Crack-Closure ModelingCrack Closure Modeling&

FASTRANPlastic wake Oxide debris

fastran # 1(a) Plasticity-induced closure

(b) Roughness-induced closure

(c) Oxide/corrosion product- induced closure

ffa

DOMINANT MECHANISMS OF FATIGUE-CRACK CLOSURE

Plastic wake Oxide debris

(a) Plasticity induced (b) Roughness induced (c) Oxide/corrosion product(a) Plasticity-induced closure

(b) Roughness-induced closure

(c) Oxide/corrosion product- induced closure

Elber, 1968 Beevers, 1979 Paris et al., 1972N 1974 S h & Rit hi 1982 S h & Rit hi 1981

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Newman, 1974 Suresh & Ritchie, 1982 Suresh & Ritchie, 1981(FASTRAN, 1977)

OUTLINE OF PRESENTATION

• Finite-Element ModelingFinite Element Modeling

• Strip-Yield ModelingStrip Yield Modeling

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FINITE-ELEMENT ANALYSIS OF FATIGUE-CRACK CLOSURE

Newman-Armen, 1974

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FINITE-ELEMENT ANALYSES OF FATIGUE-CRACK GROWTHAND CLOSURE UNDER A SPIKE OVERLOAD SIMULATION

PNewman, 1976

P

Time

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COMPARISON OF ELASTIC-PLASTIC FINITE-ELEMENT ANALYSESOF FATIGUE-CRACK CLOSURE WITH ELBER’S EQUATION

Newman 1976Newman, 1976

Plane-Stress Conditions

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MODIFIED DUGDALE MODELS IN FASTRAN

Elastic continuum

Bar elements

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BASIC CRACK SOLUTIONS REQUIRED FOR CLOSURE MODEL

Crack solutions:

Ks = fs(S d r w)Ks fs(S,d,r,w)Vs = gs(S,d,r,w,x)

K = f ( d r w bi x)K = f(,d,r,w,bi,x)V = g(,d,r,w,bi,x)

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DUGDALE’S FINITE-STRESS CONDITION

S

o ij = K / (2r)1/2 + O(r)

K = Ks + Ko = 0

c = f(S,c,o)

Finite plate with a crack and hole:= f(S c d w )

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S = f(S,c,d,w,o)

FASTRAN – Crack-Closure Based Life-Prediction Code

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-o

CRACK SOLUTION INPUT REQUIRED FOR FASTRAN

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NTYP = 1 NTYP = 0; LTYP = 1 Pre-cracking option

CONSTANT-AMPLITUDE LOADING OPTION (NFOPT = 0)

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MECHANICS OF THE ANALYTICAL CYCLE IN FASTRAN

R i fl th fl th d l

Analytical cycleSmaxh * 0 2Analytical cyclec* = 0 05

Rainflow-on-the-fly methodology

A li d

maxh c* = 0.2 c = 0.05 (NMAX = 300)

AppliedStress

S'

So

Sminb Smina

S o (So)new

Time

c*

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Time

FASTRAN Version 5.42 – Cycle-by-cycle (NMAX = 1)

CALCULATED CRACK-OPENING STRESSES AT A LOW APPLIEDSTRESS LEVEL (MIDDLE-CRACK TENSION; NTYP = 1)

1.0 2024-T3B = 0.09 in.W 3 i

0 6

0.8W = 3 in.

Smax = 10 ksi Seff / Smax

So/Smax0.4

0.6R = 0.05Pre-cracking

0.2R = -1

0.50 0.75 1.00 1.250.0

cn ci0.25

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Crack length, c, in.

