Explicit Dynamic Finite Element Method Research Articles

An Analysis of Forming Limit for Various Arc Radii of Punch in Micro Deep Drawing of the Square Cup

This paper presents an explicit dynamic finite element method (FEM) in conjunction with the forming limit diagram (FLD) to analyze the forming limit for the various arc radii of punch in micro deep drawing of square cup. In the present study, the tensile test and friction test are performed to obtain the material parameters of the electro-deposited copper foil according to the ASTM standards. Importing these properties, the numerical analysis is conducted by the explicit dynamic FEM. The FLD in numerical simulation is used as the criterion of the forming limit in micro deep drawing of the square cup. The forming limit, deformed shape, punch load-stroke relationship, height of cup and thickness distribution of square cup, are discussed and compared with the experimental results. It shows that a good agreement is achieved from comparison between simulated and experimental results. When the arc radii of punch increase with Rp=0.2, 0.5 and 0.8mm, the limit drawing ratio increases from 1.90 to 2.03 and 2.10. The forming limit of square cup increases with an increase of the arc radii of punch. From this investigation, the results of this paper can be used as reference in the relative researches and applications of micro forming.

Study on the Shifting Model of Edge Drop Control in Ultra-Wide 6-High Tandem Cold Rolling Mill

Edge drop is an important quality evaluating index for strip cross-section with the increasing of requirement for higher gauge accuracy to meet customer's demand. The mathematical model of roll shifting system plays an important role in controlling the edge drop on modern tandem cold rolling mills. Based on the explicit dynamic finite element method, a 3D finite element simulation model of rolls and strip is established for a large ultra-wide 6-high cold rolling mill with the developed EDW (edge drop control work roll) and the matched CVC intermediate roll to investigate the effect of work roll shift on edge drop of strip. Considering on the characteristics of EDW work rolls, equivalent area compensated method has been put forward to build the shifting model for edge drop control. The results indicated that the values of edge drop are less than 7μm by using the proper shifting model and the shifting model can be used to guide the practical production.

Study on the Shifting Model of Edge Drop Control in Ultra-Wide 6-High Tandem Cold Rolling Mill

Edge drop is an important quality evaluating index for strip cross-section with the increasing of requirement for higher gauge accuracy to meet customer's demand. The mathematical model of roll shifting system plays an important role in controlling the edge drop on modern tandem cold rolling mills. Based on the explicit dynamic finite element method, a 3D finite element simulation model of rolls and strip is established for a large ultra-wide 6-high cold rolling mill with the developed EDW (edge drop control work roll) and the matched CVC intermediate roll to investigate the effect of work roll shift on edge drop of strip. Considering on the characteristics of EDW work rolls, equivalent area compensated method has been put forward to build the shifting model for edge drop control. The results indicated that the values of edge drop are less than 7μm by using the proper shifting model and the shifting model can be used to guide the practical production.

Onset of Progressive Buckling by Inertia Force in Axial Impact of Straight and S-Curved Square Tubes

For the improvement of the deformation characteristic and the energy absorption efficiency of the tubular structure at impact event, a method generating the first buckling lobe using the inertia force was investigated. The solid block was attached to the wall so that its inertia force causes the partial plastic deformation that plays a role of the trigger of progressive buckling at the beginning of impact. Drop-weight impact experiment revealed that the onset of progressive buckling was achieved at the desired portion by the method. To increase the variety of tube shapes, numerical examination was conducted with the dynamic explicit finite element method. Long straight and S-curved tubes, which have square cross-section, were numerically modeled with shell elements. They were assumed to be impacted to the rigid wall to estimate the dynamic collapse behavior. The first buckling lobe generated by inertia force was demonstrated for the straight tube. The S-curved tube exhibited a bending collapse mode without the method. However, such mode was avoidable by applying the method. Then the energy absorption efficiency of the tube was drastically increased.

Numerical Simulation and Experiment Research on Thick Plate Multi-Point Forming Process with Elastic Cushion

Multi-point forming (MPF) is an advanced flexible manufacturing technology for three-dimensional sheet metal forming. The substance of MPF is replacing the conventional solid dies by a set of discrete punches called ‘‘punch group’’. Because the reconfigurable discrete punches are used, part manufacturing costs are reduced and manufacturing time is shortened. However due to the discrete contacts between the workpiece and punches, the dimple defects occurred, which are inevitable and particular for MPF. For thick plate, the surface defect is the mainly dimple defect during its MPF process. In this study, elastic cushion was proposed to prevent these surface defects. The dynamic explicit finite element method was chosen to implement the simulation of MPF process. The Hill’s anisotropic yield criterion was used to describe the workpiece material behavior, and the elastic cushion was described with using the hyperelastic material model. The method to determine each punch position to construct forming surface was introduced. The MPF process with and without using elastic cushion was simulated to study the effect of the elastic cushion on preventing the surface defects. The relevant experiment was implemented, and it verified that the elastic cushion is effective method to suppress the surface defects during the thick plate MPF process. Keyword: flexible forming process (FFP), elastic cushion, surface defects, multi-point forming (MPF), thick plate, numerical simulation

