Robust Design of Composite Bonded Pi Joints

PIRA #AER200903004Copyright 2009 by Lockheed Martin Corporation. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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Robust Design of Composite Bonded Pi Joints

Barrett D. Flansburg1 and Stephen P. Engelstad2

Lockheed Martin Aeronautics Company, Marietta, Georgia, 30063

Jim Lua3

Global Engineering and Materials, Inc., Princeton, New Jersey, 08540

An investigation was conducted for the purpose of enabling robust design of compositebonded pi joints in the presence of manufacturing flaws and impact damage. Testing wasconducted for determining the material fracture toughness and the pi joint failure pulloffloads. A software tool for evaluating pi joint reliability was constructed by couplingABAQUS, XFA (XFEM for ABAQUS), and NESSUS for use with a parametric finiteelement model with embedded cracks. A 2D model with a manufacturing flaw was validatedwith test data and used to evaluate designs which showed greater reliability than the baselinedesign. A 3D model with impact damage was correlated to test data and used to evaluate adesign showing greater reliability than the baseline design. A thin, wide, fully tapered,flexible pi base with thick uprights was found to be desired for greater reliability.

NomenclatureBVID = Barely Visible Impact DamageCAI = Composites Affordability InitiativeDCB = Double Cantilever BeamENF = End Notched Flexureg( ) = limit state functionGI = strain energy release rate for failure mode 1GIC = fracture toughness for failure mode 1GII = strain energy release rate for failure mode 2GIIC = fracture toughness for failure mode 2GIII = strain energy release rate for failure mode 3GIIIC = fracture toughness for failure mode 3UT = Ultrasonic Technology

I. IntroductionThe composite bonded pi joint is a means of joining composite skins to composite spar or rib webs without the

use of fasteners. The pi joint gets its name from the inverted pi shape as shown in Figure 1. The cured skin and webare inserted into the uncured woven composite pi-preform along with an adhesive film to be cured in an autoclave.The composite bonded pi joint offers the potential for making bonded unitized aircraft structures which are strong,durable, lightweight, and resilient when damaged. Pi joints are expected to make their flight debut on the vertical tailof the Advanced Composite Cargo Aircraft (ACCA) in 2009.

This paper presents research aimed at enabling the robust design of composite bonded pi joints, accounting forvariability in geometric dimensions, material properties, and the presence of manufacturing defects and impactdamage. The research was performed as part of the Reliability Based Structural Design Methodology (RBSDM)program under contract to the Air Force Research Laboratory (AFRL). The contractor team consisted of LockheedMartin Aeronautics Company (LM Aero) and Global Engineering and Materials, Incorporated (GEM).

1 Senior Staff Engineer, Advanced Development Programs, MZ 0663, AIAA Senior Member.2 LM Fellow, Advanced Development Programs, MZ 0663, AIAA Associate Fellow.3 Senior Principal Scientist, GEM-NJ Office, AIAA Member.Distribution A – Public Release (Case Number 88ABW-2009-0965)

50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference <br>17th4 - 7 May 2009, Palm Springs, California

AIAA 2009-2447

Copyright © 2009 by Lockheed Martin Corporation. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


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A reliability-based damage tolerance analysis and design tool for damaged pi-preform joints was developed byintegrating a fracture-based deterministic solver with the NESSUS [1] probabilistic analysis framework. A key pieceof the relibility tool was an automated delamination onset and crack growth prediction module based on theeXtended Finite Element Method (XFEM) [2], which was used as the deterministic solver. The XFEM forABAQUS (XFA) tool enables the ability to arbitrarily insert an initial delamination crack that is independent of thefinite element mesh and characterize the crack growth without re-meshing.

The research consisted of testing, validation of the analysis tools, and robust design. The testing includedevaluation of the material fracture toughness and strength testing of specimens with built-in manufacturing defectsand impact damage. The analysis tools consisted of customized software enabling probabilistic analysis of aparametric extended finite element model of the pi joint including flaws. The robust design effort includeddetermining the important parameters, calculating the sensititivities of the probability of failure to the parameters,evaluating the performance of candidate designs relative to the baseline design, and drawing conclusions about howthe reliability of the composite bonded pi joint can be improved.

