1 Alpha STAR Corp.

Workshop on Verification and Validation of Solid Mechanics and Life Prediction Software, May 9, 2012, Phoenix, AZ

ASTM Committee E08

Mohit Garg, Frank Abdi (Ph.D)

Alpha Star Corporation, Long Beach, CA, USA

and

Elvin Eren, Professor Kamran Nikbin (Ph.D)

Imperial College, London, United Kingdom

Fatigue Life Prediction for Crenellated and

Constant Thickness Steel Panels

2 Alpha STAR Corp.

Agenda

Paper Objective

Predict and test validate Fatigue Crack Growth:

Constant Thickness Panel

Delay Crack Growth in service by design of Crenellated panels

Materials: Steel (S420M, S690QL)

Fracture toughness Determination (FTD) Prediction

Fatigue crack growth (FCG) Prediction

Panels: Fatigue crack growth (a-N curve) Prediction

Constant Thickness Panel

Delay Crack Growth in service by design of Crenellated panels

Comparison of analytical and experimental test results

Summary

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Metal Lifing Approach for unMetal Lifing Approach for unMetal Lifing Approach for unMetal Lifing Approach for un----notched, and notched specimensnotched, and notched specimensnotched, and notched specimensnotched, and notched specimens

• Part I: Fracture Toughness Determination• Part II: Fatigue Crack Growth vs. stress Intensity factor • Part III: a) Fatigue Strength-Life (S-N), a-N; b) Creep Time (a-t), da/dt; c) Fatigue creep Interaction

References

1. B. Farahmand, “Fracture Toughness Determinations (FTD) and Fatigue Crack Growth”. Book Chapter - “Composites, Welded Joints,

and Bolted Joints” Kluwer Academic Publisher, 2000.

2. Metal Probabilistic: Bob Farahmand, Frank Abdi, “Probabilistic Fracture Toughness, Fatigue Crack Growth Estimation Resulting From

Material Uncertainties” ASTM Conference Paper 11569 November 6-7, 2002.

Three-Steps Fatigue Metal Approach

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Crenellation• Crenellation as a novel solution to the growing fatigue crack

– hence integrity problem has emerged aiming to retard a growing crack towards

the stringer, which has initiated in parent material.

– Growing fatigue crack perpendicular to reinforcements, considered as “worst

case” design scenario for thin-walled welded structures.

• Joining stringers to main body of structure, by using two designphilosophies:– differential design: requiring use of rivets

– integral design: requiring welding of the stringer to the main structure

Crack paths in uniformly stressed

differential and integral structures

• In fracture mechanics, differential design is more advantageous, as a potential crack in main body of structure will continue extending under the stringer,

– which may keep the stringer undamaged for a certain period

– If a crack, evolves in a structure where stringer is joined by welding,

• crack branching may occur leading to failure of stringer or separation of stringer from main structure

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Crenellated wide platesCrenellated wide platesCrenellated wide platesCrenellated wide plates

Crenellated wide plates containing butt & fillet welds

Fillet weld specimenButt weld specimen

Various crenellatedwide plates

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Summary of Results: Improvement of Fatigue Crack Growth in Summary of Results: Improvement of Fatigue Crack Growth in Summary of Results: Improvement of Fatigue Crack Growth in Summary of Results: Improvement of Fatigue Crack Growth in

Crenellated Vs. Constant Thickness Steel Panels [S420M]Crenellated Vs. Constant Thickness Steel Panels [S420M]Crenellated Vs. Constant Thickness Steel Panels [S420M]Crenellated Vs. Constant Thickness Steel Panels [S420M]

Von Mises Stress

Von Mises Stress

Von Mises Stress

Crenellated PanelConstant

Thickness Panel

Von Mises Stress

0

50

100

150

200

250

1.00E+04 1.00E+05 1.00E+06Hal

f C

rack

Le

ngt

h E

xte

nsi

on

[m

m]

N [Cycles]

S420M Steel (Stress Ratio = 0.1; Kc = 250.43 MPa.sqrt(m); KIC = 200.85

MPa.sqrt(m))

CP:Test

Sim: CP: No PFA

Sim:CP: PFA

CTP:Test

Sim:CTP: Sim:PFA

CP: Crenellated PanelCTP: Constant Thickness Panel

Variable Thickness Panel

Includes PFA & LEFM Theory

Ref: Sefika Elvin EREN, ‘Advancing The Damage Tolerance Of Laser Beam Welded Steels Using Crenellation Technique,

20.11.2011, Ph.D. Thesis in Structural Integrity, by Dipl.-Ing. Imperial College London, UK

