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Copyright © 2006 Altair Engineering, Inc. All rights reserved. 122/10/2007
Non homogeneous material and material failure
Gérard WinkelmullerDirector Radioss Development
1st European HyperWorksTechnology Conference
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1-ALE Multi-phase Material2-Austenitic steel3-Honeycomb4-Fabric5-Foam & polymer6-Failure models
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Law 37
� Two phases liquid gas mixture• Gas liquid interaction• Cavitation in liquid
� Presentation of the test• Interaction between a ship hull and fluid.• Euler Lagrange Contact interface type 18• Law 37: two phases air and water
Lagrangian
mesh
AIR fluid mesh
WATER fluid
mesh
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Law 51
� 3 phases Mïe Grüneisen EOS• Non diffusive material boundary option• Each phase can be:
– liquid or gas– Elastic solid – Elastoplastic solid (v 9.0),
• Explosive material can be added as 4th phases (new in version 9.0)
• Optional thermal conduction (v 9.0)
Law 37 Fuel tank sloshing Law 51 (non diffusive ON)
Underwater explosion
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LAW51 TESTS
Inlet (burn gases)
Cold gases
Water
Outlet
Metal plate
• This test presents a typical problem of burn gases interaction with cold gases and water
– Phase 1: Burn gases ( γ=1.2 )
– Phase 2: Air ( γ=1.4 )
– Phase 3: Water
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Austenitic steel
� Full Coupling of three factors : • Microstructure (martensite transformation)• Temperature• Work Hardening model
� Two Laws• Hänsel• U&A
� Thermal conduction (in Radioss 9.0)� In collaboration with NGV consortium
Martensite rate equation
∫ ∂∂∂=
p
p
p
mm
VV
ε
εε0
Martensite fraction
( )
( )( )TDCVV
VT
QA
BV Pm
BB
m
m
p
m ⋅+−
−
=
∂∂
+
tanh12
11exp
1
ε
VolumeC
ETT
pi ρ
int+=
Coupled thermal analysis
Mechanical behavior( ) ( )( )( )( ) m
n
pHSHSHSy VHTKKmABB αγεεσ ′→∆+++−−−= 210exp
Hänsel law
0
1000
2000
3000
4000
5000
6000
7000
0 50 100 150 200
Displacement (mm)
For
ce (
N)
Test 1 - 5m/s
Test 2 - 5m/s
Test 3 - 0.001m/s
LAW63
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Deep Drawing with thermal conduction
� Blank Temperature : 70 °°°°C
� Tools Temperature : 19 °°°°C
� Holder Force : 480 KN
� Estimated Material : 1.4301
� Constant temperature in tools
Benchmark 1Deep Drawing Single Pass
Punch
Holder
Blank
Die
Plastic strain
Temperature
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Honeycomb:Special solid elementand material law (law 58)
� Main limitation of simple homogenization approach• Crushing
• Shear behaviour
� Solution• New element with additional nodal variable
• Cosserat elasticity
Honeycomb
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Honeycomb� Compression
• With classical formulation it is not possible to take into account the initial crushing peak
Stress strain input Force output
Honeycomb
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Honeycomb� Compression
• New formulation with enriched nodal variables
– An additional nodal scalar is used to transmit the buckling information from one element to his neighbours
Honeycomb
Stress strain input Force output
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Honeycomb� Shear behaviour� Apart from the peak problem global honeycomb compre ssion is
easy to describe with a classical orthotropic mater ial. And thisfor the 1, 2 and 3 direction
� But a partial compression with some punching effect need some additional calibration.
• A partial compression in direction 1 can be adjusted with the 12 shear
• A partial compression in direction 2 can also be adjusted with the 21 shear
• But 12 shear and 21 shear are the same, and if one direction is adjusted, the other one isn’t
• What we need is a model with different shear behaviour in 12 and 21 direction. But this is impossible with classical FEM for equilibrium reasons
Cosserat elasticity
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0
0
0
≠
=
≠
z
yx
xy
m
ττ
0
0
0
≠
≠
=
z
yx
xy
m
ττ
Cosserat elasticity
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Honeycomb
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� FABRIC • Anisotropic
– Variable warp/weft angle• Physical fiber Coupling
– Nominal stretch modelization– True Poisson’s effect
— Initial Poisson’s value = 1.— Final value = 0.
