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A major dilemma faced in the nuclear industry is repair of stainless steel reactor components that have been exposed to neutron irradiation. When conventional fusion welding is used for repair, intergranular cracks develop in the heat-affected zone (HAZ). Friction stir processing (FSP), which operates at much lower peak temperatures than fusion welding, was studied as a crack repair method for irradiated 304L stainless steel. A numerical simulation of the FSP process in 304L was developed to predict temperatures and recrystallized grain size in the stir zone. The model employed an Eulerian finite element approach, where flow stresses for a large range of strain rates and temperatures inherent in FSP were used as input. Temperature predictions in three locations near the stir zone were accurate to within 4%, while prediction of welding power was accurate to within 5% of experimental measurements. The predicted recrystallized grain sizes ranged from 7.6 to 10.6 μm, while the experimentally measured grains sizes in the same locations ranged from 6.0 to 7.6 μm. The maximum error in predicted recrystallized grain size was about 39%, but the associated stir zone hardness from the predicted grain sizes was only different from the experiment by about 10%.

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The present work reviews the development of a technique to reduce the computation time of three-dimensional numerical simulations of forming processes with repetitive symmetry conditions. The method has been implemented into the 3D finite element simulation software Forge3® to handle non-standard symmetry conditions named Recurrent Boundary Conditions. The theoretical framework of the method based on miscellaneous master-slave contact penalization techniques is recalled, and its extension to simulations with deformable bodies is presented. The size of the thermo-mechanical problem is reduced by enforcing boundary conditions on auto-detected periodic surfaces for both velocity and temperature fields. The resolution method coupled with high-performance parallel computing and advanced remeshing techniques makes it possible to quickly and accurately solve complex thermo-mechanical forming problems such as gear forming and forging applications processes with helical cyclic geometries.

Pushed forward by mill complexification and harder product quality requirements, the mathematical treatment has evolved into very complex, multi-coupled models: roll deformation, thermal transfer, lubrication, and oxide scales are a few examples. The diversity of rolled products and rolling mills makes rolling process modelling a vast field indeed. Beyond general, necessarily very costly models, partial descriptions are developed for more targeted goals. Three methods share the market: the Slab Method (SM), the Upper Bound Method (UBM), and the Finite Element Method (FEM). A few modelling strategies based on the above three are described, providing accurate solutions in an industry-compatible computation time: steady-state FEM modelling; faster 2D SM with large roll flattening to build thin sheet or temper rolling force models; low-cost 3D roll stack deformation package for profile/flatness of sheets; FEM results-based UBM models of width variations in the Tandem Cold Mill; post-bite profile and flatness evolution (interstand behavior); FEM description of oxide scale behavior in descaling; SM with modern lubrication modelling. Evolutions of rolling processes are questioned to point to new demands on modelling and how to answer them.

International audience; In the context of the simulation of industrial hot forming processes, the resultant time-dependent thermo-mechanical multi-field problem (v→,p,σ,ε) can be sped up by 10-50 times using the steady-state methods while compared to the conventional incremental methods. Though the steady-state techniques have been used in the past, but only on simple configurations and with structured meshes, and the modern-days problems are in the framework of complex configurations, unstructured meshes and parallel computing. These methods remove time dependency from the equations, but introduce an additional unknown into the problem: the steady-state shape. This steady-state shape x→ can be computed as a geometric correction t→ on the domain X→ by solving the weak form of the steady-state equation v→.n→(t→)=0 using a Streamline Upwind Petrov Galerkin (SUPG) formulation. There exists a strong coupling between the domain shape and the material flow, hence, a two-step fixed point iterative resolution algorithm was proposed that involves (1) the computation of flow field from the resolution of thermo-mechanical equations on a prescribed domain shape and (2) the computation of steady-state shape for an assumed velocity field. The contact equations are introduced in the penalty form both during the flow computation as well as during the free-surface correction. The fact that the contact description is inhomogeneous, i.e., it is defined in the nodal form in the former, and in the weighted residual form in the latter, is assumed to be critical to the convergence of certain problems. Thus, the notion of nodal collocation is invoked in the weak form of the surface correction equation to homogenize the contact coupling. The surface correction algorithm is tested on certain analytical test cases and the contact coupling is tested with some hot rolling problems.

