Rigid-plastic Finite Element Analysis Research Articles

Strain gradient plasticity based finite element analysis of ultra-fine wire drawing process

Steady-state rigid-plastic finite element analysis coupled with strain gradient plasticity theory has been performed to examine the size effect of material on its plastic deformation behavior and find an optimal semi-cone angle of die which minimizes the drawing energy in the ultra-fine wire drawing process. A stream-line tracing method was adopted to calculate strain component at each element and a strain surface function was introduced to compute the equivalent strain gradient of each element. Introduction of this function enables us to use an established FE code without renewal of its main structure. Hence, the constitutive equation in FE formulation is changed to couple the strain gradient plasticity. A series of FE simulation reveals that significant differences in drawing stress are observed when material size approaches its intrinsic material length. When the strain gradient plasticity theory is reflected on the steady-state FE analysis, the optimal semi-cone angle of the die is reduced by 30%. The variation of optimal semi-cone angle is attributable to considerable increment of homogeneous deformation when the material size reaches its intrinsic material length.

A study on life estimation of hot forging die

In this study, the forging die life was investigated using fatigue life and wear quantity, which are generally considered for estimation of die life. The main aim is development of the equations to adapt finite element analysis to life estimation for a hot forging die. The Archard’s model was used to estimate the wear life of the die and Goodman’s and Gerber’s equations, using the stress-life method, were applied to estimation of the fatigue life. These techniques were applied to die life estimation for the hot forging die of a ball joint socket used in an autovehicle system. Rigid-plastic finite element analysis was first carried out for the forging process of the ball joint socket and then the elastic stress analysis was performed for the die in order to obtain fundamental data for the prediction of fatigue life. The die stress analysis requires the deforming loads of the workpiece to be translated into the contact loading of the die. In this case, the size of finite elements of the die and the workpiece is important for good interpolation of the loading. Therefore, the influence of element sizes on the interpolation results of the contact loading was also investigated. The wear volume of the die was measured using a 3-dimensional scanner of probe type. It was found that the measurement had a good agreement with the results of the finite element analysis for the die life estimation.

調質圧延におけるズーミング法を用いた表面粗さの転写解析

It is known that the transcription ratio of roughness in skinpass rolling is varied with various rolling conditions, but the relation between rolling conditions and the conditions of surface roughness of rolled strip is not well known yet. In this paper, zooming method is adopted to a rigid plastic finite element analysis, and applied to dry skin-pass rolling processes of steel to investigate the deformation behavior of the surface of strip. The profile of roll surface shape is modeled from measured profile of electrical discharge machined dull roll (ED model, Ra=2.7 mm) and shot dull roll (SD model, Ra=3.6 mm). Although the reduction of total thickness is small, it is found that the equivalent strain near the surface of strip is considerably large because of the microscopic deformation caused by transcription of the surface roughness. When the reduction is small, the surface roughness transcription ratio with ED model is larger than that with SD model. The transcription ratio increases as the reduction increase, and become almost 100% when the reduction become 6% for ED model, and 10% for SD model. The transcription ratio slightly decreases when the reduction exceeds the peak reduction because of the relative slip between the strip and the roll. The strip materials seem to have little effect on the transcription ratio. The transcription ratio becomes slightly large when the diameter of roll increases.

Finite element analysis of plastic deformation behavior during high pressure torsion processing

Recently, several methods of severe plastic deformation were developed to process bulk nanostructured materials with a grain size from 20 to 200 nm depending on a number of factors. The high pressure torsion (HPT) process has been subject of many investigations as a new method of processing bulk nanostructured materials. Nanostructures of materials can be formed both by the consolidation of nanopowders and the refinement of the coarse-grained microstructures. Because the mechanical properties of the deformed material are directly related to the amount of plastic deformation, i.e. the developed strain, understanding the phenomenon associated with strain development is very important in severe plastic deformation processes. The knowledge of absolute values and the homogeneity of internal stress and strain distributions is still very desirable in order to optimize the processes of grain size refinement and nanostructure development in the HPT process. In this study, the results of the rigid-plastic finite element analysis of the plastic deformation behavior of bulk materials during the HPT processing are presented. The deformation geometry of the workpiece was investigated. This approach of continuum mechanics for the analysis of the HPT process can be a useful tool if the material parameters are incorporated.

