Experimental and Numerical aspects of B416 Cu-Be alloy friction stir process

The Friction Stir Processing is an innovative surface engineering method, considered as a green processing technique. A good physical understanding of the process can be reached by the combined efforts of experimental examination and numerical modelling. In this study numerical and experimental investigations of Friction Stir Process (FSP) have been carried out on samples of B194 ASTM copper-beryllium alloy. The behavior of this alloy under FSP was studied using an experiment design at three levels of transversal speed (maximum speed 80 mm/min), three different normal forces (maximum force 1250 N) and two levels of rotational speed: 1000 and 2000 rpm. The treated layers have been characterized in terms of hardness and microstructure. The results obtained have shown that FSP in the tested range of parameters leads to the formation of a stirred layer with fine grains and high hardness (approximately 260% higher that the initial value of the base material). The friction between the tool and the work piece generates heat around the tool and produces microstructure modification by homogenization and refinement. These factors play a crucial role in heat generation during the process. The heat generating mechanism is influenced by the process parameters (normal load, rotational speed, transverse speed and geometric data). Thus the present study has been carried out in order to investigate the coupled effects of process parameters and the tool geometry on the thermal behavior of B194 ASTM copper-beryllium alloy under friction stir process. Numerical analyses in terms of heat generation and temperature distribution were carried out and a three-dimensional heat transfer model for friction stir process is proposed in this paper

Optimisation de la tête d'extrusion pour la fabrication de pièces thermoplastiques

Balancing the distribution of flow through a die to achieve a uniform velocity distribution is the primary objective and one of the most difficult tasks of extrusion die design. If the extrusion die is not properly designed, the exit velocity distribution may be not uniform; this can affect the thickness across thewidth of the die. The objective of our research is to ensures a homogeneous exit velocity distribution on the outlet side of the die, through the control and the optimization of the geometrical parameters and operating conditions. An optimization procedure, based on the response surface method, was proposed. All the functions are written in an explicit form by using the either diffuse approximation or the Kriging interpolation. Due to the presence of the nonlinear constraints, an iterative algorithm of type SQP, was used. To find the global optimum with precision and at lower cost an auto-adaptive research space is adopted.In the first stage the objective was to identify the rheological behaviour of a plastic using in situ experimental data. The comparison with measurements in capillary rheometry enabled us to verify the rheological parameters obtained by optimization.The results of three other applications shows the interest of the optimization of the geometrical and operating conditions of the extrusion process.A coat-hanger melt distributor is optimized numerically to ensures a homogeneous exit velocity distribution that will best accommodate for a different range of materials and multiple operating conditions. The results of numerical simulation are then validated by comparison with experimental measurements.The numerical optimization algorithm presented in this work shows its suitability and robustness as a tool for extrusion die design. It proves its capability of predicting optimal die geometry with uniform velocity distribution for a range of polymers, at satisfactory computing times for 3D Finite Element flow analysis.Au cours de cette étude, différents aspects d'optimisation ont été abordés. L'objectif de nos travaux de recherches est d'homogénéiser la répartition des vitesses à la sortie des filières, par la maîtrise et l'optimisation des paramètres géométrique et opératoires. Dans cette étude l'optimisation a été effectuée en utilisant un logiciel commercial Rem3D®, basé sur la méthode des éléments finis.Une procédure d'optimisation, basée sur la méthode de surface de réponse, a été proposée. Celle-ci nous a permis de résoudre un problème d'optimisation implicite dont l'évaluation des fonctions est très coûteuse en temps de calcul. Pour cela, toutes les fonctions sont écrites sous une forme explicite en utilisant soit l'approximation diffuse ou l'interpolation Krigeage. Compte tenu de la présence des contraintes non linéaires, un algorithme itératif de type SQP, a été utilisé. Pour localiser l'optimum global avec précision et à moindre coût, une procédure d'échantillonnage auto adaptatif de l'espace de recherche a été appliquée et plusieurs stratégies permettant de réactualiser les approximations et le point initial ont été adoptées.Dans la première étape l'objectif était d'identifier le comportement rhéologique d'une matière plastique en production. La comparaison avec des mesures en rhéométrie capillaire nous a permis de vérifier la pertinence des paramètres rhéologique obtenus par optimisation.Les résultats de trois autres applications mettent en évidence l'intérêt de l'optimisation des paramètres géométriques et opératoires du procédé d'extrusion.Une filière optimisée numériquement pour une gamme différente de polymère a été réalisée et une comparaison expérimentale a permis de valider toute la procédure de simulation et d'optimisation mise en place. Les résultats expérimentaux et de simulations montrent une bonne homogénéisation de la répartition des vitesses à la sortie de la filière optimale pour une gamme très large de débits et pour différents polymères

