Sdm 2000

H. Millwater, K. Griffin, D. WielandSouthwest Research Institute

A. West, H. Smith, M. HollyThe Boeing Co.

R. HolzwarthAir Force Research Laboratory

Probabilistic Analysis of an Advanced Fighter/Attack Aircraft Composite Wing

Structure

Sdm 2000

RTM Composites

Fiber Placed/Steered

HSM Aluminum

HIP’d Titanium Castings

Aluminum Sh Metal

Titanium Machining

Cocured Composite Dorsal AssyWith Fiberplaced Skins

Peripheral MembersCompatible With

Existing Structure

Titanium HIPCastings

RTM Carbon/Glass Hybrid SparsCobonded To Fibersteered LowerWing Skin

Sinewave Stiffened RTM SparsIncorporate Three DimensionalWoven Inserts

Assess the benefits of applying probabilistic design technology to a state-of-the-art composite wing design

Objective

Sdm 2000

RTM Composites

Fiber Placed/Steered

HSM Aluminum

HIP’d Titanium Castings

Aluminum Sh Metal

Titanium Machining

Cocured Composite Dorsal AssyWith Fiberplaced Skins

Peripheral MembersCompatible With

Existing Structure

Titanium HIPCastings

RTM Carbon/Glass Hybrid SparsCobonded To Fibersteered LowerWing Skin

Sinewave Stiffened RTM SparsIncorporate Three DimensionalWoven Inserts

Aircraft structure is a composite wing designed under an advanced lightweight aircraft structures development program.

•Represents state-of-the-art in aircraft design•Has high quality computational models available•Has experimental component test data available

Background

Sdm 2000

Structural Example

RTM Composites

Fiber Placed/Steered

HSM Aluminum

HIP’d Titanium Castings

Aluminum Sh Metal

Titanium Machining

Cocured Composite Dorsal AssyWith Fiberplaced Skins

Peripheral MembersCompatible With

Existing Structure

Titanium HIPCastings

RTM Carbon/Glass Hybrid SparsCobonded To Fibersteered LowerWing Skin

Sinewave Stiffened RTM SparsIncorporate Three DimensionalWoven Inserts

Sdm 2000

Purpose: compute probability distribution of failure load and compare with experimental results– Two test temperatures: -65 F and 75 F– Three specimens at each temperature– Pull-off load increased until failure

Edges Remain Connected

Evident Failure Surrounding Nugget

Comparison with Test Structures

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Computational Model

Skin Ply 1Skin Ply 2

.

.

.Skin Ply n

Left Flange Ply 1Left Flange Ply 2

.

.

.Left Flange Ply n

Right Flange Ply 1Right Flange Ply 2

.

.

.Right Flange Ply nr

hbl

hbr

lsl lfl lfr lsr

ta

P

M

NuggetAdhesive

Nonlinear composite analysis using BLADEM/THELMA (Boeing) Probabilistic analysis computed using NESSUS (SwRI)

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Random Variable Statistics

Composite Tape COV(%) Distribution*Modulus of Elasticity (E1) 3.2 TNORMModulus of Elasticity (E2) 2.0 TNORMShear Modulus (G12) 5.0 TNORMPoisson’s Ratio (Nu12) 11.9 TNORMPly Thickness 10.0 TNORMTensile Strength (S3) 7.8 TNORMShear Strength (T) 8.7 TNORM

Composite ClothModulus of Elasticity (E1) 6.9 TNORMModulus of Elasticity (E2) 5.0 TNORMShear Modulus (G12) 5.4 TNORMPoisson’s Ratio (Nu12) 41.5 LOGNORMALThickness 1.5 TNORMTensile Strength (S3) 4.6 TNORMShear Strength (T) 8.4 TNORM

AdhesiveInitial Shear Modulus (G) 12.8 TNORMTau Ultimate (τulτ) 9.1 TNORMGam m a Ulτim aτe (Gulτ) 22.9 TNORMNuggeτ Radius (NR) 3.0 TNORMPly Thickness 10.0 TNORMInτerlam inarShear Sτrengτh (T) 3.8 TNORM

TNORM = Truncated Normal Dist. at 3 s

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Failure Model

Structure is assumed failed when failure index >= 1.0

( ) ( )TS

FI 2

2

23

2

31

2

3

3 ττσ ++= ⎟⎟⎠

⎞⎜⎜⎝⎛

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

-6 -5 -4 -3 -2 -1 0 1 21.0

Prob. ofFailure

S3, T - Material Strengths

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Experimental ComputationalCOV (%) 2.15 8.02

