composite materials 261 and 262 - ls-dyna

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1 Composite Materials 261 and 262 Stefan Hartmann 1 David Moncayo 2 1 DYNAmore GmbH, Stuttgart, Germany 2 Daimler AG, Sindelfingen, Germany 11. LS-DYNA Forum 2012, 9. - 10. Oktober 2012, Ulm

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Page 1: Composite Materials 261 and 262 - LS-DYNA

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

Page 2: Composite Materials 261 and 262 - LS-DYNA

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

Page 3: Composite Materials 261 and 262 - LS-DYNA

3Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany

Introduction – failure mechanisms in fiber reinforced composites

Page 4: Composite Materials 261 and 262 - LS-DYNA

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

Page 5: Composite Materials 261 and 262 - LS-DYNA

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

Page 6: Composite Materials 261 and 262 - LS-DYNA

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)

Page 7: Composite Materials 261 and 262 - LS-DYNA

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

Page 8: Composite Materials 261 and 262 - LS-DYNA

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):

Page 9: Composite Materials 261 and 262 - LS-DYNA

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

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):

Page 10: Composite Materials 261 and 262 - LS-DYNA

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

Page 11: Composite Materials 261 and 262 - LS-DYNA

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):

Page 12: Composite Materials 261 and 262 - LS-DYNA

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):

Page 13: Composite Materials 261 and 262 - LS-DYNA

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):

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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):

Page 15: Composite Materials 261 and 262 - LS-DYNA

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):

Page 16: Composite Materials 261 and 262 - LS-DYNA

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

Page 17: Composite Materials 261 and 262 - LS-DYNA

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)

Page 18: Composite Materials 261 and 262 - LS-DYNA

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)

Page 19: Composite Materials 261 and 262 - LS-DYNA

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

Page 20: Composite Materials 261 and 262 - LS-DYNA

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

Page 21: Composite Materials 261 and 262 - LS-DYNA

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

Page 22: Composite Materials 261 and 262 - LS-DYNA

22Composite Materials 261 and 262 11. LS-DYNA Forum 2012, 9.-10. October 2012, Ulm, Germany

Thank you!