H.J.M. Geijselaers

The implementation of an equivalent drawbead model in a finite-element code for sheet metal forming

Drawbeads are applied in the deep-drawing process to improve the control of the material flow during the forming operation. In numerical methods these drawbeads can be simulated with an equivalent drawbead. In this paper the implementation of an equivalent drawbead model in a finite-element code is described. The input for the equivalent drawbead consists of a drawbead restraining force, a plastic thickness strain and a drawbead lift force, which are obtained from a two-dimensional drawbead simulation or from an experiment. Two different mathematical descriptions of the implementation of the plastic thickness strain are pointed out. The correlation between the simulation results gained with the different algorithms is presented in this work.

Flow front tracking in ALE/Eulerian formulation FEM simulations of aluminium extrusion

Even though Extrusion is often regarded as a semi stationary process, the defor- mations of the die at the beginning of the process can have great influence on the process later on. During filling of the die, the deformation of the die depends on the location of the flow front up to a point where parts of the profile will be opened or closed, especially in porthole dies. In this paper we present an accurate 2D method to simulate the filling of extrusion dies. The method is based on the pseudo concentration technique. We compare different options to model the pseudo material and choose the best.

A SUPG approach for determining frontlines in aluminium extrusion simulations and a comparison with experiments

In this paper we present a method to determine the frontlines inside the container and inside the extrusion die based on a steady state velocity field. Using this velocity field the convection equation is solved with a SUPG stabilized finite element method for a variable that represents the time it takes from the initial front to a certain point in the domain. When iso-lines in this field are plotted the development of fronts can be tracked. Extrusion experiments are performed with aluminium billets cut in slices. When extrusion is stopped the billet and extrudate are removed from the container and cut in half in the extrusion direction, copper foils between the slices show the frontlines. These lines show good agreement with the iso-lines from the numerical solution of convection equation

Multi-stage FE simulation of hot ring rolling

As a unique and important member of the metal forming family, ring rolling provides a cost effective process route to manufacture seamless rings. Applications of ring rolling cover a wide range of products in aerospace, automotive and civil engineering industries [1]. Above the recrystallization temperature of the material, hot ring rolling begins with the upsetting of the billet cut from raw stock. Next a punch pierces the hot upset billet to form a hole through the billet. This billet, referred to as preform, is then rolled by the ring rolling mill. For an accurate simulation of hot ring rolling, it is crucial to include the deformations, stresses and strains from the upsetting and piercing process as initial conditions for the rolling stage. In this work, multi-stage FE simulations of hot ring rolling process were performed by mapping the local deformation state of the workpiece from one step to the next one. The simulations of upsetting and piercing stages were carried out by 2D axisymmetric models using adaptive remeshing and element erosion. The workpiece for the ring rolling stage was subsequently obtained after performing a 2D to 3D mapping. The commercial FE package LS-DYNA was used for the study and user defined subroutines were implemented to complete the control algorithm. The simulation results were analyzed and also compared with those from the single-stage FE model of hot ring rolling.

Cladding of Advanced Al Alloys Employing Friction Stir Welding

Friction stir welding (FSW) is a relatively new solid-state joining technology for metals. It shows no solidification-related joint imperfections which makes it utmost suitable for hard-to-weld highly alloyed aerospace aluminium grades, like AA 2xxx and AA 7xxx. These alloys are often cladded with a thin layer of pure aluminium for corrosion protection. Friction stir welding of such materials requires removal of the clad layer prior to welding to prevent weakening of the joint by the soft clad material. This leaves the welded region vulnerable to corrosion after the joining process. Post-weld restoration of the clad layer is required to restore the protective action of the clad layer and as such to enhance the life expectancy of the welded construction. In this work the deposition of thin layers of pure aluminium on AA 2xxx and AA 7xxx alloys is studied employing an innovative FSW tool. The tool shoulder is equipped with strategically placed internal channels that allow delivery of filler type of material into the weld zone. Depending on the channel architecture used, filler material can be deposited on top of the work piece surface and/or mixed with the work piece surface region. The cladding is done in the solid state avoiding many problems with solidification and interface reactivity often observed with other surface modification techniques, such as laser surface engineering, plasma spraying or casting. Here, the filler material is deposited on top of the work piece; the modified tool is not equipped with a tool pin. The work comprises an in depth study of the influence of process conditions on the microstructural changes in the underlying work piece and on the quality of the bonding of the clad material (99.5 % aluminium) to the work piece material. Apart from the usual process conditions, such as tool rotation speed, translation speed, down force and tool angle also the delivery pressure and rate of the filler supply system can be varied. The influence of the usual process conditions on the microstructure of the underlying work piece is similar to that observed with “traditional” FSW. Changes in hardness can be related to the amount of heat generated by the welding process. Shape and dimensions of the microstructural zones found are typical for welds made without a tool pin. The effect of the small amount of clad material deposited on top of the work piece on the temperature distribution is small. The amount of heat required to heat it up is negligible to the heat required to heat up the work piece and the tool. The quality of the bonded clad layer is dependent on the amount of heat and plastic deformation generated at the interfaces between the tool, the filler material and the work piece. Tool angle, tool shape and supply rate of the filler supply system determine the layer thickness.

