validation of stress intensity solutions of complex ... of stress intensity solutions of complex...

Global Strike Systems

F-22 Program

Lockheed Martin Corporation The Boeing Company F-22 Program Proprietary

Validation of Stress Intensity Solutions of Complex Structural

Details

ASTM Workshop on Verification and Validation of Solid Mechanics and Life Prediction Software

Phoenix, Arizona

May 2012

Jeffrey Bunch, The Boeing Company Pete Caruso, Lockheed Martin Aeronautics Company

Robert Bair, U.S. Air Force F-22 Program Office

Distribution Statement D: Distribution is authorized by the Department of Defense and their contractors for Administrative or Operational Use.

(Distribution approved for Public Release 5/16/2012 88ABW‐2012‐2829). Other requests for this document shall be referred to ASC/WWUE, Building

553, 2725 C Street Wright-Patterson AFB, OH 45433-7424

F-22 Program

Lockheed Martin Corporation The Boeing Company United States Air Force 2

Objective

Verify stress intensity factors computed from crack growth analysis codes

ASME V&V 10-2006

Coupon Tests

Element Tests

Sub-Component

Tests

Component Tests

Full Scale

Test

Mil-Std-1530C

F-22 Program


Background F22 Full Scale Fatigue Test

• Cracking of the lower fillet radius observed at the wing attach lugs during the Full Scale Fatigue Test (FSFT).

• The FSFT did not provide any data for verification and validation of crack growth models

• Cracks were repaired or blended away to preserve the FSFT

• Therefore no crack growth data were collected for model validation

Frame 2

Frame 3

Frame 4

Frame 5

Frame 6

Cracks of interest occurred at the lower

fillet radius (not at the bore)

Electron Beam

Weld Line

Material:

Ti-6Al-4V Beta

Annealed

F-22 Program


Correlation Approaches for Single Datum

Cra

ck

Le

ng

th

Time

Total time to observed crack size

Back caculate crack growth curve from end point to establish an equivalent initial flaw size (EIFS).

EIFS

Shape of crack growth curve could not be validated from full scale test

due to the lack of intermediate crack observations

Cra

ck

Le

ng

th

Time

Crack Nucleation

Crack Growth

Total time to observed crack size

Uncertainty in total correlation ompounded by uncertainty in both crack initiation and crack growth

Stress based correlation factor (time to nucleate + grow crack)

Crack growth based equivalent initial flaw sizes (EIFS)

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Experimental Setup

Design and test “simple” specimen that replicates stress gradient and is similar in configuration to actual component

Constant amplitude tests

Spectrum fatigue tests

Calibrate analysis methodology

Test full scale components simulating wing bending spectrum loading

F-22 Program


Test Specimen Configurations

Lug Element Specimen

Representative geometry

~ ½ scale of frame 2 (FS 657)

Relatively simple loading fixture

18 spectrum fatigue specimens at 3 different load levels

3 constant amplitude fatigue test specimens

Specimens visually monitored for crack initiation with 40x microscope

Crack growth monitored on both faces until longest crack measured 0.5”

F-22 Program



4 Full scale component frames test articles

2 configurations

– Frame 2 upper fillet radius of lower lug

– Frame 4 lower fillet radius of lower lug

1 specimen each:

– Naturally initiated crack

– EDM notch

Cracks detected and monitored by multiple NDI techniques

– Eddy current

– Fluorescent Penetrant Inspection

– Digital microscope (primary method to measure crack length)

All Frames produced to aircraft production standards

F-22 Program


0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6

No

rma

lize

d s

tre

ss

Distance from Peak Stress Location (inches)

Full Scale Test Specimen

Lug Element Specimen


• The relative small size of the lug elements

facilitated a larger test matrix and ease of

handling and a

• Stress gradients in the critical zones were

compared to full scale components to assure

similarity between specimen configurations

~255

mm

~1.3m

~220 kg

~26 kg

F-22 Program


2 Full Scale Component Geometries tested

• Upper fillet of Frame 2 provided unique critical detail and analysis challenge

• 1 specimen tested, naturally initiated crack monitored to obtain data

• 1 specimen tested with edm notch to obtain damage tolerance data

• Lower fillet of Frame 4 representative of all lower fillet radii

• 1 specimen tested from naturally intiated crack monitored to obtain crack growth data