Preform design for precision forging of an asymmetric rib-web type component

Rib-web type aerospace and aircraft components in general have small fillet and corner radii with zero draft angles. In precision forging of such a component, the preform should be designed with a great care in order to produce appropriate metal flows. An improper preform invokes defects of underfilling and folding in the component with excessive stresses and wears in the forging equipments and dies. In the present study, it was attempted to design the preform for precision forging of an asymmetric rib-web component by predicting metal flows with the rigid-plastic finite element analysis. It was found that the key to the preform design is a proper distribution of the material, which was successfully achieved by a thorough investigation of metal flow and volume change from the result of the finite element analysis.

Analysis of torsional deformation by rigid-plastic finite element method using recurrent boundary conditions

In metal forming, there are problems with recurrent geometric characteristics and without explicitly prescribed boundary conditions. In such problems, for effective saving in computational time, so-called recurrent boundary conditions must be introduced. The present study deals with rigid-plastic finite element analysis for torsions of circular, square and rectangular bar sections. The application of recurrent boundary condition to the torsion problems has been shown to be effective and valid. The torsional torques computed by the present method are compared with those by the analytical method. Both pure torsion and warping-restraint torsion are computed and compared between the two in torque and deformation pattern. It is proven that spring-back can be predicted reasonably by rigid-plastic loading and elastic unloading.

Rigid-plastic finite element analysis of plastic deformation of porous metal sheets containing internal void defects

Using rigid-plastic finite element DEFORM-2D and -3D software, this study simulates the plastic deformation of metal sheets at the roll gap during the sheet rolling process. The study focuses specifically upon the deformation of porous metal sheets containing internal void defects. The present numerical analysis investigates the relative density distributions, the void closure behavior, the deformation mechanisms and the stress–strain distributions around the internal voids for various rolling conditions. The influences on the dimensions of the final void of the thickness reduction, the initial internal void dimensions, the friction factors and the relative density are systematically discussed. The critical rolling conditions also investigated. A series of sheet rolling experiments are performed in order to verify the validity of the simulation results. The current numerical results provide a valuable source of reference for the design of pass schedules for porous metals undergoing rolling processes.

Development of Finite Element Analysis Scheme for Micro Forming Using Grain Element and Grain Boundary Element

A numerical approach for forming simulation and manufacturing of micro part, based on the elastic and the rigid-plastic finite element methods by using grain element and grain boundary element, is proposed to simulate MEMS/micro-structural deformation behavior of material during micro forming. The idea is to present the polycrystalline material by an aggregate of so-called grain element that describes the plastic deformations of each individual grain in view of micro-structure. This grain element is connected by grain boundary element to account for shear deformation between grains. The main objective in this study is to develop the reliable finite element model and scheme for micro forming simulation with very thin sheet. The reliability for micro forming analysis is described from the comparisons of the micro-structural deformation behavior between the conventional rigid-plastic finite element analysis and the FE analysis of the developed program with very thin sheet material.

板圧延における圧延方向に平行な表面疵の変形過程の解析

The shape change of longitudinal surface micro-defects in flat rolling was investigated using a rigid-plastic finite element analysis. Rolling of plate with V-shaped scratches or rectangle defects that are parallel to the rolling direction, was simulated assuming a generalized plane strain condition. The calculated results were verified with experiments of model material, and good agreement between both results was obtained. The influence of rolling conditions, such as reduction, friction coefficient and the position of initial defect, on the shape of existing defect after rolling was evaluated. Using the developed FEM, the evolution of seam defects was also simulated, and good agreement with experimental results were obtained. The proposed prediction method can be utilized to make defect free products in flat rolling.

