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Progressive Failure Analysis of Composite Vertical Tail in Airbus A300-600R, Lecture notes of Structural Analysis

The use of solid-shell and layered-shell modeling approaches in progressive failure analyses (PFA) to determine the load, mode, and location of failure in the right rear lug of an Airbus certification test conducted in 1985. The document also explores the limitations of these methods in predicting micromechanical details of damage progression in textile-based composites.

What you will learn

  • What are the classical failure modes of a bolted joint and how are they represented in the model?
  • Why is it difficult to predict micromechanical details of damage progression in textile-based composites?
  • What are the limitations of using strength-based criteria for predicting failure beyond initiation?
  • What were the predicted failure loads, failure mode, and location of failure according to the global analysis team?
  • What are the solid-shell and layered-shell modeling approaches used for in the document?

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bg1
American Institute of Aeronautics and Astronautics
1
Paper submitted to the special session on the NTSB investigation of the AA Flight 587 accident
and part of the special sessions in honor of Dr. James H. Starnes, Jr.
NASA Structural Analysis Report on the American Airlines
Flight 587 AccidentLocal Analysis of the Right Rear Lug
I. S. Raju*, E. H. Glaessgen
, B. H. Mason
, T. Krishnamurthy
, and C. G. Dávila
NASA Langley Research Center, Hampton, Virginia, 23681
A detailed finite element analysis of the right rear lug of the American Airlines Flight 587
- Airbus A300-600R was performed as part of the National Transportation Safety Boards
failure investigation of the accident that occurred on November 12, 2001. The loads
experienced by the right rear lug are evaluated using global models of the vertical tail, local
models near the right rear lug, and a global-local analysis procedure. The right rear lug was
analyzed using two modeling approaches. In the first approach, solid-shell type modeling is
used, and in the second approach, layered-shell type modeling is used. The solid-shell and
the layered-shell modeling approaches were used in progressive failure analyses (PFA) to
determine the load, mode, and location of failure in the right rear lug under loading
representative of an Airbus certification test conducted in 1985 (the 1985-certification test).
Both analyses were in excellent agreement with each other on the predicted failure loads,
failure mode, and location of failure. The solid-shell type modeling was then used to analyze
both a subcomponent test conducted by Airbus in 2003 (the 2003-subcomponent test) and
the accident condition. Excellent agreement was observed between the analyses and the
observed failures in both cases. From the analyses conducted and presented in this paper,
the following conclusions were drawn. The moment, Mx(moment about the fuselage
longitudinal axis), has significant effect on the failure load of the lugs. Higher absolute
values of Mxgive lower failure loads. The predicted load, mode, and location of the failure
of the 1985-certification test, 2003-subcomponent test, and the accident condition are in very
good agreement. This agreement suggests that the 1985-certification and 2003-
subcomponent tests represent the accident condition accurately. The failure mode of the
right rear lug for the 1985-certification test, 2003-subcomponent test, and the accident load
case is identified as a cleavage-type failure. For the accident case, the predicted failure load
for the right rear lug from the PFA is greater than 1.98 times the limit load of the lugs.
I. Introduction
N November 12, 2001, American Airlines Flight 587 (AA 587) crashed shortly after take-off killing all 260
people on board and 5 on the ground. The composite vertical tail of the aircraft separated from the fuselage
resulting in loss of control and ultimately the loss of the aircraft.
Several teams at the NASA Langley Research Center were assembled to help the National Transportation Safety
Board with this investigation. The internal NASA team was divided into several discipline teams including a
structural analysis team that consisted of a global analysis team and a detailed lug analysis team. The global
analysis team considered global deformations, load transfer, and failure modes within the composite vertical tail as
well as failure of the composite rudder. The detailed lug analysis team focused on failure of the laminated
composite lugs that attach the tail to the aluminum fuselage. This paper describes the analyses conducted by the
detailed lug analysis team.
*Structures Discipline Expert, NASA Engineering and Safety Center, MS 155, AIAA Fellow.
Aerospace Engineer, Computational Structures and Materials Branch, MS 155, AIAA Senior Member.
O
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Partial preview of the text

Download Progressive Failure Analysis of Composite Vertical Tail in Airbus A300-600R and more Lecture notes Structural Analysis in PDF only on Docsity!

Paper submitted to the special session on the NTSB investigation of the AA Flight 587 accident

and part of the special sessions in honor of Dr. James H. Starnes, Jr.

