Numerical analysis of coupled finite element with element-free Galerkin in sheet flexible-die forming

A numerical method for coupled deformation between sheet metal and flexible-die was proposed. Based on the updated Lagrangian （UL） formulation, the elastoplastic deformation of sheet metal was analyzed with finite element method （FEM） and the bulk deformation of flexible-die was analyzed with element-free Galerkin method （EFGM）. The frictional contact between sheet metal and flexible-die was treated by the penalty function method. The sheet elastic flexible-die bulging process was analyzed with the FEM-EFGM program for coupled deformation between sheet metal and bulk flexible-die, called CDSB-FEM-EFGM for short. Compared with finite element code DEFORM-2D and experiment results, the CDSB-FEM-EFGM program is feasible. This method provides a suitable numerical method to analyze sheet flexible-die forming.

Flexible-die forming process with solid granule medium on sheet metal

Certain non-metallic granules （NMG） were selected as the research object. It was proposed to conduct the volume compression experiments as well as those on the NMG physical properties at high stress levels. Then, not only the volume compression ratio curve but also the extended Drucker-Prager linear model were obtained. In addition, through the friction strength tests, parameters of the Mohr-Coulomb model were gained, which proved in basic agreement with those of the extended Drucker-Prager linear model. Additionally, curves of the friction coefficients between the NMG and the sheet metal trader different pressures were also obtained. Based on the material performance experiments, numerical analysis in respect of flexible-die forming process with solid granule medium （SGM） was conducted. The die and device for experiments of solid granule medium forming （SGMF） on sheet metal were designed and manufactured. Typical parabolic parts were successfully trial-produced. The tests and simulation results show that the sheet formability is significantly improved for the extraordinary friction performance during interaction between the SGM and the sheet metal surface. The process control and die structure are simple, and the shaped work-pieces enjoy many advantages, such as satisfactory surface quality and favorable die fitability, which offers a brand-new method and means for processing and preparation of sheet metals.

Forming limit of textured AZ31B magnesium alloy sheet at different temperatures

Repeated unidirectional bending （RUB） was carried out to improve the texture of commercial AZ31B magnesium alloy sheets. All specimens were prepared in the rolling direction. The forming limit diagrams （FLDs） of AZ31B magnesium alloy sheet were determined experimentally by conducting stretch-forming tests at room temperature, 100, 200 and 300 ℃ Compared with the as-received sheet, the lowest limited strain of AZ31B magnesium alloy sheet with tilted texture in the FLD increased by 79% at room temperature and 104% at 100 ℃. The texture also affected the extension of the forming limit curves （FLC） in the FLD. However, the FLCs of two kinds of sheets almost overlapped at temperature above 200 ℃. It can be concluded that the reduction of （0002） texture intensity is effective to the improvement of formability not only at room temperature but also at low-and-medium temperature. The effect of texture on FLDs becomes weak with increasing temperature.

Theoretical prediction of forming limit diagram of AZ31 magnesium alloy sheet at warm temperatures

A theoretical prediction on forming limit diagram（FLD） of AZ31 magnesium alloy sheet was developed at warm temperatures based on the M-K theory. Two different yield criteria of von Mises and Hill＇48 were applied in this model. Mechanical properties of AZ31 magnesium alloy used in the prediction were obtained by uniaxial tensile tests and the Fields-Backofen equation was incorporated in the analysis. In addition, experimental FLDs of AZ31 were acquired by conducting rigid die swell test at different temperatures to verify the prediction. It is demonstrated from a comparison between the predicted and the experimental FLDs at 473 K and 523 K that the predicted results are influenced by the type of yield criterion used in the calculation, especially at lower temperatures. Furthermore, a better agreement between the predicted results and experimental data for AZ31 magnesium alloy sheet at warm temperatures was obtained when Hill＇48 yield criterion was applied.

Springback prediction for incremental sheet forming based on FEM-PSONN technology

In the incremental sheet forming （ISF） process, springback is a very important factor that affects the quality of parts. Predicting and controlling springback accurately is essential for the design of the toolpath for ISF. A three-dimensional elasto-plastic finite element model （FEM） was developed to simulate the process and the simulated results were compared with those from the experiment. The springback angle was found to be in accordance with the experimental result, proving the FEM to be effective. A coupled artificial neural networks （ANN） and finite element method technique was developed to simulate and predict springback responses to changes in the processing parameters. A particle swarm optimization （PSO） algorithm was used to optimize the weights and thresholds of the neural network model. The neural network was trained using available FEM simulation data. The results showed that a more accurate prediction of s!oringback can be acquired using the FEM-PSONN model.

