Post on 06-Dec-2021
1
Composite Materials 261 and 262
Stefan Hartmann1
David Moncayo2
1 DYNAmore GmbH, Stuttgart, Germany2 Daimler AG, Sindelfingen, Germany
11. LS-DYNA Forum 2012, 9. - 10. Oktober 2012, Ulm
2Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
� Introduction- failure mechanisms / modeling possibilities
� Summary and Outlook
� Material models 261 and 262 for intralaminar failure - *MAT_LAMINATED_FRACTURE_DAIMLER_PINHO- *MAT_LAMINATED_FRACTURE_DAIMLER_CAMANHO- summary and comparison
� Preliminary results- three point bending of flat specimen / three point bending of a hat profile / shear specimen /drop tower test
Outline
3Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
Introduction – failure mechanisms in fiber reinforced composites
4Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
� intralaminar- element: layered (thin/thick) shells
one solid element per ply- material: plasticity / damage models
� interlaminar (delamination)- cohesive elements- tiebreak contacts
Introduction – modeling possibilities
stacked shells
layered thinshell element
layered thin shell elements+ numerical „cheap“ (thickness does not
influence the critical time step size)+ combination of single layers to sub-laminates- no stresses in thickness dir. (no delamination)
layered thick shell elements+ 3D stress state+ combination of single layers to sub-laminates- thickness influences the critical time step size
solid elements+ 3D stress state- one element for every single layer (no layering) � numerical „expensive“
cohesive element
layered thinshell element
5Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
» no *SECTION_SHELL-keyword card needed» different material models allowed
*PART_COMPOSITE
Composite Lay up (Version 971)
$--------1---------2---------3---------4---------5---------6---------7---------8
$ PID| ELFORM| SHRF| NLOC| MAREA| HGID| ADOPT|
28 2 0.0 0.0 0.0 0 0
$ MID1| THICK1| BETA| MID2| THICK2| BETA2|
1 0.2 0.0 2 0.4 45.0
$ MID3| THICK3| BETA| MID4| THICK4| BETA4|
3 0.2 90.0
Listing of integrationpoints begins from the bottom
IP 1
IP 2
IP 3
0.0°
45.0°
90.0°
0.2
0.4
0.2
Introduction – layered thin shell definition with *PART_COMPOSITE
6Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
*MAT_261: [1]*MAT_LAMINATED_FRACTURE_
DAIMLER_PINHO
*MAT_262: [2]*MAT_LAMINATED_FRACTURE_
DAIMLER_CAMANHO
Material models for intralaminar failure
[1] Pinho, S.T., Iannucci, L.; Robinson, P.: “Physically-based failure models and criteria for laminated fiber-reinforced composites with emphasis on fiber kinking: Part I – Development & Part II – FE implementation”, Composites: Part A 37, 2006
[2] Maimí, P., Camanho, P.P., Mayugo, J.A., Dávila, D.G.: “A continuum damage model for composite laminates:Part I – Constitutive model & Part II – Computational implementation and validation”, Mechanics of Materials 39, 2007
(Development together with Daimler AG)
7Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
*MAT_261 (*MAT_LAMINATED_FRACTURE_DAIMLER_PINHO):
� constitutive law
( )ˆ 1 d= − ɶσ σσ σσ σσ σ4 damage parameter
; ; ;mat mac kink ad d d d
� 4 failure criteria
ad kinkd
matd macd
8Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
1a
a
t
fX
σ= =
2 2
2 2 2
1 0
1 0
m
m
T L
b
T T n L L n
kink
n T L
b
T T L
ifS S
f
ifY S S
τ τσ
µ σ µ σ
σ τ τσ
+ = ≤
− − =
+ + = >
cos(2 ) sin(2 )2 2
sin(2 ) cos(2 )2
cos( ) sin( )
m m
m
m
m
m m m
b c b c
n b c
b c
T b c
L a b c a
ψ ψ
ψ
ψ
ψ
ψ
σ σ σ σσ φ σ φ
σ στ φ σ φ
τ σ φ σ φ
+ −= + +
−= − +
= +
ɶ ɶ ɶ ɶɶ
ɶ ɶɶ
ɶ ɶ
(interaction, transformation to fracture plane - 3D)
2 2 2
1n T L
mat
t T L
fY S S
σ τ τ = + + =
(transformation to fracture plane)
(Mohr-Coulomb: Puck/Schürmann)
2 2
1T L
mac
T T n L L n
fS S
τ τ
µ σ µ σ
= + =
− − 0
:
:
fracture plane for pure compression
fracture plane under general loading
φ
φ
fiber tension (maximum stress)
fiber compression (3D-kinking model)
matrix failure: transverse tension
matrix failure: transverse compression/shear
*MAT_261 (*MAT_..._PINHO):
9Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
� linear damage laws
11 22 12 23 31
11 22 12 23 31
22 12 23 31
22 12 23 31
ˆ (1 )[ , , , , ]
ˆ (1 )[ , , , , ]
ˆ (1 )[ , , , ]
ˆ (1 )[ , , , ]
a
kink
mat
mac
d
d
d
d
σ σ σ σ σ
σ σ σ σ σ
σ σ σ σ
σ σ σ σ
= −
= −
= −
= −
ɶ ɶ ɶ ɶ ɶ
ɶ ɶ ɶ ɶ ɶ
ɶ ɶ ɶ ɶ
ɶ ɶ ɶ ɶ
σσσσ
σσσσ
σσσσ
σσσσε
σ
0σ
fε0ε
L
Γ
0
0( )
f
i fd
ε εε
ε ε ε
−=
−
, , , , :a kink b T L
Γ Γ Γ Γ Γ
fracture toughness from: CT, CC, 4-point bending, mode II interlaminar fracture (T,L)
:L
internal (characteristic) length for objectivity (localization!)