II. TestingTesting was used both to determine the

fracture toughness of the pi joint materialsand to determine the pulloff strength of the pijoint in the presence of either amanufacturing flaw or impact damage. Thefracture toughness was determined thoughthe use of double cantilever beam (DCB) andend notched flexure (ENF) testing. Thedouble cantilever beam test was used tomeasure the GIC fracture toughness value forfailure mode 1, the opening mode in whichthe crack faces are pulled apart. The testfixture for the double cantilever beam test isshown in Figure 2.

The end notched flexure test was used tomeasure the GIIC fracture toughness forfailure mode 2, the in-plane shearing mode inwhich the crack surfaces slide over oneanother. The test fixture for the end notchedflexure test is shown in Figure 3.

The DCB and ENF test specimens werefabricated using IM7-977-3 carbon/epoxy composite and AF191G epoxy adhesive. M&P Technologies fabricatedthe specimens using equipment located at Clark Atlanta University. Two laminate configurations were fabricated,

Figure 1. A composite bonded pi joint.

Figure 2. Double cantilever beam test.


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representing monolithic and bonded panels. The monolithic panel is an all 0° layup, and the bonded panelrepresents the layup configuration in the skin of the pi joint.

Fifteen cobonded and fifteen monolithic specimens were used in each test in order to approximate the statisticaldistributions of the fracture toughness values. Only room temperature dry (RTD) environments were selected forvalidation, to fit within the scope of this program. The DCB and ENF testing and data reduction proceduresfollowed those used in the Composites Affordability Initiative (CAI) [3,4]. These procedures are patterned afterASTM D5528-94a. LM Aero also conducted these same fracture toughness tests during the CAI program, howeverthe test matrix only included 5 replicates per test. In order to increase the sample size for this program, new DCBand ENF tests were performed here. Every effort was made to make the test specimens and test procedure identicalto the prior CAI tests.

The results of the testing provided mean values and coefficients of variation of GIC and GIIC for use in thesubsequent reliability analysis. The value of GIIIC, the fracture toughness for failure mode 3 (tearing), was notmeasured and was assumed to equal GIIC. Pulloff testing of pi-preform joint sub-elements subjected tomanufacturing flaws and impact damage was conducted to provide data for validation of the reliability analysismodels. Cobonded pi-preform jointspecimens were tested only at roomtemperature dry conditions, and 15replicates were utilized at each testconfiguration to measure the statisticaldistributions in the central part of thedistribution. In this way robust mean andstandard deviation statistics of the datawere measured. One test point wasincluded for manufacturing flaws, withoutoverwraps, and one test point for impactdamage, at the pi flange termination.Impact damage was inflicted on the bondedskin/stiffener panels prior to cutting theminto test specimens. Two additional panelswere used for an impact survey.

Since the primary manufacturing flawsand impact damage effects are in the skins,only symmetric pulloff tests wereconducted to separate the pi-preform from the skin. Out-of-plane shear tests have a different failure mode, whichwas not considered within the scope of this study. Figure 4 shows the location of the 0.25” Teflon strip embedded inthe joint in the pi-skin bondline at the pi flange termination, intended to represent the worst case manufacturing flawsize at the worst possible location. The pulloff test mean and standard deviation data from these specimens wasutilized to validate the 2D manufacturing flaw models.

Four 36-inch long by 8-inch wide panels were subjected to impact damage testing using the fixture shown inFigure 5. Two panels were impacted at the worst location for the joint, the point where the pi flange terminates at the

Teflon Strip in Pi / Skin BondlineAt Pi Flange Termination0.25” Wide, Full Length

0.25”

Teflon Strip in Pi / Skin BondlineAt Pi Flange Termination0.25” Wide, Full Length

0.25”Figure 4. An embedded Teflon strip simulates a manufacturing flaw.

Figure 3. End notched flexure test.


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skin. In addition, impact surveys were conducted on the other two pi joint panels to characterize barely visibleimpact damage (BVID) delamination.

For the pi-preform joints that were to be pulloff tested, the objective was to create a skin delamination not greaterthan 1/2 the width of the “T” joint coupon, which would ensure that the coupon failed in the joint and not in the skinduring testing. The pulloff test fixture limited the “T” joint coupon width to 4.0”, so the largest skin delaminationcould only be 2.0” in diameter. Thus a quick impact survey was conducted at one end of the first panel to identifythe energy required to generate a 2” diameter delamination. After each impact, the “T” joint panel was A-scanned todetermine the impact damage. It was determined that an impact of 20 ft-lbs was required to generate a delaminationof approximately 2.0” in diameter.