Influence of orthogonal shear on texture and R value in aluminum sheet

In aluminum sheet, it is known that the shear texture increases the R value and enhances the formability. In contrast to the previous studies for developing the shear texture by high-friction rolling and asymmetric rolling, a groove pressing was studied in the present investigation. In the groove pressing, the shear texture develops in the orthogonal plane to the horizontal plane of the sheet. This texture was measured and compared to the predicted one, which was obtained by combining texture theories and a rigid plastic finite element analysis. The developed texture was found to contain the {40° 45° 0°} component, which is regarded as a rotated Bs component and the maximum R value was predicted to be 3.8 in the direction of 45° to the rolling direction. This high R value may be attributed to the {40° 45° 0°} component.

Deformation Behavior of a Slab with Width Reduction in a Hot Mill

The deformation of a slab with various width reductions has been investigated using a rigid-plastic finite-element analysis. A commercial finite-element code was used to analyze a dog-bone profile, mean thickness, length of slab, and longitudinal width profile after edging and horizontal rolling. The deformation behavior of a slab in a heavy edger mill was also compared with deformation in a sizing press. It was found that the sizing press followed by horizontal rolling is more efficient in width reduction than deformation by a heavy edger mill followed by horizontal rolling. The finite-element analysis results for the deformation of a slab also show reasonable agreement with measurements from an actual mill test, and from physical modeling experiments.

Optimisation of spiral forging process design for ensuring uniform quality of forged round billet by three-dimensional rigid–plastic finite element analysis

Focusing on the spiral forging stage of the hot open die forging process, which is the final stage of finishing round billets from ingots, the influence of operational conditions on the distribution of equivalent plastic strain has been numerically analysed using a three-dimensional rigid–plastic finite element method. The mechanism via which equivalent plastic strain is accumulated at the surface of the workpiece during spiral forging is clarified. The independent influence of each major operational parameter, i.e. rotational angle and feed, is revealed, and the optimum combination of these two parameters is clarified. The influence of the coefficient of friction is also discussed, and, as a result, a fundamental scheme to optimise spiral forging process design is suggested, taking account of not only uniformity of quality but also dimensional precision of the forged round billet.

Optimization of anvil design for ensuring dimensional precision of forged round billet without forging defects by three-dimensional rigid-plastic finite element analysis

Focusing upon finding an optimum anvil design of the spiral forging stage for manufacturing a round billet to good dimensional precision directly from an octagonal work-piece without forging defects, three-dimensional rigid-plastic finite element analyses have been carried out. By analysis and laboratory experiment, the mechanism through which overlapping defects are caused in spiral forging has been quantitatively clarified and a new parameter to predict overlapping defect generation proposed. By making use of the parameter, an anvil design of the entrance side has been proposed to prevent overlapping defects. Moreover, the whole geometry of the anvil has been optimized in order to ensure dimensional precision of the final round billet. As a result, a fundamental scheme to optimize anvil design for manufacturing a round billet directly from an octagonal workpiece has been established and the total number of passes was successfully reduced in the production line.

板圧延における表面疵の変形に及ぼす圧延条件の影響

The shape change of surface micro-defects in plate rolling was investigated using a rigid-plastic finite element analysis. Rolling of plate with rectangular-shaped scratches or plunges, which lay perpendicular to the rolling direction, was simulated. The influence of rolling conditions, such as reduction, friction coefficient, roll diameter and pass schedule on the shape of existing defect after rolling was evaluated. From these results, the relationship between the shapes of surface defect before and after rolling was obtained, and the optimum condition to eliminate defects was discussed. The proposed prediction method of surface defect can be utilized to make defect free products in rolling and forging processes.

Optimization of open-die forging process design to ensure homogeneous grain size refinement of cast structures by three-dimensional rigid-plastic finite element analysis

Focusing on the rough-forging stage of the hot open-die forging process, the influence of pass schedule on the equivalent plastic strain distribution at the surface of a forged billet has been numerically analysed using a three-dimensional rigid-plastic finite element method. By analysing the circumferential distribution of the strain obtained by one forging pass, it has been clarified that the distribution is strongly influenced by the cross-sectional shape of a workpiece. By utilizing the analytical results, a new method has been developed to predict the cross-sectional shape and the strain distribution without numerically analysing all passes. As a result, a new pass schedule has been proposed to ensure homogeneous grain size refinement of cast structures and the effect of the pass schedule was verified by a real hot open-die forging experiment.

