on the development, verification and validation of a semi...
TRANSCRIPT
1ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
A. Haufe₤, M. KöstersҰ, P. DuBois¥, M. Feucht‡, S. Kolling‡ ₤ DYNAmore GmbH, Stuttgart, Germany
Ұ North Eastern University, USA¥ Consultant, Offenbach, Germany
‡ DaimlerChrysler AG, Sindelfingen, Germany
On the Development, Verification and Validation of a semi-analytical Model for Polymers
subjected to dynamic Loading
2ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
Introduction and motivation Overview on an extended V&V process Details of a new material model Verification of implementation Calibration by simple tests Validation of constitutive model Outlook
For inquiries please contact Dynamore GmbHDr. Andre HaufeIndustriestraße 2
70565 Stuttgarthttp://www.dynamore.de
Overview
3ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
More and more structural parts are made from plastics. At present important crashworthiness applications are:
Pedestrian protection (bumper, fascia, hood, adhesives) Passenger protection (cockpit, internal structures)
Their mechanical behaviour is strongly dependent on Underlaying chemical structure and production process Temperature, strain rate etc.
Many thousand different blends are available today!!
Motivation
4ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
V&V processes for complete FE models
V&V process of each individual part of the numerical model necessary:
In engineering practise the numerical model shall correlate to experimental data close enough, to allow sound predictions in a predefined range of model variations.
Element formulation, type & size
Global solution strategy
Constitutive model
… more …
Discretisation depth & modeling techniques
5ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
V&V processes for complete FE models
6ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
Extended V&V process for material model dev.
Validationof verified and calibrated
model by experiments
[Schwer 2002]
Calibrationof verified model to gain
material parameters
Verificationof implemented
constitutive model
Identificationof characteristic material behaviour with respect to
the application
Implementationinto a suitable comp. mech.
code.
7ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
Plastics is a group name comprising many different materialsMechanical response at room temperature may be glassy or rubbery,
brittle or viscous
Fiber reinforcement may cause anisotropic response Rib reinforcements represent an important modeling effort
stre
ss
1 2
34
5
strain
ε& Z
T Z
1 glasslike behaviour2 plastic or viscous flow3 low ductility
Identification challenge: Structures made of plastics
4 high ductility5 rubbery
amorphous thermoplasticcrystalline thermoplastic
thermoset plastic (Duroplast) elastomerthermoplastic
8ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
Identification:Requirements for a model targeting polymers
Plastic incompressibility is not a realistic assumption for the most polymers Hence a pressure dependency must be considered in the yield surface and the plastic potential
i. e. the plastic flow Initial isotropy – on a macroscopic level - will be disturbed eventually by straining:
Molecule chains will be stretched leading to induced anisotropic behaviour Different behaviour in tension, compression and shear direction
Homogeneousinitial state
Shear loading
Tension loading
Compression loading
Von Mises strain [-]
Vo
n M
ise
s st
ress
[M
Pa
]
9ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
Identification:Requirements for a model targeting polymers
True strain
Tru
e St
ress
In addition crazing and the development of shear bands have to be taken into account
Young’s modulus and failure strain show a strong dependency on the strain rate Sometimes even viscose effects can be observed in the elastic region Investigation on the unloading behaviour show damage effects (strain rate dependent)
[Junginger 2002]
Crazing effect Shear band development
Weak connectionTension connection Weak connection
Interlaminar defect
Amorphous region
Crystallized domainfillervoid
Separatedalien phase
End of chain
10ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
Identified yield loci for different plastics
Polycarbonate
[Vogler 2005]
Polypropylene (PP)
Polyvinylchloride (PVC) Epoxy resin CY232 (EP)
11ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
Classification of polymers (from a structural point of view) according to their mechanical behaviour
elastomers elastic foams
crushable foams Plastics/polymers
Which of the observed mechanical effects are important to consider for the targeted application of the constitutive model?
Hyperelastic/viscous behaviour
Visco-hyperelastic-visco-plastic behaviour
Identification summary: Structures made of plastics
Polymer blends show a wide range in their characteristic behaviour!
12ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
SAMP-1: Semi-Analytical Model for Polymerswith C1-continuous yield surface
vmg pσ α= −2 2
Plastic potential:
( , , )plvm vmf p A A p A pσ ε σ= − − −2 2
0 1 2 0
Yield surface:
p
f = 0
3
1
0
q
To achieve a fast and easy calibration process, test results from tension, compression and shear tests can be fed directly into SAMP-1 via table definitions:
compressiontension
shear
22 2
0 1 2
33 9 9c t c t s
s sc t c t
A A Aσ σ σ σ σσ σσ σ σ σ
− −= = =
Tension test data
tε
tσ
Compression test data
cε
cσ
Shear test data
sε
sσ
Therefore the yield surface coefficients A0,1,2 are calculated directly from stresses gained from a table lookup:
13ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
SAMP-1: Damage and failure
( ) [0,1[plχ ε =
cd
Damaging of the stresses by scalar curve definition (plastic damage)
( )( )pleff pl χ ε= −σ σ 1
0,00 0,01 0,02 0,03 0,04 0,05
0
0
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
6
6
6
6
7
7
7
7
8
8
8
8
9
9
9
9
10
10
10
10
11
11
11
11
12
12
12
12
13
13
13
13
14
14
14
14
15
15
15
15
16
16
16
16
17
17
17
17
18
18
18
18
19
Spalte B Spalte B Spalte B
wahre Dehnung [-]
wah
re S
pann
ung
[MP
a] E0Eeff1 Eeff2
Tru
e St
ress
True strain
TestApproximated effective modulus of elasticity
Failure onset defined by the parameter , further fading of the element defined by
d
ε p
ε∆ prupt
cd
1.0
pruptε∆
14ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
Verification and calibration
Verification of the implemented model was done by means of simple, strain driven one-element tests. Clearly, the input as curve definitions should be given by the model directly as output for the corresponding load cases.
Limiting cases (e. g. standard von Mises plasticity) have been checked against available constitutive models in the software package LS-DYNA.
Robustness and stability - not efficiency – were checked during the whole V&V process and was steadily improved.
Verification
The calibration process is somewhat simplified for a semi-analytical model, since test results despite being gained through small structural tests, are fed to the constitutive model directly.
Calibration
15ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
-200
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30
force
[N]
displacement [mm]
PP_EPDM tensile tests
experiment quasi staticexperiment slowly
experiment middle experiment high
simulation quasi staticsimulation slowly
simulation middlesimulation high
Calibration PP_EPDM -1-
Tensile test
48.6
mm
8x20 mmF
orce
Displacement
F
F
Tensile test conducted by Ernst-Mach-Institute/Freiburg/Germany
- for different strain rates Quasi static ≈ 1e-04 [mm/ms] Low ≈ 7e-03 [mm/ms] Medium ≈ 0.5 [mm/ms] High ≈ 8.75 [mm/ms]
- with unloading Material model calibrated for 2mm shell elements (BT, 1 point integ.)
16ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
0
50
100
150
200
250
300
350
400
450
500
0 0.5 1 1.5 2
force
[N]
displacement [mm]
tensile tests with unloading
experiment unloadingsimulation with damage
simulation no damage
Calibration PP_EPDM -1-
Tensile test
48.6
mm
8x20 mmF
orce
Displacement
Unloading at 125% yield stress
F
F
Tensile test conducted by Ernst-Mach-Institute/Freiburg/Germany
- for different strain rates Quasi static ≈ 1e-04 [mm/ms] Low ≈ 7e-03 [mm/ms] Medium ≈ 0.5 [mm/ms] High ≈ 8.75 [mm/ms]
- with unloading Material model calibrated for 2mm shell elements (BT, 1 point integ.)
17ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
0
50
100
150
200
250
300
350
400
450
500
0 5 10 15 20 25 30
force
[N]
displacement [mm]
tensile tests with unloading
experiment unloadingsimulation with damage
simulation no damage
Calibration PP_EPDM -1-
Tensile test
48.6
mm
8x20 mmF
orce
Displacement
Unloading at 80% rupture strain
F
F
Tensile test conducted by Ernst-Mach-Institute/Freiburg/Germany
- for different strain rates Quasi static ≈ 1e-04 [mm/ms] Low ≈ 7e-03 [mm/ms] Medium ≈ 0.5 [mm/ms] High ≈ 8.75 [mm/ms]
- with unloading Material model calibrated for 2mm shell elements (BT, 1 point integ.)
18ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
0
0.5
1
1.5
2
2.5
3
0 2 4 6 8 10 12 14 16
force
[N]
displacement [mm]
DKI PP_EPDM compression tests : 2.5mm mesh
experimentsimulation
Calibration PP_EPDM -2-
Compression test
To achieve this fit from tension test data, the shear
curve had to be multiplied by a factor of 2.0!