• Non linear shear with lock angle• Non linear elastic fiber
Fφα warpweft
Fabric
αt π/2
αt
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δ weft δ warp
Warp force
δ warp δ weft
Weft force
Weft force
Warp force
δ warp
Fabric tension
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Law 58 Law 19
Fabric
Airbagexample
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Fabric forming
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� LAW 65� New in Radioss 9.0� Non linear elasto-plastic law� Non linear elastic loading and non linear elastic unloading� Stress-strain functions depending on strain rate� Elastic loading : stress < yield(strain rate)� Plastic loading : stress > yield(strain rate)� Unloading : follows unloading curve shifted by plastic strain value
�
YieldstressUnloadingcurveLoading curve
Strainrate 2
Strainrate 1
Strainrate 1
Polymer Material Law
YieldstressUnloadingcurveLoading curve
Constant strainrate
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Nonlinear ‘visco’ elastic law 70
eqeqeq εεσ &,,
Law Theory :Estimate stress Tensor
),(max eqeqloadfyld εε &=Load yield stress
),(min eqequnloadfyld εε &=Unload yield stress
We use a spherical criteria for
[ ] εσσ ~~0 ∆+= D
3loadε&
1loadε&
ε
σ
1unloadε&
maxσ
minσ
⇒≤≤⇒≤≤
unloading
loading
unloadequnload
loadeqload
21
32
εεεεεε&&&
&&&
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Front rail impact
Courtesy of PSA
� Without failure
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Front rail impact
Courtesy of PSA
� With failure model
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Hyper velocity impact
� Ductile tensile rupture
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Concrete law
� Impact on ceramic
Courtesy of Eurocopter
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Composite Law 25
� Tsai Wu yield surface and hardening� Tsai Wu or Chang Chang failure criteron
resσσσσ
PW
maxσσσσ
1PW 2
PW Courtesy of Eurocopter
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Failure modelization
� New Failure models• Can be used with different material law• /FAIL/fail_model/mat_id
– Fail_model: —JOHNSON : Johnson Cook failure criteria—TULERB : Tuler Butcher criteria—WILKINS : Wilkins Failure criteria—FLD : forming limit diagram—Chang Chang : composite—BAO-XUE-WIERZBICKI failure model—USER1,2,3: user failure model
� Future improvement• Damage model improvement• X-Fem for failure propagation
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Tuler Butcher
� Tuler Butcher• Based on the concept of cumulative damage• Use for dynamic fracture.
� General criterion:
ft
fσK;λ
Courtesy of LALP
( ) Kft
f ≥−∫λ
σσ0
ft Fracture time
fσ Static stress for fracture
K;λ Material constants
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Johnson Cook
� Johnson Cook failure criterion• Derived from the following cummulative
damage law:
• Where
∑∆=
f
Dε
ε
]1)][ln(1)][exp([ *5
*4
*321 TDDDDDf +++= εεεεσσσσεεεε &
vm
m
σσσσσσσσσσσσ =*
0
*
εεεεεεεεεεεε&
&& =
0
0*
TT
TTT
melt −−=
Rivet failure
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Bao Xue Wierzbicki
-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
Round Bar Tensile Tests
Upsetting Tests
_
_
76
9
5
8
3
2
1
0.8
0.4
experiment (plane stress) experiment (axial symmetry)
Al2024-T351
σσσσm
/σσσσ
εεεεf
� failure criterion
: Equivalent strainε
σ : Equivalent stress
mσ : Mean stress
σση m= : Stress triaxiality
J3 : Third invariant of stress deviator
33
2
27
σξ J
= : Deviatoric state parameter
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Bao Xue Wierzbicki
Axial symmetry
Plane strain
Plane stress
fε
plane stress
failure criterion
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Soccer simulation with Radioss
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Soccer simulation with Radioss
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Soccer simulation with Radioss
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Soccer simulation with Radioss
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The end