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PART 1: Fracture Toughness Determination

c

U

c

UT

E

c UF

∂

∂+

∂

∂+= 2

2πσ

UP = UF + UU

UP = Total energy per unit thickness absorbed in plastic straining around the crack tip,

where UF and UU are the energy absorbed per unit thickness in plastic straining of the material beyond the

ultimate at the crack tip and below the ultimate stress near the crack tip, respectively

Energy release rate

near the crack tip for

uniform straining

Energy release rate

at the crack tip for

non-uniform straining

TE

c2

2

=πσ

Griffith Equation

Extended Griffith

equation to account

for crack tip plasticity

S tre s s

S tra in

U n ifo rm

D e fo rm a t io n

N o n -u n ifo rm

D e fo rm a t io n

U U

U F

ε fε U

σ U

σ f

N o n -u n ifo rm

s tra in in g

U n ifo rm

s tra in in g

A c e n te r c ra c k in a w id e p la te

A re a s a s s o c ia te d w ith th e u n if o r m a n d

N o n -u n if o r m s tra in in g

S tre s s

S tra in

U n ifo rm

D e fo rm a t io n

N o n -u n ifo rm

D e fo rm a t io n

U U

U F

ε fε U

σ U

σ f

N o n -u n ifo rm

s tra in in g

U n ifo rm

s tra in in g

S tre s s

S tra in

U n ifo rm

D e fo rm a t io n

N o n -u n ifo rm

D e fo rm a t io n

U U

U F

ε fε U

σ U

σ f

S tre s s

S tra in

U n ifo rm

D e fo rm a t io n

N o n -u n ifo rm

D e fo rm a t io n

U U

U F

ε fε U

σ U

σ f

N o n -u n ifo rm

s tra in in g

U n ifo rm

s tra in in g

N o n -u n ifo rm

s tra in in g

U n ifo rm

s tra in in g

A c e n te r c ra c k in a w id e p la te

A re a s a s s o c ia te d w ith th e u n if o r m a n d

N o n -u n if o r m s tra in in g

A re a s a s s o c ia te d w ith th e u n if o r m a n d

N o n -u n if o r m s tra in in g

(Theoretical Background)

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UUU hW

c

U=

∂

∂

−

−+

−−

++= βε

ε

εε

εε

σ

σεσεσ

µπσ1

1

*

1

11

n

n

TL

TU

TTU

TLTF

n

TU

TTUTUn

nk

PNUFh

Fh2T

2

Ec

FFF Wh

c

U=

∂

∂

Residual Strength Capability Equation

(A Relationship Between Crack Length & Applied Stress)

PART I: Fracture Toughness Determination [FTD]

Mixed mode fracture and thickness parameters:

μ is the thickness correction factor

K is the thickness correction factor

β is 1.3 and 0.127 for the plane stress and strain conditions, respectively

(Theoretical Background)

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Ref: Bahram Farahmand a, Kamran Nikbin, Predicting fracture and fatigue crack growth properties using tensile

properties, Engineering Fracture Mechanics 75 (2008) 2144–2155

Fracture Toughness Determination

(Theoretical Background)

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PART II: Fatigue Crack Growth [FCG]

( )

( )( )

q

c

n

p

thnn

KR

KR

K

KKfC

dN

da

−

∆−−

∆

∆−∆−

=

111

11

Forman-Newman-de Koning (FNK)

Crack Growth Rate Empirical

Relationship -NASGRO

Threshold

Region

Paris

Region

Accelerated

Region

FNK Equation Variables:C, n, p, and q ~ empirically derived constants comes from tests or virtual testing

R ~ stress ratio

∆K ~ stress intensity factor range

∆Kth

~ threshold stress intensity factor

f ~ crack opening function (incorporates the effect of closure behavior on crack growth rate under constant

amplitude loading for plasticity-induced crack closure, as defined by Newman)

(Theoretical Background)

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G: strain energy release rate

K: stress intensity factor; Kth: threshold stress intensity factor; Kc: critical stress

intensity factor, N: cycles; a: crack length

Compute Stress Intensity Factor using FE and VCCT

KvsdN

da∆.

Initial crack length a

dNRelease nodes:

a = a+da N=N+dN

stop -fracturefast

initiation

−>∆

−∆<∆

CKKIf

FCGNoKKIf th

da is fixed

(element size)

aB

vvFG

y

I∆

−≅

2

)( 4312VCCT( ) ax

Iax

KRK

EGK

Im

Im

1−=∆

=

PART III - Methodology : Virtual Crack Closure Technique (VCCT)

Ref: B. Farahmand, C. Saff, De Xie and F. Abdi, “Estimation of Fatigue and Fracture Allowables For Metallic Materials Under Cyclic Loading”.

AIAA-2007-2381, Honolulu, Hawaii, April, 2007.

12 Alpha STAR Corp.

PART III - Methodology: Critical Damage and Fracture Events

PFA•Determine: 5 stages of damage mechanism,

damage pattern & crack path, failure mechanisms.