40x60 mm
F
F
For
ce
Displacement
Compression test conducted at DKI/Germany Quasi static loading Thickness = 4.0 mm Straining measured additionally by optical analysis (GOM) Specimen was fixed at top/bottom and hold sideways to prevent
buckling The tabulated input data had to be transformed into true stress/true
equivalent plastic strain curves Material model calibrated for 2.5 mm shell elements (BT, 1 point integ.)
19ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
Calibration PP_EPDM -3-
Shear test Shear test conducted at DKI/Germany Quasi static loading Thickness = 4.0 mm Straining measured additionally by optical analysis (GOM) Specimen was fixed at top and bottom Material model calibrated for 1.0 mm shell elements (BT, 1 point integ.)
F
F
0
50
100
150
200
250
300
350
400
450
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
force
N
displacement mm
PP_EPDM - Shear Test
experimentsimulation
For
ce
Displacement
Artificially increased stiffness and strength due to enforced
convexity of yield surface.
20ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
Validation PP_EPDM
Three point bending test
0
5
10
15
20
25
30
35
40
45
0 2 4 6 8 10 12 14 16
force
[N]
displacement [mm]
Bending test : PP_EPDM : 2mm shells
experimentsimulation SAMP1
vonMises
For
ce
Displacement
SAMP-1 compared to tension test-validated von Mises input
parameters!
F
Specimen size 10 x 133 x 3.8 mm Downward prescribed displacement (quasi static) Solid elements, 1mm mesh size
Overall we see good agreement with the results of small bending validation tests so far. However, tests on component basis (bumper, fascia etc.) are still to be done.
21ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
Most critical issues have been addressed with SAMP-1 Damage and strain rate dependence Failure and unloading Load direction dependent behaviour Pressure dependent plastic potential
Features still missing: Crazing Transition to anisotropic behaviour
Future work: Further testing of material model Calibration and validation of more polymers Simulation of more component tests
LS-DYNA Forum 2005, October 21&22, Bamberg, Germany
Roadmap for public release: SAMP-1 should be available in the next release of LS-DYNA (971)
Conclusions and outlook
22ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
Thank you for your attention.
23ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
Stress update algorithms
( )( )( )
( )
1 1 1
1
1
1
1
1
1
1
1 1
1 1 11
:
:
: : :
: :
:
:
p pn n n n
p pn n n
p pn n n
pn n
n
trial pn
n
n
n
n
n
trialn n n
C
C
C C C
C C
C
C r
σ ε ε ε
ε ε ε ε
ε ε ε ε
σ ε εσ ε
σ
σ
σ
σσ
λσ
+ + +
+
+
+
+ +
+
+
+
+
+
+ + +
= − − ∆
= + ∆ − − ∆
= − + ∆ − ∆
= + ∆ − ∆
= − ∆
= − ∆
nσ
1trialnσ +
sII
sIsIII
1nσ +
24ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
Stress update algorithms:NEWTON-iteration
nσ
1trialnσ +
sII
sIsIII
1nσ +
Backward Euler return mapping or general closest-point-projection or radial return
linearization around the elastic trail state :
1 11 1
11 1 1 1
( ) 0
( )
k k kn n
kk k k k n
ff f d
fd
f
λλ
λ λ λ λ
λ
− −+ +
−− − − +
= + ∆ =∆
∆ = ∆ + ∆ = ∆ −
∆
fully implicit algorithm
25ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
Stress update algorithms:cutting plane
explicit algorithm
1 11 1
11 1 1 1
( ) 0
( )
k k kn n
kk k k k n
ff f d
fd
f
λλ
λ λ λ λ
λ
− −+ +
−− − − +
= + ∆ =∆
∆ = ∆ + ∆ = ∆ −
∆
nσ
1trialnσ +
sII
sIsIII
linearization around the elastic trail state :
26ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
Validation by three point bending test with PP-EPDM
0,00E+00 1,00E+01 2,00E+01 3,00E+01 4,00E+01 5,00E+010
2,5
5
7,5
10
12,5
15
17,5
20
22,5
25
27,5
30
32,5
Spalte C
Spalte D
SAMP-0: experimental results (tension and compression test) have been used directly as input data for this three point bending test.
Specimen size 10 x 133 x 3.8 mm Downward prescribed displacement (quasi static) 3 integration points across thickness direction
Tensile TestCompression Test
27ADMOS 2005 Barcelona / 09-2005 / Haufe et al.
Three point bending test with PP-EPDM