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.

Studying Formability Limits By Combining Conventional and Incremental Sheet Forming Process

In this work it is assessed the potential of combining conventional and incremental sheet forming processes in a same sheet of metal.This so-called hybrid forming approach is performed through the manufacture of a pre-forming by conventional forming,followed by incremental sheet forming.The main objective is analyzing strain evolution.The pre-forming induced in the conventional forming stage will determine the strain paths,directly influencing the strains produced by the incremental process.To conduct the study,in the conventional processes,strains were imposed in three different ways with distinct true strains.At the incremental stage,the pyramid strategy was adopted with different wall slopes.From the experiments,the true strains and the final geometries were analyzed.Numerical simulation was also employed for the sake of comparison and correlation with the measured data.It could be observed that single-stretch pre-strain was directly proportional to the maximum incremental strains achieved,whereas samples subjected to biaxial pre-strain influenced the formability according to the degree of pre-strain applied.Pre-strain driven by the prior deep-drawing operation did not result,in this particular geometry,in increased formability.

Improving Local Temperature Rise in Rotational Incremental Sheet Forming Process by Modifying Forming Parameters Using Response Surface Method

In rotational incremental sheet forming( RISF) process,the friction heating of rotational tool could lead to local temperature rise of the sheet and cause the improvement of sheet's formability.Lightweight metal,such as magnesium alloy,could be deformed by RISF without additional heating. The objective of this study is to investigate the effects of forming parameters,namely,tool rotational speed,feed-rate,step size and wall angle,on the local temperature rise. Using response surface methodology and central composite design( CCD) experimental design,the significance,sequence of parameters and regression models would be analyzed with AZ31 B as the experimental material,and 3D response surface plots would be shown. Combined with actual processing conditions,the measures to improve the local temperature rise by modifying each parameter would be discussed in the end. The results showed that hierarchy of the parameters with respect to the significance of their effects on the local temperature at the side wall was: feed-rate,step size,and rotational speed,while at the bottom it was: feed-rate,step size,wall angle, and rotational speed, and no significant interaction appeared. It was found that the most significant parameter was not rotational speed,but feed-rate,followed by step size,for both test positions. In addition, the local temperature would increase by elevating step size,wall angle,rotating rate,and bringing down of feed-rate.

Study on Contact Algorithm of Dynamic Explicit FEM for Sheet Forming Simulation

Based on existing algorithms, a newly developed contact search algorithm is proposed. The new algorithm consists of global search, local searching, local tracking and penetration calculation processes. It requires no iteration steps. It can deal with not only general tool surfaces with vertical walls, but also tool surfaces meshed with elements having very poor aspect ratios. It is demonstrated that the FE code employing this new contact search algorithm becomes more reliable, efficient and accurate for sheet metal forming simulation than conventional ones.

STUDY ON THE PROBLEMS OF CONTACT IN THE NUMERICAL SIMULATION OF SHEET FORMING

This study is concerned with the problems of contact in the process of numerical simulation of sheet metal forming in rigid visco-plastic shell FEM. In respect of analysis of sheet deep drawing process,for the tool model described by triangular elements, a kind of contact judging algorithm about the correlation between the node of deformed mesh and the triangular element of a tool is presented. In SPF/DB Lagrangian multiplier method is adopted to solve the contact problem between deformed meshes, and a new reliable practical dynamic contact checking algorithm is presented. As computation examples, the simulation results of metal sheet deep drawing and SPF/DB are introduced in this paper.