Sheet Metal Forming Simulation and Its Application in Stamping Process of Automobile Panels

The paper starts with a brief overview to the necessity of sheet metal forming simulation and the complexity of automobile panel forming, then leads to finite element analysis (FEA) which is a powerful simulation tool for analyzing complex three-dimensional sheet metal forming problems. The theory and features of the dynamic explicit finite element methods are introduced and the available various commercial finite element method codes used for sheet metal forming simulation in the world are discussed,and the civil and international status quo of automobile panel simulation as well. The front door outer panel of one certain new automobile is regarded as one example that the dynamic explicit FEM code Dynaform is used for the simulation of the front door outer panel forming process. Process defects such as ruptures are predicted. The improving methods can be given according to the simulation results. Foreground of sheet metal forming simulation is outlined.

Tribological behaviors between commercial pure titanium sheet and tools in warm forming

The tribological conditions between tools and sheet are the major factors affecting the product quality,forming limits and service life of tools in thin-walled titanium components warm forming.Using the orthogonal design based twist compression test in the temperature range of 25-300 °C,the significant factors affecting the coefficient of friction（Co F） and the influencing rules in CP-3 titanium sheet warm forming are clarified and discussed by changing tribological conditions such as tool material,lubrication,temperature and normal pressure.The results show that the significant factors affecting the Co F are lubrication,surface roughness,tool material,sliding velocity,normal pressure and temperature;compared with unlubricated condition,the graphite and Mo S2 greatly improve the friction condition and the maximum reduction of the Co F is 0.318;the Co Fs of Cr12 Mo V/CP-3 and QAl10-3-1.5/CP-3 tribo-pairs show a similar tendency：the Co Fs increase with increasing surface roughness and sliding velocity,and increase firstly then decrease with increasing normal pressure and temperature.

Multi-Point Forming Technology for Sheet Metal

Multi-point forming (MPF) is an advanced manufacturing technology for three-dimensional sheet metal parts. In this paper, the MPF integrated system is described that can form a variety of part shapes without the need for solid dies, and given only geometry and material information about the desired part. The central component of this system is a pair of matrices of punches, and the desired discrete die surface is constructed by changing the positions of punches though the CAD and control system. The basic MPF process is introduced and the typical application examples show the applicability of the MPF technology. Wrinkle and dimple are the major forming defects in MPF process, numerical simulation is a feasible way to predict forming defects in MPF. In conventional stamping, the mode to form sheet metal with blankholder is an effective way to suppress wrinkling; the same is true in MPF. A MPF press with flexible blankholder was developed, and the forming results indicated the forming stability of this technique. Based on the flexibility of MPF, varying deformation path MPF and sectional MPF were explored that cannot be realized in conventional stamping. By controlling each punch in real-time, a sheet part can be manufactured along a specific forming path. When the path of deformation in MPF is designed properly, forming defects will be avoided completely and lager deformation is achieved. A work piece can be formed section by section though the sectional MPF, and this technique makes it possible to manufacture large size parts in a small MPF press. Some critical experiments were performed that confirmed the validity of two special MPF techniques.

SIX SIGMA OPTIMIZATION IN SHEET METAL FORMING BASED ON DUAL RESPONSE SURFACE MODEL

Iterations in optimization and numerical simulation for the sheet metal forming process may lead to extensive computation. In addition, uncertainties in materials or processing parameters may have great influence on the design quality. A six sigma optimization method is proposed, by combining the dual response surface method （DRSM） and six sigma philosophy, to save computation cost and improve reliability and robustness of parts. Using this method, statistical technology, including the design of experiment and analysis of variance, approximate model and six sigma philosophy are integrated together to achieve improved quality. Two sheet metal forming processes are provided as examples to illustrate the proposed method.

FAST ACCURATE PREDICTION OF BLANK SHAPE IN SHEET METAL FORMING

By using the Finite Element Inverse Approach based on the Hill quadratic anisotrop-ically yield criterion and the quadrilateral element, a fast analyzing software-FASTAMP for the sheet metal forming is developed. The blank shapes of three typical stampings are simulated and compared with numerical results given by the AUTOFORM software and experimental results, respectively. The comparison shows that the FASTAMP can predict blank shape and strain distribution of the stamping more precisely and quickly than those given by the traditional methods and the AUTOFORM.

