La méthode PGD-BEM appliquée à l’équation de la chaleur nonlinéaire

National audienceDans [1] nous avons proposé une nouvelle méthode non incrémentale pour résoudre l’équation de la chaleur linéaire, la PGD-BEM. Nous proposons, une adaptation de cet algorithme dans le cas où le coefficient de conductivité thermique dépend de la température. Cette approche ne demande pas de connaître le noyau de Green de l’équation de la chaleur non-linéaire, seul le noyau de l’équation de Poisson en espace est nécessaire. Nous validons notre approche sur un exemple numérique

Estimation of track dimensions obtained in Laser Metal Deposition-powder thanks to a semi-analytical model coupled to an Eulerian thermal simulation

Originally issued from cladding, the LMD-p process widens the field of possibilities in terms of manufacturing. Depending on the targeted application, the needs regarding the track geometry are different and the ability to adapt it is a key challenge. In LMD-p, the laser beam attenuation as well as the powder particles preheating are both determined by laser-powder interactions before the powder reaches the substrate. The track dimensions are directly correlated to the melt pool size: a larger pool will tend to capture more powder resulting in a higher deposition rate. The model presented here intends to determine, for a given working distance, the partition of energy, and to estimate the area of the generated melt pool and finally the dimensions of the deposited track. It is first based on a semi-analytical approach that models the powder distribution and calculates the transmitted power to both substrate and powder particles. The attenuated power density is then an input for a light Eulerian thermal simulation from which the contour of the molten zone is extracted. Several iterations are carried out to account for the energy loss caused by the heating and melting of the powder entering the pool. Lastly, the track dimensions are estimated from the stabilized melt pool configuration. Track geometries obtained with a BeAM® machine are compared to the model predictions. Such an approach opens very interesting perspectives in studying the influence of the working distance and its optimization for a given material and/or a given application

An experiment-based method for parameter identification of a reduced multiscale parametric viscoelastic model of a laminated composite beam

Usual CAE tools simulate the behavior of composite parts from models considering the structures as being homogenized. Such approach reveals itself not to be effective when the engineer aims at determining the number of plies and the material characteristics of each ply to aim a specific dynamic behavior. To reply to this problem, we developed a multi-scale model that explicitly integrates the different design parameters of the composite structure being considered at different scales: the number of plies, the orthotropic law of each ply and the characteristics of each interface between the plies made by the matrix. This paper is detailing the method that we developed to lead to our multi-scale and parametric model. This method is coupled to an experimental approach that allows specific variables named fractional variables to be identified. These variables add to the detailed representation of the dynamic capacities of the laminated composite beams that led our study. In the case of our composite beams, the effect of damping due to the ply-interface behavior is significant, and consequently we dealt with the viscoelastic response of the laminated composite beam under dynamic load. As a result, the strategy of simulation based on our reduced, viscoelastic and multi-scale beam model is presented: solutions with low computational resources may be obtained. Keywords Fast simulation for CAE · Reduced model · Multi-scale model · viscoelastic behavior · Model parametrization · Method based on numerical and experimental approach List of symbols E Young's modulus (MPa) G Shear modulus = G 0 (MPa) v Poisson's ratio l Beam length (m) h Beam height (m) w Beam width (m) u Direction x B Xavier Fische

Additive Friction Stir Manufacturing Process: Interest in Understanding Thermal Phenomena and Numerical Modeling of the Temperature Rise Phase

Additive Friction Stir Manufacturing, or AFSM, is a new industrial process that follows the emergence of friction-based processes. The AFSM process is a solid-state additive process using the energy produced by the friction at the interface between a rotating non-consumable tool and a substrate. Friction depends on various parameters like axial force, rotation speed or friction coefficient. The feeder material is a metallic rod that flows through a hole in the tool. There is still a lack in understanding of the physical phenomena taking place during the process. This research aims at a better AFSM process understanding and implementation, thanks to numerical simulation and experimental validation performed on a prototype effector. Such an approach is considered a promising way for studying the influence of the process parameters and to finally identify a process window that seems relevant. The deposition of material through the AFSM process takes place in several phases. In chronological order these phases are the docking phase, the dwell time phase, the deposition phase, and the removal phase. The present work focuses on the dwell time phase that enables the temperature rise of the system due to pure friction. An analytic modeling of heat generation based on friction considers as main parameters the rotational speed and the contact pressure. Another parameter considered influential is the friction coefficient assumed to be variable, due to the self-lubrication of the system with the rise in temperature or the materials in contact roughness smoothing over time. This study proposes through a numerical modeling followed by an experimental validation to question the influence of the various input parameters on the dwell time phase. Rotation speed, temperature, spindle torque and axial force are the main monitored parameters during experimentations and serve as reference data for the calibration of the numerical model. This research shows that the geometry of the tool as well as fluctuations of the input parameters like axial force and rotational speed are very influential on the temperature reached and/or the time required to reach the targeted temperature. The main outcome is the prediction of a process window which is a key result for a more efficient process implementation