CRACK-OPENING STRESSESUNDER CONSTANT-AMPLITUDE LOADING

S /S f(R S / )So/Smax = f(R, Smax/o, , c/c)

R = Smin/Smax = ( + )/2o = (ys + ult)/2 = 1 for plane-stress conditions

3 f l t i diti = 3 for plane-strain conditions

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CRACK-OPENING STRESSES AS A FUNCTION OFSTRESS RATIO FOR A HIGH CONSTRAINT FACTOR

So/Smax = 2

1.0

FASTRAN c = 00.8

0.050.2

Smax/o

0.60.40.60.8Equation

0.4

0.2Smin/Smax

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-1.0 -0.5 0.0 0.5 1.0

CRACK-OPENING STRESSES AS A FUNCTION OFAPPLIED STRESS FOR VARIOUS CONSTRAINT FACTORS

0.5

0.6

= 1Plane stress

0.4

0.5

= 2

So/Smax 0.3

= 2

0.2 = 3Plane strain

0 0

0.1R = 0c = 0

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0.0 0.2 0.4 0.6 0.8 1.00.0

FATIGUE-CRACK-GROWTH RATES USING LEFM ANALYSES

10 3

10-4

10-3 2024-T3Middle crack tensionB = 2.3 mm

10-6

10-5Hudson, Phillips & Dubensky

10-7 dc/dNm/cycle R

10-9

10-8 0.70.50.30

10-11

10-10

0-1-2

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1 10 10010-11

K, MPa-m1/2

FATIGUE-CRACK-GROWTH RATES CORRELATIONUSING CRACK-CLOSURE ANALYSES

10-4

10-3 Hudson, Phillips & Dubensky2024-T3Middle crack tensionB = 2.3 mm

10-6

10-5

B 2.3 mm

= 1Fractureregime

10-7

10 6

dc/dNm/cycle

= 2

R0.7

Flat-to-slantcrack growth

10-9

10-8 = 2 0.5

0.30-1

10 11

10-10

1-2Threshold

regime

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1 10 10010-11

Keff, MPa-m1/2

FLAT-TO-SLANT FATIGUE-CRACK GROWTH

Newman and Hudson, 1966

Schijve (1966): Observed transition occurs at “constant rate”

kT

ksi-inksi-in

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Stress ratio, R

FLAT-TO-SLANT FATIGUE-CRACK GROWTH TRANSITION

Newman 1992Newman, 1992

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CONSTRAINT EFFECTS IN THREE-DIMENSIONAL CRACKED BODIES

Newman Bigelow & Shivakumar 1993Newman, Bigelow & Shivakumar, 1993

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ELASTIC-PLASTIC STRESS-INTENSITY FACTORSNewman, 1992

1.2 0.1c / r = 0.5

0.25

Newman, 1992

1.00.05

Crack Parameters:

0.6

0.8

0.25

0.5

0.1Ki / KJ

Ki = S (d)1/2 F(d/r)where d = c + = 0 elastic

0.4Kp / KJ

c / r = 0.05

0.1i J = 0 elastic = ¼ elastic-plastic

J = K 2/E0.2

p JKe / KJ

J = Kp /E

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0.1 1 10 1000.0

/ c

CRACK-CLOSURE ANALYSES OF 2024-T3 ALUMINUM ALLOY

10-4

10-3Hudson, Phillips & Dubensky2024-T3Middle crack tensionB = 2.3 mm

10-6

10-5

10

= 1

Flat to slant

Fractureregime

Keff

10 8

10-7

10 6

dc/dNm/cycle = 2 R

0 7

Flat-to-slantcrack growth

(K )

10-9

10-8 0.70.50.301

Smallcrack

regime

(Keff)T

10-11

10-10 -1-2Threshold

regime

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1 10 100Keff, MPa-m1/2

CONSTRAINT-LOSS ISSUES ON TENSION-TYPE SPECIMENS

• Tests on M(T) specimens exhibit both flat and slantfatigue-crack-growth surfaces at low and high K,

ti l id l f t i lrespectively, on a wide class of materials.

• Cracks in M(T) specimens exhibit a strong shift with the stress ratio (R) at high rates on K-rate data, consistent with lower constraint and negative T-stress.

• Measurement of crack-opening loads on M(T) specimens have not been made before, during, and after the flat-to-slant crack-growth transitionafter the flat to slant crack growth transition.

• Thus, the “constraint-loss regime” most likely occurson tension type specimens but further study is needed

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on tension-type specimens, but further study is needed.

