Cohesive Solutions for Structural Integrity and Fatigue Life Prediction

University of Bristol, 12 March 2019

Carlos G. Dávila

Durability, Damage Tolerance, and Reliability BranchNASA Langley Research CenterHampton VAUSA

NASA Advanced Composites Program

Advanced Composites Project (ACP)Postbuckled Panel with BVID, Strength and Life

2

The NASA ACP seeks to reduce the

timeline required for development

and certification of new aircraft.

High fidelity analysis methods can

reduce the testing requirements of

primary aircraft structures.

A compression-loaded skin-stringer

panel was selected as the basis of

method validation.

Technical Challenge 1:

Accurate Strength and Life Prediction

Building Block: Compression-Loaded Skin-Stringer Panel

3

Material properties

Characterization of material properties based on “first principles”

Seven Point Bend Test Results

UT scan Analysis

• Can skin/stiffener be modeled with a single interface?

4

Shell/cohesive model

• Quasi-static• Fatigue

Simplified Shell Model of 3PB Specimen

Predicted

Test

Interface law w/ bridge

Interface law – nominal tape/tape

Bridge

d

s

Shell Model

Crack initiation

Propagation

Peak load

Simplified Shell Model of 3PB Specimen

Interface law w/ bridge

Interface law – nominal tape/tape

Bridge

d

s

Shell Model

Base Bridge

Gic = 0.24 0.600 N/mm

GIIc = 0.739 3.500 N/mm

Sigc = 90 3.45 Mpa

Tauc = 93 10.34 Mpa

KI = 5E+05 1.8E+04 N/mm3

Ksh = 1.6E+05 3.0E+04 N/mm3

BK = 2.07 3

Computed (Turon’s constraint)

Standard (initiation) Calibrated (propagation)

x3.5

Gc_ss/Gc_init

x 5.7

Bridging strengths

Bridging toughness

Global-Local Analysis of Large Structures

Example: design of hat-stiffened panel

Approach

Use Abaqus SUBMODELING approach to drive local model from global displacements

Investigate effects of flange termination on stiffener debonding of postbuckled panel

Square flange

terminationTapered flange

termination

Global

modelLocal models

Cohesive

layer

Skin Skin

Tapered flangeAbrupt flange termination

Issue:Design Options

7

Global-Local Analysis of Large Structures

Critical disbond location identified by performing axial sweep of flange.

Local model out-of-plane deformation Local model disbond

Global model out-of-plane

deformation

Left flange of

stringer examined

with local models

Critical location identified

by local model

8

Fatigue

Fatigue Propagation Rate Using the Paris Law

10

Murri, NASA/TM–2013-217966

( )max

d

d

maC G

N=

Turon Fatigue Cohesive Model

11

( )( )2

1d 1 d

d d

f c

f c

pz

d dd a

N l N

− + =

Turon Fatigue Damage Law

( )max

d

d

maC G

N=

• Both Gmax and lpz are global quantities that are difficult to extract from the integration points.

• The damage rate is “non-local,” and its implementation is difficult.• The Paris law does not apply to short cracks

However:

(Composites A, 2006)

S-N or Paris Law?

12

S-N Curve Paris Law

S-N or Paris Law?

13

S-N Curve Paris Law

S-N Curve and Paris law are related

Can we develop a cohesive model based on S-N that can predict crack propagation?

Cohesive Fatigue Damage Model

14

Consider case of bar subjected to cyclic load

Assume cohesive law is envelope of fatigue damage

What damage law?

