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DIGIMAT Multi-Scale Modeling:
The Technology & Software Tools for a
Predictive Development of Reinforced
Plastic Parts
Roger A. Assaker
Skype: eX_RAR
Mobile: +32 495 52 56 52
www.e-Xstream.com
The Problem: Fiber Orientation & the UnderlyingMaterial Behavior (Simplified)
Friday, August 01, 2008 Copyright© e-Xstream engineering SA, 2003-2007 2
«E»11 «E»22 «E»33
PA Matrix
E = 3150 Mpa
Nu = 0.36
Density = 1220 kg/m3
Glass Fibers
E = 71 200 Mpa
Nu = 0.22
Density = 2600 kg/m3
Weight fraction = 0.33
4,470 MPa 10,600 MPa 4,440 MPa 8,180 MPa 4,440 MPa 12,100 MPa
1
3
Courtesy of SOLVAY
Realistic FEA of the Reinforced Plastic Parts
Software Choice
Geometric nonlinearities (Large Deformations)
Contact
Implicit/Explicit integration
Optimal mesh refinement
Optimal element choice
1st/2nd order
Tet or Hex, Triangle or Quad
Material Reinforced Plastic
Anisotropic
Heterogeneous
Nonlinear
Rate-dependent
Damage
Fatigue
Failure
Etc.Friday, August 01, 2008 Copyright© e-Xstream engineering SA, 2003-2007 3
Which Material Model ?AMODEL AS-4133 - stress-strain curves at 23°C
dumbell specimen and test samples from mold II
0
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240
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
strain (%)
str
ess (
MP
a)
dumbell
Mold II - along the flow
Mold II - across the flow
0
20
40
60
80
100
120
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0,0% 0,5% 1,0% 1,5% 2,0% 2,5% 3,0% 3,5% 4,0% 4,5% 5,0% 5,5% 6,0% 6,5% 7,0% 7,5% 8,0%
Strain
Str
es
s (
N/m
m²)
Damage, 0°, StaticDamage, 0°, 1 s-1Damage, 0°, 100 s-1Damage, 45°, StaticDamage, 45°, 1 s-1Damage, 45°, 100 s-1
TECHNYL C218 V35 Black, 23°C, Eh0
Modeling Needs
How can we design the optimal material ?
What is the relation between the material microstructure (e.g. Fiber content,
length, orientation) and its final properties (e.g. Mechanical, Thermal, Electric,…) ?
How to select the optimal material and use its anisotropy for optimal structure performance ?
What is the link between the material and structure performance ?
How can we optimally process the material and structure ?
What is the relation between the process parameters and product performance ?
How can we achieve these objectives efficiently ?
Predict the composite properties (i.e. Anisotropic, nonlinear, time-dependent, …) as a function of its microstructure.
Predict the product properties as a function the local material microstructure, as induced by the processing conditions (e.g. injection molding, draping,…)
Friday, August 01, 2008 Copyright© e-Xstream engineering SA, 2003-2007 4
DIGIMAT, The nonlinear multi-scale material & structure
modeling platform
Copyright© e-Xstream engineering, 2007
DIGIMAT to CAE, Coupling Injection Molding to Realistic FEA
Friday, August 01, 2008 Copyright© e-Xstream engineering SA, 2003-2007 6
Fiber Length Distribution
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925
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1025
1075
1125
Length [µm]
Nu
mb
er
Phase Material & Composite Microstructure
-Fiber Shape
-Fiber Weight Fraction
-Fiber Length Distribution
Fiber Orientations
Material DesignProcess Design
Structural FEA
Structure Design
Courtesy of Trelleborg & Rhodia
The Multi-Scale Modeling Approach forFiber Reinforced Engineering Thermoplastic
Friday, August 01, 2008 Copyright© e-Xstream engineering SA, 2003-2007 7
MAP
DIGIMAT
Matrix Properties
Reinforcement Properties
Composite Morphology
Fiber Length/diameter
Fiber Weight/Volume Fraction
Composite
Properties
Structural
Mesh
Fiber
Orientation
Structural FEA
Injection
Mesh
Injection
Mat Prop.
Injection
Process Param.
Fiber
Orientation
Residual
Stresses
Residual
Temperature
Micro/macro
FEA results
Injection Molding
Software
Interaction between DIGIMAT and FEA
Friday, August 01, 2008 Copyright© e-Xstream engineering SA, 2003-2007 8
FE model level
Nodal coordinates, …
Strain increments,
material state, …
Element level
Material level
Stresses and
material stiffness
Internal forces and element stiffness
e
s
Classical FE process Coupled FE/DIGIMAT process
« In code » model
FE model level
Nodal coordinates, …
Strain increments,
material state, …
Element level
Stresses and
material stiffness
Internal forces and element stiffness
Material level
Mean Field Homogenization
Composite behavior depends explicitly on the:
Behavior of each phase
Inclusion shape (Aspect Ratio)
Inclusion orientation
Inclusion evolution (finite strain)
Friday, August 01, 2008 Copyright© e-Xstream engineering SA, 2003-2007
E Σ
Local phase behavior
(Step 2)
Global behavior
Localization
(Step1)
Averaging
(Step 3)
εr σr
EHx rrr :)(ee
rrr c es :
es :)( rcc
Pros
Fast model preparation/solution
Accurate predictions
Enables fully coupled nonlinear multi-scale Analyses
Cons
Ellipsoidal inclusions
Uniformly distributed inclusions
Average per phase (micro) results
a) b) Matrix
Fibers
ei
si
a) b)
DIGIMAT-MF: Major Capabilities
Materials: Per Phase (of a composite):
Thermo-Elastic: Anisotropic, Temperature dependent.
