1. Thierry Coupez CEMEF - CIM Ecole des Mines de Paris Umr CNRS 7635
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 : Computational techniques :
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

3. 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

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

6. Industrial remeshing :
complex forging
cutting
TRANSVALOR

7. Adaptive remeshing and error estimation

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

9. 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)

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

11. Instability of a honey falling drop 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

12. Electrical device Courtesy of Schneider Electric
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 = Kg/m^3
Rem3D
Courtesy of Schneider Electric

13. 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

14. 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

15. 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

16. Foam structuration: 400 bubbles random nucleation
Mesh : nodes
elements

17. G=31%, V=1.36 G=16%, V=1.1 G=6%, V=1 G=75%, V=4.8 G=58%, V=2.1
Fraction gazeuse G, rapport des volumes V.
Dernière image : limites du maillage.
. Formes des bulles et tailles variées.
. 58% - 65% en P3 bonne description : même volume de liquide grâce à l'expansion de domaine.
. Mais la majeur partie du liquide reste dans les coins du domaine : au centre : fraction gazeuse plus importante => voir suite.

18. Flow oriented structure:
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

19. 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

20. Direct simulation of the flow of a polymeric fluid with fiber
Flow with 64 fibres
Simple shear flow
Periodical boundary condition
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

21. Concentration : 8%
15%

22. Concentration : 6%
12%

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

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

25. VALIDATION AND APPLICATION TO SIMPLE GEOMETRIES
 2D FILLING OF A PLATE
Orientation
Stretch

26. 3D COMPLEX INDUSTRIAL PARTS
 ORIENTATION AND STRESSES
Stress normal to flow axis
Shearing

27. Conclusion Forming process simulation : Futures challenges :
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