International audience; Calculation time of some material forming processes is tremendously expensive which makes reducing computational time one of the most urgent challenges in this domain. Among strategies that have been developed to speed-up calculations, one of the most flexible solutions is to utilize enhanced linear solvers such as Multi-Grid algorithm. It consists in using several levels of meshes of the same domain in order to more efficiently solve the systems of equations derived from the discretized problem. The speed-up results from the efficiency of coarse meshes in computing the low frequencies of the residual while fine meshes are more efficient in reducing the high frequencies of the residual. The method is integrated in the commercial software Forge® and applied to the industrial cogging process. The obtained results show that the speed-up depends on the number of nodes; for an industrial scale mesh of 50,000 nodes, the multigrid technique allows dividing the computational time by a factor of two.

International audience; 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.

International audience; Numerical simulation of linear friction welding (LFW) of Titanium alloys is considered with the Forge® software, using a JMatPro constitutive model with the aim of supporting process design for the welding of dissimilar materials, such as Titanium and Inconel. Relying on forces and temperature experimental measurements, friction and other unknown parameters of the model have to be calibrated.

International audience; The problem of multi-objective optimization (MOP) is approached from the theoretical background of the Game Theory, which consists in finding a compromise between two rational players of a bargaining problem. In particular, the Kalai and Smorodinsky (K-S) model offers a balanced and attractive solution resulting from cooperative players. This approach allows avoiding the computationally expensive and uncertain reconstruction of the full Pareto Frontier usually required by MOPs. The search for the K-S solution can be implemented into methodologies with useful applications in engineering MOPs where two or more functions must be minimized. This paper presents an optimization algorithm aimed at rapidly finding the K-S solution where the MOP is transformed into a succession of single objective problems (SOP). Each SOP is solved by meta-model assisted evolution strategies used in interaction with an FEM simulation software for metal forming applications. The proposed method is first tested and demonstrated with known mathematical multi-objective problems, showing its ability to find a solution lying on the Pareto Frontier, even with a largely incomplete knowledge of it. The algorithm is then applied to the FEM optimization problem of wire drawing process with one and two passes, in order to simultaneously minimize the pulling force and the material damage. The K-S solutions are compared to results previously suggested in literature using more conventional methodologies and engineering expertise. The paper shows that K-S solutions are very promising for finding quite satisfactory engineering compromises, in a very efficient manner, in metal forming applications.

International audience; For many material forming processes steady-state formulations allows reducing numerical simulation time by an order of magnitude with respect to more conventional approaches. In the presented approach, the steady regime is iteratively computed by a free surface algorithm that alternates computations of the metal forming flow over a known geometry and known contact surfaces, with computations of domain corrections to satisfy free and contact surface conditions. Several weak formulations of the second problem equations are investigated to get a robust algorithm suitable for parallel computations with unstructured meshes. Analytical problems show the necessity to introduce an upwind shift within these weak formulations. Contact inequations enforces this necessity by requiring a more dramatic shift. A robust and accurate algorithm is so obtained, which is successfully applied to 3D complex metal forming processes like rolling. In the wire drawing application, computational time is reduced by more than fifteen with respect to the incremental calculation of the steady-state.

International audience; The numerical simulation of Friction Stir Welding (FSW) is carried out using an Arbitrary Lagrangian or Eulerian (ALE) formulation. Its computational cost is reduced by appealing to the parallel version recently developed within the Forge software. The accuracy of the numerical model is increased by enhancing the state variables remapping algorithm and by introducing a better suited time integration scheme based on the cylindrical coordinates. The pin and shoulder threads are modelled in order to account for this crucial phenomenon on material heating. The developed model provides quite satisfactory temperature fields for the FSW of a butt joint of 6061 aluminium, as compared to experimental results. It allows simulating welding defects such as tunnels holes or flashes. The study then focuses on numerical simulations and experimental measurements of a lap joint of a 7175 aluminium sheet on a 2024 aluminium sheet for an aeronautical application.

International audience; In the field of materials forming processes, the use of simulation coupled with optimization is a powerful numerical tool to support design in industry and research. The finite element software Forge®, a reference in the field of the two-dimensional and three-dimensional simulation of forging processes, has been coupled to an automatic optimization engine. The optimization method is based on meta-model assisted evolutionary algorithm. It allows solving complex optimization problems quickly. This paper is dedicated to a specific application of optimization, inverse analysis. In a first stage, a range of reverse analysis applications are considered such as material rheological and tribological characterization, identification of heat transfer coefficients and, finally, the estimation of Time Temperature Transformation curves based on existing Continuous Cooling Transformation diagrams for steel quenching simulation. In a second part, a novel inverse analysis application is presented in the field of cold sheet forming, the identification of the material anisotropic constitutive parameters that allow matching with the final shape of the component after stamping. The advanced numerical methods used in this kind of complex simulations are described along with the obtained optimization results. This article shows that automatic optimization coupled with Forge® can solve many inverse analysis problems and is a valuable tool for supporting development and design of metals forming processes.