Elasto-Plastic: Small deformations/Large rotations
• Pressure dependent (Drucker-Prager)
• Continous Damage (4 parameters model)
Visco-elastic: Linear, small deformations/Large rotations
Elasto-Viscoplastic: Large deformations.
Hyperelastic (5 models): Large deformations
Micro-structure:
N-Phase (e.g. fibers + mineral inclusions, distribution of fiber “lengths”)
General Orientation (e.g. Orientation Tensor from MOLDFLOW)
Inclusion Coating (i.e. Fiber/Matrix Interface)
Voids
Micro & Macro Failure Indicators
1st & 2nd Order Incremental Homogenization Methods:
Mori-Tanaka
Interpolative Double Inclusion (High Concentrations/Contrast)
Thermo-Mechanical Static & Dynamic (Impact) Loading
Nonlinear, strongly coupled CAE Interfaces
Friday, August 01, 2008 Copyright© e-Xstream engineering SA, 2003-2007 10
10
s
1
E0
1
E = E0 (1–D)
e
MAP: 2D & 3D mapping
Mesh Types Mid-plane(Triangles)Shell (Triangle or Quad)
3D (Tet) 3D (Tet or Hex)
Mesh Format Abaqus
ANSYS
LS-DYNA
PAM-CRASH
Mapped Data: fiber Orientation
Initial Stresses
Initial Temperature
Mapping Error Indicators Global (Contour plot)
Local (Histogramme)
Model Scaling/Positioning
Data post-processing Synchronized
Contour or vector plotsFriday, August 01, 2008 Copyright© e-Xstream engineering SA, 2003-2007 11
SOME APPLICATIONS
Friday, 01 August 2008 Copyright© e-Xstream engineering SA, 2003-2006 13
FAT B85 : FE & Material Models (PP-LGF)
DIGIMAT Material Model
PP-Matrix :
• E= 1500 MPa
• = 0.3
Fibres :
• E = 72000 MPa
• = 0.22
• Volume Fraction = 19.46 % (40 % Weight Fraction)
• Aspect ratio : 100 (Long Fibers)
• Orientation : MOLDFLOW 5.1
ABAQUS FEA Model # Elements =12632 (S3R)
# Nodes = 6365
# DOF = 38190
Material : PP-LGF with DIGIMAT 1.6
Initial Stresses: MOLDFLOW 5.1 Courtesy of:
www.renault.com
Friday, 01 August 2008 Copyright© e-Xstream engineering SA, 2003-2006 14
FAT B85: Structural Stiffness
Fixed
P3 : 20daNP1: 20daN
P2: 20daN
Structural Stiffness (MDA-Test)/Test
P1 -3.75%
P2 +8.07%
P3 -6.97%Courtesy of:
Friday, 01 August 2008 Copyright© e-Xstream engineering SA, 2003-2006 15
FAT B85: Modal Response
Eigen Freq. (MDA-Test)/Test
7 1.68%
8 0.96%
9 -3.66%
10 -2.76%
11 -1.84%
12 -1.06%
13 -2.83%
14 -4.45%
15 1.46%
16 2.09%
17 0.47%
18 2.21% 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Mode Number
Ein
ge
n F
req
ue
nc
y [
Hz]
Test
MDA Predictions
Courtesy of:
Friday, 01 August 2008 Copyright© e-Xstream engineering SA, 2003-2006 16
3-Point Bending Beam: Problem Definition
ABAQUS FE Model Number of Elements=30,532 Number of Nodes= 31,528 Number of DOF=154,089
Material : PA 35% GF Matrix :
• Young’s modulus: 2.75 E+09 Pa• Poisson ratio : 0.37
• yield_stress = 4.0e+07 Pa
• hardening_model = exponential linear
• hardening_modulus = 3.67e+07
• hardening_exponent = 3.2e+02
• hardening_modulus2 = 3.0e+07• Density: 1.13 E+03 Kg/m3
Fibers :• Young’s modulus: 7.2e+10 Pa• Poisson ratio: 0.22• Density:2.47e+03 Kg/m3
• Weight fraction : 35 % • Aspect ratio :
– 25– Fiber length Distribution
• Fiber Orientation– Moldflow (DSM)
Axial Young's Modulus Vs Fiber Length
0
2000
4000
6000
8000
10000
12000
14000
16000
0 200 400 600 800 1000 1200
Fiber Length [µm]
Ax
ial
Yo
un
g's
Mo
du
lus
[M
Pa
]
Ln = 248
µm
Lw = 321 µm
ELw = 12147
ELn = 11379
EFLD = 10560
LFLD = 197
µm
Fiber Length Distribution
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Length [µm]
Nu
mb
er
Courtesy of: DSM