NASA Structural Analysis Report on the American Airlines

Flight 587 Accident–Local Analysis of the Right Rear Lug

I. S. Raju

, E. H. Glaessgen

, B. H. Mason

, T. Krishnamurthy

, and C. G. Dávila

NASA Langley Research Center, Hampton, Virginia, 23681

A detailed finite element analysis of the right rear lug of the American Airlines Flight 587

- Airbus A300- 600 R wasperformedaspartoftheNationalTransportationSafetyBoard’s

failure investigation of the accident that occurred on November 12, 2001. The loads

experienced by the right rear lug are evaluated using global models of the vertical tail, local

models near the right rear lug, and a global-local analysis procedure. The right rear lug was

analyzed using two modeling approaches. In the first approach, solid-shell type modeling is

used, and in the second approach, layered-shell type modeling is used. The solid-shell and

the layered-shell modeling approaches were used in progressive failure analyses (PFA) to

determine the load, mode, and location of failure in the right rear lug under loading

representative of an Airbus certification test conducted in 1985 (the 1985-certification test).

Both analyses were in excellent agreement with each other on the predicted failure loads,

failure mode, and location of failure. The solid-shell type modeling was then used to analyze

both a subcomponent test conducted by Airbus in 2003 (the 2003-subcomponent test) and

the accident condition. Excellent agreement was observed between the analyses and the

observed failures in both cases. From the analyses conducted and presented in this paper,

the following conclusions were drawn. The moment, M x (moment about the fuselage

longitudinal axis), has significant effect on the failure load of the lugs. Higher absolute

values of M x give lower failure loads. The predicted load, mode, and location of the failure

of the 1985-certification test, 2003-subcomponent test, and the accident condition are in very

good agreement. This agreement suggests that the 1985 - certification and 2003 -

subcomponent tests represent the accident condition accurately. The failure mode of the

right rear lug for the 1985-certification test, 2003-subcomponent test, and the accident load

case is identified as a cleavage-type failure. For the accident case, the predicted failure load

for the right rear lug from the PFA is greater than 1.98 times the limit load of the lugs.

I. Introduction

N November 12, 2001, American Airlines Flight 587 (AA 587) crashed shortly after take-off killing all 260

people on board and 5 on the ground. The composite vertical tail of the aircraft separated from the fuselage

resulting in loss of control and ultimately the loss of the aircraft.

Several teams at the NASA Langley Research Center were assembled to help the National Transportation Safety

Board with this investigation. The internal NASA team was divided into several discipline teams including a

structural analysis team that consisted of a global analysis team and a detailed lug analysis team. The global

analysis team considered global deformations, load transfer, and failure modes within the composite vertical tail as

well as failure of the composite rudder. The detailed lug analysis team focused on failure of the laminated

composite lugs that attach the tail to the aluminum fuselage. This paper describes the analyses conducted by the

detailed lug analysis team.

Structures Discipline Expert, NASA Engineering and Safety Center, MS 155, AIAA Fellow.

Aerospace Engineer, Computational Structures and Materials Branch, MS 155, AIAA Senior Member.

O

First, an overview of the problem, including the vertical tail plane (VTP) structure, is presented. Second, the

various models developed for the right rear lug are described. Third, details of the material modeling, contact

modeling, and progressive failure analysis (PFA) for solid-shell type modeling are presented. Fourth, a brief

discussion of an alternative modeling approach, layered-shell modeling, is presented. Fifth, the global-local

connection processes used to virtually embed the local lug model within a global model of the VTP are described.

Sixth, the results of the analyses are presented. Finally, the results and lessons learned are discussed.

II. Description of the Problem

The vertical tail plane (VTP) of an Airbus A300-600R is connected to the fuselage with 6 lugs (3 on the right-

hand side and 3 on the left-hand side) through a pin and clevis connection (see Figures 1a to 1d). Six yokes (not

shown in figures) also connect the VTP to the fuselage and take some of the lateral loads. The air loads on the VTP

during the 12 seconds before the VTP separated from the fuselage were evaluated and were supplied to the NASA

structures teams by the National Transportation Safety Board (NTSB) and Airbus. The air loads were derived from

digital flight data recorder (DFDR) data obtained after the accident.

The NASA global analysis team and the Airbus team evaluated the loads on each of the lugs and determined that

the right rear lug (see Figure 1d) carried the largest loads compared to the design allowable. The lug analysis team,

therefore, focused on the detailed analysis of the right rear lug. The objectives of the lug analysis team were to

predict the failure load, mode, and location in the right rear lug for the loading conditions that the right rear lug

experienced during the accident.

