Post on 30-Jun-2020
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
4 Alpha STAR Corp.
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
6 Alpha STAR Corp.
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
7 Alpha STAR Corp.
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)
9 Alpha STAR Corp.
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)
11 Alpha STAR Corp.
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
13 Alpha STAR Corp.
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
15 Alpha STAR Corp.
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
17 Alpha STAR Corp.
• 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
18 Alpha STAR Corp.
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",
19 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
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