F

Time

Cohesive Fatigue Damage Model

15

( )*

d

d

DD

N

= +

* c

f cD

− =

−

( )max

0

1d

FDf c

DN D

D

−−

= +

Number of cycles to failure obtained by integrating dN from A to B

A B

S-N curve

Consider damage law:

S-N Curve Corresponding to Damage Model

16

( )max

0

1d

FDf c

DN D

D

−−

= +

Damage model entirely defined by parameters and

S-N Diagram for Delamination

17

• A single line appears to fit the S-N curve from N = 1 to 107

• The parameters and of the damage model can be obtained by fitting experimental results

R = min/ max = 0.1

Endurance limit vs. tensile strength (R = -1)

18

[Chart generated with CES Edupack, GrantaDesign, S. Gorsse]

Goodman Diagram (GD)

19

e

c

mean

amp

0

R = −1

R = 1

R = 0.5R = 0 1

meanamp

e

c

= −

1

2

eR

c R

=

−

The GD is design tool that represents the locus of stress states corresponding to a runout stress or a given number of cycles to failure

R = min/ max

S-N curves for Different R Ratios

20

2

ceR

R

=

−2 cycles

Test data for R = 0.1

S-N curves are “anchored” at two points

Determination of Model Coefficients and

21

Experimental S-N data desirable but not needed to determine and

( )*

d

d

DD

N

= +

Flowchart of UMAT

22

Fatigue model was implemented as a UMAT user-written material subroutine for Abaqus cohesive elements

Analysis of Double Cantilever Beam Specimen (DCB)

23

Applied load remains constant

Detail of propagation zone

Propagation Rates for DCB Specimen

24

Test: Murri, NASA/TM–2013-217966

Analyses of DCB were conducted with 4 different applied loads (displacement control)

R = 0.1

R-Curve Effect on DCB Specimen

25

Test: Murri, NASA/TM–2013-217966

R-curve

Quasi-static response of DCB using superposition of bridging laws

Delamination Propagation Rates for DCB with R-Curve

26

Predicted delamination growth rates in a DCB specimen for several values of applied displacement (red) and applied force (green).

R = 0.1

Delamination Propagation Rates for DCB with R-Curve

27

Predicted delamination growth rates in a DCB specimen for several values of applied displacement (red) and applied force (green).

R = 0.1

Delamination Propagation Rates for DCB with R-Curve

28

Predicted delamination growth rates in a DCB specimen for several values of applied displacement (red) and applied force (green).

R = 0.1

Delamination Propagation Rates for DCB with R-Curve

29

Comparison of predicted delamination growth rates with R-curve bridging included with experimental results

R = 0.1

MMB – Delamination Propagation Rate

30

Test: Ratcliffe, 2014

MMB tests and analyses conducted under force control

Mode ratio = 0.5

R = 0.1

Effect of Stress Ratio R on Propagation Rates

31

( )* 1

d

d

m R

R

a GC

N G

−

=

Effect of Stress Ratio R on Propagation Rates

32

( )* 1

d

d

m R

R

a GC

N G

−

=

( )* 1m m R

= −

( )*

d

d

DD

N

= +

Present model

Allegri Model (2012)

Comparison with Allegri Model

33

( )*

d

d

DD

N

= +

Damage Model Allegri Model (2012)

S-N law

( )( )( )

1max

1

0

1d

1

FDf

c

N D

D D

−

=

− +

( )

( )

maxd

d 1 c

DD

N D

+ =

−

or,

( )1

b

R

=−

Paris Law

2m

Fatigue: Three Point Bend (3PB) Specimen

Skin/stiffener separation

3PB: Delamination Length vs. Cycle Count

Progression of cracks and delaminations in a 3PB specimen

Increasing load

Simplified Model of 3PB Specimen

37

Symmetric model Sigc = 90 MPaMesh: 0.072 mm

Concluding Remarks

38

Fatigue Cohesive Constitutive Model:• Based on S-N curve rather than Paris law.• Relies on relationships between S-N and Paris.• Simplified loading procedure keeps load constant during analysis.• Fatigue Model Parameters Obtained Without Test Data.

R-Curve Effects Modeled Using Cohesive Superposition• R-curve effect explains differences between load control and

displacement control.• R-curve is intended to capture effect of blunting, delving,

bridging, and migrations.

Initial Evaluation Conducted on 3PB Specimens• Extreme nonlinearity in results highlights the difficulty in

predicting fatigue.

• Additional work needed to confirm that the model can predict the propagation rates for different materials and loading conditions.