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Numerical simulation of forming processes: present achievements and future challenges Thierry Coupez CEMEF - CIM Ecole des Mines de Paris Umr CNRS 7635

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Plan Forming process simulation : –Large deformations : forging, stamping,… –Free surface flow : Injection molding, casting –Multi-modeling : flow, deformation, heat transfer, liquid solid transition Computational techniques : –EF solver : mixed FE, incompressibility, viscoelasticity –EF Lagranian, remeshing, –EF Eulerian, vof, levelset New chalenge : structure prediction –Multiscale modeling –Multiphase Example : Foam : form nuclation, bubble growth, and cell construction Fibers reinforced polymer : suspension to long fiber high concentration –Physic property: Polymer : macromolecular orientation in polymer Cristalysation –Computational Chalenges : Multiphases calculation : liquid, solid, gas Transition : critalynity, mixture solid liquid (dendrite, spherolite) Macroscopic descriptor

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Computational Material forming Solid material : –High temperature : viscoplasticity, –Low temperature : plasticity, elastoplasticity Fluid material : –Low viscosity :liquid metal (foundry), Newtonian incompressible liquid (turbulence) –Low viscosity : Newtonian, reactive material, thermoset, –High viscosity : Pseudopalsticity, viscoelasticity thermoplastic polymer Liquid solid transition

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Mechanical approaches FE for both solid and fluid problems –Implicit –Iterative solver (linear system), parallel (Petsc) –Stable (Brezzi Babuska) Mixed Finite Element (incompressibility) (P1+/P1) Large deformations (Forge3 : forging ): –Lagrangian description Flow formulation (velocity) Unilateral contact condition Remeshing Flow (Rem3D : injection moulding) –Stokes and Navier Stokes solver (velocity, pressure) –Transport equation solver (Space time discontinuous Galerkin method) Heat transfer coupling –Rheology temperature dependent –Convection diffusion (Dicontinuous Galerkin method) –Thermal shock –Phase change, structural coupling

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Forging example : Large deformations Lagrangian FE Formulation Key issue : remeshing FORGE3®

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TRANSVALOR Industrial remeshing : complex forging cutting

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Adaptive remeshing and error estimation

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free surface flow Polymer injection moulding (Rem3D) Metal casting Filling process Mixing Foaming Material Liquid state to solid state Gas liquid solid…

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MOVING FREE SURFACES AND INTERFACES Eulerian approach –the diffuse interface approach –Transport equation solver –Capture of interfaces –Space time finite element method –Mesh adaptation R-adaptivity (~ALE) Conservative scheme Free surface Free surface = Interface fluid / empty space (air)

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A fluid column crushing under its own weight. High Reynolds. Incompressible Navier Stokes and moving free surface Mesh adaptation: interface tracking

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3D Crushing column of liquid a rectangular box 3D Navier Stokes + moving free surfaces + Mesh adaptation + Space time FE Instability of a honey falling drop

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Electrical device Courtesy of Schneider Electric Rem3D Material : Polysulfure de phénylène (PPS, thermoplastique semi-cristallin) Carreau law + arrhenius : K = 588 Pa.S m= 0.7 E= 33 kJ/mole k= 0.3 W/m °C = Kg/m^3

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Multiscale modelling in material forming Examples : –Foam, –Fibre reinforced polymer, –constitutive equation based on the macromolecule orientation Structure descriptors : microscale to macroscale –Microscale : modelling by direct multidomain simulation of moving bubbles or fibres in a sample volume of liquid –Macroscale : Concentration, gas rate Distribution of bubble size, fibre shape factor, Orientation tensor: fibres, macromolecules, … –Flow oriented structure : micro-macro Evolution equation of the orientation tensor : closure approximation Interaction description (fibre fibre, entangled polymer, bubble density) Influence of the structure on the rheology End use property

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Foaming modelling by direct computation of bubble growth structure parameters : density (gas rate) (10% G 99.5%) size (number) and shape of cells Computation ingredients : Multidomains (individual bubble) (transport equation solver STDG, VoF, r-adaptation) Compressile gas in incompressible liquid (stable MFE method ) from nuclei to bubble and cells Fluid domain f n gas bubbles gi The sample domain Inflation of a large number of bubbles in a representative volume

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Interaction by direct calculation of the expansion of several bubbles : validation : retrieve ideal structure cubic bubble bubbles configuration Inflated configuration Cubical shape of trapped central bubble

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Mesh : nodes elements Foam structuration: 400 bubbles random nucleation

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G=6%, V=1 G=16%, V=1.1 G=31%, V=1.36 G=50%, V=1.8 G=58%, V=2.1 G=75%, V=4.8

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Orientation : - Fibre reinforced polymer - viscoelasticity by molecular orientation Flow oriented structure: –Macroscale descriptor : orientation tensor –Orientation evolution (rigid fibre): Physical model : –Closure approximation –Interaction modelling – Orientation and stretch Macromolecule orientation modelling

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Fibres fibres interaction Closure approximation Macroscopic modelling : Equation model for a2 evolution : Closure approximation : a4 from a2 Interaction between fibres (concentration) Microscale simulation : Direct computation of the flow of N fibres in a viscous fluid Exact calculation of a2 and a4 from a statistical representative volume of fluid oriented Isotropic

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Direct simulation of the flow of a polymeric fluid with fiber Periodical boundary condition Simple shear flow Flow modification Impact of the fibre on the flow (vertical velocity component) Flow with 64 fibres MFE flow solver Interaction by Vof for each fibre Fibre motion by bi-particle tracking

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Concentration : 8% 15%

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Concentration : 6% 12%

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MATERIAL MODELLING VISCOELASTICITY : a molecular approach POMPOM MODEL: REPTATION THEORY BASIS One chain interacts with other chains, but is transversely blocked, even though it finds no obstacles in its path REPTATION TUBE MODEL The chain is still in the tube and has arms The arms allow the stretch of the chain Reptation of the arms Stretch of the chain Reptation of the chain when the arms penetrate in the tube Stretch is the other variable of the pompom model

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MATERIAL BEHAVIOUR MODELLING: VISCOELASTICITY POMPOM MODEL: EVOLUTION EQUATIONS Determination of molecular orientation: variation due to macroscopic flow relaxation diffusion Determination of chain stretch: Elastic force Arm force Extra-stress explicit computation: Stress explicit computation: And conservation of momentum...

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VALIDATION AND APPLICATION TO SIMPLE GEOMETRIES 2D FILLING OF A PLATE OrientationStretch

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3D COMPLEX INDUSTRIAL PARTS ORIENTATION AND STRESSES Stress normal to flow axis Shearing

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Conclusion Forming process simulation : –Large deformation and Lagrangian approach : forging, rolling, deep- drawing, machining –Flow and Eulerian approach : injection moulding of polymer, casting, mixing –Numerical techniques : Stable Mixed Finite Element method (incompressibility), Meshing technique (h-adaptation, r-adaptation, remeshing, anisotropic mesh), Transport solution, level set, Volume of Fluid, parallel computing Futures challenges : –Complex material : structure and morphology –Multiphase: liquid solid, liquid gas –Multiscale computing –Phase transition –End use property and microstructure prediction

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