Modelling of aluminium sheet forming at elevated temperatures

The formability of Al–Mg sheet can be improved considerably, by increasing the temperature. By heating the\ud sheet in areas with large shear strains, but cooling it on places where the risk of necking is high, the limiting drawing ratio\ud can be increased to values above 2.5. At elevated temperatures, the mechanical response of the material becomes strain rate\ud dependent. To accurately simulate warm forming of aluminium sheet, a material model is required that incorporates the\ud temperature and strain-rate dependency. In this paper simulations are presented of the deep drawing of a cylindrical cup,\ud using shell elements. It is demonstrated that the familiar quadratic Hill yield function is not capable of describing the plastic\ud deformation of aluminium. Hardening can be described successfully with a physically based material model for temperatures\ud up to 200 �C. At higher temperatures and very low strain rates, the flow curve deviates significantly from the mode

Prediction of sheet necking with shell finite element models

In sheet forming simulations, the prediction of localised necking is an important goal. A pragmatic\ud approach is to compare calculated principal strains with a forming limit curve (FLC). However, the FLC’s\ud are known to depend on the strain path and most experimental FLC’s are determined for straight deformation\ud paths. Localisation can also be determined numerically with a Marciniak–Kuczynski analysis (M–K). It is\ud recognised that a FEM analysis with shell elements resembles the M–K analysis very much. For uniform\ud deformations a band with slightly reduced thickness is necessary to trigger localisation. In practical forming\ud conditions, however, the non-uniformity of the process automatically triggers localisation and an arbitrary initial\ud imperfection is not needed. FEM models have the additional benefit that boundary conditions, non-proportional\ud deformation and e.g. friction with the tools are completely included

Efficient implicit FEM simulation of sheet metal forming

For the simulation of industrial sheet forming processes, the time discretisation is\ud one of the important factors that determine the accuracy and efficiency of the algorithm. For\ud relatively small models, the implicit time integration method is preferred, because of its inherent\ud equilibrium check. For large models, the computation time becomes prohibitively large and, in\ud practice, often explicit methods are used. In this contribution a strategy is presented that enables\ud the application of implicit finite element simulations for large scale sheet forming analysis.\ud Iterative linear equation solvers are commonly considered unsuitable for shell element models.\ud The condition number of the stiffness matrix is usually very poor and the extreme reduction\ud of CPU time that is obtained in 3D bulk simulations is not reached in sheet forming simulations.\ud Adding mass in an implicit time integration method has a beneficial effect on the condition number.\ud If mass scaling is used—like in explicit methods—iterative linear equation solvers can lead\ud to very efficient implicit time integration methods, without restriction to a critical time step and\ud with control of the equilibrium error in every increment. Time savings of a factor of 10 and more\ud can easily be reached, compared to the use of conventional direct solvers.\ud

An algorithm to make your implicit code competitive with an explicit code for large scale problems

To intensify the use of implicit finite element codes for solving large scale problems, the computation\ud time of these codes has to be decreased drastically. A method is developed which decreases the\ud computational time of implicit codes by factors. The method is based on introducing inertia effects into the\ud implicit finite element code in combination with the use of iterative solvers. Deep drawing simulations are\ud performed to investigate the performance of the dynamics contributions in combination with iterative solvers.\ud It is concluded that the computation time can be decreased by a factor 5-10

