Rigid-plastic Finite Element Method Research Articles

A nonlinear rigid-plastic analysis for metal forming problem using the rigid-plastic point collocation method

A rigid-plastic point collocation method is applied to the analysis of plane strain forging, which is a nonlinear rigid-plastic problem of bulk metal forming. In general, the bulk metal forming problems are nonlinear and large deformation problems, used to be analyzed with the conventional rigid-plastic finite element methods. While the conventional rigid-plastic finite element methods have some shortcomings such as necessities of mesh generation, remeshing and numerical integration for these methods. The rigid-plastic point collocation method not only is a kind of truly meshless method, but also is a kind of no integration and no fundamental solution method. In this paper, the first, a linear elastic cantilever beam problem is analyzed by using the point collocation method, into which the concepts of the considered nodes and the unconsidered nodes are introduced. The numerical solution of the problem is compared with the exact solution of it, and quite high accuracy of the numerical solution has been achieved. The second, a plane strain metal forming problem has been analyzed by using the rigid-plastic point collocation method. Because the considered nodes and the unconsidered nodes are used, no renoding is needed. The solution of the rigid-plastic problem is compared with a conventional rigid-plastic finite element solution, and reasonable results have been obtained.

Hybrid Type Rigid Plastic Finite Element Analysis for Bearing Capacity Characteristics of Surface Uniform Loading

ABSTRACT In the geotechnical engineering design, rigid plastic analysis is usually used to estimate a factor of safety or an ultimate capacity. Although based on a simple assumption of rigid-plastic material behaviour, limit analysis has a rigorous theoretical background called limit theorems. The implementation of limit analysis to finite element method is recognised as rigid-plastic finite element method. The author recently proposed a new formulation of hybrid type rigid-plastic finite element method based on the interior point method, named primal-dual rigid-plastic finite element method (PDRPFEM). In this paper, characteristics of primal-dual rigid-plastic finite element method are illustrated in contrast to the ordinary rigid-plastic finite element method based on the upper bound theorem. Advantages of the primal-dual rigid-plastic finite element method in the numerical calculations are also explained. In addition to this, as a real rigid-plastic boundary value problem, bearing capacity problems of surface uniform loading on weightless Tresca material (c, φ = 0) are solved by the primal-dual rigid-plastic finite element method. Numerical solutions are compared to the analytical solutions to investigate numerical accuracies of the primal-dual rigid-plastic finite element method.

Simplified Three-Dimensional Finite Element Simulation of Shear Spinning Process Based on Axisymmetric Modeling

A simplified three-dimensional method for simulating plastic deformation in a shear spinning process of disks in a comparatively short computing time is proposed on the basis of the rigid-plastic finite element method using axisymmetric modeling. In this method, the shear spinning process is approximated as a forming process with a ringed die having the same cross-sectional shapes as the roller. The effects of the virtual shear deformation in the hoop direction and the incremental deformation in the shear spinning process are introduced into the axisymmetric modeling. A shear spinning process of disks having a taper flange is simulated by the proposed method. The forming limit is predicted from the pileup just before touching the roller in the finite element simulation. In addition, an actual shear spinning process of a large wheel disk for a bus and truck is simulated.

Process design and blank modification in the multistage rectangular deep drawing of an extreme aspect ratio

We have carried out finite element analysis to achieve the multistage deep drawing of a rectangular configuration with an extreme aspect ratio, focusing on the process design. Analysis of a rectangular deep drawing process with an extreme aspect ratio is very difficult in regard to the design process parameters, including the intermediate die profile. To solve these difficulties, a numerical approach using a finite element method was performed. A series of multistage rectangular deep drawing experiments were conducted, and the deformed configuration was compared to the results of the finite element analysis. Additionally, to minimize the amount of removed material after the trimming process, a finite element simulation was applied to a blank modification. The analysis incorporated brick elements in a rigid-plastic finite element method with an explicit time integration scheme using LS-DYNA3D software.

3차원 강소성 유한요소법을 이용한 환상압연공정중 형상결함의 예측

3차원 강소성 유한요소법을 이용한 환상압연공정중 형상결함의 예측

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.

Finite element modelling of mixed film lubrication in cold strip rolling

A finite element model for mixed film lubrication in cold strip rolling has been developed. In this paper, a full 3D rigid–plastic finite element method (FEM) was used to simulate the cold strip rolling, taking into account the friction variation in the roll bite which involves a mixed film lubrication regime. A roll with embedded pins was employed to measure the variation of the coefficient of friction. The simulation results such as rolling force and torque have been validated by experimental results, which indicate that the developed model can give a reliable prediction. This paper contributes to Professor Wang’s 70th birthday celebration. The first author has been significantly inspired by Professor Z.R. Wang’s distinguished work in metal forming since he was an undergraduate at the Northeastern University, PR China, which has benefited him significantly in the development of his academic career.

