Rigid-plastic Finite Element Method Research Articles

Finite element analysis and experiment on multi-wedge cross wedge rolling for asymmetric stepped shaft of C45

A rigid-plastic finite element method (FEM) simulation model for a multi-wedge cross wedge rolling (MCWR) was developed to analyze an asymmetric stepped shaft. To evaluate the MCWR process and better understand its deformation characteristics, the material flowing mechanisms, temperature distributions, strain and rolling force were analyzed. The correctness of the finite element simulation is experimentally verified. Numerical simulations and experiments led to the following conclusions: when α=36° and β=7.5°, the quality of the work piece can be significantly improved. Finally, the development of the asymmetric stepped shaft is applied to industrial production.

Study of the rigid plastic finite element method using triangular element with drilling and strain degrees of freedoms

Study of the rigid plastic finite element method using triangular element with drilling and strain degrees of freedoms

Experimental study on material flow in cold rolling

Abstract Material flow in roll bite occurred during symmetric or asymmetric rolling of thin sheet was investigated by model rolling experiment in this study. The sheet samples with fine grids drawn by laser processing on longitudinal-thickness cross-section at the middle of the sheet width were used for the experiment to visualize material flow. By measuring the changes of roughness in the cross section after rolling, it was confirmed that the rolling was conducted practically in plane strain conditions in the cross section. Also the changes of vertical ruled lines before and after rolling reflect material flow throughout the roll bite. It clearly shows the characteristic that the inclination angle of the ruled line due to rolling increases monotonically as the different speed ratio increases. To compare the material flow of model rolling experiment, two dimensional steady-state rolling analyses using rigid plastic finite element (FE) method have been conducted. The profiles of the ruled line observed in the experiments have a good agreement with the calculated results. Also the calculated results of equivalent plastic strain reveal non-monotonical relations between the strain and the different speed ratio (i.e. maximal of the strain observed at certain different speed ratio). This qualitative discrepancy observed between the measured angles and the calculated strains in relation to the different speed ratio suggests that measurement of the angle of the ruled lines is not sufficient to characterize plastic strain.

Discussion on size effect of footing in ultimate bearing capacity of sandy soil using rigid plastic finite element method

Currently, many formulas are used to calculate the ultimate bearing capacity. However, these formulas have disadvantages when being applied in practice since they can only be applied for calculating simple footing shapes and uniform grounds. Most formulas do not take into account the size effect of the footing on the ultimate bearing capacity, except for the formula by the Architectural Institute of Japan. The advantage of using the finite element method (FEM) is its applicability to non-uniform grounds, for example, multi-layered and improved grounds, and to complicated footing shapes under three-dimensional conditions. FEM greatly improves the accuracy in estimating the ultimate bearing capacity. The objective of this study is to propose a rigid plastic constitutive equation using the non-linear shear strength property against the confining pressure. The constitutive equation was built based on experiments for the non-linear shear strength property against the confining pressure reported by Tatsuoka and other researchers. The results from tests on Toyoura sand and various other kinds of sand indicated that, although the internal friction angle differs among sandy soils, the normalized internal friction angle decreases with an increase in the normalized first stress invariant for various sands despite dispersion in the data. This property always holds irrespective of the reference value of the confining pressure in the normalization of the internal friction angle. The applicability of the proposed rigid plastic equation was proved by comparing it to the ultimate bearing capacity formula by the Architectural Institute of Japan, which is an experimental formula that takes into account the size effect of the footing. The results of rigid plastic finite element method (RPFEM) with the proposed constitutive equation were found to be similar to those obtained with the Architectural Institute of Japan’s formula. It is clear that RPFEM, with the use of the non-linear shear strength against the confining pressure, provides good estimations of the ultimate bearing capacity of the footing by taking account of the size effect of the footing.

ULTIMATE BEARING CAPACITY OF FOOTING ON SANDY SOIL AGAINST COMBINED LOAD OF VERTICAL, HORIZONTAL AND MOMENT LOADS

Rigid plastic finite element method employing the rigid plastic constitutive equation, which considers non-linear shear strength properties against confining pressure, is used for the assessment of ultimate bearing capacity of footing on sandy soils against the combined load of vertical, horizontal and moment loads. The numerical results were compared with the results predicted by semi-empirical bearing capacity formulate of Architectural Institute of Japan and others. The comparison is conducted in terms of vertical and horizontal loads plane and vertical and moment loads plane. The limit load is expressed in normalization form by the limit vertical load, Vo. Results show that the normalized vertical load decreases with the increase in the normalized horizontal load and/or moment load. Effect of non-linear shear strength on the normalized limit load space in vertical, horizontal and moment loads is clearly indicated. The normalized horizontal load is obtained greater than that of linear shear strength property.