Modeling of the Austenite-Martensite Transformation in Stainless and TRIP Steels

The transformation of austenite to martensite is a dominant factor in the description of the constitutive behavior during forming of TRIP assisted steels. To predict this transformation different models are currently available. In this paper the transformation is regarded as a stress induced process based on the thermodynamic action of the local stresses during transformation. A threshold for the thermodynamic action, above which transformation will occur, can be easily measured in a properly instrumented tensile test. The martensitic transformation is a diffusionless lattice shear. It is characterized by a habit plane normal n and a shear vector m, which are both defined with respect to the austenite lattice coordinate system. Therefore the thermodynamic action in each material grain strongly depends on the orientation of the grain with respect to the applied stress. Uniaxial tensile tests on both a non-textured austenitic stainless steel and one with a strong crystallographic texture were performed in both the rolling and the transverse directions. Both materials show mechanically induced phase transformation from austenite to martensite. When a strong texture is present in the austenite, differences between transformations during deformation in different directions can be observed clearly. The stress induced transformation theory, in combination with the textures measured before and after deformation, is used to explain and model the difference in transformation behavior when straining in various directions. During deformation the texture changes. This can have consequences for modeling of the transformation during non-proportional deformation.

Free surface modeling of contacting solid metal flows employing the ALE formulation

In this paper, a numerical problem with contacting solid metal flows is presented and solved with an arbitrary Lagrangian-Eulerian (ALE) finite element method. The problem consists of two domains which mechanically interact with each other. For this simulation a new free surface boundary condition is implemented for remeshing of the boundary elements. It uses explicitly that the integral of the convective velocity along a boundary element remains zero. Steady state solutions are obtained only if the integral of the convective velocities along each free surface boundary element remains zero. The new remeshing option for the free surface is tested on a cladding problem employing friction stir welding (FSW). The problem describes two elasto-viscoplastic aluminum material flows which mechanically interact.

A Gradient-Based Strategy for the Optimization of Stiffened Composite Structures Subject to Multiple Load Cases and Multiple Failure Criteria

This work aims at investigating the applicability of the level-set based thickness optimization method, earlier proposed by the authors, to a realistic structure. The design has to have sufficient stiffness and strength while the structural mass is minimized. The concerned composite structure is subjected to multiple load cases. The proposed method guarantees the fulfillment of the design guidelines, namely symmetry, covering ply, disorientation, percentage rule, balance, and contiguity of the layup. The stiffeners divide a composite structure into several smaller panels. The manufacturability of a resulting design is guaranteed as plies are continuous among adjacent panels (the design is blended). The proposed method is successfully applied to the mass minimization problem of the stiffened top and bottom skin of a wing torsion box. The structure, subject to two load cases, is optimized where local buckling and allowable strain are the constraints of the problem.

Numerical Forming Simulations and Optimisation in Advanced Materials

With the introduction of new materials as high strength steels, metastable steels and fibre reinforced ncomposites, the need for advanced physically valid constitutive models arises. In finite deformation problems nconstitutive relations are commonly formulated in terms the Cauchy stress as a function of the elastic Finger tensor and nan objective rate of the Cauchy stress as a function of the rate of deformation tensor. For isotropic materials models this nis rather straightforward, but for anisotropic material models, including elastic anisotropy as well as plastic anisotropy, nthis may lead to confusing formulations. It will be shown that it is more convenient to define the constitutive relations in nterms of invariant tensors referred to the deformed metric. Experimental results are presented that show new ncombinations of strain rate and strain path sensitivity. An adaptive through- thickness integration scheme for plate nelements is developed, which improves the accuracy of spring back prediction at minimal costs. A procedure is ndescribed to automatically compensate the CAD tool shape numerically to obtain the desired product shape. Forming nprocesses need to be optimized for cost saving and product improvement. Until recently, a trial-and-error process in the nfactory primarily did this optimization. An optimisation strategy is proposed that assists an engineer to model an noptimization problem that suits his needs, including an efficient algorithm for solving the problem.