Theoretical and experimental analysis of the rolling process of bimetallic rods Cu-steel and Cu-Al

In this study, the authors present the results of their theoretical and experimental analysis of the rolling process of bimetallic rods in stretching passes. The bimetallic rods had different ratios of the yield stress between components. The original rods were round (21.7mm diameter) steel and aluminium rods, covered with 2.8mm copper layer. A numerical model for hot stretching passes rolling was proposed. In the model, the deformation of a bimetallic material was analysed by three-dimensional rigid–plastic finite-element method. The model simulated metal flow during rolling of bimetallic rods in round–oval series. The results of the experiments were compared with the finite-element calculations of the stress distribution and spread of Cu-steel and Cu-Al rods in the deformation zone. The analysis demonstrated that an appropriate selection of shape and size of oval pass allows production of even distribution of the copper layer in the bimetallic roll products. The results of comparison of calculated spread and experimental data confirmed good ability of proposed mathematical model, that is recommended for roll pass design at rolling of bimetallic rods.

Face stabilizing method for shallow tunnels in loose sandy ground

The overburden, stiffness of the ground, underground water level and the size of a tunnel are influential factors for tunnel face stability. The Ushikagi double-track tunnel was constructed by the shotcrete tunneling method, or the so-call New Austrian Tunneling Method (NATM) on the Touhoku Shinkansen line (between Hachinohe and Shin-Aomori). The tunnel is 2,070 m long drilled in a loose sandy ground at a high groundwater level. The overburden of the tunnel is 2-10 m thick throughout the whole section. For this reason, we worried about the face stability of the tunnel and carried out soil stabilization test as a means to keep the face stability. The soil near the crown was improved by a mixing method from the ground surface for 90 m from the entrance of the tunnel. When the tunnel was bored after the ground improvement, we measured some convergences, stresses of the primary lining, displacement and earth pressure of the ground, etc. to investigate the effect of the measure on the face stability. We evaluated the face stability with and without the measure applied by the elastic FEA, based on the plastic theory (so-call rigid-plastic FEA or RPFEA), such as the one to calculate the balance of the mass in front of a face. (1) This paper describes an outline of the construction, results of measurements and analyses, and a study on the mechanism of stabilization. Following things are contained: The ground improvement for a loose sandy ground. (2) The results of some convergences, displacement and earth pressure of the ground. (3) Two-dimensional finite element method (elastic analysis). (4) Two-dimensional rigid plastic finite element method (ultimate analysis). (5) About the stabilization based on the results of measurements and evaluation. (A). Reprinted with permission from Elsevier. For the covering abstract see ITRD E124500.

Explanation of the mushroom effect in the rotary forging of a cylinder

Rotary forging is an incremental forging process and is available to form various axisymmetrical parts from cylindrical billets. However, under certain conditions, a cylindrical billet is liable to be formed into a mushroom-shape after rotary forging, but not a drum shape in upsetting. A 3D rigid–plastic finite element method is used to simulate the rotary forging process to reveal the deformation mechanism of the mushroom shape workpiece. The stress, strain rate and strain distributions at different positions of the workpiece and at different times during the process are presented, and then the deformation zones are presented in detail for analyzing the deforming patterns. The reasons why the part with H0/D=0.5–1.0 (ratio of initial height to diameter) is formed into a mushroom shape are analyzed and it is concluded that these are non-uniform deformation under the effect of the eccentric loading and the different deforming degrees along the tangential direction at various heights of the workpiece. However, this kind of effect can be used to manufacture a part with a flange from a cylinder, instead of being regarded as a defect.

A rigid-plastic finite element analysis of temper rolling process

A study on temper rolling process has been carried out using rigid-plastic finite element method. Rigid-plastic formulation can be used to predict the roll force and roll torque and to study the deformation field of the rolled sheet. Hitchcock’s formula for roll deformation does not consider the effect of frictional traction on the roll deformation. Hence, to account for high friction present in temper rolling, the roll deformation is computed in an iterative manner using theory of elasticity solution considering roll as an elastic half space. The study reveals that some of the assumptions made for approximate theory of temper rolling are not valid. The deformation field consists of a central rigid (actually elastic) zone and is highly non-homogeneous across the thickness of the strip. Longitudinal stress is not uniform across the thickness of the sheet, hence one-dimensional analysis of the process does not seem to be appropriate. Whereas a rigorous analysis is possible using elasto-plastic finite element formulation at the expense of large amount of computational time, a study using rigid-plastic formulation may be used to understand the qualitative effects of process parameters.

A rigid-plastic finite element analysis of temper rolling process

A study on temper rolling process has been carried out using rigid-plastic finite element method. Rigid-plastic formulation can be used to predict the roll force and roll torque and to study the deformation field of the rolled sheet. Hitchcock’s formula for roll deformation does not consider the effect of frictional traction on the roll deformation. Hence, to account for high friction present in temper rolling, the roll deformation is computed in an iterative manner using theory of elasticity solution considering roll as an elastic half space. The study reveals that some of the assumptions made for approximate theory of temper rolling are not valid. The deformation field consists of a central rigid (actually elastic) zone and is highly non-homogeneous across the thickness of the strip. Longitudinal stress is not uniform across the thickness of the sheet, hence one-dimensional analysis of the process does not seem to be appropriate. Whereas a rigorous analysis is possible using elasto-plastic finite element formulation at the expense of large amount of computational time, a study using rigid-plastic formulation may be used to understand the qualitative effects of process parameters.