Analysis on Shear Deformation for High Manganese Austenite Steel during Hot Asymmetrical Rolling Process Using Finite Element Method

Based on the rigid-plastic finite element method (FEM), the shear stress field of deformation region for high manganese austenite steel during hot asymmetrical rolling process was analyzed. The influences of rolling parameters, such as the velocity ratio of upper to lower rolls, the initial temperature of workpiece and the reduction rate, on the shear deformation of three nodes in the upper, center and lower layers were discussed. As the rolling parameters change, distinct shear deformation appears in the upper and lower layers, but the shear deformation in the center layer appears only when the velocity ratio is more than 1.00, and the absolute value of the shear stress in this layer is changed with rolling parameters. A mathematical model which reflected the change of the maximal absolute shear stress for the center layer was established, by which the maximal absolute shear stress for the center layer can be easily calculated and the appropriate rolling technology can be designed.

Rigid Plastic FE Slope Stability Analysis Combined With Rain Fall Water Infiltration

This paper presents a new slope stability analysis regarding rainfall-induced landslides by coupling a saturatedunsaturated seepage analysis and a rigid plastic finite element method (RP-FEM). Currently, a more valid and reliable disaster prevention system detecting the risk of slope instability due to sudden intense rainfall is required in Japan. However, conventional slope stability methods often fail to predict this new type of landslides. Therefore, the aim of this study is to propose the new slope stability analysis method in the context of rainfall infiltration. This method introduces the effect of seepage force, an increase of unit weight and a reduction of apparent cohesion due to the change in soil suction to obtain the slope stability load factors and collapse mechanisms. Consequently, this method can provide the relatively accurate and valid analysis results, which can be well compared with experimental data. Moreover, it is ascertained that this method can evaluate the different type of slope failure mechanisms: an initial small failure at the toe of the slope caused by the seepage forces and a large-scale failure due to the degradation of the soil apparent cohesion.

Experiments and Simulation on Mannesmann Piercing Process in the Drill Steel Manufacture

Steel drill rods are employed in the mining industry to drill blast holes in rock, for them a high-quality metal surface and accurate geometrical parameters are essential. Drill steel is a special material exclusively designed for drill rods. To estimate the microstructure and dimensional stability of drill steel, a rigid plastic finite element method (FEM) was applied in examining the Mannesmann piercing in the drill steel manufacture. The three-dimensional thermal-force coupling FEM models were computer-generated with different plug positions. The metal deformation during the piercing process was analyzed in detail. The stress-strain state of the metal ahead of the plug was simulated to obtain formation characteristics during the Mannesmann piercing. The effect of the plug position on force and strain rates was also studied with simulation. The results demonstrate that the dimensional stability of hollow drill rods can be enhanced by advancing the plug position.

Analysis of Deformation Behavior in Backward–Radial–Forward Extrusion Process

The forming characteristics of backward–radial–forward extrusion process were investigated by the effect of some important die design geometry parameters. Some major flow faults such as separation height and length, asymmetric ratios of height and angle are introduced and the effects of process parameters are studied on them. The workpiece material was AL1050 and the simulation work was performed by the rigid-plastic finite element method. The validity of the simulation results obtained in this study was verified by using the experimental test data in terms of forming load and material flow. There is reasonably good agreement between the simulation and the experiment. The die geometry and frictional condition have a significant influence on the material flow into the die cavities. The work presented in this paper might be used for basic data in the design of the backward–radial–forward extrusion process.

Formation and Simulation of Negative Shear Zone

Cutting-direction burr/fracture is one of the important factors that influence the edge quality and performance of precision parts.The formation of negative shear zone decisions the edge quality of workpiece. A finite element model has been established to investigate the mechanism of negative formation in machining H64 brass. The negative shear zone formation process is simulated with rigid-plastic nonlinear finite element method. The cutting direction burr forms when the stress of principal shear zone great than it in negative, the cutting direction fracture forms when the stress of principal shear zone less than it in negative and there is a crack in the area near the tool tip and grow along the negative shear zone .