Friday, 01 August 2008 Copyright© e-Xstream engineering SA, 2003-2007 17
3-Point Bending Beam
Courtesy of: DSM
von Mises Stresses
In PAGF
Accumulated Plastic Strain
In PA matrix
Friday, 01 August 2008 Copyright© e-Xstream engineering SA, 2003-2006 18
Reaction Force / Intrusion
-11000
-9000
-7000
-5000
-3000
-1000
1000
0 1 2 3 4 5 6 7 8 9 10
Intrusion (mm)
Re
ac
tio
n F
orc
e (
N)
DIGIMAT ar=16 ElastoPlastic NLGEOM
DIGIMAT ar=16 Elastic NLGEOM
SHF ar=16 NLGEOM
SHF ar=25 NLGEOM
DIGIMAT AR=16 ElastoPlastic NLGEOM
(Quad mesh)Experience
3-Point Bending Beam: F/d Curves
-35%
Target
Measured RF= 6,883 N
Predicted RF (Tri mesh) = 7,170 N (+4%)
Predicted RF (Quad mesh) = 6720 N (-2.4%)Courtesy of: DSM
Copyright© e-Xstream engineering SA, 2003-2008 19
Multi-Scale Modeling of Passenger Airbag Container
Moldflow’s Injection Molding Mesh: Number of nodes: 584,123
Number of elements: 3,369,976
Element type: C3D4
Abaqus Structural Mesh: Number of nodes: 368,852
Number of elements: 194,794
Element type: C3D10, C3D10M
Material: AKULON K224-PG8 (40% Glass filled
Impact Modied Polyamide)
Matrix: Impact Modified Polyamide• type = elastoplastic
• Young Modulus = 2350 MPa
• Poisson Ratio = 0.38
• Yield stress =30 MPa
Fibers: E-Glass • Type = elastic
• Density = 2.54 E+3
• Young Modulus = 72 000 MPa
• Poisson Ratio = 0.22
• Weight fraction = 40%
• Aspect ratio (L/D) = 20
• Orientation = Moldflow3D (.xml)
Courtesy of: AUTOLIV & DSM
Moldflow Injection Molding Simulation
Friday, 01 August 2008 Copyright© e-Xstream engineering SA, 2003-2008 20Courtesy of: AUTOLIV & DSM
Quasi-Static/Monotonic: Elasto-Plastic DIGIMAT Material
Friday, August 01, 2008 Copyright© e-Xstream engineering SA, 2003-2007 21Courtesy of: AUTOLIV & DSM
DIGIMAT to Abaqus Nonlinear Multi-ScaleAnalyses: Results & CPU
Loadings Linear Cyclic
CPU Time 82 h 05 m 41 h 13 m
Elapsed time 25 h 56 h 28 m
# CPUs(Opteron 64 bits)
4 1
Friday, 01 August 2008 Copyright© e-Xstream engineering SA, 2003-2008 22
RF @ Imposed D ExperimentalForce
DIGIMAT to Abaqus Difference
Linear(to 10.5mm)
~ 6477 N 6203.49 N -4.2%
Cyclic(to 7mm)
~ 4765N 3949.18 N -17 %
Courtesy of: AUTOLIV & DSM
Multi-Scale Impact & Failure Simulation
LS-DYNA FE Mesh
3,630 Elements
3,646 Nodes
16 composite shell sections with different thicknesses.
5 integration points across the thickness
Characteristic dimension : 400x50x30 mm.
Loading & BC :
Simply supported beam
Initial velocity: V0 =-5 m/sec
Friday, August 01, 2008 Copyright© e-Xstream engineering SA, 2003-2007 23
Fixed
Initial velocity
FixedCourtesy of :
Impact & Failure Analysis: Aligned Fibers
Friday, August 01, 2008 Copyright© e-Xstream engineering SA, 2003-2007 24
Failure Prediction: Effect of Injection Gate Location
Friday, August 01, 2008 Copyright© e-Xstream engineering SA, 2003-2007 25
Courtesy of :
DIGIMAT to PAM/CRASH: Impact & Failure
Friday, August 01, 2008 Copyright© e-Xstream engineering SA, 2003-2007 26
Conclusions
Mean Field homogenization is a powerful technology to predict
the anisotropic, nonlinear and rate-dependent behavior of
mutli-phase materials in general and of reinforced plastics in
particular.
Fully coupled multi-scale modeling bridges the gap between
the manufacturing process and the final part performance via
the material microstructure.
DIGIMAT offer the tools and modeling process for the optimal
and predictive design of reinforced plastic parts.