• 1 specimen tested with edm notch to obtain damage tolerance data

F-22 Program


Test Matrix

Test Type Load

Spectrum

Reference

Stress

# Data collected

Element Constant

Amplitude

3 Initiation and Growth

Element Spectrum 6 Initiation and Growth



Frame 2 Component Spectrum 1 Initiation and Growth

Frame 4 Component Spectrum 1 Initiation and Growth

Frame 4 Component Spectrum 1 Growth from EDM notch

F-22 Program


Analysis: Crack Growth Program

In-House source code used to compute lives

Retardation moded: Modified Generalized Willenborg model

da/dN equation: Tabular lookup of digitized da/dN curve

Program contains library of geometric details for computing stress intensity factors

solutions based on accepted and validated sources (e.g. Kathirisen and Brussat, Newman and Raju, etc.)

Effects of stress gradient accounted for using Green’s function to generate beta-modification factors

A1 T

B A2

σA2(y) σA1(x)

F-22 Program


Lug Element Test Results

Results for 18 specimens grouped by stress level

Variability in crack size when naturally initiated cracks detected affect direct comparisons

A1

A2 Face

Side

Face

Side

F-22 Program


Test Results

Test results element tests typically did not match

Neither the end point or the shape of the curve were accurately predicted

Analysis does not predict results

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6C

rac

k L

en

gth

(in

)Lifetimes

(1 Life = 8000 flt hrs)

Test

Prediction

Data for lug element specimen "LE-10"

F-22 Program


Full Scale Component Results

3.02.52.01.51.00.50.0

35

30

25

20

15

10

5

0

Crack Growth Life

Cra

ck A

1 (

mm

)

Frame 2, Upper Fillet

Frame 4, EDM Notch at Lower Fwd Fillet

Frame 4, Lower Aft Fillet

Frame 4, Lower Fwd Fillet

Full Scale Components Crack A1 vs Crack Growth Life

Full scale component results from 3 test articles

Frame 4 crack initiation test article naturally initiated 2 cracks

Each crack monitored separately

F-22 Program


Analysis of Test Data

Data assessed by plotting growth rate per flight hour (da/dF) vs DK curves

Analogous to da/dN curves

Curves are specific to Material and load spectrum

Independent of test article geometry

d

a/d

F (L

en

gth

/Flig

ht H

r)

Reference Stress Intensity Factor

Spectrum da/dF Curve

Ti-6Al-4V Beta Annealed Forging

Wing Bending Spectrum

F-22 Program


Predicted crack growth curve shape does not match test results

Consistent behavior observed for lug element and full scale test articles

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

10.0 100.0

Spec

tru

m C

rack

Gro

wth

Rat

e (m

/flt

-hr)

Reference Stress Intensity Factor (Mpa√m)

Frame 4, EDM notch at lwr fwd fillet, A1

Frame 4, EDM Notch at Lwr Fwd Fillet, A2

Frame 4, Lower Aft Fillet, A1

Frame 4, Lower Aft Fillet, A2

Frame 4, Lower Fwd Fillet, A1

Frame 4, Lower Fwd Fillet, A2

Frame 4, Lwr Fillet Predicted da/dF

For given low value of stress

intensity predicted growth

rates are slower than test

For larger stress intensities,

predicted growth rates are faster

than test.

F-22 Program


Ratio of Test Derived Stress Intensity Factors to analytical Stress Intensity Factors

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 5.0 10.0 15.0 20.0

Kte

st/K

an

aly

tical

Crack Length (mm)

Ratio of Ktest/Kanalytical for Lug Element Specimens

A1 Crack Segment @ 780 MPa






All Frame 4 A1 Crack Segment

All Frame 4 A2 Crack Segments

F-22 Program


Comparisons with Simpler geometry

Open hole specimen in uniaxial tension

From previous tests and analysis of a common geometry and same material and similar load spectrum

Good agreement between test and prediction

Basic stress intensity solutions are accurate

Eliminates issues regarding retardation model

A1

A2

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

0.0 5.0 10.0 15.0

Str

ess I

nte

nsit

y F

acto

r (

MP

a√m

)

Crack Length (mm)

Stress Intensity Comparison for Assessement of Crack From a Hole in Finite Width

Plate

Boundary Element, A1

Stress Intensity Library, A1



0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

0.0 1.0 2.0 3.0

Cra

ck

Le

ng

th (

mm

)

Blocks

Crack Growth Result Comparison




Stress Intensity Library

F-22 Program


Lug Element Tests with Constant Amplitude Loading

Test derived Stress Intensity Factors for constant amplitude specimens follow same trend as for spectrum tests.