Comparison of Rigid-Plastic and Elastoplastic Finite Element Predictions of a Tensile Test of Cylindrical Specimens

In this paper, finite element predictions of a tensile test of cylindrical specimens obtained by rigid-plastic and elastoplastic finite element methods are compared in terms of tensile load-elongation curve and deformed shape. The flow stress curve used for this study is obtained by a scheme of obtaining flow stress at large strain from tensile test of cylindrical specimen using rigid-plastic finite element method. The two predictions are compared in a quantitative manner and discussed not only to find some similarity but also to distinguish the elastoplastic finite element method from the rigid-plastic finite element method.

Study of Formability of Steel Thick Plates for Offshore Structures

A jack-up rig or a self-elevating unit is a type of mobile platform that consists of a buoyant hull fitted with a number of movable legs, capable of raising its hull over the surface of the sea. The buoyant hull enables transportation of the unit and all attached machinery to a desired location. Once on location the hull is raised to the required elevation above the sea surface on its legs supported by the sea bed. The legs of such units may be designed to penetrate the sea bed, may be fitted with enlarged sections or footings, or may be attached to a bottom mat. Generally Jack up rigs are not self-propelled and rely on tugs or heavy lift shipsfor transportation. Formability problems in offshore structure construction where particularly high-strength steels are used for chords and racks. Attainment of mechanical properties is not usually difficult, although procedural trials are advisable. Fatigue cracking is probably the major cause of service failure of jack-up rigs, and the use of high-strength steels, which permits higher static stress limits, can exacerbate this problem. Roll forming process is one of the most widely used processes in the world for forming metals. It can manufacture goods of the uniform cross section throughout the continuous processing. However, process analysis is very difficult because of the inherent complexity. Therefore, it is time-consuming and much money is needed for manufacturing goods. In order to overcome this difficulty, a new computational method based on the rigid-plastic finite element method is developed for the analysis of roll forming process.

Repetitive upsetting extrusion process and microstructure evolution of AZ61 magnesium alloy

The rigid plastic finite element method was used to simulate the repetitive upsetting extrusion (RUE) process of an AZ61 magnesium alloy. Flow nets, field variables and the influence of initial blank temperature and RUE passes on the RUE process were analysed systematically. The results showed that large accumulated strain induced by multi-pass operation could be obtained by RUE process. The applied load versus displacement curves were obtained by RUE process test and the forming principle was revealed. Microstructure evolution during RUE process was demonstrated by microstructure observation, which revealed that the RUE strain induced process has a pronounced effect on grain refinement. Under the conditions of 340°C and 1 mm s−1, the initial cast structure with average grain size of 95 μm evolved to fine and uniform DRX grains with average grain size of 6·9 μm after three RUE passes.

Analysis and experimental studies of internal voids in multi-wedge cross wedge rolling stepped shaft

In this study, a rigid-plastic finite element method (FEM) simulation model for a multi-wedge cross wedge rolling (MCWR) was developed to analyze the generation mechanisms of internal defects. Two feature parts in MCWR, rod area and store area, were defined to analyze the internal defects mechanisms. The difference of stress states between the rod and store areas was pointed out and an insight into generation mechanism was concluded. Based on simulation, the influence of mold parameters was discussed and an optimized parameter group was achieved. The results indicate that the internal voids in the store and rod areas were extended from microcracks produced by shear stress cycle, and then develop to cracks due to the overlarge first principle tension stress caused by metal backflow. In a certain range, a smaller forming angle and a reasonable area reduction is good for avoid center voids in store area. Subsequently, the industrial test manifested the feasibility of study results.

Determination of the Observation Area for Metallographic Microstructure of GH4033 Superalloy in a Uniaxially Thermo-Mechanical Compression Experiment

Based on two-dimensional (2D) rigid-plastic finite element (FE) method, the optimum observation area for metallographic microstructure and the influence of the height–diameter ratio on which were analyzed for the cylindrical samples with the diameter of 8 mm and different heights from 8 to 16 mm in nonuniform compressive experiments. It is shown that the representative metallographic observation area relevant to the applied deformation condition is located at about 0.835 of the radius from the center of the sample to the solder joint between the sample and the thermocouples. At the same time, the microstructure in that area is more appropriate as the height of the sample is 12 mm. The related parameters of GH4033 superalloy were adopted in the FE analysis, and the validity of this analysis was verified by the compressive experiments.