An Analysis of Forming Limit in Micro Deep Drawing of the Square Cup for Anisotropic Foil

This paper presents an explicit dynamic finite element method (FEM) in conjunction with the forming limit diagram (FLD) to analyze the forming limit for the SPCC foil in micro deep drawing of square cup. In the present study, the tensile, anisotropic and friction test are performed to obtain the material parameters of the alloy foil according to the ASTM standards. Importing these properties, the numerical analysis is conducted by the explicit dynamic FEM. The FLD in numerical simulation is used as the criterion of the forming limit in micro deep drawing of the square cup. The forming limit, punch load-stroke relationship, deformed shape and thickness distribution of square cup, are discussed and compared with the experimental results. It shows that a good agreement is achieved from comparison between simulated and experimental results. The limit drawing ratio in micro deep drawing of square cup is 2.08 in this paper. From this investigation, the results of this paper can be used as reference in the relative researches and applications of micro forming.

Numerical Analysis of Steel Fiber Reinforced High Strength Concrete Walls Subjected to Blasting Load

In this paper, the dynamic response of concrete wall and steel fiber reinforced high strength concrete (SFRHSC) wall under blast load is simulated with the explicit dynamic finite element method. The J-H-C model is used for SFRHSC and the material parameters are determined based on the test results. The damage and strain rate effects are considered in above material model. The influences of scaled distance on the dynamic responses of walls are investigated and discussed.

Dynamic Crushing of Hexagonal Honeycombs under In-Plane Loading

The in-plane dynamic crushing of hexagonal honeycombs was numerically studied by means of explicit dynamic finite element method using ANSYS/LS-DYNA. Under the assumption that the edge length and thickness were the same, the metal honeycomb models filled with convex and concave cells were established. And then the effects of expanding angle and impact velocity on the plateau stress and the energy absorption capacities of hexagonal honeycombs were discussed in detail. Numerical results show that the energy absorption capacities of convex hexagonal honeycombs are stronger than the concave ones. These results will provide some useful guides for the dynamic energy absorption design of cellular materials.

Wear resistance and induced cutting damage of aeronautical FRP components obtained by machining

Abstract A cutting induced-damage process involving matrix cracking, fiber fracture and interlaminar delamination often occurs when machining composite materials. Compared to metals, relatively little research has been carried out in this topic. Generally, damage mechanisms in machining composites include four types of wear modes: transverse matrix cracking, fiber–matrix interface debonding, fiber rupture and inter-ply delamination. The surface quality plays an important role in the improvement of fatigue life and wear resistance of composite components. In the case of high speed machining composite materials, the surface quality of the finished product may be improved by modifying the machining parameters. Due to the complex nature of this process, we focus here on the effect of cutting parameters on surface damage of the machined component and thus wear resistance. The later has been predicted using dynamic explicit finite element method. In this investigation a progressive failure analysis has been adopted for analysing damage process within the fiber reinforced polymer (FRP) workpiece. After damage is detected, selective stiffness degradation is applied to the workpiece material. It has been shown in this study that matrix cracking and interface shearing occur first, followed by wear of fibers. The damage progression in the matrix and interface occurs in parallel directions to the fiber axis. A random growth of fiber fracture has been observed and mainly localized in a plane with a specific direction. The effect of fiber orientation on wear resistance of the composite structure and cutting induced damage process has been investigated. Damage progression was found to be strongly influenced by the fiber orientation of the FRP composite.

Testing Techniques to Eliminate Frictional Effect and to Achieve Constant Strain-Rate in Split Hopkinson Pressure Bar Impact Compression System

In order to obtain the intrinsic stress – strain relationship by split Hopkinson pressure bar (SHPB) impact compression system, two testing techniques to eliminate the frictional effect and hold the prescribed constant strain-rate are demonstrated. The extrapolation method eliminating frictional effect at the tool – specimen interface was exhibited. Several specimens with different height were used for changing the initial diameter / height ratio in the method, where the circular plates were laminated. In order to maintain the constant strain-rate during compression, the incident pulse was adjusted to elevate in accordance with the compression force, where the tapered cylindrical striker bar was applied. Test material is a fully annealed pure aluminum. The intrinsic stress – strain relationship at strain-rate of 1000 /s was determined and the strain-rate sensitivity was also determined. The numerical simulation of the SHPB impact compression system was also performed using the dynamic explicit finite element method. The additional evidence for these experimental techniques to accomplish the elimination of friction and the constant strain-rate was shown.