A1

A2 Face

Side

Face

Side

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 5.0 10.0 15.0 20.0

Kte

st/K

an

aly

tical

Crack Length (mm)

Ratio of Ktest/Kanalytical for Constant Amplitude Lug Element Test Specimens

A1 Crack Segment, Constant Amplitude Lug Element

A2 Crack Segment, Constant Amplitude Lug Element

F-22 Program


Boundary Element Model for Lug Element

Boundary Condition: fix at the

4 clamping bolt locations

Loading: load in the lug bore

Initial Mesh w/o crack

Mesh w/ crack

(local auto remesh)

Mesh on the crack surface

(auto remesh)

(minimum mesh size ~0.005”)

F-22 Program


Lug Element Test Results

Stress Intensity factors from Boundary Element Code Closely match test derived factors

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

0.00 0.10 0.20 0.30 0.40 0.50

Str

ess I

nte

nsit

y,

K(A

1)

Crack Length Along Specimen Side, A1 (inches)

Test Derived (6 specimens), 138 ksi

BEASY, LE-10, 138 ksi

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

0.00 0.20 0.40 0.60 0.80

Str

ess I

nte

nsit

y,

K(A

2)

Crack Length Along Specimen Face, A2 (inches)

Test Derived (6 specimens), 138 ksi

BEASY, LE-10, 138 ksi

Similar results for tests conducted at 125 and 113 ksi

a

cA1

A2

Some deviation at

small crack lengths

F-22 Program


Beta factors for small crack effect

y = 40925x4 - 12738x3 + 1461.9x2 - 75.357x + 2.5618

0.0

0.5

1.0

1.5

2.0

2.5

0 0.02 0.04 0.06 0.08 0.1

crack size (in)

Beta

Facto

r

Empirical “Short Crack” Beta Test Factor Derived from Lug Element Tests For cracks < 2.54 mm (0.1”), a correction was applied to account

for short crack effects

Necessary to match growth rates for cracks small cracks

Beta factors used to modify the stress intensity factor for small cracks derived from evaluation of lug element specimens

For Ti-6Al-4V Beta Annealed, 2.54 mm (0.1”) is approximately 2 to 3 grain diameters. A range where microstructural features can strongly influence crack growth.

F-22 Program


Results for Lug Element Test Validation of BEASY on Lug Element Test Specimens

0.0

0.1

0.1

0.2

0.2

0.3

0.3

0.4

0.4

0.5

0.5 0.7 0.9 1.1 1.3 1.5 1.7

Lifetimes

Cra

ck L

en

gth

(in

)

Test Results

Pre-Test Predictions

Pred. with BEASY

Post Test Correlation

Pre-test prediction using

Green’s function methods

“Post-diction” forcing

prediction to match test Prediction of test results

using BEASY

Crack growth predictions using stress intensity factors from the boundary element analysis match test results

F-22 Program


Area of concern

Models for Full Scale Components

Frame 4

Frame 2

F-22 Program


K1 vs Crack Length, Forward Fillet Crack

0

20

40

60

80

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

A2 (in)

K (

ksi*

sq

rt(i

n))

w / beta_str beasy

K1 vs Crack Length, Forward Fillet Crack

0

20

40

60

80

100

0 0.1 0.2 0.3 0.4 0.5 0.6

A1 (in)

K (

ksi*

sq

rt(i

n))

w / beta_str beasy

Stress intensity factors

derived using current

method higher than those

obtained from BEASY

Frame 4 Component Test Results, Forward Crack

Frm4 D5, Forward Fillet Crack

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

15000 20000 25000 30000 35000 40000

Unfactored Life (hours)

A2 (

in)

testing w/ beta_str w/ beta_beasy

1.0 2.0 3.0 4.0 5.0

Test Lifetimes

Frm4 D5, Forward Fillet Crack

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

15000 20000 25000 30000 35000 40000


A1 (i

n)


1.0 2.0 3.0 4.0 5.0

Test Lifetimes

Forward

Aft

Predictions using BEASY

derived stress intensities

closely match test results

F-22 Program


K1 vs Crack Length, Aft Fillet Crack

0

20

40

60

80

0 0.1 0.2 0.3 0.4 0.5 0.6

A1 (in)

