numerical simulation of forming processes: present achievements and future challenges thierry coupez...
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Numerical simulation of forming processes: present achievements and
future challenges
Thierry CoupezCEMEF - CIM
Ecole des Mines de ParisUmr CNRS 7635
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
• 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• 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
Forging example :Large deformationsLagrangian FE FormulationKey issue : remeshing
FORGE3®
TRANSVALOR
Industrial remeshing : • complex forging• cutting
Adaptive remeshing and error estimation
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
– the diffuse interface approach
– Transport equation solver
– Capture of interfaces
– Space time finite element method
– Mesh adaptation• R-adaptivity (~ALE)
• Conservative scheme
fluid air
Freesurface
)()( tt airfluid
Free surface = Interface fluid / empty space (air)
0.
))(2.(
v
gpv
A fluid column crushing under its own weight. High Reynolds.
Incompressible Navier Stokes and moving free surface
Mesh adaptation: interface tracking
3D Crushing column of liquida rectangular box
3D Navier Stokes + moving free surfaces +Mesh adaptation + Space time FE
Instability of ahoney falling drop
Electrical device
Courtesy of Schneider Electric Rem3D
Material : Polysulfure de phénylène (PPS, thermoplastique semi-cristallin)
Carreau law + arrhenius :K = 588 Pa.Sm= 0.7E= 33 kJ/molek= 0.3 W/m °C = 1.64 10 Kg/m^3
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
Foaming modelling by direct computation of bubble growthstructure 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
n
igf i
1
)(
Inflation of a large number of bubbles in a representative volume
Interaction by direct calculation of the expansion of several bubbles : validation : retrieve ideal structure cubic bubble
6 + 1 bubbles configuration
Inflated configuration
Cubical shape of trapped central bubble
Mesh : 98 000 nodes
550 000 elements
Foam structuration:
400 bubbles random nucleation
G=6%, V=1 G=16%, V=1.1G=31%, V=1.36
G=50%, V=1.8 G=58%, V=2.1
G=75%, V=4.8
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
N
i
iiii
N
i
ii
ppppN
a
ppN
a
14
12
1
1
Fibres fibres interaction
Closure approximation
)(2):2(242222
2 anICaaaaaDt
aDdI
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 fluidExact calculation of a2 and a4 from a statistical representative volume of fluid
oriented Isotropic
00
012a
5.00
05.02a
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
Concentration :
8%
15%
Concentration :
6%
12%
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 chainReptation of the chain when the arms penetrate in the tube
Stretch is the other variable of the pompom model
mequilibriuat lengthndeformatioafter length
MATERIAL BEHAVIOUR MODELLING: VISCOELASTICITY
POMPOM MODEL: EVOLUTION EQUATIONS
Determination of molecular orientation: dtdS
Tvv
SS
variation due to macroscopic flow
31 Iλb
S
relaxation
SS v
:2
diffusion
Determination of chain stretch:dtd
Elastic force
S:vε
Arm force
1
0
11 υ
s
eλ
Extra-stress explicit computation:
NM
i
is τvεηpσ1
2
I
ISτ 23 iii G
Stress explicit computation:
And conservation of momentum...
02 τγ pvη
VALIDATION AND APPLICATION TO SIMPLE GEOMETRIES
2D FILLING OF A PLATE
Orientation Stretch
3D COMPLEX INDUSTRIAL PARTS
ORIENTATION AND STRESSES
Stress normal to flow axis
Shearing
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