International audience; 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.

International audience; In order to support the design of such a complex process like Friction Stir Welding (FSW) for the aeronautic industry, numerical simulation software requires (1) developing an efficient and accurate Finite Element (F.E.) formulation that allows predicting welding defects, (2) properly modeling the thermo-mechanical complexity of the FSW process and (3) calibrating the F.E. model from accurate measurements from FSW experiments. This work uses a parallel ALE formulation developed in the Forge® F.E. code to model the different possible defects (flashes and worm holes), while pin and shoulder threads are modeled by a new friction law at the tool / material interface. FSW experiments require using a complex tool with scroll on shoulder, which is instrumented for providing sensitive thermal data close to the joint. Calibration of unknown material thermal coefficients, constitutive equations parameters and friction model from measured forces, torques and temperatures is carried out using two F.E. models, Eulerian and ALE, to reach a satisfactory agreement assessed by the proper sensitivity of the simulation to process parameters.

International audience; In metal forming simulations, the transfer of data from one mesh to another can be very often required such as, in ALE formulation at each time step or in Lagrangian formulation at each remeshing step. Its accuracy is one of the main concerns for researchers, since the accumulation of generated diffusion can lead to larger numerical error and create convergence problems. Since 1992, the Super convergent Patch Recovery method (SPR) introduced by Zienkiewicz & Zhu [1], was a major breakthrough for the methods to estimate errors in FE solution. Later, it has also been used to recover nodal fields from integration points, in order to transfer data between two meshes [10]. The original method raises some difficulties to treat the domain boundaries. They have not quite properly been handled, in particular in the frame of parallel implementation, despite the fact that, surface phenomena, such as contact and friction, play such an important role in metal forming applications. In the present paper, it is presented a modified iterative SPR method which deals with boundary points with the same order of accuracy as the interior points. It does not require increasing the patch size and it is easier to implement in parallel environment. Also, when interpolating the field on new mesh, a new and consistent technique (P0+ transport) of enriched field has been used. It involves building a P1+ field by mixing the recovered SPR nodal field with the known field at integration points. Results are presented in form of convergence rate and L2 error norm, for several analytical functions for a SPR based transfer operator against a simple volumetric based transfer operator, before being applied to an actual metal forming problem. All computations presented here have been done by using four processors in parallel environment.

International audience; Coupling of evolutionary algorithms (EA) with meta-models (MM) is used to investigate the concept of the optimal die semi-angle in wire drawing. Traditional process design by minimization of the wire drawing force highlights an optimal die angle which increases with friction factor and reduction ratio. When wire drawing optimization is applied on the Latham and Cockcroft damage criterion, an optimal die semi-angle no longer appears: in this mono-objective optimization, the lowest industrially achievable die angle is recommended. Thanks to EA-MM coupling, multi-objective optimizations have been performed and the Pareto optimal front has been precisely plotted so as to find the best compromise. Simultaneous optimization of damage and wire drawing force suggests a refined vision of the optimal die semi-angle concept. Choosing a lower angle than the traditional optimum allows damage to be decreased without a significant increase of the drawing force. However, it is shown that a die semi-angle slightly above the optimum should be selected, for fear of friction drift; this explains the rather high traditional value of the angle.

During the last decades, simulation software based on the Finite Element Method (FEM) has significantly contributed to the design of feasible forming processes. Coupling FEM to mathematical optimization algorithms offers a promising opportunity to design optimal metal forming processes rather than just feasible ones. In this paper Sequential Approximate Optimization (SAO) for optimizing forging processes is discussed. The algorithm incorporates time-consuming nonlinear FEM simulations. Three variants of the SAO algorithm--which differ by their sequential improvement strategies--have been investigated and compared to other optimization algorithms by application to two forging processes. The other algorithms taken into account are two iterative algorithms (BFGS and SCPIP) and a Metamodel Assisted Evolutionary Strategy (MAES). It is essential for sequential approximate optimization algorithms to implement an improvement strategy that uses as much information obtained during previous iterations as possible. If such a sequential improvement strategy is used, SAO provides a very efficient algorithm to optimize forging processes using time-consuming FEM simulations.

