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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 . Plan. Forming process simulation : Large deformations : forging, stamping,… Free surface flow : Injection molding, casting

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numerical simulation of forming processes present achievements and future challenges

Numerical simulation of forming processes: present achievements and future challenges

Thierry Coupez

CEMEF - CIM

Ecole des Mines de Paris

Umr CNRS 7635

slide2
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
computational material forming
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
mechanical approaches
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
forge3

Forging example :

Large deformations

Lagrangian FE Formulation

Key issue : remeshing

FORGE3®
slide6

Industrial remeshing :

    • complex forging
    • cutting

TRANSVALOR

free surface flow
free surface flow
  • Polymer injection moulding (Rem3D)
  • Metal casting
  • Filling process
  • Mixing
  • Foaming
  • Material Liquid state to solid state
  • Gas liquid solid…
moving free surfaces and interfaces eulerian approach

Free

surface

MOVING FREE SURFACES AND INTERFACESEulerian 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 = Interface fluid / empty space (air)

slide10

Incompressible Navier Stokes and moving free surface

A fluid column crushing under its own weight. High Reynolds.

Mesh adaptation: interface tracking

slide11

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

electrical device
Electrical device

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

r = 1.64 10 Kg/m^3

Rem3D

Courtesy of Schneider Electric

multiscale modelling in material forming
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
slide14

Fluid domain f

The sample domain

n gas bubbles gi

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

Inflation of a large number of bubbles in a representative volume

slide15

Interaction by direct calculation of the expansion of several bubbles : validation : retrieve ideal structure cubic bubble

Cubical shape of trapped

central bubble

6 + 1 bubbles configuration

Inflated configuration

slide16

Foam structuration: 400 bubbles random nucleation

Mesh : 98 000 nodes

550 000 elements

slide17

G=31%, V=1.36

G=16%, V=1.1

G=6%, V=1

G=75%, V=4.8

G=58%, V=2.1

G=50%, V=1.8

orientation fibre reinforced polymer viscoelasticity by molecular orientation
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
slide19

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

Macroscopic modelling :

Equation model for a2 evolution : Closure approximation : a4 from a2

Interaction between fibres (concentration)

Closure approximation

Fibres fibres interaction

direct simulation of the flow of a polymeric fluid with fiber

Periodical boundary condition

Direct simulation of the flow of a polymeric fluid with fiber

Flow with 64 fibres

Simple shear flow

Flow modification

Impact of the fibre on the flow (vertical velocity component)

  • MFE flow solver
  • Interaction by Vof for each fibre
  • Fibre motion by bi-particle tracking
slide23

One chain interacts with other chains, but is transversely blocked, even though it finds no obstacles in its path

Stretch is the other variable of the pompom model

REPTATION

TUBE MODEL

MATERIAL MODELLING

VISCOELASTICITY : a molecular approach

 POMPOM MODEL: REPTATION THEORY BASIS

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

slide24

diffusion

Determination of molecular orientation:

variation due to macroscopic flow

relaxation

Elastic force

Arm force

Determination of chain stretch:

Extra-stress explicit computation:

Stress explicit computation:

And conservation of momentum...

MATERIAL BEHAVIOUR MODELLING: VISCOELASTICITY

 POMPOM MODEL: EVOLUTION EQUATIONS

slide25

VALIDATION AND APPLICATION TO SIMPLE GEOMETRIES

 2D FILLING OF A PLATE

Orientation

Stretch

slide26

3D COMPLEX INDUSTRIAL PARTS

 ORIENTATION AND STRESSES

Stress normal to flow axis

Shearing

conclusion
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