Rigid-Plastic Finite Element Simulation of Cold Forging and Sheet Metal Forming by Eulerian Meshing Method

A computational technique of rigid-plastic finite element method by using the Eulerian meshing method was developed to deal with large deformation problem in metal forming by replacing the conventional way of applying complicated remeshing schemes when using the Lagrange’s elements. During metal forming process, a workpiece normally undergoes large deformation and causes severe distortion of elements in finite element analysis. The distorted element may lead to instability in numerical calculation and divergence of non-linear solution in finite element analysis. With Eulerian elements, the initial elements are generated to fix into a specified analytical region with particles implanted as markers to form the body of a workpiece. The particles are allowed to flow between the elements after each deformation step to show the deforming pattern of material. Four types of cold forging and sheet metal clinching were conducted to investigate the effectiveness of the presented method. The proposed method is found to be effective by comparing the results on dimension of the final product, material flow behaviour and punch load versus stroke obtained from simulation and experiment.

Effects of Feed Angle on Mannesmann Piercing in Drill Steel Production

Drill steel is a special steel specifically tailored for drilling rods. To understand the microstructure properties and dimensional accuracy of the drill steel, a rigid plastic finite element method was used to analysis Mannesmann piercing in steel drilling production. The three-dimensional thermal force coupling FEM models were computer generated with different feed angle. The metal deformation during the piercing process was analyzed in detail. The influence of feed angle on deformation, force, velocity and strain was obtained through simulations.

Numerical Simulation of GH4169 Alloy Section of Hot Roll Forming

A hot roll forming process of GH4169 alloy complex sections described in this paper is a new forming process of GH4169 alloy sections. The rolling 6o, 7o, 8o pass and rectangular, wedge-shaped, irregular blank are designed. Rolling models has been developed using the rigid-plastic finite element method on DEFORM. The rolling force and pass fullness and the distribution of various field-variables such as temperature and effective strain can be obtained from the simulated result. The finally optimizing rolling process shows that the pass slopes with 6o on the roll, the cross-section of the blank is irregular, and the rolling processes are using one pass to do two passes rolling through changing the value of the roll gauge. The simulated results show the temperature of the workpiece is about 1030~1080°C, the inner temperature is greater than the surface temperature, the surface temperature is minimum, and the effective strain is about 0.3~2, which meet the requirement of the GH4169 alloy structure property, and they are significance to the other hot roll forming process of GH4169 alloy sections.

Influence of punch geometries on the divided material flow in a double cup extrusion process

This paper provides an analysis of the deformation patterns in a backward can extrusion combined simultaneously with a forward can extrusion process, which is known as a double cup extrusion process. The main objective of this study is to examine the divided material flow characteristics in DCEP. Analyses were conducted in a numerical manner by employing a rigid-plastic finite element method. Among many process parameters, the major design factors chosen for analysis include the reduction in area (RAB), the wall thickness ratio (TR), the punch nose radius (R), and the friction condition. The simulation results were summarized in terms of relationships between the process parameters and the ratios of extruded length and volume, and between the process parameters and force requirements, respectively. Comparisons between a multi-stage forming process in sequential operations and one-stage combined operation were also made in terms of the forming load and pressure exerted on the tool. The force requirement and self-regulating characteristics were more greatly influenced by the wall thickness ratio among the selected major design factors. And more severe load to form the same shape is expected in sequential operations than in a combined extrusion process.

Finite Element Simulation of Aluminum ECAP Material Flow

To enhancing strength and toughness of metals, severe plastic deformation (SPD) grain refinement was a typical method. As one of the SPD method, equal channel angular pressing is an effective method in fabricating ultra-fine grain metallic materials. In this paper, the rigid-plastic finite element method was used to analyze the aluminum alloy ECAP processing, to reveal the material flow character and its effect on microstructure evolution. The simulation results were agreed with plastic mechanics and experiment well, and it was shown that distribution of maximum principal stress was not uniform, material located at the front-end of sample flow easily and material located at the top of die channel corner flow difficultly.