Sheet Metal Forming Optimization by Using Surrogate Modeling Techniques

Surrogate assisted optimization has been widely applied in sheet metal forming design due to its efficiency. Therefore, to improve the efficiency of design and reduce the product development cycle, it is important for scholars and engineers to have some insight into the performance of each surrogate assisted optimization method and make them more flexible practically. For this purpose, the state-of-the-art surrogate assisted optimizations are investigated. Furthermore, in view of the bottleneck and development of the surrogate assisted optimization and sheet metal forming design, some important issues on the surrogate assisted optimization in support of the sheet metal forming design are analyzed and discussed, involving the description of the sheet metal forming design, off-line and online sampling strategies, space mapping algorithm, high dimensional problems, robust design, some challenges and potential feasible methods. Generally, this paper provides insightful observations into the performance and potential development of these methods in sheet metal forming design.

Investigation of Surface Damage in Forming of High Strength and Galvanized Steel Sheets

Powdering/exfoliating of coatings and scratching galvanized steels and high strength steels （HSS）, are the main forms of surface damage in the forming of which result in increased die maintenance cost and scrap rate. In this study, a special rectangular box was developed to investigate the behavior and characteristics of surface damage in sheet metal forming （SMF） processes. U-channel forming tests were conducted to study the effect of tool hardness on surface damage in the forming of high strength steels and galvanized steels （hot-dip galvanized and galvannealed steels）. Experimental results indicate that sheet deformation mode influences the severity of surface damage in SMF and surface damage occurs easily at the regions where sheet specimen deforms under the action of compressive stress. Die corner is the position where surface damage initiates. For HSS sheet, surface damage is of major interest due to high forming pressure. The HSS and hot-dip galvanized steels show improved ability of damage-resistance with increased hardness of the forming tool. However, for galvannealed steel it is not the forming tool with the highest hardness value that performs best.

A Study on Super Speed Forming of Metal Sheet by Laser Shock Waves

Metal sheet plastic deformation or forming is gener at ed through a mechanical pressure or a thermal variation. These pressure variatio ns or thermal variations can be created by a variety of means such as press form ing, hydroforming, imploding detonation and so on. According to the magnitude of the strain rates all these forming methods can be divided into quasi-static fo rming and dynamical forming. Up to now there are no reports of forming methods w ith the strain rates above 10 5sec -1, even though the exploding forming. In this article, we work on a dynamic super-speed forming method driven by lase r shock waves and advanced a novel concept of laser shock forming. The initial o bservation of the laser shock forming is done through a bugle testing with speci mens of SUS430 sheet metal, using a neodymium-glass laser of pulse energy 10J～ 3 0J and duration of 20 ns (FWHM). The investigation revealed that the plastic de formation during the laser shock forming is characterized as ultrahigh strain ra te up to 10 7sec -1. We indicate that plastic deformation increases nonlin early when the energy density of the laser varies. By investigating the hardness and residual stress of the surfaces, we conclude that laser shock forming is a combination technique of laser shock strengthening and metal forming for introdu cing a strain harden and a compressive residual stress on the surface of the wor k-piece, and the treated surface by laser shock forming has good properties in fatigue and corrosion resistance. This technique can achieve forming wit h or without mould.

Study on Theory and Application of the Energy Method used for Analyzing Compressive Instability in Sheet Forming

It is pointed out that there was serious weakness w he n using the energy method for studying compressive plastic instability in sheet forming in the past. Where applying the deduced instability strengths to relativ e engineering analysis, theoretical solutions were away from practices. Its basi c reason is that simplified process in mathematical analysis of elastic bending energy was completely applied to that of plastic bending energy. Where the cambe r expressed by function of displacement normal to a plate was approximated to re alistic deflective camber, the displacement of deflected plate to compressed dir ection was neglected. With the aid of the improved instability strengths, the pr edictions on both critical buckling dimension of blank in cup deep-drawing with out blankholder through cylindrical die or conical die and the minimum blankhold er pressure to prevent buckling under constant load are universally in agreement with both experimental results and experiential data. On the bases of above-mentioned improvement, the approximate expressions for bo th the curvature and the twist used in equation of the energy of elastic bending are also ameliorated. Thus the obtained general equations for both the energy a nd the work done by internal force in plastic bending of a plate are more precis e than before. In the analyses of plastic buckling of shell with bending moment, the effect of bending moment is considered through the work done by simulative bending for ce. The method proposed in this paper can not only simplify analyses but also ge t practical result.

