Adaptive 2D finite element simulation of metal forming processes

The development and integration of available current methods and the development of new methods for an adaptive finite element analysis of metal forming processes are presented. The analysis includes large-strain, elastic–plastic, and thermal effects. Many numerical methods such as mesh generation, simulation of the contact between the workpiece and tool and die, and optimization of the finite element mesh are integrated and incorporated. In addition, an algorithm is developed which can detect certain severely distorted elements where the area of integration is approaching zero. The advantage of correcting these regions of locally distorted elements is demonstrated. These numerical methods are implemented in a finite element program developed for simulating metal forming processes, with the emphasis on automating the analysis. Examples include an axisymmetric stress simulation of a coldheading process, a plane strain simulation of an extrusion process and a plane strain simulation of orthogonal metal cutting, all with noticeable thermal effects. The orthogonal cutting forces and feed forces calculated are compared with two sets of experimental data, with good agreement.     

Automatic adaptive remeshing for finite element simulation of forming processes

An automatic remeshing scheme has been developed to enable finite element simulation of even complicated forming processes. It has been demonstrated that for many practical applications the incorporation of this technique in the existing computer codes is indispensable not only for more accurate solutions but sometimes just for striving to obtain solutions. In order to avoid the tedious procedures of, e.g. interrupting the analysis, performing rediscretization, mapping of current state variables and preparing the new set of boundary conditions, methods for automating the remeshing procedures and the related accuracy problems have been presented. Several examples, such as a heading process, an extrusion process through a square die, and a one-blow impression-die forging process with flash have been successfully tested out with this automatic remeshing scheme.     

A mesh re-zoning technique for finite element simulations of metal forming processes

Based on some fundamental properties of finite element approximations, a mesh re-zoning scheme is proposed for finite element simulations of metal forming problems. It is demonstrated that this technique is indispensable in analysing many difficult forming processes, especially when there exist corners or very irregular shapes on the boundaries. The algorithm is tested by a backward extrusion process and direct extrusion through a square die.     

Three-dimensional finite element contact algorithm for metal forming

This work presents a three-dimensional rigid plastic finite element formulation. The workpiece is discretized with eight node hexahedral isoparametric elements. Friction is included in the formulation by means of a shear stress depending on the relative velocity between the workpiece and the tool. Special attention is given to the contact problems, and a three-dimensional contact algorithm based on a discretization of the tool surface with triangular elements is presented. Finally, some selected examples are solved, in order to show the capabilities of the formulation.     

Plane strain finite element simulation of shear band formation during metal forming

A plane strain finite element formulation and solution procedure for shear band failure during the plane strain metal forming process are developed and presented. The large strain elastic-plastic formulation includes a 5-node 10-degree-of-freedom (d.o.f.) ‘crossed-triangle’ element, a 4-node 8-d.o.f. element with selective reduced integration, an 8-node 16-d.o.f. element and a 4-node 8-d.o.f. element with an embedded shear band. The formulation includes an elastic-plastic material model with a modified Gurson yield function and combined isotropic-kinematic hardening. The solution procedure is based on a Newton–Raphson incremental-iterative method with an orthogonal projection of zero or negative eigen-modes when required. Two different examples of plane strain tension test are studied with results compared with available numerical solutions to evaluate the present formulation and solution procedure of the four different elements. The results demonstrate that both types of the 4-node quadrilaterals are comparable to the 5-node crossed-triangle element as well as the 8-jiode element. To further validate and to demonstrate the predictive capability and practical applicability of the present development, two plane strain metal forming examples are investigated. The first application is a numerical simulation of a sheet-stretching test with results compared with experimental data for a commercially pure aluminium–magnesium 5182-O sheet. The load vs. extension history and the through-thickness strain are compared. The good agreement suggests that it is possible to numerically determine the parameters needed for the modified Gurson yield function. The second application is a numerical simulation of the formation of dead metal zones in the extrusion process. A plane strain extrusion of a short aluminium billet through straight-sided dies is presented and characteristic features of the formation of dead metal zone are observed.     

