during bending and unbending loadings in sheet metal forming process.

Force-controlled sheet metal stretch-forming process based on loading at discrete points

Stretch-forming based on loading at discrete points (SF-LDP) is a new stretch-forming process, by controlling the loading trajectory at each discrete point; the process can fulfill the sheet metal deformation along the prescribed forming path. In this paper, force-controlled SF-LDP process was proposed and discussed. The sheet metal deformations in SF-LDP were numerically analyzed and it is shown that the strains remain in a fixed ratio during the forming process and the three principal axes of strain are stationary and in the longitudinal, transverse, and thickness directions, respectively. Based on the characteristic analysis on the SF-LDP process, a precision design method for the loading trajectory described by stretch-forming force was presented, and the time course of the stretching force at each loading point is determined by taking into account the effect of material hardening and the friction between the sheet metal and stretch-forming die. A force-controlled SF-LDP process for a spherical surface part was designed and the loading trajectories were employed in the experiment, the measured results on the formed part demonstrate that the force-controlled SF-LDP process achieves qualified product without forming imperfections.

A triangular prism solid and shell interactive mapping element for electromagnetic sheet metal forming process

In this paper, a novel triangular prism solid and shell interactive mapping element is proposed to solve the coupled magnetic–mechanical formulation in electromagnetic sheet metal forming process. A linear six-node “Triprism” element is firstly proposed for transient eddy current analysis in electromagnetic field. In present “Triprism” element, shape functions are given explicitly, and a cell-wise gradient smoothing operation is used to obtain the gradient matrices without evaluating derivatives of shape functions. In mechanical field analysis, a shear locking free triangular shell element is employed in internal force computation, and a data mapping method is developed to transfer the Lorentz force on solid into the external forces suffered by shell structure for dynamic elasto-plasticity deformation analysis. Based on the deformed triangular shell structure, a “Triprism” element generation rule is established for updated electromagnetic analysis, which means inter-transformation of meshes between the coupled fields can be performed automatically. In addition, the dynamic moving mesh is adopted for air mesh updating based on the deformation of sheet metal. A benchmark problem is carried out for confirming the accuracy of the proposed “Triprism” element in predicting flux density in electromagnetic field. Solutions of several EMF problems obtained by present work are compared with experiment results and those of traditional method, which are showing excellent performances of present interactive mapping element.

A multi-deformable bodies solution method coupling finite element with meshless method in sheet metal flexible-die forming

Abstract In this paper, a multi-deformable bodies solution method which includes both sheet metal elastoplastic deformation and bulk deformation of pressure-transmitting medium (PTM) in sheet metal flexible-die forming was proposed. The elastoplastic deformation of sheet metal was analyzed with finite element method (FEM), and the bulk deformation of PTM was analyzed with a meshless method, called element-free Galerkin method (EFGM). Aiming at the coupled deformation characteristics and strong nonlinear features between sheet metal/FEM and PTM/EFGM, a node-to-point contact method based on slave-master concept was employed to treat the frictional contact between these two deformable bodies. A numerical example of sheet metal flexible-die forming was presented to demonstrate the effectiveness of the proposed method.