Deterministic and robust optimisation strategies for metal forming proceesses

Product improvement and cost reduction have always been important goals in the metal forming industry. The rise of\ud Finite Element simulations for metal forming processes has contributed to these goals in a major way. More recently, coupling\ud FEM simulations to mathematical optimisation techniques has shown the potential to make a further contribution to product\ud improvement and cost reduction.\ud Mathematical optimisation consists of the modelling and solving of optimisation problems. Although both the\ud modelling and the solving are essential for successfully optimising metal forming problems, much of the research published until\ud now has focussed on the solving part, i.e. the development of a specific optimisation algorithm and its application to a specific\ud optimisation problem for a specific metal forming process.\ud In this paper, we propose a generally applicable optimisation strategy which makes use of FEM simulations of metal\ud forming processes. It consists of a structured methodology for modelling optimisation problems related to metal forming.\ud Subsequently, screening is applied to reduce the size of the optimisation problem by selecting only the most important design\ud variables. Screening is also utilised to select the best level of discrete variables, which are in such a way removed from the\ud optimisation problem. Finally, the reduced optimisation problem is solved by an efficient optimisation algorithm. The strategy is\ud generally applicable in a sense that it is not constrained to a certain type of metal forming problems, products or processes. Also\ud any FEM code may be included in the strategy.\ud However, the above strategy is deterministic, which implies that the robustness of the optimum solution is not taken\ud into account. Robustness is a major item in the metal forming industry, hence we extended the deterministic optimisation\ud strategy in order to be able to include noise variables (e.g. material variation) during optimisation. This yielded a robust\ud optimisation strategy that enables to optimise to a robust solution of the problem, which contributes significantly to the industrial\ud demand to design robust metal forming processes. Just as the deterministic optimisation strategy, it consists of a modelling,\ud screening and solving stage.\ud The deterministic and robust optimisation strategies are compared to each other by application to an analytical test\ud function. This application emphasises the need to take robustness into account during optimisation, especially in case of\ud constrained optimisation. Finally, both the deterministic and the robust optimisation strategies are demonstrated by application to\ud an industrial hydroforming example

Stable incremental deformation of a strip to high strain

This paper presents the effect of combined stretching and bending on the achieved strain in\ud incremental sheet forming ISF. A simple two dimensional model of strip undergoing stretching and\ud travelling three point bending in cyclic form is used. The numerical model presents the effect of the\ud ratio of stretching velocity to roll-set speed on the achieved strain and its distributio

Advanced sheet metal forming

Weight reduction of vehicles can be achieved by using high strength steels or aluminum. The formability of aluminum can be improved by applying the forming process at elevated temperatures. A thermo-mechanically coupled material model and shell element is developed to accurately simulate the forming process at elevated temperatures. The use of high strength steels enlarges the risk of wrinkling. Wrinkling indicators are developed which are used to drive a local mesh refinement procedure to be able to properly capture wrinkling. Besides, to intensify the use of implicit finite element codes for solving large-scale problems, a method is developed which decreases the computational time of implicit codes by factors. The method is based on introducing inertia effects into the implicit finite element code. It is concluded that the computation time is decreased by a factor 5-10 for large-scale problems

A metamodel based optimisation algorithm for metal forming processes

Cost saving and product improvement have always been important goals in the metal\ud forming industry. To achieve these goals, metal forming processes need to be optimised. During\ud the last decades, simulation software based on the Finite Element Method (FEM) has significantly\ud contributed to designing feasible processes more easily. More recently, the possibility of\ud coupling FEM to mathematical optimisation algorithms is offering a very promising opportunity\ud to design optimal metal forming processes instead of only feasible ones. However, which\ud optimisation algorithm to use is still not clear.\ud In this paper, an optimisation algorithm based on metamodelling techniques is proposed\ud for optimising metal forming processes. The algorithm incorporates nonlinear FEM simulations\ud which can be very time consuming to execute. As an illustration of its capabilities, the\ud proposed algorithm is applied to optimise the internal pressure and axial feeding load paths\ud of a hydroforming process. The product formed by the optimised process outperforms products\ud produced by other, arbitrarily selected load paths. These results indicate the high potential of\ud the proposed algorithm for optimising metal forming processes using time consuming FEM\ud simulations

Improvement of implicit finite element code performance in deep drawing simulations by dynamics contributions

To intensify the use of implicit finite element codes for solving large scale problems, the computation time of these codes has to be decreased drastically. A method is developed which decreases the computational time of implicit codes by factors. The method is based on introducing inertia effects into the implicit finite element code in combination with the use of iterative solvers. Another advantage of introducing inertia effects into an implicit finite element code is that it stabilizes the computation, especially when the problem is under-constrained. The dynamics contributions are successfully implemented for both the plane strain element (only displacement d.o.f.) and the Mindlin shell element (displacement and rotational d.o.f.). Deep drawing simulations are performed to investigate the performance of the dynamics contributions in combination with iterative solvers. It is concluded that the computation time can be decreased by a factor 5–10