Rigid-plastic FEM Research Articles

Simulation of the ultimate bearing capacity of a spread foundation on sandy soils: rigid plastic FEM approach with inclined load and size effect incorporating stress-dependent non-linear yield function

Simulation of the ultimate bearing capacity of a spread foundation on sandy soils: rigid plastic FEM approach with inclined load and size effect incorporating stress-dependent non-linear yield function

End bearing capacity of a single incompletely end-supported pile based on the rigid plastic finite element method with non-linear strength property against confining stress

An Incompletely End Supported Pile (IESP) is a pile in a soft soil layer underlain by a hard soil layer that does not reach the bottom hard layer in practice. This study estimates the end bearing capacity of IESP by using an inhouse Rigid Plastic FEM code (RPFEM), considering shear strength non-linearity of soil against confining pressure, and soil-foundation interaction. The effect of the distance between the pile tip and the bottom hard soil layer (d/B) on the end-bearing capacity of IESP was mainly investigated for three types of soil: cohesive soils, cohesionless soils and intermediate soils. Also, theratio (r) of the end bearing capacity of the pile when it reaches the bottom hard layer to that of the pile when the bottom layer has no influence was was considered. By considering the shear strength non-linearity, the end bearing capacity was accurately estimated. The estimations were consistent with previous analytical, experimental and numerical solutions. It is found that the end bearing capacity inversely decreases with the distance d/B and becomes constant around d/B = 3. Based on the results, a formula for estimating the end bearing capacity of IESP is proposed. Comparisons with methods in existing literature confirmed the reliability of the proposed equation.

ULTIMATE VERTICAL BEARING CAPACITY OF CLAYEY SQUEEZE BREAKDOWN USING RIGID-PLASTIC FINITE ELEMENT METHOD

The relations of ultimate bearing capacity for foundations are specified in the guideline published by the Architectural Institute of Japan for design of building foundations. The rigid-plastic finite element method developed by Tamura and Ohtsuka has been employed to estimate the ultimate bearing capacity of footings. The characteristic of this method is that, in contrast to deformation analysis, it applies limited soil constants; only the strength parameters, such as cohesion and friction angle, are used since the method deals with the limit state directly by disregarding the deformation of the building and ground. In this study, a series of rigid plastic finite element analyses were performed to compare the ultimate bearing capacities of spread foundation for clayey squeeze breakdown obtained by simulations and the formulae of the Architectural Institute of Japan. The change in the failure mode of the ground was discussed considering the geometrical ratio between the width of the footing and the surface clay layer. In addition, inclined load was considered for clayey squeeze breakdown. The applicability of rigid plastic FEM to the assessment of ultimate vertical bearing capacity of clayey squeeze breakdown was demonstrated.

Aluminum tube extrusion with the porthole die for deconcentrated welding lines

In this paper, a study on the aluminum tube extrusion with a porthole die for deconcentrated welding lines is carried out. The porthole die is consisted of a die mandrel with six inlet ports and two die caps. The aluminum material is extruded into six segments in the die mandrel with six inlets and then inner three of them are welded to compose the inner tube in fist die cap and the others are welded to compose the outer tube in the second die cap. The outer tube has different position of the welding lines to them of the inner tube. In the second die cap, two tubes are welded. The metal flow in the extrusion is analyzed with rigid plastic FEM. The position of welding lines between the inner and the outer tube are predicted. The extrusion experiment is performed and the design of the porthole die is modified to balance the position of the welding line. The extruded profile is tested to evaluate the improvement of the mechanical properties compared to the general porthole extrusion. It is confirmed that the mechanical properties are improved compared to the general porthole extrusion tube.

Novel Analytic Model for the Projected Contact Zone Based on the Flow Line Element Method in Alloyed Bar Rolling

For obtaining the profile and the projected area of contact zone exactly during alloyed bar rolling by Round-Oval-Round pass sequence, the analytic model for the length contact and contact boundary curve were built firstly by considering the influence of the spread of the outgoing workpiece on the effective height of outgoing workpiece and roll mean radius, and then the contact surface was discretized by finite flow line elements. Moreover, the radius equation and bite angle equation of different flow lines were derived and they were all expressed as the function of the position angle, then any flow line on the contact surface can be determined since the position angle has been given. Finally, since the analytic equation for the projected area of contact surface was hard to be integrated directly, the analytic model was proposed by summing up the area of discretized parts on the contact surface. Based on the analytical model of contact boundary and flow line element, 3-dimension contact surface was rebuilt by mathematical software, and the validity of analytic model was examined by the bar rolling experiments and the numerical simulation of alloyed bar rolling by rigid-plastic FEM software. Compared with the existing models, the precision of the projecting area of contact zone was improved obviously. So, it can be applied in alloyed bar rolling to predict the projected area of contact zone and velocity of outgoing workpiece exactly.