A novel micro-rolling&incremental sheet forming hybrid process:Deformation behavior and microstructure evolution

Thin-walled metal parts with functional micro-featured surface have broad application prospects in the fields of resistance reduction,noise reduction,etc.In this study,a novel micro-rolling&incremental sheet forming hybrid process(μR-ISF)is proposed to fabricate thin-walled metal parts with microgroove arrays.An analytical model which relates the rolling force and microgroove depth in the micro-rolling stage was first established.Then,the formation mechanism of microgroove morphology during both micro-rolling stage and macro-shape forming stage are investigated.After the micro-grooved sheet being incrementally formed,a significant reduction(between 21%to nearly 60%)is occurred in the depth of both transverse and longitudinal grooves compared to the flat sheet.Meanwhile,the width of transverse grooves decreases slightly by about 10%on average,while the width of longitudinal microgrooves increases significantly by more than 30%on average.After micro-rolling,85°{102}tensile twins appear on the micro-grooved sheet and the percentage of 65°{112}compressive twins increases.After incremental forming,the percentage of low-angle grain boundaries and the density of geometrically necessary dislocations in the formed part increase significantly,and the grain size distribution becomes more uniform.The present work provides a new strategy for the fabrication of 3D metal thin-walled components with surface micro-features.

A toolpath strategy for improving geometric accuracy in double-sided incremental sheet forming

The double-sided incremental forming(DSIF)improved the process flexibility compared to other incremental sheet forming(ISF)processes.Despite the flexible nature,it faces the challenge of low geometric precision like ISF variants.In this work,two strategies are used to overcome this.First,a novel method is employed to determine the optimal support tool location for improving geometric precision.In this method,the toolpath oriented the tools to each other systematically in the circumferential direction.Besides,it squeezed the sheet by the same amount at the point of interest.The impacts of various support tool positions in the circumferential direction are evaluated for geometric precision.The results demonstrate that the support tool should support the master tool within 10°to its local normal in the circumferential direction to improve the geometric accuracy.Second,a two-stage process reduced the geometric error of the part by incrementally accommodating the springback error by artificially increasing the step size for the second stage.With the optimal support tool position and two-stage DSIF,the geometric precision of the part has improved significantly.The proposed method is compared to the best DSIF toolpath strategies for geometric accuracy,surface roughness,forming time,and sheet thickness fluctuations using grey relational analysis(GRA).It outperforms the other toolpath strategies including single-stage DSIF,accumulative double-sided incremental forming(ADSIF),and two-stage mixed double sided incre-mental forming(MDSIF).Our approach can improve geometric precision in complex parts by successfully employing the support tool and managing the springback incrementally.

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.

Experimental and numerical investigation on surface quality for two-point incremental sheet forming with interpolator

The unsatisfied surface quality seriously impedes the wide application of incremental sheet forming(ISF)in industrial field.As a novel approach,the interpolator method is a promising strategy to enhance the surface quality in ISF.However,the mechanism for the improvement of surface quality and the influence of interpolator properties on surface roughness are not well understood.In this paper,the influences of process variables(i.e.tool diameter,step size and thickness of interpolators)on the forming process(e.g.surface roughness,forming force and geometric error)are investigated through a systematic experimental approach of central composite design(CCD)in two-point incremental sheet forming(TPIF).It is obtained that the increase in thickness of interpolators decreases the surface roughness in direction vertical to the tool path while increases the surface roughness in direction horizontal to the tool path.Nevertheless,the combined influence between thickness of interpolators and process parameters(tool diameter and step size)is limited.Meanwhile,the placement of interpolator has little influence on the effective forming force of blank.In addition,the geometric error enlarges with the increase of step size and thickness of interpolator while decreases firstly and then increase with an increase in tool diameter.Finally,the influencing mechanism of the interpolator method on surface quality can be attributed to the decrease of thecontact pressure due to the increase of contact area with the unchanged contact force.Meanwhile,the interpolator method eliminates the sliding friction on the surface of blank due to the stable relative position between the blank and the interpolator.

The influence of ultrasonic vibration on parts properties during incremental sheet forming