20 ft-lb impacts were performed on the first two panels, at 4” wide spacing, for follow-on machining into pullofftest specimens. Following the 20 ft-lb impacts, impact surveys at three locations were conducted in the interest ofidentifying BVID energy levels and associated delamination sizes. A single 80 ft-lb impact was performed on thethird panel, with no visible dent, and from then on all impact energies were 100 ft-lbs. The measured dent depthsfor these 100 ft-lb impacts ranged from .001” to .01”, much smaller than the BVID criteria dent depth of .06” to0.1”. Following the impacts, the four impacted panels were sent to Laser UT for thorough non-destructiveinspection (NDI) of the delamination shapes, sizes, and depths. Following NDI, the 20 ft-lb panels were machinedinto 4” wide specimens and pulloff tested. The resulting mean and standard deviation of the pulloff load were usedin the validation and correlation of the 3D reliability analysis model.

III. 2D Robust Design for Manufacturing FlawsTo evaluate the reliability of the pi joint design in the presence of a manufacturing flaw, three different software

tools were integrated: the ABAQUS finite element analysis program [5], the XFEM (eXtended Finite ElementMethod) fracture analysis toolkit for ABAQUS, and the NESSUS probabilistic analysis software. The interaction ofABAQUS, XFEM, and NESSUS is shown in Figure 6. NESSUS selected values for the random parameters basedon input normal distributions and wrote out data files for the fracture toughness, geometric and material propertyparameters, and the crack size and location. NESSUS then called RBSDM, a custom program written in C++ toserve as an interface between NESSUS and the finite element analysis. RBSDM first ran ABAQUS CAE using acustom XFEM Python script to generate the finite element model from its parametric definition. Then ABAQUSwas run to analyze the finite element model and XFEM was used to perform the crack analysis and write out theresulting strain energy release rates GI and GII at the crack tip. RBSDM then calculated the limit state function g( )using the mode mix formula to account for the two failure modes. The value of the limit state function was returnedto NESSUS for use in the iterative probabilistic analysis algorithm. When the algorithm iteration was completed,NESSUS wrote out the resulting probability of failure, the random parameter importance levels, and the sensitivitiesof the probability of failure to the mean and standard deviation values of each of the random parameters.

The parametric finite element model of the 2D pi joint is shown in Figure 7. The model included geometricparameters for the widths and thicknesses of the pi joint, web, skin, and adhesives. The model was subjected to avertical pulloff load (P) and was constrained using simple supports on the skin on each side of the pi joint. Materialproperty parameters were used to represent the stiffnesses of the pi joint, web, skin, and adhesives. Additionalparameters were used to specify the size and location of cracks within the skin and web. Each parameter’s variabilitywas represented using a normal distribution having a mean and standard deviation based on test data where possibleor otherwise estimated.

Figure 5. Apparatus used for impact testing of pi joints.


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t1

w1

w2

t2

w3

t3

t4

w4

x1

w5

t5z1

x2

z2

w7

P

w6

t6

t7

w8

w9

Figure 7. 2D parametric finite element model with manufacturing flaws.

NESSUS ParametersInput.txt

Cracks.data

Allowable_g.txtGIC, GIIC

RBSDM.exe

ABAQUS CAE

ABAQUSModel

ABAQUSXFEM

serr_out.datGI, GII

rbsdm.outg = 1 – (GI/GIC + GII/GIIC)

Probability ofFailure,

ImportanceLevels,

Sensitivities

NESSUS ParametersInput.txt

Cracks.data

Allowable_g.txtGIC, GIIC

RBSDM.exe

ABAQUS CAE

ABAQUSModel

ABAQUSXFEM

serr_out.datGI, GII

rbsdm.outg = 1 – (GI/GIC + GII/GIIC)

Probability ofFailure,

ImportanceLevels,

Sensitivities

Figure 6. Interaction of ABAQUS, XFEM and NESSUS.


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NESSUS was used to calculate the probability of failure for 0.25” delaminations at various depths within theskin and web. For any specified pulloff load, the critical flaw location was found to be between the pi base adhesiveand the skin under the outer edge of the pi base. As expected, the probability of failure was negligible for verticalflaws within the web. More surprisingly, the probability of failure was also found to be negligible for horizontalflaws below the surface of the skin, indicating that overwraps covering the end of the pi base could be very useful inpreventing the peeloff of the pi base.

