1-Progressive Damage Analysis (Davila)

Aircraft Aging and Durability ProjectAircraft Aging and Durability Project

Progressive Damage AnalysisProgressive Damage Analysis

of Compositesof Composites

Carlos G. Carlos G. DávilaDávila

Cheryl A. RoseCheryl A. Rose

External CollaboratorsExternal Collaborators

Pedro P. Pedro P. CamanhoCamanho

Pere MaimíPere Maimí, Albert , Albert TuronTuron

Damage Mechanisms in Laminated CompositesDamage Mechanisms in Laminated Composites

fiber

kinking

ST Pinho, Imperial

College, UK

P Camanho, U. Porto, PT

+45º

-45º

0º

90º

R Olsson,

Imperial College, UK

C Soutis,

Sheffield, UK

E Gamstedt, SE

Finite Element Idealization of Structural DamageFinite Element Idealization of Structural Damage

Through-the-thickness crackThrough-the-thickness crack• fracture mechanics and modifications

•strain softening

Intralaminar Intralaminar DamageDamage•continuum damage models (CDM)

Delamination/DebondingDelamination/Debonding• fracture mechanics approaches

•cohesive elements

High Fidelity 3D ModelsHigh Fidelity 3D Models•RVE models (unit cell)

• transversely isotropic damage model (TIDM)

LaRC04 in Continuum Damage Model (CDM)LaRC04 in Continuum Damage Model (CDM)

Gibbs Free Energy

Strains:

Lamina Secant Relation

Rate of Damage Growth

fi: LaRC04 failure criteria as activation functions

Softening

Compression Tension

CDM ensures consistent material degradation

and mesh-independent solution

Progressive Damage AnalysisProgressive Damage Analysis

Damage Modes:

Tension Compression

Damage Evolution:

Thermodynamically-consistent material

degradation takes into account energy

release rate and element size for each mode.

LaRC04 Criteria

• In-situ matrix strength prediction

• Advanced fiber kinking criterion

• Prediction of angle of fracture (compression)

• Criteria used as activation functions within

framework of damage mechanics

• Ongoing work: refinements of theory in 3D

stress state and more accurate material

nonlinearity

!

"

Critical (maximum) finite element size:

Bazant CBT:

Validation of Progressive Damage AnalysisValidation of Progressive Damage Analysis

Prediction of size effects in notched composites•Stress-based criteria predict no size effect.

•LEFM, Point-Stress Method need empirical calibration.

•CDM damage model predicts scale effects w/out calibration.

Hexcel IM7/8552 [90/0/45/-45]3s CFRP laminate

(Camanho, 2007)

Challenges in Progressive Damage AnalysisChallenges in Progressive Damage Analysis

Splitting

Crack jumping

P. Camanho, 2007

E. Iarve, 2007

NRANRA

AwardsAwards

B. Cox, 2007

Interactions between matrix cracks

and delamination

Quasi-static Cohesive Damage ModelQuasi-static Cohesive Damage Model

t!0

LaRC Decohesion Element

Mixed-Mode

Fracture

Bilinear Traction-Displacement Law

CGd

F

=! ""#"

0 )(

"# "f

K(1-d)K

$#

Gc

(Technology adopted by ABAQUS, Inc.)

Validation of Mixed-Mode Validation of Mixed-Mode Delamination Delamination ModelModel

DCB, ENF and MMB test over PEEK/AS4 composite

Shell Cohesive ElementsShell Cohesive Elements

D

T

ShellD

T

Shell 33and FRFRKRK ==

Shell cohesive elements allowsimpler, more efficient analysis models

Formulation

Shell kinematics (FSDT)

Example: MMB test Analysis results

jShellkj

kD

Shellzj

yj

xj

j

j

j

j

j

Dk

k

k w

v

u

t

t

w

v

u

URU =

!!!!

"

!!!!

#

$

!!!!

%

!!!!

&

'

(((((((

)

*

+++++++

,

-±

=

!"

!#

$

!%

!&

'

3

3

or

000100

002

010

02

0001

.

.

.m

Shell cohesive element calculation

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7 8

Applied load, N.

Applied displacement, mm.

Linear

Test [Reeder, 2002]

Shell analysis

3D AnalysisTuron 2006

G = 1.123 N/mmc

Results indicate goodcorrelation between 3Danalysis, shell analysis,and experimental results

Shell Analysis

Test

3D Analysis

Gc=1.12 N/mmLinear


Applie

d load,

N.

Efficient Analyses w/ Shells & Cohesive ElementsEfficient Analyses w/ Shells & Cohesive Elements

Matrix cracks

Displacements

magnified 8X

Skin-flange interface,

decohesion elements

Skin-flange

interface

Delamination

Matrix failures

Layers of materialintegration points

Matrix failures

3D Model Shell Model

Efficient Analyses Efficient Analyses w/ w/ Shells & Cohesive ElementsShells & Cohesive Elements

Load

0°

Lugs

Failure Mode:

Cleavage

14-layer shell model of lug

Lugs

Simulation of Fatigue Simulation of Fatigue Delamination Delamination GrowthGrowth

Cohesive element: quasi-static + fatigue damage

Quasi-static damage Fatigue characterization (Paris Law) ENF - Fatigue structural simulation

Threshold

Overload

Cyclic load

• New cohesive law uses Paris Law to account for fatigue

damage growth (Turon-Camanho, 2007).