유한요소해석을 이용한 환봉 단조공정 최적화

Three-dimensional rigid-plastic finite element analysis has been performed to optimize open die forging process to make round bar. In the round bar forging, it is difficult to optimize process parameters in the operational environments. Therefore in this study, finite element method is used to analyze the practice of open die forging, focusing on the effects of reduction, feeding pitch and rotation angle for optimal forging pass designs. The soundness of forging process has been estimated by the smoothness and roundness of the bar at various combination of feeding pitches and rotation angles. From the test result, process conditions to make round bar having precise dimensional accuracy have been proposed.

Optimisation of open die forging condition and tool design for ensuring both internal quality and dimensional precision by three-dimensional rigid–plastic finite element analysis

Focusing on the rough forging stage of the hot open die forging process, the influences of anvil design and pass schedule on the internal quality of forged billet have been numerically analysed using a three dimensional rigid-plastic finite element method. By analysing the strain distribution newly added by one forging stroke, it has been clarified that the region where a workpiece contacts an anvil can be divided into four zones according to the deformation and, in the zone where a dead metal region arises at the surface, high strain is obtained at the centre. As a result, as regards the anvil edge shape design, it was found that it is effective to select an arc of small radius to obtain high strain at the centre. Moreover, in order to ensure both internal quality and dimensional precision of a forged surface, it has been revealed that it is effective to apply a small curvature to the flat surface of an anvil. The results have enabled a fundamental scheme to optimise tool design for ensuring both internal quality and dimensional precision to be established.

Optimisation of spiral forging process design for ensuring dimensional precision of forged round billets by three-dimensional rigid–plastic finite element analysis

Focusing on the spiral forging stage of the hot free forging process, which is the final stage to finish round billets from ingots, the optimisation of the operational conditions for ensuring dimensional precision of the final round billet has been carried out mainly by numerical analysis. In the analysis, a three-dimensional rigid-plastic finite element method was used and the validity of the analysis was examined by laboratory experiments using lead billets. The independent influence of each chosen major operational parameter, i.e. the rotational angle and the feed, has been clarified and critical and suitable ranges of the operational parameters for ensuring dimensional precision have been specified. As a result, the optimum combination of rotational angle and feed has been clarified and a fundamental scheme to optimise spiral forging process design has been suggested taking account of not only dimensional precision but also productivity. Moreover, it is suggested that the optimum rotational angle can be determined independently of the anvil geometry.

Rigid–plastic finite element analysis of hydroforming process and its applications

An finite element method (FEM) program, HydroFORM-3D, for the analysis and design of tube hydroforming processes, has been developed, and then applied to the hydroforming process for an automobile rear axle housing and subframe. This paper includes the theoretical background of the program. By using the developed program and the ductile fracture criterion, the process design for the straight tube hydroforming process of a rear axle housing, is presented. The potential failure site for the rear axle housing predicted by the numerical simulation is consistent with experimental results. The preform design of the typical pre-bent tube hydroforming process of forming a subframe, which concentrates on the determination of initial diameter of the tubular blank, is suggested.

Finite element analysis for the lamination process of a precision motor core using progressive stacking dies

In order to increase the productivity of electrical parts, manufacturing processes using progressive dies have been widely used in the industry. Motor cores have been fabricated using progressive stacking dies with lamination in order to obtain better electro-magnetic properties. For proper design of the process, a prediction of the process is required to obtain relevant design parameters. In this work, rigid–plastic finite element analysis is carried out in order to simulate the lamination process of the motor core. The effects of the embossing depth and the number of stacked sheets are investigated and compared with experimental results. The forming process can then be predicted successfully from the results of analyses, enabling the development of an appropriate design for the die and the process.