•Advantage: not requires predefined crack path.

•Disadvantage: removing damaged elements

can create stress singularity.

Fracture Mechanics Theory•Disadvantage: predefined crack path,

fracture toughness

•Advantage: stress singularity

Ref: Xie D and Biggers, Jr. SB, “Progressive crack growth analysis using interface element based on the virtual crack closure technique, “, Finite Elements in Analysis and Design, 2006, Vol 42, page 977-984.

Damage Initiation/growth, and Fracture initiation/growth, Residual Strength

Crack growth strategy in composite under

static loading with GENOA/PFA

Displacement

Load

1212

12

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Part 1: Fracture Toughness Prediction Vs. Test (Steel S420M)Part 1: Fracture Toughness Prediction Vs. Test (Steel S420M)Part 1: Fracture Toughness Prediction Vs. Test (Steel S420M)Part 1: Fracture Toughness Prediction Vs. Test (Steel S420M)

Output: Fracture Toughness vs. Thickness

Ref: B. Farahmand, “Fatigue and Fracture Mechanics of High Risk Parts”, Chapman and Hall, 1997

Input

0

100

200

300

400

500

600

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Eng. Stress [MPa]

Eng. Strain [mm/mm]

Input: Stress-Strain Curve

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Part 1: Fracture Toughness [S690 QL]Part 1: Fracture Toughness [S690 QL]Part 1: Fracture Toughness [S690 QL]Part 1: Fracture Toughness [S690 QL]

Plane Strain Fracture

Toughness

Plane Stress Fracture

Toughness @ 6mm

KC @ 6.0mm = 151.6 MPa.sqrt(m)

KC @ 11.54mm = 130.0 MPa.sqrt(m)

KIC = 83.25 MPa.sqrt(m)

Plane Stress Fracture

Toughness @ 11.45mm

Test @ 11.54 mm =

131.68 MPa.sqrt(m)

Output: Fracture Toughness vs. Thickness

InputInput: Stress-Strain Curve

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Part 2: Fatigue Crack Growth Prediction Vs. Test (Steel]Part 2: Fatigue Crack Growth Prediction Vs. Test (Steel]Part 2: Fatigue Crack Growth Prediction Vs. Test (Steel]Part 2: Fatigue Crack Growth Prediction Vs. Test (Steel]

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

10 100 1,000

da/dN [mm/cycles]

? K [MPa.sqrt(m)]

S420M Steel (Stress Ratio = 0.1; Kc = 250.43 MPa.sqrt(m); KIC = 200.88 MPa.sqrt(m))

GENOA FCG

Test

• Same FCG curve was used for both constant thickness and variable thickness panels.

• For FE Analysis the blue curve was used to predict the a-N curve for constant thickness and

variable thickness panels.

S420M Steel, R=0.1, K1C= 200.88 (MPa.sqrt(m))

S690QL Steel, R=0.1, K1C= 83 (MPa.sqrt(m))

Prediction VS Test

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PART 2: Fatigue Crack Growth (Steel S420M)PART 2: Fatigue Crack Growth (Steel S420M)PART 2: Fatigue Crack Growth (Steel S420M)PART 2: Fatigue Crack Growth (Steel S420M)

• Fracture Toughness value was taken from the test and KIC estimated from FTD code

• beta1, beta2 values were adjusted slightly to match the test curve (rotation of FCG curve)

• Kth Ratio was adjusted slightly to match the dKth value

• Imperial Test Specimen stopped before possible net-section yielding (indicated by blue line)

• Software FCG curve shows net-section yielding region (right side of blue line)

• FCG Curve and Imperial Test are in good agreement

dK [MPa.sqrt(m)]

da/d

N [

Cycle

s/m

m]

Output: Fatigue Crack Growth Vs. dkInput

Predicted K1c

Net section yield

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• Fracture Toughness (KIC and KC) values were estimated from FTD code

• beta1, beta2,Kth Ratio values were adjusted slightly

dK [MPa.sqrt(m)]

PART 2: Fatigue Crack Growth (Steel S690QL)PART 2: Fatigue Crack Growth (Steel S690QL)PART 2: Fatigue Crack Growth (Steel S690QL)PART 2: Fatigue Crack Growth (Steel S690QL)

Output: Fatigue Crack Growth Vs. dkInput

Predicted K1c

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Constant & Variable Thickness Specimens (Fatigue)Constant & Variable Thickness Specimens (Fatigue)Constant & Variable Thickness Specimens (Fatigue)Constant & Variable Thickness Specimens (Fatigue)Constant Thickness

Variable Thickness

Various Crenellated M(T)200 specimen of AISI 304 steel

Ref: "S.E. Eren, “Advancing the Damage Tolerance of Laser Beam Welded Steels using the Crenellation Technique,”, Ph.D. Thesis, Imperial College

