Marco Schwarze

Characterization and Simulation of High-Speed-Deformation-Processes

The combination of the processes deep drawing and electromagnetic pulse forming is a promising way to cope with the ever higher complexity of new sheet metal designs. A cooperation between the Institute of Materials Science (IW) of the Leibniz Universitat Hannover and the Institute of Applied Mechanics (IFAM) of the RWTH Aachen is investigating these processes both experimental and in simulation. Aim is the characterization of the combined process. Therefore the material properties of the investigated aluminum alloy EN AW 6082 T6 have to be determined quasi-static as well as at high speed. These properties are then used as a basic for the simulations. Anisotropic behaviors as well as dynamic hardening effects are investigated in the quasi-static state. Several experiments for analyzing “Bauschinger” respectively “Ratcheting effects” have been conducted resulting in a new measuring set-up for thin sheets. For the determination of high speed forming limit diagrams a novel testing device on the basis of the Nakajima-test has been developed allowing for strain rates of approximately 103 s. Both testing methods are described in this paper; the results are then used to adapt the simulation models for the combined processes. The high speed deformation process is simulated by means of finite elements using a material model developed at the IFAM. The finite strain constitutive model combines nonlinear kinematic and isotropic hardening and is derived in a thermodynamic setting. It is based on the multiplicative split of the deformation gradient in the context of hyperelasticity. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong–Frederick kinematic hardening which is widely adopted as capable of representing the above metal hardening effects. To prevent locking * This work is based on the results of PAK 343 “Hochgeschwindigkeitsblechumformung”; the authors would like to thank the “Deutsche Forschungsgemeinschaft DFG” for its financial support

Stability of Mixed Finite Element Formulations – A New Approach

To guarantee stability of non-linear mixed finite element formulations is still an unsolved problem. In the present contribution firstly a unified finite element technology for linear-elastic problems is described where the effect of locking can be well explained and the issue of instability is not relevant. The extension to large deformation models reveals the difficulty of differentiating between physcially relevant and artificial bifurcations. Powerful finite element technologies should be able to exhibit the first kind but not show the second kind of bifurcations. In the paper a strategy is developed to detect and to avoid such non-physical instabilities.

Efficient Finite Element and Contact Procedures for the Simulation of High Speed Sheet Metal Forming Processes

A large variety of forming processes is used in industrial manufacturing processes. The numerical simulation of such processes puts high demands on the finite element technology. Usually first order isoparametric elements are preferred because of their robustness and numerical efficiency. Unfortunately, these elements tend to undesired numerical effects like ”locking”, predominant in situations characterized by plastic incompressibility or pure bending. To overcome this problem, several authors [1, 2, 4] propose finite element formulations based on the concept of reduced integration with hourglass stabilization by applying the ”enhanced strain method”. The main advantage of the proposed new isoparametric solid-shell formulation with linear ansatz functions is the fact that the undesirable effects of locking are eliminated. The previously described element technique can be applied to analyze specific problems of high speed forming into a cavity: Working with contact surfaces discretized by first order finite elements leads to discontinuities of the normal patch vector and, subsequently, to non-smooth sliding [5]. In quasi-static forming processes these discontinuities will not influence the contact forces noticeably. However, in dynamic investigations the sudden change of contact forces due to the rough surface description leads to a very high acceleration of the contact nodes. To avoid this effect, a smoothing algorithm will be described.

Neue Finite-Elemente-Technologie zur Simulation elektromagnetischer Blechumformung

Kurzfassung Diese Abhandlung beschreibt eine neue Finite-Elemente-Formulierung, die sich hervorragend zur Simulation von Umformprozessen, insbesondere von Blechumformung, eignet. Wesentliche Vorteile des entwickelten Solid-Shell-Elements sind die vollständige Eliminierung von unerwünschten Locking-Effekten sowie seine numerische Effizienz. In diesem Beitrag werden die wesentlichen Ideen der Elementformulierung vorgestellt. Als numerisches Beispiel dient hierfür die Berechnung der elektromagnetischen Blechumformung.

Towards the Contact and Impact Modeling in Finite Element Simulations of High Speed Forming