*MAT_261 (*MAT_LAMINATED_FRACTURE_DAIMLER_PINHO):
10Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
1D plasticity formulation with combined isotropic/kinematic hardening –coupled with linear damage model
Nonlinearity defined via*DEFINE_CURVE
*MAT_261 (*MAT_LAMINATED_FRACTURE_DAIMLER_PINHO):
� in-plane shear behavior
11Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
11 11
1 1 1
11 11
22 22
2 2 2
22 22
d d d
d d d
σ σ
σ σ
σ σ
σ σ
+ −
+ −
−= +
−= +
( )
( )
( )
21
1 1 2
12
1 2 2
6 12
10
1
10
1
10 0
1
d E E
HE d E
d G
ν
ν
−
−
= − −
−
� constitutive relation1
: :−= → =ε σ σ εε σ σ εε σ σ εε σ σ εH H
5 damage variables
� 4 failure criteria (LaRC03/04)
1 1 1
2 2 2
1 1 1
2 2 2
0
0
0
0
F r
F r
F r
F r
φ
φ
φ
φ
− − −
− − −
+ + +
+ + +
= − ≤
= − ≤
= − ≤
= − ≤
damage activation functions
( ) ( ) ( ) ( ) ( )1 1 1 1 1 2 2 2 2 6 2, ; ; ; ;d r r d r d r d r d r− − + + + − − + + +
*MAT_262 (*MAT_LAMINATED_FRACTURE_DAIMLER_CAMANHO):
12Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
� failure surface (assembly of 4 sub-surfaces)
*MAT_262 (*MAT_LAMINATED_FRACTURE_DAIMLER_CAMANHO):
13Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
(transformation to fracture plane - 2D)
(assumption: crack perpendicular to mid-surface)
(transformation to fracture plane)
fiber tension (maximum strain – LaRC04 )
fiber compression (LaRC03)
matrix failure: transverse tension (LaRC04)
matrix failure: transverse compression/shear (LaRC04)
2
11 12 12
1
TX
σ ν σφ +
−=
ɶ ɶ
2
12 22
1
m m
L
LS
σ µ σφ −
+ =
ɶ ɶ
11 22
12 12
11 22 11 22
22 12
sin(2 ) cos(2 )2
cos(2 ) sin(2 )2 2
m C C
m C C
σ σσ ϕ σ ϕ
σ σ σ σσ ϕ σ ϕ
−= − +
+ −= − −
ɶ ɶɶ ɶ
ɶ ɶ ɶ ɶɶ ɶ
2 2
22 22 12
2 22
2
12 22
2 22
(1 ) ( 0)
( 0)
T T L
L
L
gY Y S
S
σ σ σφ σ
σ µ σφ σ
+
+
= − + + ≥
+= <
ɶ ɶ ɶɶ
ɶ ɶɶ
(in-plane shear & transverse tension)
(in-plane shear & small transverse compression)
2 2
2
eff eff
T L
T LS S
τ τφ
−
= +
[ ]22 0 0 0
0 12 22 0
cos( ) sin( ) cos( ) cos( )
cos( ) cos( )sin( )
eff
T T
eff
L L
τ σ α α µ α θ
τ α σ µ σ α θ
= − −
= +
ɶ
ɶ ɶ
*MAT_262 (*MAT_LAMINATED_FRACTURE_DAIMLER_CAMANHO):
14Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
� evolution of threshold (internal) variables
{ }
{ }
1 1
1 /2 1 /2 1 /2
1 1 1
1 /2 1 /2 1 /2 1 /2
max 1, ,
max 1, , ,
n n n
n n n n
r r
r r r
φ
φ
+ +
− − − − − −
+ + +
+ + + + − − + +
=
=
compression:
tension:
� evolution of damage variables
bi-linear in fiber direction linear in transverse direction
( )( ) ( )
( )
, ,1
m X G n X md r
E E rε= − −
, , , ,XT XC YT YC SL
G G G G G
fracture toughness from: CT, CC, DCB, - , 4-ENF
:ℓ internal (characteristic) length for objectivity (lokalization!)