K (

ksi*

sq

rt(i

n))

w / beta_str Beasy

K1 vs Crack Length, Aft Fillet Crack

0

20

40

60

80

100

0 0.1 0.2 0.3 0.4 0.5 0.6

A2 (in)

K (

ksi*

sq

rt(i

n))

w / beta_str Beasy

Analysis using BEASY

Derived Beta Factors

PREdict both the shape and

the end point of the crack

growth curve for the frame

4 specimen

Frame 4 Component Test Results, Aft Fillet Crack

1.0 2.0 3.0 4.0 5.0

Test Lifetimes

Frm4 D5, Aft Fillet Crack

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

15000 20000 25000 30000 35000 40000


A2

(in

)


Frm4 D5, Aft Fillet Crack

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

15000 20000 25000 30000 35000 40000


A1

(in

)


1.0 2.0 3.0 4.0 5.0

Test Lifetimes

Forward

Aft

F-22 Program


Comparison of Frame 4 Component Test Crack Growth Results

0.0

5.0

10.0

15.0

20.0

25.0

0.0 0.5 1.0 1.5 2.0 2.5

Cra

ck L

en

gth

(m

m)

Test Lifetimes

Crack Growth Predictions Using Boundary Element Model (BEM) Stress Intensity Factors Compared to Test Results

Prediction with BEM Stress Intensities, Specimen 4C, A1 Crack Segment

Prediction with BEM Stress Intensities, Specimen 4C, A2 Crack Segment

Specimen 4C Measurements, A1 Crack Segment

Specimen 4C Measurements, A2 Crack Segment

Specimen 5D Measurements, A1 Crack Segment

Specimen 5D Measurements, A2 Crack Segment

Frame 4 component crack growth

test results.

Specimen 5D – naturally initiated

crack

Specimen 4C – Crack from EDM

flaw

F-22 Program


Frame 2 Upper Fillet Analytical Results and Test Correlation

Analytical results are from crack growth analysis with different stress intensity solutions:

• Predictions using the original method with Green’s Function

• Predictions using stress intensities from boundary element analysis and a

1.27 mm x 1.27mm (0.05”x0.05”) initial flaw

• Predictions using stress intensities from boundary element analysis and a

2.84mm x 2.41 mm (0.112”x0.095”) initial flaw to match the initial observed flaw from test

0.0

10.0

20.0

30.0

40.0

1 1.5 2 2.5 3 3.5 4

A1 C

rack

Leng

th

(mm

)

Test Lifetimes

Frm2 Specimen 7A, Upper Fillet Crack

0.0

5.0

10.0

15.0

20.0

25.0

1 1.5 2 2.5 3 3.5 4

A2 C

rack

Leng

th

(mm

)

Test Lifetimes


0.0

20.0

40.0

1 1.5 2 2.5 3 3.5 4A2 (m

m)

Test Lifetimes


Test Results

Prediction with Green's Function

BEM Analysis Matching Test Flaw Sizes

BEM Analysis with 1.27mm x 1.27mm damage tolerance initial f law

F-22 Program


A

A

View A-A

Crack origins at lower corners

Stress intensity factors computed from boundary element tool improves crack growth “pre-”dictions in complex geometric details

Cross section of fracture surface

shows greater complexity than

provided by simplified stress

intensity solution

Full Scale Component Results When the structure cross section geometry gets complex

simplified stress intensity solutions unable to model full range of crack lengths

Boundary element tool accurately accounts for effects of geometric boundary and complex loading

F-22 Program


Conclusion

A rigorous test program was executed to understand crack growth behavior in full scale structures

Two sources of error were observed affecting model accuracy

Incorrect stress intensity factors

Short crack effect for cracks less than 2.54 mm (0.1 in) or 2 to 3 grain diameters

FEM based approach validated against test data to improve stress intensity data

Empirical modification implemented to account for short crack effect

F-22 Program


Observations

Properly designed element specimens that match stress gradient and material processing can match behavior of full scale structures

Methods can be validated and verified utilizing the smaller less expensive element specimens

Methods should be calibrated using specimens that look like the structures being modeled

Previous methods calibration and validation tests focused on specimens that looked like standard stress intensity solutions (i.e. cracks growing from a round hole in a finite width plate)

Future emphasis on integral structures, larger forgings, etc, require verification and validation tests that represent details in the structure

F-22 Program


Questions?

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