Pour appliquer les algorithmes d’optimisation multi-objectifs a des problemes de mise en forme des metaux tres couteux en temps de calcul, nous etudions le couplage de l’algorithme genetique NSGA-II propose par Deb a un metamodele inspire de la methode des differences finies sans maillage de Liszka et Orkisz. Nous soulignons l’importance d’ameliorer iterativement le metamodele au cours des iterations d’optimisation, et la possibilite de determiner avec precision des fronts optimaux de Pareto des problemes multi-objectifs etudies en moins d’une centaine de calculs.

International audience; Multiobjective optimization problems are considered in the field of nonsteady metal forming processes, such as forging or wire drawing. The Pareto optimal front of the problem solution set is calculated by a Genetic Algorithm. In order to reduce the inherent computational cost of such algorithms, a surrogate model is developed and replaces the exact the function simulations. It is based on the Meshless Finite Difference Method and is coupled to the NSGAII Evolutionary Multiobjective Optimization Algorithm, in a way that uses the merit function. This function offers the best way to select new evaluation points: it combines the exploitation of obtained results with the exploration of parameter space. The algorithm is evaluated on a wide range of analytical multiobjective optimization problems, showing the importance to update the metamodel along with the algorithm convergence. The application to metal forming multiobjective optimization problems show both the efficiency of the metamodel based algorithms and the type of practical information that can be derived from a multiobjective approach.

International audience; The accurate 3D finite element simulation of the Friction Stir Welding (FSW) process requires a proper knowledge of both material and interface behaviors, but friction, the key phenomenon of this process, is quite difficult to model and identify. According to the extreme encountered conditions and the highly coupled nature of the material flow, simple tribological tests are not representative enough, so the welding process itself has been utilized in most analyses of the literature, although its complexity has led to use simplified numerical models and approaches. The recent development of more accurate 3D simulation software, which allows modeling the entire complexity of the FSW process, makes it possible to follow a much more rigorous inverse analysis (or calibration) approach. FSW trials are conducted on an Al 6061 aluminum plate with an unthreaded concave tool. Forces and tool temperatures are accurately recorded at steady welding state, for different welding speeds. The numerical simulations are based on an Arbitrary Lagrangian Eulerian (ALE) formulation that has been implemented in the Forge3® F.E. software. The main feature of the numerical approach is to accurately compute the contact and frictional surface between the plate and the tool. A first study using Norton's friction model show the great sensitivity of welding forces and tool temperatures to friction coefficients, the need to take into account the changes brought to the contact surface by slight friction variations (thanks to the ALE formulation), the possibility to get very accurate calibrations on forces, and the impossibility to properly render the tool temperature profile. On the other hand, the use of Coulomb's friction model allows obtaining realistic temperature profiles and so calibrating a friction coefficient that offers an excellent agreement with experiments, on forces as much as on tool temperatures, for various welding speeds.

International audience; This paper studies efficient techniques to find the optimal set of solutions (Pareto front) for multiobjective optimization problems in the context of time expensive evaluation of functions. These techniques make use of a meta-model based on the Meshless Finite Difference Method (MFDM) coupled with evolutionary Multi-Objective algorithm (here: NSGA-II) in order to minimize the time consuming evaluations and to achieve a faster convergence to the Pareto front. The different studied methods differ in the choice of master points, the evolution of the meta-model, and the updating of elitism. They are studied and compared on several analytical functions, with only 100 exact evaluations of the objective function. The obtained results show the efficiency of these techniques.

International audience; On introduit deux algorithmes hybrides d'optimisation évolutionnaire basés sur le principe d'approximation du critère en se servant d'un nombre limité d'évaluations exactes de la fonction et de son gradient. Le premier algorithme utilise un ansatz discontinu avec classification de la génération courante. Le second utilise l'interpolation de Liszka-Orkisz et garde mémoire des évaluations exactes des générations précédentes. Ces deux méthodes sont appliquées à un problème 3D d'optimisation de forme en forgeage, avec un critère combinant l'énergie totale de forgeage et une fonction de mesure de défaut. On présente des resultants numériques qui illustrent l'efficacité de ces algorithmes.

International audience; 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.n = 0. 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.n = 0 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.

International audience; The aim of this paper is to study the simulation of cogging process using a thermo-mechanical partitioned algorithm. The thermal and mechanical problems are solved separately. The mechanical problem is based on the balance equation whereas the thermal problem is based on the heat equation. The two physics are coupled trough the mechanical parameters that depends on the thermal problem and vice versa. The results obtained using the software Forge3 show that the mechanical deformation is high inside the zone of deformation and negligible outside whereas the temperature is high overall the mesh with a gradient at the zone of contact between the dies and the work piece.