Failure due to pull-off load (75 degrees; 3 test structures)

Comparison of Computational and Experimental Results

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Probabilistic Sensitivity Factors (75)

Variable dprob/dmean Normalized (%) dprob/dstdev Normalized(%)

Cloth E1 -1.57E-10 0.97 -7.08E-11 0.11Cloth E2 6.56E-11 0.15 -1.25E-11 0.00Cloth G12 2.60E-10 0.01 -1.25E-11 0.00Cloth Nu12 1.08E-03 0.00 -1.40E-04 0.00Cloth Thick -0.2081 3.12 -4.51E-02 0.01Tape E1 1.22E-10 2.14 -3.88E-11 0.03Tape E2 3.52E-10 0.08 -1.60E-11 0.00Tape G12 -1.36E-09 0.36 -1.44E-10 0.00Tape NU12 2.19E-04 0.00 -7.01E-06 0.00Tape Thick 1.577 50.72 -3.382 55.62Adhesive Goct -7.92E-09 1.46 -6.93E-09 1.54Adhesive Tau-ult -2.22E-08 0.01 -7.13E-10 0.00Adhesive Gam-ult 3.34E-04 0.00 -1.24E-05 0.00Adhesive Thickness -1.72E-02 0.00 -7.94E-04 0.00Nugget Radius 7.27E-02 26.35 -8.91E-02 5.92Cloth Ten strength 7.62E-07 7.72 -1.16E-06 14.16Cloth Shear Str. 3.77E-07 6.92 -6.45E-07 22.61Tape Ten Str. -1.41E-16 0.00 -7.16E-11 0.00Tape Shear Str. -9.18E-17 0.00 -4.89E-11 0.00Adhesive Shear Str. -3.51E-16 0.00 -1.61E-10 0.00

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Comparison of Computational and Experimental Results

Failure locations and mean failure load agree. Amount of variation in pull-off load is several times that from test Expected reason:

• Computational results were developed using material property data collected over several years.

• Test structures were manufactured as one structure then sectioned.

• Variations in material properties and geometries likely to be significantly less than that used in computation.

• Computational results expected to be more accurate of fleet.

• Use of test results as indicative of fleet may be unconservative.

Sdm 2000

Skin Ply 1Skin Ply 2

.

.

.Skin Ply n

Left Flange Ply 1Left Flange Ply 2

.

.

.Left Flange Ply n

Right Flange Ply 1Right Flange Ply 2

.

.

.Right Flange Ply nr

hbl

hbr

lsl lfl lfr lsr

ta

P

M

NuggetAdhesive

Failure: pull-off load in bonded joint of spar/wing Severe down bending load (ultimate load) 20 independent random variables - material properties Geometrically Nonlinear NASTRAN analysis of wing - local analysis of composite joint Failure probability and sensitivities computed

Probabilistic Analysis of a Composite Wing

Spar 3 Location of Load Extraction

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WING-BLADE ANALYSIS Methodogy

NASTRANNon-linear Global

ALAFS Model

BLADEMDetailed Blade

Model

BLADEM_POSTExtraction of FailureIndex from Results

BLADEM_PREPreprocessor to Create BLADEM Input File

Force Post-ProcessorExtract Free-Body Forces

for Sub-model Region

Prob. Distrib.

lsl lfl lfr lsr

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Material property

inputPatran Nastran PatranNon-linear

bdfNon-linear

op2

Nastran Linearbdf

Linearop2PatranFreebody

exeFreebody

data

Blademinput

Bladem/Thelma

ThelmaResults

NESSUS

NESSUS

1

2 3

7

4

9

6

8

5

Computational Procedure

Link NESSUS, PATRAN, NASTRAN, THELMA

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Structural Deformation At Nominal Values

Post-buckled Wing Skin

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Joint STRESSES

Highly stressed region

lsl lfl lfr lsr

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Random Variables

Mat’l Variable COV(%) DistributionTape Modulus of elasticity - E1 (tension &

compression)1.3 TNORM

Tape Modulus of elasticity - E2 (tension &compression)

4.5 TNORM

Tape Modulus of elasticity - E3 (= E2)Tape Shear modulus - G12 (tension &

compression)2.7 TNORM

Tape Shear modulus - G23 (tension &compression) = E2/(2*(1+Nu23))