Optimization of the extrusion die for the manufacture of thermoplastic parts

L’objectif de nos travaux de recherches est d’homogénéiser la répartition des vitesses à la sortie des filières, par la maîtrise et l’optimisation des paramètres géométrique et opératoires. Une procédure d’optimisation, basée sur la méthode de surface de réponse, a été proposée. Toutes les fonctions sont écrites sous une forme explicite en utilisant soit l’approximation diffuse ou l’interpolation Krigeage. Compte tenu de la présence des contraintes non linéaires, un algorithme de type SQP, a été utilisé. Pour localiser l’optimum global avec précision, une procédure d’échantillonnage auto adaptatif de l’espace de recherche a été adoptée. Les résultats d’optimisation mettent en évidence l'intérêt de l’optimisation des paramètres géométriques et opératoires du procédé d’extrusion. Une filière optimisée numériquement pour une gamme différente de polymère a été réalisée et une comparaison expérimentale a permis de valider toute la procédure de simulation et d’optimisation mise en place.The objective of our research tasks is to homogeneous the velocity distribution on the outlet side of the die, through the control and the optimization of the geometrical parameters and operating conditions. An optimization procedure, based on the response surface method, was proposed. All the functions are written in an explicit form by using the either diffuse approximation or the Kriging interpolation. Due to the presence of the nonlinear constraints, an iterative algorithm of type SQP, was used. To find the global optimum with precision and at lower cost an auto-adaptive research space is adopted. The results of three other applications highlight the interest of the optimization of the geometrical and operational parameters of the extrusion process. A die optimized numerically for multiple operating conditions and materials was produced. An experimental comparison allowed us to validate all the procedure of simulation and optimization put in place

Optimisation de la tête d'extrusion pour la fabrication de pièces thermoplastiques

L objectif de nos travaux de recherches est d homogénéiser la répartition des vitesses à la sortie des filières, par la maîtrise et l optimisation des paramètres géométrique et opératoires. Une procédure d optimisation, basée sur la méthode de surface de réponse, a été proposée. Toutes les fonctions sont écrites sous une forme explicite en utilisant soit l approximation diffuse ou l interpolation Krigeage. Compte tenu de la présence des contraintes non linéaires, un algorithme de type SQP, a été utilisé. Pour localiser l optimum global avec précision, une procédure d échantillonnage auto adaptatif de l espace de recherche a été adoptée. Les résultats d optimisation mettent en évidence l'intérêt de l optimisation des paramètres géométriques et opératoires du procédé d extrusion. Une filière optimisée numériquement pour une gamme différente de polymère a été réalisée et une comparaison expérimentale a permis de valider toute la procédure de simulation et d optimisation mise en place.The objective of our research tasks is to homogeneous the velocity distribution on the outlet side of the die, through the control and the optimization of the geometrical parameters and operating conditions. An optimization procedure, based on the response surface method, was proposed. All the functions are written in an explicit form by using the either diffuse approximation or the Kriging interpolation. Due to the presence of the nonlinear constraints, an iterative algorithm of type SQP, was used. To find the global optimum with precision and at lower cost an auto-adaptive research space is adopted. The results of three other applications highlight the interest of the optimization of the geometrical and operational parameters of the extrusion process. A die optimized numerically for multiple operating conditions and materials was produced. An experimental comparison allowed us to validate all the procedure of simulation and optimization put in place.NANCY-INPL-Bib. électronique (545479901) / SudocALBI-ENSTIMAC (810042301) / SudocSudocFranceF

Optimisation of extrusion flat die design and die wall temperature distribution, using Kriging and response surface method

International audienceA new optimisation methodology for the design of coat-hanger dies is presented. Two approaches are presented to optimise the velocities distribution across the die exit. In the first approach, we predict the optimal shape of a coat hanger die; in the second approach, to keep the same geometry and avoid design of a new die, we optimise the temperature of regulation in heterogeneous way. This method involves coupling a three-dimensional finite element simulation software and an optimisation strategy. For this optimisation, the Sequential Quadratic Programming algorithm and the global response surface method with Kriging interpolation are used

Comparaison between two designs of experiment using the response surface method in order to optimize the velocity distribution in a coat hanger die