Trial Computation of Dynamic Axial Compression of Adhesive-Bonded Tubular Structure

The dynamic axial compression of adhesive-bonded tubular structures with hat-shaped cross-section was numerically investigated using dynamic explicit finite element method. The numerically modeled Type I tubular structure consisted of a hat-shaped part and a flat plate. Type II consisted of two hat-shaped parts. The hat flange portion was assumed to be joined by adhesive bonding. The impact velocity of 10 m/s was given. Parametric computation was performed, where thicknesses of the plate and adhesive layer, and mechanical properties of the plate material were varied. As the result of computation, separation behavior of the hat flange portion was almost avoided for the case where the strength of plate material was lower. However, it was clearly observed for the higher strength material, though the plate was thin. The separation of the flange portion in Type I structure was more remarkable in comparison with that in Type II. The crush strength increased as the thickness of the adhesive layer thickened, when the plate thickness was thin and the strength was low. The Type II structure exhibited larger crush strength than that of Type I.

Linear finite elements with orthogonal discontinuous basis functions for explicit earthquake ground motion modeling

The dynamic explicit finite element method is commonly used in earthquake ground motion modeling. In this method, the element mass matrix is approximately lumped, which may lead to numerical dispersion. On the other hand, the orthogonal finite element method, based on orthogonal polynomial basis functions, naturally derives a lumped diagonal mass matrix and can be applied to dynamic explicit finite element analysis. In this paper, we propose finite elements based on orthogonal discontinuous basis functions, the element mass matrices of which are lumped without approximation. Orthogonal discontinuous basis functions are used to improve the accuracy and reduce the numerical dispersion in earthquake ground motion modeling. We present a detailed formulation of the 4-node tetrahedral and 8-node hexahedral elements. The relationship between the proposed finite elements and conventional finite elements is investigated, and the solutions obtained from the conventional explicit finite element method are compared with analytical solutions to verify the numerical dispersion caused by the lumping approximation. Comparison of solutions obtained with the proposed finite elements to analytical solutions demonstrates the usefulness of the technique. Examples are also presented to illustrate the effectiveness of the proposed method in earthquake ground motion modeling in the actual three-dimensional crust structure. Copyright © 2010 John Wiley & Sons, Ltd.

FEM Simulation and Analysis of Variable Parameters for the Three-Roll Cylindrical Bending of Plate Process

A three-dimensional model is developed to study the dynamic process of three-roll plate bending using finite element method (FEM). In this work, the continuous three-roll bending configuration with cylindrical rolls is used to bend a thick plate into a cylindrical shape. It presents the geometrical setup and the finite element model. This 3D simulation is based on the elastic plastic explicit dynamic FEM under the ANSYS/LS-DYNA environment. Effect of initial strain and change of material properties during deformation is neglected. In order to investigate the influence of parameters on the process, top roller position, friction between rolls and plate, and temperature are also discussed. It is found that the simulation program is a feasible and economical method to study the influence of these parameters, and the FEM simulation can also provide engineers with a convenient analytical tool for optimizing process parameters.

A hybrid approach for estimating the drawbead restraining force in sheet metal forming

In order to achieve better part quality in sheet metal forming the rate of the material flow into the die cavity must be efficiently controlled. This control is obtained using a restraining force supplied either by the blankholder tool, drawbeads or both. When the restraining force required is too high, the use of drawbeads is necessary, although excessive blank deformation may be produced. Some other disadvantages such as adjustment difficulties during die try-outs to determine the actual Drawbead Restraining Force (DBRF) may also be encountered. One way to solve these problems and to reduce the number of die try-outs - which are very much time consuming - is to introduce/define accurate enough drawbead concepts. The present study will make use of a method that has been developed using the similitude approach in order to understand the influence of the most important parameters on DBRF and to establish a pre-estimate DBRF theory. Data bases have been developed throughout Explicit Dynamic Finite Element Method (EDFEM) based simulations. The results are compared with experimental data bases provided by Nine (1978) and with the analytical model of Stoughton (1988) results. The average of absolute error with respect to experimental data bases was around 6% and, for the studied cases, the maximum discrepancy was found to be below 11%. For the analytical and experimental cases, the average of absolute error was approximately 5% and, for the studied cases, the maximum error was below 7%. In terms of precision, the predictions derived from this approach are adequate when compared with analytical and experimental results. For this reason, the approach has been validated and accepted as a contribution to STAMPACK®, a commercial explicit dynamic finite element based system for forming processes numerical simulation.