Mathematical model of neutral line on the contact zone in alloyed bar rolling by the round-oval-round pass sequence

For determining the neutral line on the contact zone to determine the relative slip condition between the contact surface of rolling pieces and the roll, the contact boundary curve was proposed by obtaining the radius of flow line and the bite angle of points on the contact boundary based on the flow line method, and then the contact surface was discretized as flow line elements to build a novel analytic model to reconstruct the geometry of contact surface. Moreover, the velocity of flow lines on the contact surface along the direction of X-axis was derived by the condition of steady-state incompressible flow, and the function of neutral line was obtained by determining the neutral radius and the neutral angle of the points on the neutral line. In addition, the three-dimensional rectangular coordinates of points on the neutral line were derived.Based on these mathematical models, the three dimensional geometry of contact surface and neutral line were drawn up by mathematical software. The validity of the theoretical model was verified by rolling experiments of alloyed bar and the numerical simulation by rigid-plastic FEM software. Compared with the experimental data and simulation results, the prediction error is acceptable and the results of the mathematical model is satisfying.

Research on the characteristics of forward slip and backward slip in alloyed bar rolling by the round-oval-round pass sequence

For determining the neutral line on the contact zone to distinguish the forward slip zone and backward slip zone on the contact surface between the deformed pieces and the roll, the contact surface was discretized as finite flow line elements to build a novel analytic model to reconstruct the geometry of contact surface. Moreover, the velocity of flow lines on the contact surface along the direction of x-axis was derived by the condition of steady-state incompressible flow, and the function of neutral line was obtained by determining the neutral radius and the neutral angle of the points on the neutral line. In addition, the forward slip coefficient and backward slip coefficient was derived and the relative slip condition of contact surface between the roll and the rolled pieces was determined. Based on these mathematical models the geometry of contact surface and neutral line were drawn up by mathematical software. The validity of the theoretical model was verified by rolling experiments of alloyed bar and the numerical simulation by rigid-plastic FEM software. Compared with the experimental data and simulation results, the prediction error of the mathematical model is acceptable and results from the mathematical model are satisfying.

Effect of grooved roll profiles on microstructure evolutions of AZ31 sheets in Periodical Straining Rolling process

Magnesium alloy sheets have very attractive features such as lightweight, high specific strength, vibration absorption and high electromagnetic shielding although it is well known that the strong (0001) basal texture of magnesium alloy sheets limits the plastic formability at room temperature. Therefore, texture and microstructure control of magnesium alloys are of importance for improvement of sheet formability. Many processes for controlling microstructures have been proposed and their effectiveness has been discussed. The authors have already proposed the novel rolling process called “Periodical Straining Rolling” or in a short, PSR process that employs the pinion-like or worm-gear-like grooved roll to introduce periodically localized plastic strain in rolled sheet. This process is aimed to control strain distribution to generate microstructure and texture gradient by adapting the proposed process to the conventional strip rolling process. The hot rolling experiment of AZ31 magnesium alloy sheet was conducted with sine curve grooved and continuous arc curve grooved platens to examine the feasibility of the proposed process. As a result, the apparent texture gradients in both the longitudinal and thickness directions are observed from as-PSR processed sheets so that it is proved that the PSR process is able to weaken the (0001) basal texture and increase microstructure evolution of AZ31 sheets. The optimal roll profile for PSR process is also discussed, being compared with microstructure and crystallographic changes and strain distribution/material flow analysis by rigid plastic FEM simulation.

Study on Compacting Mechanism of Plate Cross Wedge Rolling High-Speed Rail Screw Spike

A thermal mechanical coupled model for High-Speed rail screw spike had been established with the aid of FE software Deform-3D by using rig id-plastic FEM. According to the results of finite element simulation, the metal flowing rules in plastic deforming were discussed. Stress and strain field distribution of Screw Spike were concrete researched. It has important theoretical sense and using values on solving part precision forming and workpiece quality improvement of plat cross wedge rolling.