Efficient implicit finite element analysis of sheet forming processes

The computation time for implicit finite element analyses tends to increase disproportionally with increasing problem size. This is due to the repeated solution of linear sets of equations, if direct solvers are used. By using iterative linear equation solvers the total analysis time can be reduced for large systems. For plate or shell element models, however, the condition of the matrix is so ill that iterative solvers do not reach the huge time‐savings that are realized with solid elements. By introducing inertial effects into the implicit finite element code the condition number can be improved and iterative solvers perform much better. An additional advantage is that the inertial effects stabilize the Newton–Raphson iterations. This also applies to quasi‐static processes, for which the inertial effects finally do not affect the results. The presented method can readily be implemented in existing implicit finite element codes. Industrial size deep drawing simulations are executed to investigate the performance of the recommended strategy. It is concluded that the computation time is decreased by a factor of 5 to 10. Copyright © 2003 John Wiley & Sons, Ltd.     

A particle finite element method for analysis of industrial forming processes

We present a generalized Lagrangian formulation for analysis of industrial forming processes involving thermally coupled interactions between deformable continua. The governing equations for the deformable bodies are written in a unified manner that holds both for fluids and solids. The success of the formulation lays on a residual-based expression of the mass conservation equation obtained using the finite calculus method that provides the necessary stability for quasi/fully incompressible situations. The governing equations are discretized with the FEM via a mixed formulation using simplicial elements with equal linear interpolation for the velocities, the pressure and the temperature. The merits of the formulation are demonstrated in the solution of 2D and 3D thermally-coupled forming processes using the particle finite element method.     

A finite element model for thermomechanical analysis of sheet metal forming

A thermal model based on explicit time integration is developed and implemented into the explicit finite element code DYNA3D to model simultaneous forming and quenching of thin‐walled structures. A staggered approach is used for coupling the thermal and mechanical analysis, wherein each analysis is performed with different time step sizes. The implementation includes a thermal shell element with linear temperature approximation in the plane and quadratic in the thickness direction, and contact heat transfer. The material behaviour is described by a temperature‐dependent elastic–plastic model with a non‐linear isotropic hardening law. Transformation plasticity is included in the model. Examples are presented to validate and evaluate the proposed model. The model is evaluated by comparison with a one‐sided forming and quenching experiment. Copyright © 2004 John Wiley & Sons, Ltd.     

Analysis of superplastic metal forming by a finite element method

A finite element velocity method for analysing the superplastic sheet metal forming process is presented. This method is developed from the principle of virtual work and is based on the use of isoparametric continuum elements. The large inelastic deformation of the superplastic material is modelled as the behaviour of an incompressible non-linear viscous flow material. The contact and friction problem is solved by using the compatibility load step method, which is an extension of an earlier work. The finite element method is applied to selected problems to illustrate the applicability of the solution procedure.     

Adaptive generation of hexahedral element meshes for finite element analysis of metal plastic forming process

A method for the adaptive generation of hexahedral element mesh based on the geometric features of solid model is proposed. The first step is to construct the refinement information fields of source points and the corresponding ones of elements according to the surface curvature of the analyzed solid model. A thickness refinement criterion is then used to construct the thickness-based refinement information field of elements from digital topology. The second step is to generate a core mesh through removing all the undesired elements using even and odd parity rules. Then the core mesh is magnified in an inside–out manner method through a surface node projection process using the closest position approach. Finally, in order to match the mesh to the characteristic boundary of the solid model, a threading method is proposed and applied. The present method was applied in the mesh construction of different engineering problems. The resulting meshes are well-shaped and capture all the geometric features of the original solid models.     

A proposal to deal with contact and friction by blending meshfree and finite element methods in forming processes

In this work a computational model based on a meshless method, the Element Free Galerkin Method (EFG), is applied in the simulation of forging processes. Contact and friction are handled by blending finite elements with the EFG in order to overcome the difficulty of meshless methods in dealing with essential boundary conditions. Special interface finite elements are established between the tools and the workpiece, allowing to impose directly those conditions. An application example in forging is analyzed and the numerical solution of the proposed model is compared with experimental results as well as with a traditional finite element solution.     

A finite element analysis of damage propagation during metal forming process

In this paper damage propagation during metal forming process is investigated with the concept of continuum damage mechanics. An isotropic damage model based on the theory of materials of type N is adopted to describe the damage process of a ductile material with large elasto-viscoplastic deformation. To solve the finite elasto-viscoplasticity problem, a reasonable kinematic strain measure for largely deformed solids is used and the damage constitutive equations based on thermodynamical framework are developed. The stiffness degradation of the loaded material is chosen as a damage measure. An extended interior penalty method is used to impose the contact condition on the boundary. The highly nonlinear equilibrium equations are reduced to the incremental weak form and approximated by the total Lagrangian finite element method. The displacement control method along with the modified Riks' continuation technique based on displacement parameter is used to solve the incremental iterative equations. As numerical examples, upsetting, backward extrusion and punch problems are simulated and the results of damage propagation and J₂ stress contours with and without damage are presented. For punch problems, spring back and residual stresses are also presented.     