The reliability model was validated by comparing the predicted reliability with the pulloff test results for pijoints with embedded manufacturing flaws described above. Figure 8 shows a comparison of the cumulativeprobability of failure versus pulloff load for three different fracture toughness values with the test data. The test datawas bounded by the monolithic specimen fracture toughness curve on the low end and by the cobonded fracturetoughness curves on the high end. The reliability prediction obtained using the CAI cobonded fracture toughnessvalues most closely predicted the test results. The CAI cobonded fracture toughness values differed from thecobonded fracture toughness values obtained in this research primarily in the value of GIIC. The CAI cobondedfracture toughness values were used for the robust design effort because of the better agreement with the test.

The validation effort led to several conclusions. First, the mode mix equation used in the limit state function isclearly important in the reliability calculations. Second, the fracture toughness values used in the reliability analysisdramatically affect the predicted performance. Third, it is important to measure the fracture toughness for the actuallayup where the delamination is located, which was not achieved in this research due to the complexity of the weaveused in the pi-preform base. Fourth, the reliability model somewhat overpredicts the pulloff load performance of thepi joint.

Using the validated reliability model with the CAI cobonded fracture toughness values, NESSUS was run todetermine the sensitivities of the probability of failure to the mean values of all of the parameters. The results areshown in Figure 9. The magnitudes of the sensitivities indicate which parameters have an important influence on theprobability of failure. Based on these importance levels, only 11 of the 32 random parameters were selected to retainvariability in subsequent analyses in order to reduce computation time. The signs of the sensitivities indicate the

2D Baseline Design Pulloff Load Cumulative Density Function0.25" Crack in Base Adhesive Extending to End of Pi Base

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0.2

0.3

0.4

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0.8

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0 100 200 300 400 500 600 700 800 900 1000 1100 1200

Pulloff Load (lb/in)

Cu

mu

lati

veP

rob

abili

tyo

fF

ailu

re

Monolithic Fracture Toughness

Test Data June 2008

CAI Cobonded Fracture Toughness

Cobonded Fracture Toughness

Figure 8. Validation of 2D reliability model with manufacturing flaws.


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direction that the mean value of the parameter should be changed in order to reduce the probability of failure.Parameters with positive sensitivities should have their mean values reduced, while parameters with negativesensitivities should have their mean values increased. Table 1 summarizes the directions that the retained randomparameter mean values should be changed in order to decrease the probability of failure.

Table 1. Design directions for 2D retained random parameters.

Parameter Description Direction Pi?

t4 Pi Base Thickness Decrease Yes

t5 Skin Thickness Increase No

w7 Support Width Decrease No

w1 Pi Base Inner Width Increase Yes

w2 Pi Base Outer Width Increase Yes

sk_e11 Skin E11 Increase No

t2 Pi Upright Thickness Increase Yes

base_e11 Pi Base E11 Decrease Yes

t3 Web Thickness Increase No

t1 Pi Base Adhesive Thickness Decrease Yes

sk_g12 Skin G12 Increase No

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Mea

nS

ensi

tivit

ies

t1 t2 t3 t4 t5 t6 t7 w1

w2

w3

w4

w7

w8

w9

bas

e_e

11

base

_e2

2

ba

se_

g12

up

_e11

up

_e22

up

_g1

2

sk_e

11

sk_

e22

sk_

g12

wb

_e11

wb

_e22

wb

_g1

2

bad

h_

e11

bad

h_e

22

bad

h_g

12

uad

h_e

11

uad

h_e

22

ua

dh

_g12

Parameter

Baseline Design Mean Sensitivities - All ParametersCAI Co-Bonded Fracture Toughness

Figure 9. 2D baseline design sensitivities to mean parameter values.


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Examining the results shown in Table 1, it is seen that the reliability of the pi joint is increased by increasing thestiffness of the skin and/or decreasing the stiffness of the pi base. In other words, a stiff skin with a compliant pibase is desired to increase the reliability of the pi joint. Of the retained random parameters, only six are relevant tothe design of the pi joint. Therefore, only changes in these six parameters were considered in the robust designanalysis.