International audience; 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.

International audience; Friction stir welding on aluminum alloy is seen as an alternative solution to riveting 2024 and 7075 aluminum alloys pieces in order to lighten aircraft structure. On these alloys, mechanical properties are linked to structural hardening due to solid state precipitation. A coupling approach is proposed in order to manage the precipitates distribution evolution taking place during the process and predict final properties. At macro-scale, a model is used to get the thermal evolution in the different parts of the welded zone. At micro-scale, a time-efficient precipitation simulation is developed based on a reliable thermodynamic description. A particle size distribution approach (PSD) is proposed to predict the nucleation, growth, dissolution and coarsening of stable and metastable phases. An accurate yield strength model is applied on the final distribution. Calibration is performed on differential scanning calorimetry studies (DSC), hardening test and tensile tests for both isothermal, non-isothermal and weld samples.

International audience; The problem of contact between a part and a tool or between two deforming bodies is analysed in view of metal forming processes. For simplicity, only the case of viscoplastic materials is considered. The velocity formulation is presented, with different time integration schemes. The contact with a rigid tool is considered first and various forms of contact formulations are described: nodal contact, integral formulation with a penalty or with a Lagrange multiplier method. Time integration is considered which results in various explicit or implicit contact formulations. Special attention is paid to the contact between two deforming bodies or to the self contact when a fold is generated in the workpiece.

International audience; Le procédé de soudage par friction malaxage (FSW) permet le soudage à l’état solide d’alliages d’aluminium sans apport de matière et sans présenter de défauts de fissuration à chaud. Il est développé depuis une vingtaine d’années. Il apparait ainsi être, dans le domaine aéronautique, une alternative intéressante au rivetage, en conduisant à un allègement des structures. La garantie d’une tenue mécanique fiable, dans le cadre d’alliages à durcissement structural, nécessite de connaitre l’évolution des mécanismes de précipitation. La simulation représente une opportunité d’étudier ces évolutions, à travers l’étude des processus de germination, croissance, dissolution et coalescence des précipités. Le modèle proposé dans cette étude est un modèle de classe préconisé pour les traitements anisothermes et développé par Myhr et Grong. Il permet de simuler l’ensemble des phénomènes caractéristiques de la précipitation. Ce modèle est couplé au logiciel Thermocalc de calcul des équilibres thermodynamiques, et appliqué à l’étude de l’évolution de la précipitation de la phase S, lors du soudage FSW des alliages AA2024. Une calibration préalable de ce modèle est effectuée grâce aux résultats expérimentaux obtenus via une analyse DSC sur des échantillons prétraités. La simulation de ces essais conduit également à valider le modèle, en prédisant l’ensemble des évolutions des flux de chaleur attendues. Cette validation est étendue pour différents traitements anisothermes. Dans un second temps, le modèle est couplé à la simulation de l’évolution thermomécanique de pièces soudées, dans le cadre d’un suivi de particules. L’évolution des différents cellules du modèle, correspondant à des évolutions thermiques spécifiques (Fig1) permet de cartographier et prédire l’état de précipitation afin d’en déduire les propriétés mécaniques finales du joint soudé

International audience; The basic formulation for finite element modeling of metal forming processes is briefly recalled with the aim of treating the case of multi body interactions. This situation occurs when the tools are considered as deformable, when the work-piece includes several materials or when the physical structure is analyzed at the micro scale. The classical approach utilizes separate meshes for each body and the contact is enforced using different numerical methods: the complete coupling, the master and slave approach and a quasi-symmetrical formulation. The single mesh method with different constitutive equations corresponding to each material is more computationally effective, but its use is restricted to the cases when the contact between the different bodies does not evolve. Finally the Euler formulation can be used with a level set method for the description of the interfaces between different materials and its application to recrystallization for example.