[ ]( )0 1d ∈ →
[ ]( )1r ∈ → ∞
no damage due to crack (tension);crack closure
m
n
*MAT_262 (*MAT_LAMINATED_FRACTURE_DAIMLER_CAMANHO):
15Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
1D elasto-plastic formulation with combined iso/kin hardening – coupled to a linear damage evolution law
SLG
l
12ε
12σ
LS
*MAT_262 (*MAT_LAMINATED_FRACTURE_DAIMLER_CAMANHO):
16Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
*MAT_261 (Pinho) *MAT_262 (Camanho)
failure criterion may use 3D-stress state failure criterion based on plane stress assumption
fiber tension
maximum stress criterion maximum strain criterion
fiber compression
complex 3D-fiber kinking model, expensivesearch for controlling fracture plane
use constant fiber misalignment angle based onshear and longitudinal compressive strength
matrix failure: transverse tension
search for controlling fracture plane assume perpendicular fracture plane
matrix failure: transverse compression/shearsearch for controlling fracture plane assume constant fracture plane angle (i.e. 53 )
in-plane shear treatment1D-plasticity model with combined (iso/kin)
hardening based on *DEFINE_CURVE1D-plasticity model with combined (iso/kin)
linear hardening
damage evolutionlinear damage based on fracture toughness bi-/linear damage based on fracture toughness
17Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
*MAT_261: (*MAT_LAMINATED_FRACTURE_DAIMLER_PINHO) (together with Daimler AG)� solid, shell, tshell (3,5)� linear elastic orthotropic� coupled failure criteria (plane stress) – fracture plane:
fiber tens./compr., matrix tens./compr.� complex 3D fiber kinking model� 1D plasticity formulation for in-plane shear� linear damage evolution based on fracture toughness
*MAT_262: (*MAT_LAMINATED_FRACTURE_DAIMLER_CAMANHO) (together with Daimler AG)� solid, shell, tshell (3,5)� linear elastic orthotropic� coupled failure criteria (plane stress) – fracture plane� 1D plasticity formulation for in-plane shear� bi-linear damage evolution based on fracture toughness
S.T. Pinho, L. Iannucci, P.Robinson:Physically-based failure models and criteria for laminated fibre-reinforced composites with emphasis on fibre kinking:Part I: Development & Part II: FE implementation, Composites: Part A 37 (2006) 63-73 & 766-777
P. MaimÍ, P.P. Camanho, J.A. Mayugo, C.G. Dávila:A continuum damage model for composite laminates:Part I: Constitutive model & Part II: Computational implementation and validation, Mechanics of materials 39 (2007) 897-908 & 909-919
Material Models in LS-DYNA (Intralaminar)
18Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
Preliminary results – three point bending of flat specimen
� single shell with a thickness of 4mm / carbon fibers in epoxy resin- [0 ]5s (fibers in longitudinal direction of the plate) - [90 ]5s (fibers in transverse direction of the plate)
19Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
Preliminary results – three point bending of a hat profile
matrix failure
� single shell with a thickness of 2mm / carbon fibers in epoxy resin- [90 /0 /45 /-45 /0 /90 /-45 /45 /0 /90 ]
Shell sublaminatesLocal failure
InterfacesLocal failure
20Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
Preliminary results – shear specimen
� single shell with a thickness of 2mm / carbon fibers in epoxy resin- [45 /-45 ]3S
Experiment Simulation
Shear plasticity
tensiletest
21Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
� two continuum damage models implemented into LS-DYNA- advanced, coupled failure surfaces (transformation to fracture plane)- bi-linear/linear damage evolution laws (based on fracture toughness)- 1D elasto-plastic formulation for in-plane shear non-linearity
� preliminary results - material models able to represent general behavior, especially non-linearity in shear
� many detailed numerical studies necessary for further improvements - comparison and parameter studies with experiments- different element formulations and modeling techniques (stacked shells)
Summary
Outlook
Acknowledgement
� Thank for technical support to:Prof. Pedro Camanho, Dr. Pere Maimí & Dr. Silvestre Pinho
22Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany
Thank you!