In finite element simulations of high speed sheet metal forming processes the contact between workpiece and forming tools has to be modeled very carefully. Several important aspects have to be taken into account. Robust and locking-free finite element formulations are required to model the sheet forming process, the die has to be considered as a deformable component, and the description of the contact constraints between workpiece and forming tools is a significant source of shortcomings in modeling. The contact and impact simulation makes high demands on the robustness of finite element formulations. For this reason finite elements with low order ansatz functions are preferred. Furthermore, they prove to be advantageous when automatic meshing tools are applied. To overcome the undesired effects of locking we work with an improved version of the innovative solid-shell concept proposed by [11]. It is based on the concept of reduced integration with hourglass stabilization. The use of this solid-shell finite element allows us to test the influence of the modeling of the die and the contact constraints in a very efficient way. An overview of so-called macro and micro deformations of forming tools in sheet metal forming simulations can be found in [8]. We show that the deformation of the die has a noticeable influence in electromagnetic sheet metal forming. However, in most commercial finite element codes taking into account elastically deformable forming tools requires a full finite element discretization of the die which leads to very high computational effort. Therefore users often assume the tools as being rigid and apply node-based spring-dashpot systems to improve the modeling of the interaction between sheet metal and die. But also in this case local interactions cannot be taken into account realistically. As a possible remedy we investigate a fully elastic description of the forming tools in combination with model reduction techniques. These significantly reduce the number of degrees-of-freedom in the finite element simulation. For this reason we present different alternatives of this technique.

Modeling and Simulation of 3D EMF Processes

A recent interest in potential industrial applications of electromagnetic forming processes has inspired a demand for adequate simulation tools. Aiming at the virtual design of industrial applications, the purpose of this work is to develop algorithmic formulations particularly suitable to reduce the enormous computational cost inherent to 3D simulations. These formulations comprise a carefully chosen discretization, highly accurate methods for data transfer between electromagnetic and mechanical subsystems, an efficient solid shell formulation, and a termination criterion for the electromagnetic field computation. As a result the simulation time is reduced by about one order of magnitude.

A new solid‐shell finite element technology incorporating plastic anisotropy in forming simulations

In the recent years shell finite element formulations which include only displacement degrees‐of‐freedom, the so‐called solid‐shells, have been successfully applied in sheet metal forming (see e.g. [1]). A very efficient strategy to deal with the problem of locking which occurs in bending‐dominated problems and in the limit of incompressibility is the method of reduced integration with hourglass stabilization [12]. Further advantages of these finite element technologies are their robustness with respect to severe mesh distortion and the low computational cost. A disadvantage is, however, the necessity to develop a suitable hourglass stabilization which adapts to both, the changing geometry and the usually highly non‐linear material behaviour. Most earlier finite element technologies are based on the assumption that the material behaviour is initially isotropic. In the present contribution we develop an approach to include initial and deformation‐induced anisotropy. Prerequisite for that is the development of a suitable material law. In contrast to many other current papers ([10], [13], [2], [7], [14]) we aim at a purely continuum mechanical modelling to arrive at optimal numerical efficiency.In the recent years shell finite element formulations which include only displacement degrees‐of‐freedom, the so‐called solid‐shells, have been successfully applied in sheet metal forming (see e.g. [1]). A very efficient strategy to deal with the problem of locking which occurs in bending‐dominated problems and in the limit of incompressibility is the method of reduced integration with hourglass stabilization [12]. Further advantages of these finite element technologies are their robustness with respect to severe mesh distortion and the low computational cost. A disadvantage is, however, the necessity to develop a suitable hourglass stabilization which adapts to both, the changing geometry and the usually highly non‐linear material behaviour. Most earlier finite element technologies are based on the assumption that the material behaviour is initially isotropic. In the present contribution we develop an approach to include initial and deformation‐induced anisotropy. Prerequisite for that is the development...

Finite Element Technology In Forming Simulations - Theoretical Aspects And Practical Applications Of A New Solid-Shell Element

Finite element simulations of sheet metal forming processes are highly non‐linear problems. The non‐linearity arises not only from the kinematical relations and the material formulation, furthermore the contact between workpiece and the forming tools leads to an increased number of iterations within the Newton‐Raphson scheme. This fact puts high demands on the robustness of finite element formulations. For this reason we study the enhanced assumed strain (EAS) concept as proposed in [1]. The goal is to improve the robustness of the solid‐shell formulation in deep drawing simulations.

Analysis of forming processes with efficient finite element procedures

Forming technologies are widely used in the manufacturing processes of industries. The numerical simulation of such processes makes high demands on the finite element technology. Element formulations which do not show the undesirable effect of locking in the cases of nearly incompressible material behaviour like during the plastification and in large deformations with extreme bending, are required. Unfortunately classical low order isoparametric element formulations show the effect of locking. An underestimation of the deformation associated with an overestimation of the stress state can be observed. To overcome this problem several autors [1], [4] propose finite element formulations based on the concept of reduced integration with hourglass stabilization by using the enhanced strain method. Especially for the efficient numerical simulation of sheet forming processes so-called solid-shell elements are developed [2], [4]. The starting point of the present formulation is the same three-field variational functional on which many three-dimensional enhanced strain concepts are based. A new aspect is the Taylor expansion of the first Piola-Kirchhoff stress tensor with respect to the normal through the center of the element. Together with a constant Jacobi matrix due to the computation in the center of the element this concept leads to a powerful element formulation with only two Gauss points over the thickness. Furthermore continuum mechanical laws can be implemented without additional assumptions about the kinematics or the stress state.