International audience; The 3D finite element simulations of processes like multi-pass rolling or drawing often result into exorbitant computational times that make the numerical approach almost infeasible while only the “stationary” step of the process is actually of interest for the industry. Therefore, it can be advantageously simulated by resorting to steady-state formulations which allows reducing the calculation time by, at least, an order of magnitude with respect to more conventional methods where the steady regime is incrementally calculated. A general and robust formulation is developed; it is suitable for parallel computing, compatible with unstructured meshes and general enough to apply to a wide range of forming processes. It consists in alternatively resolving the “simple” steady-state material forming problem for a given domain geometry and then computing the domain corrections that allow satisfying the free surface condition. Within the “simple forming problem”, a Streamline Upwind Petrov Galerkin (SUPG) method is used to integrate the state variables along the streamlines. For the domain geometry correction, a Least Squares formulation with an Upwind shift is introduced. The two resolutions are coupled by the contact equations. This method is applied to several metal forming problems such as 3D rolling and drawing. Results show the high efficiency of the method with respect to an incremental resolution. Computational time is reduced by a factor ranging between 20 and 30. Results are as accurate as with an incremental method. Convergence is always reached whatever the initial geometry of the domain at the beginning of the iterative algorithm.

International audience; A Multi-Mesh Multi-Physics (MMMP) method is developed to reduce the very long computational time required for simulating incremental forming processes such as cogging or ring rolling. It consists in using several finite element meshes on the same domain to solve the different physics of the problem. A reference mesh is used to accurately store the results and history variables, while the different computational meshes are optimized to solve each physic of the problem. The MMMP algorithm consists in two main key-steps: the generation of the different unstructured meshes and the data transfer between the meshes. The accuracy of the method is supported by using meshes that are embedded by nodes. The method is applied to the simulation of the cogging metal forming process for which it shows as accurate and more than ten times faster than the standard method with a single mesh

A method for computing shape sensitivity in the frame of non-linear and non-steady-state forging is presented. Derivatives of tool geometry, velocity and state variables with respect to the shape parameters are calculated by a direct differentiation of discrete equations. Because of the important part played by the accuracy of finite element calculations, an efficient transfer method is used between meshes during remeshings and the contact algorithms are carefully differentiated. The resulting inverse design procedure is successfully applied to two industrial examples of forging of automobile parts, with fold-over and piping defects occurring during the intermediate designs. It makes it possible to suggest reasonable preform shapes, with or without any available knowledge of the forging process. Copyright © 2001 John Wiley & Sons, Ltd.

The problem of contact between a part and a tool or between two deforming bodies is analysed in view of metal-forming processes. For simplicity, only the case of viscoplastic materials is considered. The velocity formulation is presented. The contact with a rigid tool is considered first and various forms of contact formulations are described: nodal contact, integral or discrete formulation with a penalty or with a Lagrange multiplier method. The time integration is considered which results in various explicit or implicit contact formulations. A special attention is paid to the contact between two deforming bodies or to the self-contact when a fold is generated in the work-piece. Some 2-D and 3-D application examples illustrate the effectiveness of the proposed formulations and algorithms. Copyright © 1999 John Wiley & Sons, Ltd.

The finite element analysis of deformation of viscoplastic material involves contact between the tool and the workpiece. Here unilateral contact condition with the possibility of nodes originally in contact, losing contact subsequently, is analysed in non‐steady state forming processes. Friction has been taken into consideration through a potential function. Node to node contact is analysed and contact forces at the node are used to decide if the node is to be released. Two different algorithms are presented for treating the nodal contact condition. The one step explicit method with projections on the surface of contact was already implemented in the FORGE2® software. An implicit scheme is proposed and compared with the existing scheme. The advantages of this scheme are numerically shown by solving some examples. It is observed that the volume losses are reduced. This makes it possible to use larger time steps or increase the computational accuracy.

International audience; A contact smoothing technique is developed in the frame of metal forming applications, especially for processes where the contact area is quite small with respect to the component size. In fact, the non-smoothness of contact surfaces discretized by finite elements shows to be a key problem to the simulation accuracy. The smoothing technique is based on building a higher order quadratic interpolation of the curved surface, using the node positions and their normal vectors, as proposed by Nagata. Within a local and easy to parallelize procedure, accurate normal vectors are calculated at each node from the existing discretized surface by considering a patch of surrounding elements and following a normal voting strategy. Corner and edges are automatically detected by analysing eigenvalues of derived covariant matrix. The efficiency and reliability of the resulting contact model are assessed on several examples, such as ironing a bulk parallelepiped or a plate, before being applied to metal forming processes, such as wire drawing, rolling of long products and orbital forging

International audience; Improvements in parallel computing and adaptive remeshing have permitted to simulate a wide range of metal forming processes within few hours or days on modern multi-core workstations. However, they do not tackle the issues encountered in incremental forming processes, making them very challenging. Multi-mesh methods opens very interesting doors in this domain, making possible to take advantage of adaptive remeshing techniques (optimizing the ratio precision/cost) without its usual drawbacks (loss of information and diffusion issues).We present in this article a fully parallel Dual-Mesh implementation in the commercial FEA software FORGE®, compatible with a wide range of other FEM facilities. Speed-up larger than 4 are common for incremental forming simulations, and speed-up larger than 10 can be reached in favorable cases. Parallel efficiency is the same than for our standard computations (>80% for more than 2000 nodes per core).