Using NESSUS, probabilities of failure were calculated and plotted versus each of the six pi joint retainedrandom parameters. The results showed that the optimum pi joint design has a fully tapered pi base which is as thin,wide, and flexible as possible, with thick uprights. For practical manufacturing reasons, it was felt that the pi basecould not be reduced in thickness from the baseline mean value. Also, reducing the pi base adhesive thickness wasdeemed to be not an effective means of improving the pi joint reliability. Finally, changing the pi joint base E11stiffness would require changing the weave in the base, which would require a complex analysis and a change in themanufacturing process. The simplest design changes promising the greatest improvements in reliability were tochange the geometry only – the width of the pi base and the thickness of the pi upright. Based on these assumptions,three candidate pi joint designs were selected for comparison of reliability to the baseline design and to each other.The baseline and candidate pi joint designs are shown in Figure 10.

NESSUS was used to calculate the probability of failure of the Baseline Design and the three candidate designsfor a range of values of pulloff load. The results are plotted in Figure 11 in the form of cumulative probabilitycurves. The Baseline Design provides the lowest pulloff load capability for any given reliability. Candidate Design 1provides approximately 64% greater mean pulloff load capability than the baseline, verifying that the combinationof a thicker pi upright and a wider pi base provide greater reliability. Candidate Design 2 provides approximately76% greater mean pulloff load capability than the Baseline Design, verifying that increasing the tapered portion ofthe pi base provides more benefit than increasing the untapered portion. Candidate Design 3 provides approximately112% greater mean pulloff load capability than the Baseline Design, verifying that a nearly fully tapered pi baseprovides the maximum reliability benefit.

The 2D robust design analysis showed that the pi joint probability of failure could be significantly reduced if theparameters were changed in the directions indicated by the NESSUS-calculated sensitivities. No minima werefound, indicating that the optimum parameter values are set by manufacturing limitations or failure modes other than

Baseline Design Candidate Design 1

Candidate Design 2 Candidate Design 3

Baseline Design Candidate Design 1

Candidate Design 2 Candidate Design 3

+50%

+25% +25%

+50%+50%

+45%

+50%

-74% +105%

Figure 10. 2D baseline and candidate designs.


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delamination propagation. The parameters w1, w2, and t2 (the pi base widths and upright thickness) were found tobe the most practical design changes to the pi joint promising significant increases in reliability. A thin, wide, fullytapered flexible pi base with thick uprights was found to be desired for reliability. Reducing the pi base stiffness bychanging the fabric weave is another viable option for improving the reliability, but it is not as simple as changingthe pi dimensions.

IV. 3D Robust Design for Impact DamageInitially, it was assumed that a circular delamination representing impact damage could be inserted into the finite

element model within the skin and that failure could be predicted using the strain energy release rates around theperimeter of the delamination. However, the testing of impact-damaged specimens indicated that a different failuremode was at work. Rather than failing at the delamination location within the skin, the pi joints failed by peeloff ofthe pi base from the skin. To model this failure mode, the 3D model incorporated two cracks: an assumed “starter”flaw at the edge of the pi base extending the full length of the model and a circular delamination within the skin, asshown in Figure 12. The starter flaw allowed the model to fail at the edge of the pi base while the delamination flawrepresented the NDI-measured impact delamination.

The 3D model was initially used to predict the failure pulloff load for the pristine pi joint having no impactdamage. Only the starter flaw was used for this comparison. Figure 13 shows the comparison of the predicted failurepulloff load ( g( )=0 ) for the pristine pi joint with the experimental test result using an arbitrarily-selected starterflaw width of 0.05”. Curves are shown for two different co-bonded fracture toughness values, those obtained fromthe current research and those obtained in the previous CAI testing. As was found in the 2D analysis, the CAIfracture toughness values produced better agreement with the test due to the lower GIIC value. Therefore, the CAIfracture toughness values were used for the subsequent analysis. Figure 13 shows that the 3D model overpredictedthe pristine failure pulloff load using this arbitrarily-selected starter flaw width. The model was correlated to thepristine failure load by increasing the starter flaw width.

Prior to correlation, the 3D model significantly overpredicted the 20 ft-lb test failure load. The delaminationdiameter and depth were considered as correlation parameters, however it was found that neither of these parametershad enough influence to account for the overprediction of the failure load. Instead, the 3D model was correlated tothe 20 ft-lb test failure load by reducing the fracture toughness values to account for microcracking and other diffuseinternal damage within the skin.

