Center for Aircraft Structural Life ExtensionProviding Structural Integrity Technology to the Aerospace Community

3-D Crack Growthand Residual Strengthand Residual Strength

May 2009

Ms. Sarah GalyonDr James GreerDr. James Greer

Dr. Saravanan ArunachalamMr. Matthew Hammond

Dr. Scott Fawaz

Project Goals

Develop mixed mode I/II fatigue crack trajectory dataDevelop mixed mode I/II residual strength dataUse state of the art crack prediction tools to model mode I/II crack growthD l i i d l t di t i d dDevelop an engineering model to predict mixed mode crack growth

Develop mode I and mode II crack growth rate data for p guse in models

Assess correlation of predicted and measured crack trajectory and crack growth ratestrajectory and crack growth ratesDetermine the effect of mixed mode loading on residual strengthg

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MethodologyL 

T 

Mode I Mode I/II Mode II

 

  /

an  an anao  ao aoa a  a

θ1 θ2

im

IIIIII

im

IIIIIIIII

III KCdNdaKC

dNda

dNda

dNda

dNda θθ sin,cos

/

Δ=Δ=⇒+=

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IIIIIIIII dNdNdNdNdN /

First order approximation, if inadequate, then pursue advanced methods

3-D Crack GrowthProject Overviewj

■ Mixed mode (Mode I/II) determination of crack trajectory and residual strength.

Prediction of crack growth rate, crack trajectory with stress analysis and life prediction toolsstress analysis and life prediction tools, FRANC3D/NG.

Engineering prediction of mixed mode I/II crack trajectory.

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Mixed Mode (I/II) Test Matrix

Mode I/II Fatigue Test MatrixMaterial Orientation R Specimen Loading Loading ReplicatesMaterial Orientation R Specimen

TypeLoading Loading

AngleReplicates

2024- LTKeq≈6.9 ksi√in at

0°30°2024

T351LT

0.1 ARCANksi√in at

the start of each test

33060°75°

2024-T351

TL0.1

ARCANKeq≈6.9 ksi√in at

the start of each test

0°

330°60°

48 total specimens for mixed mode testing

each test75°

Third set of 0° samples were replaced with a test at 15°

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Arcan Test Fixtures

ARCAN sample

Thickness=0.063”

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Arcan Specimen and Fixture

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ARCAN specimen in fixture

Initial Load Determination

Original test matrix required ARCAN testing with a constant stress of 15 ksiThe stresses are not constant across the ARCAN specimensIt was decided to use the same K = √(K 2+K 2) for theIt was decided to use the same Keq= √(KI

2+KII2) for the

start of each test for all loading orientationsAfter the initial loading all tests are K-increasing as the fatigue crack propagates-there is no attempt to control Keq after the start of the testA FEA model was used to determine the initial loadingA FEA model was used to determine the initial loading for the ARCAN specimens

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FEA Model of ARCAN Specimens

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Finite element stress contours (x, or horizontal) for the ARCAN specimen under four displacement conditions

SIF Plots from Patran/Nastran

VCCT method has been used to calculate analytical Mode I and Mode II SIFs

√Equivalent SIF, Keq = √(KI2 + KII

2), “carpet plots” are used to start each constant amplitude fatigue test under similar SIF conditionsPlots include SIF as a function of both mode mixity and crack length

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Current LT Crack Trajectory Results

2

2.5Representative LT Crack Trajectory Data

1

1.5

0

0.5

2 1 5 1 0 5 0 0 5 1 1 5 2 2 5 3

-1

-0.5

‐2 ‐1.5 ‐1 ‐0.5 0 0.5 1 1.5 2 2.5 3

-2

-1.5

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-2.5ARCAN Specimen IISA24LT 0 Degree 406,737 cycles IISA59LT 15 Degrees 169,232 cycles

IISA58LT 30 Degrees 120,875 cycles IIA64LT 60 Degrees 71,443 cycles IIA60LT 75 Degrees 96,328 cycles