The integration of ultrasonic vibration into sheet forming process can significantly reduce the forming force and bring benefits including the enhancement of surface quality,the enhancement of formability and the reduction of spring-back.However,the influencing mechanisms of the high-frequency vibration on parts properties during the incremental sheet forming(ISF)process are not well known,preventing a more efficient forming system.This paper comprehensively investigates the effects of different process parameters(vibration amplitude,step-down size,rotation speed and forming angle)on the micro-hardness,minimum thickness,forming limit and residual stress of the formed parts.First,a series of truncated pyramids were formed with an experimental platform designed for the ultrasonic-assisted incremental sheet forming.Then,microhardness tests,minimum thickness measurements and residual stress tests were performed for the formed parts.The results showed that the surface micro-hardness of the formed part was reduced since the vibration stress induced by the ultrasonic vibration within the material which eliminated the original internal stress.The superimposed University,Beijing 100083,People’s Republic of China ultrasonic vibration can effectively uniform the residual stress and thickness distribution,arid improve the forming limit in the case of the small deformation rate.In addition,through the tensile fracture analysis of the formed part,it is shown that the elongation of material is improved and the elastic modulus and hardening index are decreased.The findings of the present work lay the foundation for a better integration of the ultrasonic vibration system into the incremental sheet forming process.

FEM-based strain analysis study for multilayer sheet forming process

Fiber metal laminates have many advantages over traditional laminates （e.g., any type of fiber and resin material can be placed anywhere between the metallic layers without risk of failure of the composite fabric sheets）. Furthermore, the process requirements to strictly control the temperature and punch force in fiber metal laminates are also less stringent than those in traditional laminates. To further explore the novel method, this study conducts a finite element method-based （FEM-based） strain analysis on multilayer blanks by using the 3A method. Different forming modes such as wrinkling and fracture are discussed by using experimental and numerical studies. Hydroforming is used for multilayer forming. The Barlat 2000 yield criteria and DYNAFORM/LS-DYNA are used for the simulations. Optimal process parameters are determined on the basis of fixed die-binder gap and variable cavity pressure. The results of this study will enhance the knowledge on the mechanics of multilayer structures formed by using the 3A method and expand its commercial applications.

Formation mechanism and modeling of surface waviness in incremental sheet forming

mproving and controlling surface quality has always been a challenge for incremental sheet forming (ISF), whereas the generation mechanism of waviness surface is still unknown, which impedes the widely application of ISF in the industrial field. In this paper, the formation mechanism and the prediction of waviness are both investigated through experiments, numerical simulation, and theoretical analysis. Based on a verified finite element model, the waviness topography is predicted numerically for the first time, and its generation is attributed to the residual bending deformation through deformation history analysis. For more efficient engineering application, a theoretical model for waviness height is proposed based on the generation mechanism, using a modified strain function considering deformation modes. This work is favorable for the perfection of formation mechanism and control of surface quality in ISF.

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.

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.

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; asimplified model of the blank holder during the drawing process was established andthe effects of related parameters on the forming processes were also studied. At thesame time, a finite--element numerical simulation program SPID was developed. Thedistribution of strain and relationship of stress--stroke simulated were compared withexperimented, the results are well coincided with each other. It is verified that theanalytical 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.

Experimental Investigation of the Effect of the Material Damage Induced in Sheet Metal Forming Process on the Service Performance of 22MnB5 Steel

The use of ultra-high strength steels through sheet metal forming process offers a practical solution to the lightweight design of vehicles.However,sheet metal forming process not only produces desirable changes in material properties but also causes material damage that may adversely influence the service performance of the material formed.Thus,an investigation is conducted to experimentally quantify such influence for a commonly used steel（the 22MnB5 steel） based on the hot and cold forming processes.For each process,a number of samples are used to conduct a uniaxial tensile test to simulate the forming process.After that,some of the samples are trimmed into a standard shape and then uniaxially extended until fracture to simulate the service stage.Finally,a microstructure test is conducted to analyze the microdefects of the remaining samples.Based on the results of the first two tests,the effect of material damage on the service performance of 22MnB5 steel is analyzed.It is found that the material damages of both the hot and cold forming processes cause reductions in the service performance,such as the failure strain,the ultimate stress,the capacity of energy absorption and the ratio of residual strain.The reductions are generally lower and non-linear in the former process but higher and linear in the latter process.Additionally,it is found from the microstructure analysis that the difference in the reductions of the service performance of 22MnB5 by the two forming processes is driven by the difference in the micro damage mechanisms of the two processes.The findings of this research provide a useful reference in terms of the selection of sheet metal forming processes and the determination of forming parameters for 22MnB5.