Lionel Fourment

Error Estimation And Accurate Mapping Based ALE Formulation For 3D Simulation Of Friction Stir Welding

An Arbitrary Lagrangian Eulerian (ALE) formulation is developed to simulate the different stages of the Friction Stir Welding (FSW) process with the FORGE3® F.E. software. A splitting method is utilized: a) the material velocity/pressure and temperature fields are calculated, b) the mesh velocity is derived from the domain boundary evolution and an adaptive refinement criterion provided by error estimation, c) P1 and P0 variables are remapped. Different velocity computation and remap techniques have been investigated, providing significant improvement with respect to more standard approaches. The proposed ALE formulation is applied to FSW simulation. Steady state welding, but also transient phases are simulated, showing good robustness and accuracy of the developed formulation. Friction parameters are identified for an Eulerian steady state simulation by comparison with experimental results. Void formation can be simulated. Simulations of the transient plunge and welding phases help to better understand t...

Efficient formulations for quasi-steady processes simulations: Multi-mesh method, arbitrary Lagrangian or Eulerian formulation and free surface algorithms

Numerical simulation of forming processes like rolling may require prohibitive computational times. Calculations can be speeded-up by different recently developed numerical methods. If the process can be considered as steady, then the steady-state can be directly computed using an iterative approach based on free surface corrections: the domain shape is computed alternately with the resolution of mechanical equations. In the frame of 3D unstructured meshes, complex shapes and parallel calculations, it is proposed to use a global formulation based on a least square functional with an upwind shift for taking into account contact conditions. It is shown to converge from any initial shape of the domain. If the process is only quasi-steady, then the computational cost can be reduced by considering a smaller part of the domain, which is made possible by an Arbitrary Eulerian or Lagrangian formulation. A general formulation is developed, which applies to a wide range of forming processes. In rolling, the observe...

An upwind least square formulation for free surfaces calculation of viscoplastic steady-state metal forming problems

Despite using very large parallel computers, numerical simulation of some forming processes such as multi-pass rolling, extrusion or wire drawing, need long computation time due to the very large number of time steps required to model the steady regime of the process. The direct calculation of the steady-state, whenever possible, allows reducing by 10–20 the computational effort. However, removing time from the equations introduces another unknown, the steady final shape of the domain. Among possible ways to solve this coupled multi-fields problem, this paper selects a staggered fixed-point algorithm that alternates computation of mechanical fields on a prescribed domain shape with corrections of the domain shape derived from the velocity field and the stationary condition v.nxa0=xa00. It focuses on the resolution of the second step in the frame of unstructured 3D meshes, parallel computing with domain partitioning, and complex shapes with strong contact restraints. To insure these constraints a global finite elements formulation is used. The weak formulation based on a Galerkin method of the v.nxa0=xa00 equation is found to diverge in severe tests cases. The least squares formulation experiences problems in the presence of contact restraints, upwinding being shown necessary. A new upwind least squares formulation is proposed and evaluated first on analytical solutions. Contact being a key issue in forming processes, and even more with steady formulations, a special emphasis is given to the coupling of contact equations between the two problems of the staggered algorithm, the thermo-mechanical and free surface problems. The new formulation and algorithm is finally applied to two complex actual metal forming problems of rolling. Its accuracy and robustness with respect to the shape initialization of the staggered algorithm is discussed, and its efficiency is compared to non-steady simulations.

Application of multi-grid method on the simulation of incremental forging processes

Numerical simulation becomes essential in manufacturing large part by incremental forging processes. It is a splendid tool allowing to show physical phenomena however behind the scenes, an expensive bill should be paid, that is the computational time. That is why many techniques are developed to decrease the computational time of numerical simulation. Multi-Grid method is a numerical procedure that permits to reduce computational time of numerical calculation by performing the resolution of the system of equations on several mesh of decreasing size which allows to smooth faster the low frequency of the solution as well as its high frequency. In this paper a Multi-Grid method is applied to cogging process in the software Forge 3. The study is carried out using increasing number of degrees of freedom. The results shows that calculation time is divide by two for a mesh of 39,000 nodes. The method is promising especially if coupled with Multi-Mesh method.

Multi-Objective Optimization of Metal Forming Processes Based on the Kalai and Smorodinsky Solution

The Game Theory is a good method for finding a compromise between two players in a bargaining problem. The Kalai and Smorodinsky (K-S) method is a solution the bargaining problem where players make decisions in order to maximize their own utility, with a cooperative approach. Interesting applications of the K-S method can be found in engineering multi-objective optimization problems, where two or more functions must be minimized. The aim of this paper is to develop an optimization algorithm aimed at rapidly finding the Kalai and Smorodinsky solution, where the objective functions are considered as players in a bargaining problem, avoiding the search for the Pareto front. The approach uses geometrical consideration in the space of the objective functions, starting from the knowledge of the so-called Utopia and Nadir points. An analytical solution is proposed and initially tested with a simple minimization problem based on a known mathematical function. Then, the algorithm is tested (thanks to a user friendly routine built-in the finite element code Forge®) for FEM optimization problem of a wire drawing operation, with the objective of minimizing the pulling force and the material damage. The results of the simulations are compared to previous works done with others methodologies.

Computational Strategies for Speeding-Up F.E. Simulations of Metal Forming Processes

An overview of various numerical methods developed for speeding-up computations is presented in the field of the bulk material forming under solid state, which is characterized by complex and evolving geometries requiring frequent remeshings and numerous time increments. These methods are oriented around the axis that constitutes the meshing problem. The multi-mesh method allows to optimally solve several physics involved on the same domain, according to its finite element discretization with several different meshes, for example in the cogging or cold pilgering processes. For quasi steady-state problems and problems with quite pronounced localization of deformation, such as Friction Stir Welding (FSW) or High Speed Machining, an Arbitrary Lagrangian or Eulerian formulation (ALE) with mesh adaptation shows to be imperative. When the problem is perfectly steady, as for the rolling of long products, the direct search for the stationary state allows huge accelerations. In the general case, where no process specificity can be used to solve the implicit equations, the multigrid method makes it possible to construct a much more efficient iterative solver, which is especially characterized by an almost linear asymptotic cost.