We present a fully parallel Bi-Mesh method which permits to dramatically speed-up incremental forging computations by taking advantage of the localization of the deformation area. Working on two meshes at each time step, one to solve the mechanical problem and one to solve the thermal problem and store the results, permits to take advantage of recent adaptive remeshing techniques without suffering from the usual remapping issues. This method has been successfully implemented in the commercial software FORGE and is compatible with a wide range of other FEM facilities. Speed-up larger than 4 are common and speed-up larger than 10 can be reached in favorable cases.

11th International Conference on Numerical Methods in Industrial Forming Processes, NUMIFORM 2013; Shenyang; China; 6 July 2013 through 10 July 2013; International audience; 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 observed computational cost reduction varies between 2 and 7 in parallel. If an incremental Lagrangian approach is inescapable, then the multi-mesh method makes it possible to reduce the computational cost by using several meshes on the same domain. Each mesh is optimal for a particular physic of the domain. This approach provides speed-ups up to 10 in a parallel computing environment

Most forming processes are multi-stages processes. Typically, a standard forging sequence consists of three operations: Pre-forming, Blocker, Finisher, which are followed by heat-treatments. We call this the complete manufacturing chain. Simulation-wise, all these stages have to be computed one after the other; we call this the 'simulation chain'. From the optimization point of view, it is quite challenging because the process parameters which could be modified usually belong to the early stages of forming (blocker) while the quality or non-quality of the formed part only appears during the last stage (finisher or heat treatment). For any modification on the early stage, all the following stages have to be re-computed to evaluate the benefit of the modification. This is time consuming and then often people renounce to do it. In this paper, we show how the concept of 'simulation chain' used in the Forge software can be coupled with automatic optimization techniques to address this point. In order to get a ...

This paper is the second part of a two-part article about shape optimization of metal forming processes. This part is focused on numerical applications of the optimization method which has been described in the first paper. The main feature of this work is the analytical calculations of the derivatives of the objective function for a non-linear, non-steady-state problem with large deformations. The calculations are based on the differentiation of the discrete objective function and on the differentiation of the discrete equations of the forging problem. Our aim here is to show the feasibility and the efficiency of such a method with numerical examples. We recall the formulation and the resolution of the direct problem of hot axisymmetrical forging. Then, a first type of shape optimization problem is considered: the optimization of the shape of the initial part for a one-step forging operation. Two academic problems allow for checking the accuracy of the analytical derivatives, and for studying the convergence rate of the optimization procedure. Both constrained and unconstrained problems are considered. Afterwards, a second type of inverse problem of design is considered: the shape optimization of the preforming tool, for a two-step forging process. A satisfactory shape is obtained after few iterations of the optimization procedure.

We suggest a shape optimization method for a non-linear and non-steady-state metal forming problem. It consists in optimizing the initial shape of the part as well as the shape of the preform tool during a two-step forging operation, for which the shape of the second operation is known. Shapes are described using spline functions and optimal parameter values of the splines are searched in order to produce, at the end of the forging sequence, a part with a prescribed geometric accuracy, optimal metallurgical properties and for a minimal production cost. The finite element method, including numerous remeshing operations, is used for the simulation of the process. We suggest using a least-squares-type algorithm for the unconstrained optimization method (based on external penalty) for which we describe the calculation of the derivatives of the objective function. We show that it can reduce to calculations which are equivalent to the derivative calculations of steady-state processes and to evolution equations. Therefore, the computational cost of such an optimization is quite reasonable, even for complex forging processes. Lastly, in order to reduce the errors due to the numerous remeshings during the simulation, we introduce error estimation and adaptive remeshing methods with respect to the calculation of derivatives.