The Effect of Temperature Condition on Material Deformation and Die Wear

The characteristics of temperature change on die and billet are very complex during the deformation process because of the interaction between them and some unstable external factors. In this paper, the numerical simulation model for the crank shaft die forging was established by means of the rigid-plastic FEM method. The model was validated by optical non-contact 3D measurement—ATOS. Based on available research results, this paper explored the effect of temperature conditions on material deformation and die wear. Three parameters, press velocity and initial temperature of billet and die, were chosen to illustrate the effects. From the experimental results, the effect of process parameters on deformation ability of the material is simple, while the effect on die wear is relatively complicated. The press velocity plays an important role on die wear when the initial temperature of the billet has larger influence on material deformation. A conclusion can be drawn that when the initial temperature of the billet is 1100 °C, the initial temperature of the die is 250 °C, and the velocity is kept in the range of 200-300 mm/s, the optimum solution for deformation ability of the material and die wear can be obtained. It is possible for the conclusion to be extended further for the control of temperature condition to optimize die life and material deformation.

剛塑性有限要素法を用いた二層系粘性土地盤の直接基礎の支持力解析

The ultimate bearing capacity formulas of foundation and penetration foundation have been specified in the guideline published by Architectural Institute of Japan for design of building foundation. The rigid plastic finite element method was developed by Tamura and Ohtsuka and has been applied to estimate the ultimate bearing capacity of footing. The characteristic of this method is to employ limited soil constants in comparison with deformation analysis. It only uses the strength parameters as cohesion, c and friction angle, φ since it deals with the limit state directly by disregarding the deformation of building and ground. Through a series of rigid plastic finite element analyses, the comparison of ultimate bearing capacities of penetration foundation between the simulation results and the formula of Architectural Institute of Japan was conducted for two layered soil system of clay. The change in failure mode of ground was discussed with the geometrical ratio between the width of footing and the height of surface layer. The strength ratio of the surface and the second layers of ground was clearly shown to affect the formation of failure mode. The applicability of rigid plastic FEM was demonstrated to the assessment of ultimate bearing capacity of two layered clayey soil system.

Research on Roll-Forging Process Simulation for Thick-Walled Hollow Part

Based on the rigid-plastic FEM program DEFORM-3D, the forming process of roll-forging for the thick-walled hollow parts has been simulated. The effect reduction on elongation and width-extension has been presented, and the difference between hollow part and solid part has been investigated in elongation and width-extension. This project can provide a reference for guiding the actual roll-forging for thick-walled hollow part.

Influence of tool parameters on internal voids in cross wedge rolling of aluminum alloy parts

The internal void of cross wedge rolling (CWR) part can be treated as porous material due to their similar physical property and deformation characteristics. Aiming at the CWR process of aluminum alloy 7075 workpiece, the numerical simulation model for internal void was established by means of the rigid-plastic FEM method for the porous material. The relative density was used to research the influence of three primary parameters on the internal void in CWR process, including the forming angle α1, the stretching angle β and the area reduction ΔA. The experimental results show that the expansion of internal void occurs in the stretching zone, and the knifing zone just has a little influence on it. The stretching angle has a great influence on the internal void, while the area reduction has a small influence on it. The size of internal voids decreases with the increase of area reduction, stretching angle and forming angle. When designing the CWR tool geometry and operating conditions, to prevent the internal void, the area reduction is suggested to be 55%–65%, the stretching angle to be 8°–10°, and the forming angle to be 29°–32°.

A NR–BFGS method for fast rigid-plastic FEM in strip rolling

RPFEM (rigid-plastic finite element method) has been widely applied in rolling process with the development of computer technology. However, it is unavailable for online application due to the large computational time. During iterative solution of RPFEM, the convergence speed is greatly determined by the optimization method. In order to improve computational efficiency and convergence, the NR (Newton–Raphson) method and BFGS (Broyden–Fletcher–Goldfarb–Shanno) quasi-Newton method are discussed, respectively, and an NR–BFGS (NR and BFGS) method is proposed and constructed for fast calculation of RPFEM. Moreover, the RPFEM code is developed using Compaq Visual Fortran language and the different strip rolling processes have been solved successfully to show the efficiency and accuracy with the different optimization methods. The calculated results have a good agreement with the measured value and the RPFEM has higher accuracy. Compared with other two methods, the NR–BFGS method has the remarkable advantages to reduce the CPU time and the iterations of RPFEM code. From the numerical results, it is found that the CPU time, stability and the accuracy of RPFEM code in the solution procedure by the NR–BFGS method can meet the requirements of online application of FEM in the strip rolling process.