International audienceBalancing the distribution of flow through a die to achieve a uniform velocity distribution across the die exit is one of the most difficult tasks of extrusion die design. The objective of this paper is to obtain a homogeneous velocities distribution at the die exit. In order to keep the same geometry and avoid design and manufacture of a new die, it seems very important to control the die thermally. For this, we optimize the wall temperature of regulation of a coat hanger die in a heterogeneous way, (i.e. the wall temperature may not be constant in the entire die). The temperature of regulation of the melt enables us to locally control the viscosity, which influences the flows in the various zones. The flow analysis results are then combined with an automatic optimisation algorithm that is based on a response surface methodology and a non linear constraint algorithm SQP with several strategies to provide a new profile of the die wall temperature distributions. Two designs of experiment are used and both results are then compared. Typically, for extrusion die design, the objective function states that the average velocity across the die exit is uniform. Constraints are used to limit and /or to control the pressure drop in the die

Application of a response surface method to the optimal design of the wall temperature profiles in extrusion die

International audienceA new approach to the optimal design of the die wall temperature profile in polymer extrusion processes is presented. In this approach, optimization of the design variables is conducted by a Response Surface Method (RSM) and the Sequential Quadratic Programming (SQP) algorithm. Design of experiment (DoE) needed for the construction of the response surface is used to evaluate the objective and the constraint functions on the basis of a finite element method (FEM). Two designs of experiments are used and the performances of the optimization results are compared with respect to efficiency and ability to obtain a global optimum. Typically, for extrusion die design, the objective function states that the average velocity across the die exit is uniform. Constraints are used to limit the pressure drop in the die. For this purpose, we optimize the wall temperature profile of a coat hanger die in a heterogeneous way, (i.e. the wall temperature may not be constant in the entire die). The melt temperature enables us to locally control the viscosity, which influences the flows in the various zones. The effect of the design variables in the objective and constraint functions is investigated using Taguchi method. The flow analysis results are then combined with an automatic optimization algorithm to provide a new profile of the die wall temperature distributions

Contribution of AI and machining learning in advanced material characterization

Artificial intelligence (AI) includes many mathematical methods such as optimization algorithms, approximation technics (surface response), etc. Some methods brought more focus especially in machine learning (ML) and deep learning (DL) algorithms. Their applications is becoming an important tool in the fields of materials and mechanical engineering. It is due to their incredible capability of predictions of parameters and mechanics behaviours. This allows design of new materials and optimal structures beyond intuitions. Parameter identification of complex materiel for instance, involves massive design spaces that are intractable for conventional methods. In addition, simulation of such model under different loading often required days of finite element analysis with high performing computer

The optimal design of sheet metal forming processes: application to the clinching of thin sheets

The production of high-strength clinched joints is the ultimate goal of the manufacturing industry. The determination of optimum tool shapes in the clinch forming process is needed to achieve the required high strength of clinched joints. The design of the tools (punch and die) is crucial since the strength of the clinched joints is closely related to the tools geometry. To increase the strength of clinched joints, an optimisation procedure using the response surface methodology, based on an adaptive moving target zone, is presented. The cost function studied here is defined in terms of the maximum value of the tensile force computed during the simulation of the sheets separation. Limitations on the geometrical parameters due to feasibility issues are also taken into account. The kriging interpolation is used to provide an approximation to the optimisation problem and to build the response surfaces

mathematique, poutre , modelisation

International audienceA refined beam theory that takes the thickness-stretching into account is presented in this study for the bending vibratory behavior analysis of thick functionally graded (FG) beams. In this theory, the number of unknowns is reduced to four instead of five in the other approaches. Transverse displacement is expressed through a hyperbolic function and subdivided into bending, shear, and thickness-stretching components. The number of unknowns is reduced, which involves a decrease in the number of the governing equation. The boundary conditions at the top and bottom FG beam faces are satisfied without any shear correction factor. According to a distribution law, effective characteristics of FG beam material change continuously in the thickness direction depending on the constituent’s volume proportion. Equations of motion are obtained from Hamilton’s principle and are solved by assuming the Navier’s solution type, for the case of a supported FG beam that is transversely loaded. The numerical results obtained are exposed and analyzed in detail to verify the validity of the current theory and prove the influence of the material composition, geometry, and shear deformation on the vibratory responses of FG beams, showing the impact of normal deformation on these responses which is neglected in most of the beam theories. The obtained results are compared with those predicted by other beam theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of FG beams