Tape Shear modulus – G13 (tension &compression) = G12 = G31

Tape Poisson’s ratio – Nu12 5.1 TNORMTape Poisson’s ratio – Nu23 = 0.3Tape Poisson’s ratio – Nu31 (=E2*Nu12/E1)Cloth Modulus of elasticity - E1 5.8 TNORMCloth Modulus of elasticity - E2 6.2 TNORMCloth Modulus of elasticity - E3 6.2 TNORMCloth Shear modulus - G12 1.8 TNORMCloth Shear modulus - G23 2.2 TNORMCloth Shear modulus - G31 (=G23)Cloth Poisson’s ratio – Nu12 62.5 LOGNORMA

LCloth Poisson’s ratio – Nu23 7.3 TNORM

Tape 2 Modulus of elasticity - E1 (Cloth Nu31 =E3*Nu23/E1 Tape 2)

2.7 TNORM

Adhesive Modulus of elasticity – E 9.1 TNORMAdhesive Shear modulus – G 9.1 TNORM

Tape Tensile Strength 6.1 TNORMTape Shear Strength 4.7 TNORMCloth Tensile Strength 6.9 TNORMCloth Shear Strength 8.2 TNORM

Sdm 2000

System Reliability Results

]

[] [][

1

11

ePlyNRightFlangePlyRightFlang

PlyNLeftFlangePlyLeftFlangeSkinPlyNSkinPlyadhesivenugget

FF

FFFFFFPionin any regfailurePbladeP

∪

∪∪∪∪∪∪==

LLL

Consider failure of the joint as failure in any location or ply, i.e., adhesive, nugget, flanges or skin

Results indicate failure governed entirely by failure in 1st ply of left flange.

Sdm 2000

Probabilistic Sensitivity Results

Random Variable dprob/dmean Normal-ized (%) dprob/dstdev Normal-ized (%)

Tape E1 -1.77E-08 1 -3.35E-10 0Tape E2 -1.21E-07 0 -2.07E-09 0Tape G12 -7.47E-07 1 -1.17E-08 0Tape Nu12 -7.52E-01 0 -1.13E-02 0Cloth E1 -1.02E-007 2 -3.76E-009 0Cloth E2 2.76E-07 17 -2.85E-08 5Cloth E3 4.13E-07 1 -6.47E-09 0Cloth G12 1.23E-07 0 -2.89E-09 0Cloth G23 1.50E-06 4 -2.96E-08 0Cloth Nu12 0.2874 0 -0.1046 0Cloth Nu23 2.45E-01 0 -4.70E-03 0Cloth Nu31 -9.37E-10 0 -1.55E-10 0Adhesive E 1.46E-07 0 -6.36E-09 0Adhesive G 6.21E-06 0 -1.56E-07 0Tape Tensile Strength 2.21E-12 0 -1.64E-06 0

Tape Shear Strength 9.96E-14 0 -1.12E-07 0

Cloth Tensile Strength -8.15E-04 74 -1.88E-04 95

Cloth Shear Strength -2.17E-07 0 -8.77E-08 0

*

*

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Probability of Failure was too high from original design

Several redesigns were explored deterministically– Effective redesigns were:

» Increase nugget radius (from prob. sensitivities)» Remove ply from right flange» Soften E2 modulus of cloth (from prob. sensitivities)

Probabilistic Redesign

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Probabilistic Redesign

Probability Density Function after Redesign

Pf ~ 10-30

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Probabilistic Redesign Conclusions

A many order of magnitude improvement in safety was obtained with a small amount of effort

Probabilistic sensitivity factors indicated 2 of the 3 elements to change - nugget radius and E2 of the cloth

– The effect of E2 would have been difficult to ascertain without the sensitivity analysis

Exploratory analyses were performed determinstically (quickly) to indicate a promising design

Sdm 2000

Summary and Conclusions

Computed distribution of probability of failure loads were compared with test results. Failure region and mean failure load agree. Computed scatter was several times that of test. Expected reason - test structures do not exhibit realistic amount of variation that would be seen in fleet. Computational results expected to be more representative of fleet. Use of test results as indicative of fleet may be unconservative.Test procedures may need to be modified in order to represent better the variation seen in production.

Test Structures

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Summary and Conclusions

Probabilistic analysis of a state-of-the-art composite wing is practical using standard probabilistic and structural analysis tools. Probability of failure of a post-buckled wing/joint subjected to a severe down bending load was determined

– Combined probabilistic analysis (NESSUS) with geometrically nonlinear NASTRAN analysis with local composite THELMA analysis

Wing/Joint Analysis

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Summary and Conclusions

Wing/joint structure was redesigned by modifying three variables: nugget radius, removing ply from right flange and reducing E2 material property.Probabilistic sensitivities give valuable insight into the redesign. Redesigned structure’s probability of failure was reduced by many orders of magnitude