Preliminary LT and TL Orientation Comparison

2

2.5Representative TL Crack Trajectory Data

1

1.5

0

0.5

2 1 5 1 0 5 0 0 5 1 1 5 2 2 5 3

‐1

‐0.5

‐2 ‐1.5 ‐1 ‐0.5 0 0.5 1 1.5 2 2.5 3

‐2

‐1.5

ARCAN S i IISA54TL 0 D 543 175 l IISA68TL 15 D 138 668 l

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‐2.5

ARCAN Specimen IISA54TL 0 Degree  543,175 cycles IISA68TL 15 Degrees  138,668 cycles

IIA66TL 30 Degrees  169,670 cycles IISA48TL 60 Degrees  171,318 cycles IIA61TL 75 Degrees  172,500 cycles

Sixty Degree Crack Trajectory Comparisonp

2

2.560 Degree Crack Trajectory Comparison

1

1.5

0

0.5

2 1 5 1 0 5 0 0 5 1 1 5 2 2 5 3

-1

-0.5

‐2 ‐1.5 ‐1 ‐0.5 0 0.5 1 1.5 2 2.5 3

-2

-1.5

Specimen IISA23LT 60 Degrees; 281,395 cycles; 460 lbs IISA17LT 60 Degrees; 193,000 cycles; 540 lbs

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-2.5IISA64LT 60 Degrees; 71,443 cycles; 620 lbs IISA53TL 60 degrees; 94096 cycles; 420 lbs IISA41TL 60 degrees;148,315 cycles; 540 lbs

IIA48TL 60 degrees; 171,318 cycles; 620lbs

Residual Strength Test MatrixMode I/II Residual Strength Test Matrix

Material Orientation R Specimen Type

Loading Loading Angle

ReplicatesType Angle

2024-T351

LT0.1 ARCAN

ConstantDisplacement

Test

0°

330°60°75°

Constant 0°2024-T351

TL0.1

ARCAN Displacement Test 3

30°60°75°

■ For the third set of tests the 0° test was replaced with a test at 15°

75

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Residual Strength Analysis3000 Load vs. Displacement for LT and TL ARCAN Specimens

2000

2500IISA33LT 0 Degree

IISA42TL 0 Degrees

IISA30LT 30 Degrees

1500

Load

, lbs

IISA30LT 30 Degrees

IISA43TL 30 Degrees

IISA25LT 60 Degrees

1000

IISA44TL 60 Degrees

IISA21LT 75 Degrees

IISA45TL 75 Degrees

500

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00 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

Displacement, in

MODELING EFFORTS

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SIF Plots from Patran/Nastran

Known (experimental) crack trajectories have been used to calculate SIFs for realistic cracking scenarios

Regular mesh was modified to incorporate experimental crack trajectoryChecks were run to ensure mesh changes did not gadversely affect FE resultsSIFs were calculated in the plane of the crack (local coordinate system)coordinate system)

Keq = √(KI2 + KII

2) is independent of the coordinate system, but KI and KII are notF t it i d l t f k di ti dFuture criteria development for crack direction and extension may benefit

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SIF Development using Patran/Nastran

Plots for SIFs as crack grows

Experimental result

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Residual Strength Testing Results

FE models used to generate R-curve plot for test

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Mixed-Mode Specimen Modelingwith FRANC3D-NG

FRANC3D-NG is the “Next Generation (NG)” version of Cornell Fracture Group’s crack growth modelingof Cornell Fracture Group s crack growth modeling code

Includes meshing capabilityPreserves boundary nodes for global/local modeling of large or complex modelsHas hooks for multiple solvers (ANSYS, Nastran, etc.)p ( , , )

ABAQUS used in this effortCornell Fracture Group considers NG to be a “beta” codecode

Multiple executable versions were provided by CFG and used in this programExtensive assistance received from CFG

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Mixed-Mode Specimen ModelingGlobal/Local Submodeling Approach

Developed global model of 20-noded hexahedral elementsDefined local model and identified boundary nodesExtracted local model and ported to FRANC3D-NGFRANC3D NG h d b d l (l l d l) ithFRANC3D-NG remeshed submodel (local model) with 10-noded tetrahedral elements, accounting for flaw at each crack growth step

refined, structured mesh in vicinity of crack tipFRANC3D-NG reinserted the local tetrahedral mesh into the global modelinto the global model