Thermal Coupled FEM Analysis of Precision Roll Forging Performing of Automobile Front Axle

According to the characters, technological condition and requirements of automotive front axle forging, both the process of exact roll-forging billet and die design are studied, as the result, roll- forging die of front axle billet, pre-completed roll-forging die and final roll-forging die are design respectively, finally the groove with hat cross-section is analyzed and top pressure rolling method is proposed during blank-making roll-forging process. The precision rolling forging performing deformation process of automobile front axle is simulated with finite element software Deform-3D by using 3D thermo-mechanical coupled rigid plastic FEM. The metal flow process, equivalent stress and strain field, temperature field and load status of rolling die are analyzed, and they are consistent with experiments. This provides a dependable theoretical basis for understanding the deforming mechanism and selecting reasonable parameters for the precision rolling forging performing of front axle.

A Research on the Forward Slip Coefficient in Alloyed Bar Rolling by the Round-Oval-Round Pass Sequence

For predicting the forward slip coefficient and veocity of outgoing workpiece exactly during alloyed bar rolling by Round-Oval-Round pass sequence, the influence of the spred of the outgoing workpiece and its contact boundary condition was considered and the calculating formula for the effective height of outgoing workpiece and the mean roll radius was proposed individually. Moreover, the new parameters were substituted into the Shinokura and Takai Formula to modify it. Then a modified forward slip coefficient firmula was proposed. The validity of the theoretical model has been examined by the bar rolling experiment and the numerical simulation using three-dimensional rigid-plastic FEM. Compared with the Shinokura and Takai dormula, the predict accuracy of the modified formula was improved apparently. So, it can be applied in alloyed bar rolling to predict the the forward slip coefficient and veocity of outgoing workpiece exactly.

Rigid Plastic FEM Model of Fast Solution to Strip Rolling

Rigid plastic finite element method (RPFEM) is one of the most efficient numerical methods during the rolling process. Realizing FEM online application has been main target for many researchers. The influence of compile method, elements number, compressible parameter, friction factor and convergent criteria were investigated and RPFEM model of fast solution to strip rolling was proposed in this work. Compile method and compressible parameter have less influence on calculated rolling force. However, the iteration steps are reduced and computational efficiency is improved greatly with compile method of release and compressible parameter 0.01. The change of calculated rolling force becomes less but iteration steps become more and more with the increment of elements number. Both accuracy and efficiency is satisfying with the change of elements number from 50 to 200. In addition, the typical rolling schedule from a certain plant has been solved with the developed program FFEM-2D by FORTRAN. The predicted rolling force has a good agreement with the measured value. The iteration steps change from 12 to 36 and computational time is less than 200(ms) with the model in one pass rolling. Therefore, the accuracy is satisfying and computational time fully meets the basic requirements of FEM online application. Keywords: Rolling; RPFEM; Fast solution; Computational time

Improved Rotative Mid-Point Mensuration and Newton-Raphson Method in 2-D Flat Rolling Simulation

Newton-Raphson (N-R) method has been employed to solve the system of simultaneous equations arising in Rigid-Plastic finite element simulation. The combination of the improved rotative mid-point mensuration and the N-R method, named the M-P method is designated to solve the equations of velocity increment in Rigid-Plastic FEM. The CPU times required for calculation by the M-P method and the N-R method are compared and it is found that the CPU time required for calculation of the N-R method is more than the M-P method. The calculated rolling forces by the M-P method and the N-R method are compared and it is found that the former correlates better with the measured value. Numerical tests and application show that the M-P method is feasible and steady.

Rigid-Plastic FEM Simulation of Orthogonal Cutting Process

This paper presents a rigid-plastic finite element method for orthogonal cutting process by adopting Lagrange method. The rigid-plastic FEM analysis model is established and the rigid-plastic FEM analysis toolkit was developed. Meanwhile, two relevant key problems are discussed systematically, including the rule of chip-workpiece separation and the criterion of tool-chip separation. At last, a simulation example of planing an aluminium alloy (ZL-301) workpiece was conducted. The effects of the cutting stroke, the tool rake angle and the friction coefficient on chip were observed. The numerical simulation results have a good agreement with their experimental ones. It is indicated that the presented FEM model and algorithm are efficient and correct.

An approach for reduction of the volume loss in the rigid-plastic FEM using two-step updating procedure

The volume loss, as a direct consequence of the geometry updating procedure used in the conventional penalty rigid-plastic finite element method (RPFEM), is primarily caused by the application of the widely used forward Euler time integration method. In order to decrease this undesired consequence, the combination of the two-step Adams–Bashforth time integration method and the volumetrically elastic and deviatorically RPFEM is proposed as a new approach. The cylinder upsetting process was simulated using in-house finite element code. The results of simulations, obtained for the various levels of friction factors and height reductions, show that the proposed method gives a significantly lower volume loss. Also, the results of the friction factor determination procedure utilising the ring compression test for three lubrication conditions demonstrate the capabilities of the proposed method.