Probability of Failure Versus LoadBaseline and Candidate Designs

0.25" Manufacturing Flaw at End of Pi Base

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0 500 1000 1500 2000 2500Load (lb/in)

Cum

ula

tive

Pro

babi

lity

ofF

ailu

re

Baseline DesignCandidate Design 1Candidate Design 2Candidate Design 3

Figure 11. Performance comparison of 2D baseline and candidate designs.


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Limit State Function g( ) Vs Pulloff Load for Pristine Pi Joint0.05" Starter Flaw at Edge of Pi Base

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800Pulloff Load P (lbs/inch)

Lim

itS

tate

Fu

nct

ion

g(

)

CAI Co-Bonded

Co-Bonded

20 Ft-Lb Test

NJC Pristine Test

0.0

Pristine Test Result20 Ft-Lb Test Result

Figure 13. Pre-correlation comparison of 3D model with test results for pristine pi joint.

D

x2

y2L

L/2

x

y

z

Starter Flaw

Circular Delamination

D

x2

y2L

L/2

x

y

z

Starter Flaw

Circular Delamination

Figure 12. The 3D model includes a starter flaw and circular delamination.


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The 3D model was correlated to match both the pristine test failure pulloff load and the 20 ft-lb test failurepulloff load as shown in Figure 14. Point 1 shows the predicted failure pulloff load for an arbitrary 0.05” starter flawwidth. Point 2 shows the failure pulloff load correlated to the pristine failure pulloff load by increasing the starterflaw width to 0.071”. Point 3 shows the negative limit state function that results from adding the delamination flawto the model at the pristine test failure pulloff load. Point 4 shows the positive limit state function that results at the20 ft-lb test failure pulloff load using the full fracture toughness values. Point 5 shows the final correlation with theanalysis failure pulloff load correlated to the 20 ft-lb test failure pulloff load by reducing the fracture toughnessvalues by a factor of 0.44 to account for microcracking and other internal damage.

Using the correlated 3D model, the importance levels and sensitivities were calculated for the 20 ft-lb impactdamage delamination with 41 random parameters. Only the 12 most important random parameters were retained inthe subsequent analyses in order to reduce the computation time. Figure 15 shows the sensitivities to the meanparameter values for the retained random parameters.

The retained parameters for the 3D model with impact damage are essentially the same as for the 2D model witha manufacturing flaw. They include the thickness and width of the pi base, the thickness of the pi upright, and thethickness and stiffness of the pi base adhesive. The signs of the sensitivities indicate the directions the parametersshould be changed in order to increase the pi joint reliability. Table 2 shows the retained parameters and thedirections each should be changed to increase the reliability. Table 2 also indicates if the parameter is relevant to thedesign of the pi-preform.

Limit State Function g( ) Vs Pulloff Load3D Model Correlation

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0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

Pulloff Load P (lbs/inch)

Lim

itS

tate

Fu

nct

ion

g(

)

CAI Co-Bonded a=0.05"20 Ft-Lb TestNJC Pristine Testa=0.071", Starter Flaw Only, Full Fracture Toughnessa=0.071", Starter Flaw + Delam, Full Fracture Toughnessa=0.071", Starter Flaw + Delam, Reduced Fracture Toughness

2

3

4

50.01

Pristine Test Result20 Ft-Lb Test Result

Figure 14. Correlation of the 3D model.


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As with the 2D robust design analysis, the 3D robust design analysis indicates that the reliability of the joint isincreased by using a thin, wide, flexible pi base with thick uprights. Therefore, the same candidate designs wereconsidered as shown in Figure 10. Because of the greater runtime required for the 3D analysis, only the BaselineDesign and Candidate Design 2 were analyzed for reliability in the presence of impact damage. Figure 16 shows the

Table 2. Design directions for 3D retained random parameters.

Parameter Description Direction Pi?

w2 Pi Base Outer Width Increase Yes

crk2_y2 Delamination Depth Increase No

t4 Pi Base Thickness Decrease Yes

w1 Pi Base Inner Width Increase Yes

sk_e11 Skin E11 Increase No

t5 Skin Thickness Increase No

t2 Pi Upright Thickness Increase Yes

ckk2_dia Delamination Diameter Decrease No

t1 Pi Base Adhesive Thickness Decrease Yes

t3 Web Thickness Increase No

badh_g12 Base Adhesive G12 Decrease Yes

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

Mea

nS

ensi

tivit

ies

T1

T2

T3

T4

T5

W1

W2

Ba

seE

11

Ski

nE

11

Ba

seA

dh

esiv

eG

12

De

lam

inat

ion

De

pth

Del

amin

atio

nD

iam

ete

r

Parameter

Baseline Design Mean Sensitivities - Retained Random Parameters

Figure 15. 3D baseline design sensitivities to the mean values of the retained random parameters.