NC INCREMENTAL SHEET METAL FORMING PROCESS AND VERTICAL WALL SQUARE BOX FORMING

The forming principle and deformation analysis of NC incremental sheet metalforming process as well as the process planning, experiment and key process parameters of verticalwall square box forming are presented. Because the deformation of sheet metal only occurs around thetool head and the deformed region is subjected to stretch deformation, the deformed region of sheetmetal thins, and surface area increases. Sheet metal forming stepwise is to lead to the whole sheetmetal deformation. The forming half-apex angle 9 and corner radius R are the main processparameters in NC incremental forming of vertical wall square box. According to sine law, a verticalwall square box can't be formed by NC incremental sheet metal forming process in a single process,rather, it must be formed in multi processes. Thus, the parallel line type tool path process methodis presented to form the vertical wall square box, and the experiment and analysis are made toverify it.

DEFORMATION ANALYSIS OF SHEET METAL SINGLE-POINT INCREMENTAL FORMING BY FINITE ELEMENT METHOD SIMULATION

Single-point incremental forming （SPIF） is an innovational sheet metal forming method without dedicated dies, which belongs to rapid prototyping technology. In generalizing the SPIF of sheet metal, the deformation analysis on forming process becomes an important and useful method for the planning of shell products, the choice of material, the design of the forming process and the planning of the forming tool. Using solid brick elements, the finite element method（FEM） model of truncated pyramid was established. Based on the theory of anisotropy and assumed strain formulation, the SPIF processes with different parameters were simulated. The resulted comparison between the simulations and the experiments shows that the FEM model is feasible and effective. Then, according to the simulated forming process, the deformation pattern of SPIF can be summarized as the combination of plane-stretching deformation and bending deformation. And the study about the process parameters＇ impact on deformation shows that the process parameter of interlayer spacing is a dominant factor on the deformation. Decreasing interlayer spacing, the strain of one step decreases and the formability of blank will be improved. With bigger interlayer spacing, the plastic deformation zone increases and the forming force will be bigger.

Comparative study on forming limit prediction of AA7075-T6 sheet with M−K model and Lou−Huh criterion

In order to effectively predict the fracture of AA7075-T6 sheet, the forming limit curves of AA7075-T6 high-strength sheet were drawn according to Morciniak Kuczyski (M K) model and Lou Huh criterion, respectively. The errors between the predicted values of the two theoretical prediction models and experimental values were calculated by error analysis. The forming limit curves were verified by the punch stretch test to evaluate the prediction accuracy of M K model and Lou Huh criterion. The error analysis results show that the mean error of Lou Huh criterion with the optimal parameters for all tensile specimens is 25.04%, while the mean error of M K model for all tensile specimens is 74.24%. The prediction accuracy of Lou Huh criterion in predicting the fracture of AA7075-T6 sheet is higher. The punch stretch test results show that the forming limit curve drawn by Lou Huh criterion can effectively predict the fracture of AA7075-T6 sheet, but the prediction accuracy of M K model is relatively poor.

Numerical simulation and experimental investigation of incremental sheet forming process

In order to investigate the process of incremental sheet forming (ISF) through both experimental and numerical approaches, a three-dimensional elasto-plastic finite element model (FEM) was developed to simulate the process and the simulated results were compared with those of experiment. The results of numerical simulations, such as the strain history and distribution, the stress state and distribution, sheet thickness distribution, etc, were discussed in details, and the influences of process parameters on these results were also analyzed. The simulated results of the radial strain and the thickness distribution are in good agreement with experimental results. The simulations reveal that the deformation is localized around the tool and constantly remains close to a plane strain state. With decreasing depth step, increasing tool diameter and wall inclination angle, the axial stress reduces, leading to less thinning and more homogeneous plastic strain and thickness distribution. During ISF, the plastic strain increases stepwise under the action of the tool. Each increase in plastic strain is accompanied by hydrostatic pressure, which explains why obtainable deformation using ISF exceeds the forming limits of conventional sheet forming.

STUDY ON THE FINITE ELEMENT NUMERICAL SIMULATION OF SHEET METAL FORMING

Based on the Finite Element Theory of Rigid Plastic,relevant problems during plas-tic simulation on sheet metal forming were technologically studied and simplified;a simplified model of the blank holder during the drawing process was established and the effects of related parameters on the forming processes were also studied.At the same time,a finite--element numerical simulation program SPID was developed.The distribution of strain and relationship of stress--stroke simulated were compared with experimented,the results are well coincided with each other.It is verified that the analytical program is reliable.

EXPERIMENTAL TESTING OF DRAW-BEAD RESTRAINING FORCE IN SHEET METAL FORMING

Due to complexities of draw-bead restraining force calculated according to theory and depending on sheet metal forming properties experiment testing system, a simplified method to calculate draw-bead restraining force is put forward by experimental method in cup-shaped drawing process. The experimental results were compared with numerical results and proved agreement. It shows the method is effective.