Boundary nodes preserved20-noded hex and 10-noded tet elements have same order along element edges, so nodes are matched

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Mixed-Mode Specimen ModelingGlobal/Local Submodeling Approach

Flaw insertion and re-meshing

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Mixed-Mode Specimen ModelingGlobal/Local Submodeling Approach

Simulation Parameters80 to 100 increments (solutions) to grow crack from 0.12 in to 0.9 in

about 15 hours of computer time (2 work days)some user intervention required during analysisq g y

Growth rate determined by user-supplied da/dN vs. ΔKcurve

Growth rates were anisotropic with material orientationGrowth rates were anisotropic with material orientation, but supplying orthotropic crack growth rate properties not yet an option for FRANC3D-NG

Growth direction determined by comparing tensile andGrowth direction determined by comparing tensile and shear stresses near crack tip

Engineering judgment used to develop shear (pure mode II) it i t t d t il blII) criteria, as no test data were available

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Mixed-Mode Specimen ModelingGlobal/Local Submodeling Approach

Rate and Direction Criteria (other options are available within the code menus

Crack growth rate

Crack growth direction

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FRANC3D-NG vs. TESTING(30° Case)

■ Photo of part of post-test 30° Arcan specimen indicating three

i t l k thexperimental crack paths (blue, green, and black)

■ FRANC3D-NG di t d th ( d)predicted path (red).

■The yellow reference line indicates 30° from h i t lhorizontal.

■The photo orientation matches that of the

i t d ispecimen as mounted in the test frame.

■The color inset image is th FRANC3D NG lt

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the FRANC3D-NG result as depicted in ABAQUS.

FRANC3D-NG vs. TESTING(60° Case)

■Photo of part of post-test 60° Arcan specimen indicating two experimental crack paths (blue and green)

■The FRANC3D-NG predicted path (red).

■The yellow reference line indicates 60° from horizontal.

■The photo orientation matches that of the specimen as mounted in the test frame.

■The color inset image

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is FRANC3D-NG result as depicted in ABAQUS.

Engineering Model

4.00

60 Degree TL Prediction and Data Comparison

IISA53TL

3.00

3.50 IISA41TL

IISA48TL

Predication 1

Prediction 2

2.00

2.50

k Le

ngth

, cm

Prediction 2

Predication 3

1.00

1.50Cra

ck

0 00

0.50

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0.000 20000 40000 60000 80000 100000 120000 140000 160000 180000

Cycles

Conclusions From ProgramTestingg

Overall mixed mode crack growth produces scattered data with regards to crack trajectory and fatigue lifeBased on our current results more testing in needed to fully understand mixed mode loadingThe residual strength of the specimens in adverselyThe residual strength of the specimens in adversely affected by mixed mode loading compared to purely tension loading.

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Conclusions From Program Modelingg

Predicted number of cycles to a given crack length are reasonablePredicted paths differ from those seen in experiments

For example current FRANC3D NG model the 30° predicted path isFor example, current FRANC3D-NG model the 30° predicted path is steeper than the test data, while the 60° is shallower.

Some possible reasons for differencesThe current model assumes a perfectly rigid fixture with no “play” atThe current model assumes a perfectly rigid fixture with no play at pins and joints—only the flexibility of the specimen is includedThe model assumes isotropic propertiesThe model assumes linear elastic material behaviorThe model assumes linear elastic material behaviorFurther material characterization is needed to accurately determine the correct mode II critical K value; this value determines the shear stress level at which crack kinking occursIt could also be that none of FRANC3D’s built-in criteria are best for AA2023-T351

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Conclusions from Program Modeling (cont.)g ( )

The engineering prediction was able to model 3 of the 4 cases predicted with reasonable accuracy.

Final ConclusionsM t ti i i d t d t d i d d■ More testing is required to understand mixed mode crack propagation and growth

■ With more adjustments to the inputs it is possible that j p pFRANG3D NG could accurately model the mixed mode crack growthM f th k f thi h ld b■ Many of the unknowns from this program should be resolved with the follow-on program using 0.25 inch titanium plate

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