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cumulative probability of failure versus pulloff load for the Baseline Design and Candidate Design 2. Figure 17shows the probability density curves for the same data.

Probability Density Versus Pulloff LoadCorrelated Baseline Design and Candidate Design 2

0.0000

0.0010

0.0020

0.0030

0.0040

0.0050

0.0060

0.0070

0.0080

0.0090

0.0100

0 500 1000 1500 2000 2500 3000 3500


Pro

bab

ility

Den

sity

TestCorrelated Baseline DesignCandidate Design 2

Figure 17. Probability density versus pulloff load for 3D Baseline Design and Candidate Design 2.

Cumulative Probability of Failure Versus Pulloff LoadCorrelated Baseline Design And Candidate Design 2

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Cu

mul

ativ

eP

rob

abili

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fF

ailu

re

TestCorrelated Baseline DesignCandidate Design 2

Figure 16. Performance comparison of 3D Baseline Design and Candidate Design 2.


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As expected, the Baseline Design exactly matches the mean test failure load because it was correlated to the testvalue. However, the distribution for the Baseline Design also matches the distribution for the test data very well,indicating that the variability in the 3D model is realistic. Candidate Design 2 shows more than double the meanfailure pulloff load of the Baseline Design, indicating that the increases to the pi base width and upright thickness doincrease the reliability at any given load. However, the Candidate Design 2 curve shows much more variability thaneither the Baseline Design or the test data. This is more easily seen in the probability density curves shown in Figure17. The Baseline Design shows a similar height and width of the probability density curve to the test data, while theCandidate Design 2 curve is very short and wide, indicating much greater variability. This increased variability isunexplained and will require additional analysis and tests to validate these results.

V. Summary and ConclusionsTesting was conducted to measure the fracture toughness and failure pulloff load of composite bonded pi joints

in the presence of manufacturing flaws and impact damage. ABAQUS, XFA, and NESSUS were coupled to allowprobabilistic failure analysis of pi joints with embedded cracks. A 2D analysis model for pi joints withmanufacturing flaws was developed and validated using the test data. A 3D analysis model for pi joints with impactdamage was correlated to the test data. To correctly simulate the peeloff failure mode observed in testing, it wasnecessary to incorporate two cracks in the 3D model – a starter flaw at the edge of the pi-preform base and a circulardelamination within the skin. The 3D model was correlated to the pristine failure load using the starter flaw widthand to the 20 ft-lb impact test load by reducing the fracture toughness values to simulate internal damage caused bythe impact.

The 2D robust design analysis for manufacturing flaws and the 3D robust design analysis for impact damagereached the same essential conclusions regarding the desired characteristics of the pi joint for improved reliability. Athin, wide, fully tapered, flexible pi base with thick uprights was found to be desired. Candidate designs with thesecharacteristics were shown by analysis to provide up to twice the mean failure pulloff load as the baseline design.Additional testing will be required to validate these findings.

Acknowledgements

The work reported herein was performed for the Air Force Research Laboratory/Air Vehicle Directorate(AFRL/RBSA) under the Air Vehicles Technology Integration Program (AVTIP) Delivery Order Contract. Theauthors would like to acknowledge the guidance provided by Dr. Edwin E. Forster, who served as the programmonitor.

References

1. NESSUS, Software Package, Ver. 8.3, Southwest Research Institute, San Antonio, TX, 2008.

2. Shi, J., Lua, J., Waisman, H., Liu, P., Belytschko, T., Sukumar, N., and Liang, Y., “XFEM Toolkit for Automated CrackOnset and Growth Prediction”, AIAA 2008-1763, Schaumburg, IL, April 2008.

3. Deobald, Lyle, “Composite Affordability Initiative Double Cantilever Beam Test”, August 2002.

4. Deobald, Lyle, “Composite Affordability Initiative End Notch Flexure Test”, August 2002.

5. ABAQUS, Software Package, Ver. 6.7, SUMULIA, Providence, RI, 2007.

Documents

Robust Design of Composite Bonded Pi Joints