사각 빌렛 자유단조시 내부기공폐쇄거동 유한요소해석

Finite element analysis of open die forging process to make rectangular billet has been performed in this study. Three dimensional rigid-plastic finite element method was used to analyze the effects of process variables, forging pass design and die configurations on the void closure phenomena to maximize the internal deformation for better structural homogeneity and center-line consolidation of the rectangular billet. The effect of anvil width ratio, anvil pitch, anvil shape and number of pass has been estimated by the degree of void closure ratio. Although it is difficult to optimize process parameters in the operational environments, favourable process conditions are suggested for better product quality.

Numerical Analysis on the Dissimilar Channel Angular Pressing by Multi-Pass Rolling

The dissimilar channel angular pressing (DCAP or CCSS) based on the equal channel angular pressing (ECAP) was numerically modeled and analyzed by means of a rigid-plastic two-dimensional finite element method. Multi-pass rolling is performed in two different manners; the feeding direction of samples into the DCAP-channel is maintained in Route A and the feeding direction is reversed in the Route B. The deformation of AA1100 sheets during the DCAP process comprises three distinct processes of rolling, bending and shearing. The shear deformation of an amount of 0.5 was concentrated at the corner of the DCAP-channel where the abrupt change in the direction of material flow occurred. Because differences in the shear deformation in Route A and Route B led to the different strain states throughout the thickness of the aluminum sheet, the strain history in the DCAP-channel was analyzed in various thickness layers by the shear and effective strain components.

A Study on the Process Design of Cold-Forged Automobile Parts

The cold forging processes of automobile parts such as piston-pin, valve-spring retainer(VSR) and power-assisted steering part (PAS) are analyzed by the rigid-plastic finite element method. The results of the simulation on the piston-pin are summarized in terms of the strain distribution and load-stroke relationship. Based on the analysis on the current processes of VSR and PAS, the new novel processes for improving the conventional process sequences are designed. As a design criterion, the improved processes satisfy the new condition such as an initial billet size, the production time and the limit value of forming load and pressure etc. The present simulation results and the newly developed process gave rise to an improvement in manufacturing processes for cold-forged automobile parts. Furthermore, the numerical analysis for the processes in this study provides a new design concept for forming processes and a basis for the selection of forging equipments.

混合型シェイクダウン解析法のアルゴリズムに関する研究

An algorithm of hybrid type shakedown analysis based on the interior point method is investigated from the theoretical point of view. Instead of time domain description of repeated external loads, an external load domain which is a convex polygon in the load space including its origin is installed. In addition, any external loads are expressed as a linear combination of basis vectors which correspond to the corners of the external load domain. This expression is called a descretisation of repeated external loads, because these basis vectors are independent of time. By using this descretisation of repeated external loads, a mathematical structure of shakedown analysis is very similar to that of limit analysis. Therefore, hybrid type algorithm of rigid plastic finite element method can be extended to shakedown analysis. Some fundamental numerical results are also reported.

混合型剛塑性有限要素法による摩擦性材料の支持力解析

Rigid plastic analysis is widely used for the analyses of metal forming process or bearing capacity characteristics. From the mathematical point of view, rigid plastic analysis essentially belongs to convex programming. In this context, one of the authors proposed a hybrid type rigid plastic finite element method based on the primal dual interior point method (PDRPFEM) as an efficient numerical tool. In this paper, PDRPFEM is extended to more general rigid plastic boundary value problems including dead loads which is independent of a load factor and frictinal materials. Formulation of this extension is explained in details. Numerical performance of this extension is also investigated in comparison with the previous analytical solutions.

Effect of Pass Schedule on Cross-Sectional Shapes of Circular Seamless Pipes Reshaped into Square Shapes by Hot Roll Sizing Mill

A heavy gauge square steel pipe is manufactured by a hot roll sizing process, in view of difficulty in manufacturing such a pipe with sharp corners by cold roll forming. In this paper, the effect of pass schedule on a cross-sectional shape is discussed by referring to experimental measurements, and results calculated by the rigid-plastic finite element method. The experiment was carried out at the last step of the sizing process for seamless pipes. The comers of a product become sharper as the magnitude of total reduction increases. In the case of a two-roll type roller, the comer near the roll flange becomes sharper than the comer near the groove bottom. The hollow depth at the sides is small when the incremental reduction at each sizing stand is high at the early reshaping stage with a large bending curvature ((D 0 /2)/R i , R i : bending radius, Do: initial external diameter of a circular seamless pipe) and low at the late reshaping stage with a small bending curvature.

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.

Finite element simulation of cold rolling of thin strip

In this work, the authors use a full 3D rigid plastic finite element method (FEM) to simulate the thin strip rolling taking into account the modelling of friction variation in the roll bite. A comparison of the computed results with measured values was conducted. The characteristics of the distribution of the velocity along the width of strip at the exit of the roll bite and the spread of strip for the different crown factors are presented in this paper. The modelling of the shape, profile and flatness for cold rolling of thin strip with friction variation is also discussed.