Numerical simulation of forming processes: present achievements and future challenges

1
Numerical simulation of forming processes
present achievements and future challenges

• Thierry Coupez
• CEMEF - CIM
• Ecole des Mines de Paris
• Umr CNRS 7635

2
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)

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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

4
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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FORGE3
Forging example Large deformations Lagrangian
FE Formulation Key issue remeshing
6

• Industrial remeshing
• complex forging
• cutting

TRANSVALOR
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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 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)
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Incompressible Navier Stokes and moving free
surface
A fluid column crushing under its own weight.
High Reynolds.
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
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/m3
Rem3D
Courtesy of Schneider Electric
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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

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
Cubical shape of trapped central bubble
6 1 bubbles configuration
Inflated configuration
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Foam structuration 400 bubbles random
nucleation
Mesh 98 000 nodes 550 000 elements
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G31, V1.36
G16, V1.1
G6, V1
G75, V4.8
G58, V2.1
G50, V1.8
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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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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)
Fibres fibres interaction
Closure approximation
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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

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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
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
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MATERIAL BEHAVIOUR MODELLING VISCOELASTICITY
? POMPOM MODEL EVOLUTION EQUATIONS
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VALIDATION AND APPLICATION TO SIMPLE GEOMETRIES
? 2D FILLING OF A PLATE
Orientation
Stretch
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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