• Propagation law bounded by threshold and overload fracture.

• Model accounts for mode mixity GI/GII and load ratio, R.

• Model uses “standard” material properties.

• “Cycle Jump” strategy used to reduce re-calculations of

structural response.

m

cG

GC

N

A

!!"

#$$%

& '=

(

(0=

!

!

N

A


Double Cantilever Beam

0,2 0,3 0,4 0,5 0,6 0,7 0,80,911E-6

1E-5

1E-4

1E-3

0,01

dA

/dN

GImax

/GIc

Numerical Experimental

Asp, Sjogren, Greenhalgh, J.

Comp. Tech. Res., 2001.

Mixed Mode Propagation


Fatigue growth of facesheet debond

Material

Characterization

Model of sandwich with fatigue cohesive elements Predicted

Life

Pressure

Traction-Displacement Laws for R-curve EffectsTraction-Displacement Laws for R-curve Effects

Experiments show that toughnessGc is a function of crack length, a.

A trilinear traction law for cohesive elements and forcontinuum damage models can account for thetoughening effect of fiber bridging and fiber pullout.

F

TestOriginal

Gc=75

Original, Gc=150

Lo

ad

, N


Modified

Trilinear

F

Test results: Pinho, ’06, Imperial College, UK.

Damage Toleranceanalysis of fuselage

Original and modifiedsoftening law for R-Curve

F

Symmetric FE model of CT specimen

High Fidelity Analyses: High Fidelity Analyses: Micromechanical levelMicromechanical level

0º

90º

Matrix crack

Delamination

90º

0º

0º

Transversely Isotropic Damage Model

High Fidelity Analyses: TIDMHigh Fidelity Analyses: TIDM

Transversely Isotropic Damage ModelTransversely Isotropic Damage Model

Compliance Matrix

*l

GdtdY

Fracture=! &

Damage defined in principal directions

Dissipated energy for crack growth is

regularized in terms of element size

(Maimí, 2007)

Micromechanical Level: TIDMMicromechanical Level: TIDM

90

0

90

High Fidelity Analyses: Process of Matrix CrackingHigh Fidelity Analyses: Process of Matrix Cracking

[0/904/0]

Transversely Isotropic Damage ModelTransversely Isotropic Damage Model


TIDM analysis is 3D and provides complete

picture of crack propagation


Test: J. Varna, Composites Science and Tecnology, 2001.

[02/904]s [±15/904]s

[±

30/904]s

[±40/904]s

Test

Analysis

Ex/E0

x %xy/%0xy Ex/E

0xy %xy/%

0xy

Comparison of measured and predicted Young’s Modulus

and Poisson’s coefficient using TIDM damage model

Validated Tools - Target: SAA w/ Industry PartnersValidated Tools - Target: SAA w/ Industry Partners

Approach:

•Collaborative SAA research between NASA and U.S. RotorcraftCompanies through CRI (T.K. O’Brien)

•Develop analytical methodologies to predict composite structure fatiguelife and damage tolerance

•Define/conduct delamination characterization testing needed foranalysis input parameters (specimens provided by Sikorsky/Bell)

Validation Test Articles:

Helicopter main rotor blade spar subjected to

tension/torsion fatigue loading

•• DurabilityDurability

Sikorsky

Stiffened tilt-rotor wing skin panel, post

BVID, compression fatigue loading, residual

strength

•• Damage ToleranceDamage Tolerance

Bell

Damage Models: Summary of ProgressDamage Models: Summary of Progress

Continuum damage model:Continuum damage model:! Uses LaRC04 criteria to account for all failure mechanisms.

! Energetic regularization using element size avoids mesh-dependency.

" Improved kinematic representation of ply damage needed when damage mode

interaction is important.

Cohesive models:Cohesive models:! Rigorous kinematic representation of a strong discontinuity.

! Possesses built-in energetic regularization.

! Newly developed shell and fatigue cohesive models.

" Previous information of the possible fracture planes is required.

Traction Curves for R-Curve Effect:Traction Curves for R-Curve Effect:! R-Curve toughening can be modeled with trilinear traction-displacement laws.

High-Fidelity 3D Models:High-Fidelity 3D Models:! Transversely Isotropic Damage Model can capture all modes of matrix cracking:

• crack initiation and propagation through the thickness and along the fibers.• process of crack saturation.• linking of matrix transverse cracks and delamination.

" Requires several elements through the thickness of every ply.

Documents

1-Progressive Damage Analysis (Davila)