CONSTRAINT-LOSS ISSUES ON BEND-TYPE SPECIMENS

• Tests on C(T) and ESE(T) specimens generally exhibit• Tests on C(T) and ESE(T) specimens generally exhibitonly flat fatigue-crack surfaces (no flat-to-slant crack-growth transition) for a wide class of materials (but flat-to-slant crack growth has occurred on some materials).

• Deep cracks in C(T) and ESE(T) specimens exhibitlittl hift ith t ti (R) K tvery little or no shift with stress ratio (R) on K-rate

data, maybe due to high constraint and positive T-stress.

• Measurement of crack-opening loads on cracks greater than ~65% of the width exhibit a rapid dropin crack-opening loads, consistent with no R-shift incrack-growth-rate data.

• Th th “ t i t l i ” d t

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• Thus, the “constraint-loss regime” does not appearto occur on bend-type specimens.

VARIABLE-AMPLITUDE LOADING OPTION (NFOPT = 1)

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SPECTRUM LOADING OPTIONS IN FASTRAN

• TWIST or MINI-TWIST - Transport Spectra (NFOPT = 2 or 3)

• FALSTAFF - Fighter Spectra (NFOPT = 4)

• SPACE SHUTTLE Load Spectra (NFOPT = 5)p ( )

• Gaussian (R ~ -1) Load Sequence (NFOPT = 6)

• Felix-28 or Helix-32 Helicopter Load Sequence (NFOPT = 7)

• Spectrum Read from List of Stress Points (NFOPT = 8)Spectrum Read from List of Stress Points (NFOPT 8)

• Spectrum Read from Flight-by-Flight Loading (NFOPT = 9)

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• Spectrum Read from Flight Schedule (NFOPT = 10)

CRACK CONFIGURATION OPTIONS IN FASTRAN

• Two-dimensional crack configurations (14)- Middle-crack tensionMiddle crack tension- Compact and bend type specimens- Crack(s) from an open hole- Crack in a pressurized cylinder- Crack in a pressurized cylinder- Periodic array of cracks at holes- User defined crack configuration

Th di i l k fi ti (10)• Three-dimensional crack configurations (10)- Surface crack (tension or bending loads)- Surface or corner crack(s) at an open hole - AGARD small-crack specimen- Periodic array of surface or corner cracks

at pin-loaded holes

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p

LABORATORY SPECIMENS

99

Example of user defined crack configuration

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p g(NTYP = -99 Crack(s) from hole)

RIVETED AIRCRAFT JOINT CRACK CONFIGURATION

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AGARD SMALL-CRACK SPECIMEN

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CRACK CLOSURE CORRECTION FOR FREE SURFACE

K=0 = R KB

K=90 = KAK=90 KA

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FATIGUE-CRACK-GROWTH RATE OPTIONS

• Equation: dc/dN = C1 KeffC2 f(Kth) / g(KIe)

f(K ) 1 (K /K )p- f(Kth) = 1 – (Ko/Keff)p

Ko = C3 (1 – C4 R) or Ko = C3 (1 – R)C4

- g(KIe) = 1 – (Kmax/KIe)q

• Table Look up: dc/dN = f(K ) (Max 35 points)• Table Look-up: dc/dN = f(Keff) (Max 35 points)

- dc/dN = C1i KeffC2i (i = 1 to 34)

- dc/dN = C1i KeffC2i f(Kth) / g(KIe)

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• Crack growth (da/dN = dc/dN or da/dN # dc/dN)

CRACK-GROWTH-RATE TABLE LOOK-UP

K f(C C R)Ko = f(C3, C4, R)

KIe = g(KF, m)

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FRACTURE CRITERIA

• Two-Parameter Fracture Criterion – KF and mTwo Parameter Fracture Criterion KF and m- m = 0 LEFM (KIe = KF)- m = 1 Plastic-collapse criteria (KF = large value)p ( F g )

• Cyclic fracture toughness exceeded (Kmax > C5)

• Plastic-zone size exceeds net-section region

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