Longitudinal crack on slab surface at straightening stage during continuous casting using finite element method

Deformation behavior of slab at the straightening stage during continuous casting was simulated by the explicit dynamic finite element method, and the stress distribution along the width direction of the slab and its change regularity at slab center during continuous casting were obtained. The influence of distribution and change of stress on the propagation of longitudinal cracks on slab surface was discussed. The results show that the tensional stress appears on slab surface at the inner arc side and the compressive stress appears on slab surface at the outer arc side at stages 6–8 in straightening zone during continuous casting. Longitudinal cracks generally appear on slab top surface and do not appear on slab bottom surface, which are also observed in industry.

Numerical simulation of friction stir spot welding process for aluminum alloys

Thermo-mechanical simulations of the Friction Stir Spot Welding (FSSW) processes were performed for AA5083-H18 and AA6022-T4, utilizing commercial Finite Element Method (FEM) and Finite Volume Method (FVM) codes, which are based on Lagrangian and Eulerian formulations, respectively. The Lagrangian explicit dynamic FEM code, PAM-CRASH, and the Eulerian Computational Fluid Dynamics (CFD) FVM code, STAR-CD, were utilized to understand the effect of pin geometry on weld strength and material flow under the unsteady state condition. Using FVM code, material flow patterns near the tool boundary were analyzed to explain weld strength difference between welds by a cylindrical pin and welds by a triangular pin, whereas the frictional energy concept using the FEM code had a limited capacity to explain the weld strength difference.

Finite Element Analysis on the Roll Milling Process of Twisted Oblate Tube

The roll milling process for manufacturing a twisted oblate tube was presented and applied in the forming of twisted oblate copper tube successfully. A finite element simulation of the roll milling process for forming a twisted oblate 1010 steel tube was implemented on the basis of the elastic-plastic explicit dynamic finite element method under the ANSYS/LS-DYNA environment. The simulation accuracy was verified by comparing the forming force from simulation with the experimental results. The forming effect, change curve of forming force, tube stress distribution and influences of forming parameters on forming force were investigated. The simulation results can be guidance to the manufacturing process improvement and manufacturing equipment design of the twisted oblate steel tube.

テーラードブランク材突合せ過程における<br>ギャップ矯正機構とその予測手法

Recently, tailored blank sheets have been widely and frequently used in automotive parts such as door inner and body side inner parts in order to reduce the weight of a car body and the number of parts. The control of the gap between batting blank sheets with different thicknesses below 0.1mm and the appropriate choice of the material for producing a tailored blank sheet are considered as main subjects in the development of new stamping parts using laser-welded tailored blank sheets. Therefore, in this study, we investigated the mechanism of gap control in a batting process and developed a dynamic explicit finite element method (FEM) for predicting the gap in a batting process in a testing machine. We also investigated a contact algorithm and friction to increase computation accuracy. The accuracy of the prediction of the gap by the proposed FEM has been verified with experimental measurement data for simple rectangle steel sheets and blanks of body side inner parts. The effects of the design variables of a batting machine on the gap were also investigated using the proposed FEM, and an equation for predicting gap was proposed.

絞りスピニング加工における<br>破断発生メカニズムとその予測手法

We have developed a numerical simulation technique of a spinning draw process using a dynamic explicit Finite Element Method (FEM) for evaluating formability. Oyane’s equation for the ductile fracture criterion was applied. In order to shorten computation time, the velocity of die roller movement and the velocity of die rotation of the material are increased in the analytical model. If the velocity of the die roller in the axial direction is increased, the velocity of die rotation is adjusted to obtain the same extent of damage as that in the actual spinning draw process. An accurate evaluation of fracture initiation in a spinning draw process can be performed within a short computation time. It was confirmed that numerical simulation is a useful tool for investigating the formability of a spinning draw process. Finally, we have developed an optimization method for forming parameters using the response surface method on the basis of the finite element analysis (FEA) results of a spinning draw process. In this study, we also presented the application of the proposed analytical model for verifying whether the optimized condition realized high-quality products without fracture.

Explicit Finite Element Analysis of the Plunge Stage of Tool in Friction Stir Welding

The investigation of the plunge stage of the tool during friction stir welding (FSW) is the basis of understanding the nature of FSW, which is especially important for friction stir spot welding. In this study, the plunge stage of FSW tool was numerically examined by dynamic explicit finite element method with more attention to the temperature evolution. It was found that the high temperature region around the stirred zone extended with increasing the rotation speed. The heat affected zone expanded with the increase of inserting time, but the highest temperature around the stirred zone changed little. The range of the stirred zone changed little with the variations of the rotation speed and inserting time. The simulation result on the temperature field was in comparable agreement with the experimental one.