International audience; A finite‐element model for calculating the die temperature profile for a hot‐forging operation is presented. The workpiece is modelled as a thermo‐viscoplastic material, while the dies are considered undeformable. Heat transfer between the dies and the workpiece is modelled using an iteratively coupled, fixed‐point calculation of the temperature in each domain. Transfer of temperature boundary conditions across contact interfaces is performed for non‐coincident meshes, using a boundary integration point contact analysis. Two industrial‐type examples are presented. In the first example, the effectiveness of the transfer of the temperature boundary conditions for a non steady‐state forging process is evaluated and determined to be satisfactory. Then weakly‐ and strongly‐coupled temperature resolutions are compared. It was found that the strongly‐coupled resolution may be necessary in order to obtain reasonably accurate results. In the second example, the weakly‐coupled resolution is compared to a constant‐temperature die approach for a relatively slow forging process, which shows the influence of the die temperature on the flow of the material.

The analysis of error estimation is addressed in the framework of viscoplasticity problems, this is to say, of incompressible and non‐linear materials. Firstly, Zienkiewicz—Zhu (Z2) type error estimators are studied. They are based on the comparison between the finite element solution and a continuous solution which is computed by smoothing technique. From numerical examples, it is shown that the choice of a finite difference smoothing method (Orkisz’ method) improves the precision and the efficiency of this type of estimator. Then a Δ estimator is introduced. It makes it possible to take into account the fact that the smoothed solution does not verify the balance equations. On the other hand, it leads us to introduce estimators for the velocity error according to the L2 and L∞norms, since in metal forming this error is as important as the energy error. These estimators are applied to an industrial problem of extrusion, demonstrating all the potential of the adaptive remeshing method for forming processes.

International audience; A major dilemma facing the nuclear industry is repair or replacement of stainless steel reactor components that have been exposed to neutron irradiation. When conventional fusion welding is used for weld repair, the high temperatures and thermal stresses inherent in the process enhance the growth of helium bubbles, causing intergranular cracking in the heat-affected zone (HAZ). Friction stir processing (FSP) has potential as a weld repair technique for irradiated stainless steel, because it operates at much lower temperatures than fusion welding, and is therefore less likely to cause cracking in the HAZ. Numerical simulation of the FSP process in 304L stainless steel was performed using an Eulerian finite element approach. Model input required flow stresses for the large range of strain rates and temperatures inherent in the FSP process. Temperature predictions in three locations adjacent to the stir zone were accurate to within 4% of experimentally measure values. Prediction of recrystallized grain size at a location about 6mm behind the tool center was less accurate, because the empirical model employed for the prediction did not account for grain growth that occurred after deformation in the experiment was halted.

International audience; In this paper, we describe the numerical simulation of high rate hot forging processes, for which inertia effects are noticeable. A weakly coupled thermo-mechanical method is used to compute the deformation of the workpiece and the tool wear is also predicted. In this paper we study the influence of inertia forces in high velocity hot forging for some industrial-type problems.

1st International Conference on Computational Contact Mechanics, ICCCM09, September 16, 2009 - September 18, 2009; International audience; This paper describes the effect of tool discretization on the simulation of metal forming processes, especially for processes where the contact area is quite small with respect to the component size. The smoothing of contact surfaces, which are defined by linear triangles, is based on a higher order quadratic interpolation of the curved surface. This interpolation is derived from the node positions and their normal vectors, as proposed by Nagata. The normal vectors are calculated at each node from the existing discretized surface by considering a patch of surrounding elements and using a consistent strategy. The efficiency and reliability of the resulting contact model are assessed on several examples, such as the indentation of a parallelepiped and the drawing of a wire

http://link.aip.org/link/?APCPCS/1252/487/1; International audience; This paper describes the effect of tool discretization accuracy on the simulation of forming processes, especially for processes where the contact area is quite small with respect to the component size. For smoothing contact surface discretized by linear triangles, an algorithm is followed to develop a higher order quadratic interpolation of the curved surface from the positions and normal vectors of the nodes, as proposed by Nagata. Normal vectors are calculated at each node from the existing discretized surface by considering a patch of surrounding elements. This is accomplished by the mean of normal voting strategy. The efficiency and reliability of the resulting contact model are checked through several examples like indenting and ironing a bulk parallelepiped. It is also applied to complex ring rolling, form rolling and extrusion problems

http://link.aip.org/link/?APCPCS/1252/27/1; International audience; The classical scientific basis for finite element modeling of metal forming processes is first recalled. Several developments in advanced topics are summarized: adaptive and anisotropic remeshing, parallel solving, multi material deformation. More recent researches in numerical analysis are outlined, including multi grid and multi mesh methods, mainly devoted to decrease computation time, automatic optimization method for faster and more effective design of forming processes. The link of forming simulation and structural computations is considered with emphasis on the necessity to predict the final mechanical properties. Finally a brief account of computation at the micro scale level is given.