A three field element via Augmented Lagrangian for modelling bulk metal forming processes

A new 2D quadrilateral element is developed for the modelling of 2D incompressible rigid/viscoplastic problems: the QMITC-3F. The element formulation is based on the interpolation of three fields: velocities, strain rates and pressures. The incompressibility constraint is enforced using an Augmented Lagrangian technique. The new element is used in conjunction with the flow formulation and the pseudo-concentrations technique for modelling bulk metal forming processes.Dedicated to J. C. Simo     

A multi-layer triangular membrane finite element for the forming simulation of laminated composites

Continuous fibre reinforced thermoplastics offer a cost reduction compared to thermosets due to promising fast production methods like diaphragm forming and rubber pressing. Forming experiments of pre-consolidated four-layer 8H satin weave PPS laminates on a dome geometry demonstrated that inter-ply friction is a dominant parameter in forming doubly curved components. Therefore, simulations of this process as sequentially draping the individual layers are invalid. A multi-layer triangular membrane finite element has been developed for efficient simulation of laminated composite forming processes with only one element in the thickness direction. Contact logic between the individual plies is avoided. The simulations were validated by comparison to the experiments mentioned and agree well. The multi-layer membrane element has shown to be capable of predicting the material instabilities during forming. They appeared to be unsuited for realistic wrinkling simulations due to their lack of a bending stiffness.     

A Lagrangian cell‐centred finite volume method for metal forming simulation

The current article presents a Lagrangian cell‐centred finite volume solution methodology for simulation of metal forming processes. Details are given of the mathematical model in updated Lagrangian form, where a hyperelastoplastic J₂ constitutive relation has been employed. The cell‐centred finite volume discretisation is described, where a modified discretised is proposed to alleviate erroneous hydrostatic pressure oscillations; an outline of the memory efficient segregated solution procedure is given. The accuracy and order of accuracy of the method are examined on a number of 2‐D and 3‐D elastoplastic benchmark test cases, where good agreement with available analytical and finite element solutions is achieved. Copyright © 2016 John Wiley & Sons, Ltd.     

Investigation of anisotropy problems in sheet metal forming using finite element method

This paper discusses the results of the numerical study of rectangular cup drawing of steel sheets using finite element methods. To be able to verify the results of the numerical solutions, an experimental study was done where the material behavior under deformation was analyzed. A 3D parametric finite element (FE) model was built using the commercial FE-package ABAQUS/Standard. ABAQUS allows analyzing physical models of real processes putting special emphasis on geometrical non-linearities caused by large deformations, material non-linearities and complex friction conditions. Friction properties of the deep drawing quality steel sheet were determined by using the pin-on-disc tribometer. The results show that the friction coefficient depends on the measured angle from the rolling direction and corresponds to the surface topography. A quadratic Hill anisotropic yield criterion was compared with von Mises yield criterion having isotropic hardening. The sensitivity of constitutive laws to the initial data characterizing material behavior is also presented. It is found out that plastic anisotropy of the matrix in ductile sheet metal has influence on deformation behavior of the material. When the material and friction anisotropy are taken into account in the finite element analysis, this approach gives better approximate numerical results for real processes.     

A semi‐discrete shell finite element for textile composite reinforcement forming simulation

A triangular shell element for the simulation of textile composite reinforcements forming is proposed. This element is made up of unit woven cells. The internal virtual works are added on all woven cells of the element. They depend on tensions, in‐plane shear and bending moments that are directly those given by the experimental tests that are specific to textile composite reinforcement. The element has only displacement degrees of freedom; the bending curvatures are obtained from the displacement of the neighbouring elements. A set of example shows the efficiency of the approach and the relative roles of the tensile, in‐plane shear and bending rigidities. Especially their influence on the appearance and the development of wrinkles in draping and forming tests is analysed. Copyright © 2009 John Wiley & Sons, Ltd.