London, 2012",

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Used 12880 shell (S4R) element for full model & Virtual Crack Closure Technique combined with fatigue analysis and reading the fatigue crack growth curve from previous slide

a -N (S 420M S te e l; R = 0.1; F m a x = 243.5 kN;

F m in = 24.35 kN)

0

50

100

150

200

250

1.00E + 04 1.00E + 05 1.00E + 06

N [Cycle s]

Half

Cra

ck L

en

gth

Exte

nsio

n [

mm

]

Simula tion

Tes t

Half Crack Extension

Fmax = 243.5 kN

Fmin = 24.35 kN

Stress Ratio = 0.1

PART 3: Fatigue Crack Growth (Constant Thickness)PART 3: Fatigue Crack Growth (Constant Thickness)PART 3: Fatigue Crack Growth (Constant Thickness)PART 3: Fatigue Crack Growth (Constant Thickness)

(Steel S420M)

20 Alpha STAR Corp.

Used 12880 shell (S4R) element for full model & Virtual Crack Closure Technique combined with fatigue analysis and reading the fatigue crack growth curve from previous slide

Fmax = 243.5 kN

Fmin = 24.35 kN

Stress Ratio = 0.1

0

50

100

150

200

250

1.00E + 04 1.00E + 05 1.00E + 06 1.00E + 07

Half Crack Length Extension

[mm]

N [Cycles]

a-N (S 420M S teel; R = 0.1; Fm ax = 243.5 kN; Fm in= 24.35 kN)

S im: Co n sta n t Th ickn e ss

Te st

S im: V a ria b le Th ickn e ss

50

70

90

110

130

150

170

190

210

230

2.50E+06 2.60E+06 2.70E+06 2.80E+06 2.90E+06

Half Crack Length Extension

[mm]

N [Cycles]

a-N (S420M Steel; R = 0.1; Fmax = 243.5 kN; Fmin=24.35 kN)

Sim: Variable Thickness

2.13E6 Cycles

PART 3: Fatigue Crack Growth, Variable Thickness [S420M)PART 3: Fatigue Crack Growth, Variable Thickness [S420M)PART 3: Fatigue Crack Growth, Variable Thickness [S420M)PART 3: Fatigue Crack Growth, Variable Thickness [S420M)

21 Alpha STAR Corp.

Used 3220 shell (S4) element for full model & Virtual Crack Closure Technique combined with fatigue analysis and reading the fatigue crack growth curve from previous slide

50

70

90

110

130

150

170

190

210

230

2.50E+06 2.60E+06 2.70E+06 2.80E+06 2.90E+06

Half Crack Length Extension

[mm]

N [Cycles]

a-N (S420M Steel; R = 0.1; Fm ax = 243.5 kN; Fm in=24.35 kN)

Sim: Variab le Th ickness

Half Crack Extension

Fmax = 243.5 kN

Fmin = 24.35 kN

Stress Ratio = 0.1

Crack Growth Peak are due to change in panel thickness

PART 3: Fatigue Crack Growth, Variable Thickness [S420M)PART 3: Fatigue Crack Growth, Variable Thickness [S420M)PART 3: Fatigue Crack Growth, Variable Thickness [S420M)PART 3: Fatigue Crack Growth, Variable Thickness [S420M)

22 Alpha STAR Corp.

Half Crack

ExtensionFmax = 243.5 kN

Fmin = 24.35 kN

Stress Ratio = 0.1

Variable Thickness

Panel

Max

Stress

Max

Stress

1.00E+06cycles

PART 3: Fatigue Crack Growth, Variable Thickness [S690QL)PART 3: Fatigue Crack Growth, Variable Thickness [S690QL)PART 3: Fatigue Crack Growth, Variable Thickness [S690QL)PART 3: Fatigue Crack Growth, Variable Thickness [S690QL)

1.56E+06cycles

23 Alpha STAR Corp.

SUMMARY

� Life Assessment of metallic components can be performed Progressive Failure Analysis

� To precisely model the statically/cyclically loaded parts, GENOA recommends its unique 4-steps approach� PART 1 : Fracture Toughness Determination (FTD); requires full material SS curve

� PART II : Fatigue Crack Growth (FCG) Behavior (da/dN versus ∆K)

� PART III: Progressive Failure Analysis (PFA) in conjunction with Virtual Crack Closure technique (VCCT) for linearly elastic materials and Discrete Cohesive Zone Modeling (DCZM) for parts made of softer material

� Each above mention PART Steel (S420M, and S690QL) were validated at RT

� Improvement of Fatigue Crack Growth in Crenellated Vs. Constant Thickness Steel Panels

� These predictive methods are anticipated to reduced fatigue testing and expenses at the coupon and component scales