The lug analysis team considered the right rear lug region shown in Figure 1d. The lug is a continuation of the

skin of the vertical tail with two pre-cured fitting halves cured to either side of the skin in the vicinity of the lug hole

(the fitting extends to rib 4, as shown in Figure 1d). The region modeled consists of the right rear lug, rib 1, the rear

spar, and 6 stringers from rib 1 to rib 5. Two different modeling approaches were used. The first modeling

approach involved the development of a finite element (FE) model of the region shown in Figure 1d using three-

dimensional (3D) elements in the region of the two pre-cured fitting halves of the lug and shell elements for the rest

of the model and is termed the solid-shell model. The second modeling approach involved the development of an

FE model of the region shown in

Figure 1d using shell elements

throughout and is termed the layered-

shell model. In the layered-shell

model, the 3D region of the first

approach is modeled as shell layers

that are connected by decohesion

elements representing multi-point

constraints. The results obtained by

these approaches were validated by

comparison with reference solutions

for simplified configurations. The

two approaches were also verified by

comparing the finite element results

with Airbus experimental results.

III. Modeling

The coarse 3D model (part of the

solid-shell series of models) and

layered-shell model were developed

by modifying an Airbus-developed

model of the same region. The

damage modeling applied to each

modeling approach was developed

independently, which provided a

degree of independent verification of

the results from both methods. During

the course of the investigation, two

other solid-shell models were also

Fin

Lugs

Rudder

Fin

Lugs

Rudder

Fin

Lugs

Rudder

(a) A300-600R Empennage (b) Major Components of Vertical

Tail Plane (VTP)

Rib 1

Stringers

Rib 1 Lug

Rib 4

Stringers

Lug

Rib 5

Rear

Spar

Clevises mounted on

the fuselage

Yoke connection at

rear spar

Pin and

Bushing

Rib 1

Stringers

Rib 1 Lug

Rib 4

Stringers

Lug

Rib 5

Rear

Spar

Rib 1

Stringers

Rib 1 Lug

Rib 4

Stringers

Lug

Rib 5

Rear

Spar

Clevises mounted on

the fuselage

Yoke connection at

rear spar

Pin and

Bushing

Clevises mounted on

the fuselage

Yoke connection at

rear spar

Pin and

Bushing

(c) VTP-Fuselage Connections (d) Construction of Fin near

Right Rear Lug

Figure 1. Vertical Tail Plane Mounted on the Fuselage.

C. 1985 - Certification Test Model

Two test specimens (called X2/2 and X2/1) were tested by Airbus in 1985. One FE model was used to represent

both test specimens. To simulate the configurations of the X2/2 and X2/1 test specimens, an FE model was created

from the coarse 3D model by deleting all the elements above rib 4 and forward of stringer 6 as shown in Figure 4a.

This model had 23216 nodes and 19149 elements. The boundary conditions used with this model are shown in

Figure 4b.

Z

X

Y

x, u,

(F X

)

y, v, (F Y

)

z, w,

(F Z

)

 Y

,

(M Y

)

 X

,

(M X

)

 Z

,

(M Z

)

Z

X

Y

Z

X

Y

x, u,

(F X

)

y, v, (F Y

)

z, w,

(F Z

)

 Y

,

(M Y

)

 X

,

(M X

)

 Z

,

(M Z

) x, u,

(F X

)

y, v, (F Y

)

z, w,

(F Z

)

 Y

,

(M Y

)

 X

,

(M X

)

 Z

,

(M Z

)

(a) Solid-Shell Model (b) Layered Shell Model

CLAMPED

(u=v=w=

 x

= y

= z

=0)

HARD SIMPLE SUPPORT

v’=w’= 0

 x

’= y

’= z

’=

PINNED

(u=v=w=0)

v= x

=

u=

Z

X

Y

Z’

X’

Y’

CLAMPED

(u=v=w=

 x

= y

= z

=0)

HARD SIMPLE SUPPORT

v’=w’= 0

 x

’= y

’= z

’=

PINNED

(u=v=w=0)

v= x

=

u=

Z

X

Y

Z

X

Y

Z’

X’

Y’

Z’

X’

Y’

(c) Initial Airbus Boundary Conditions

Figure 3. Finite Element Models of Right Rear Lug (colors are for visualization purposes only).

Z

X

Y

Solid

Element

Region

Shell

Element

Region

CLAMPED

(u=v=w=

 x = y = z =0)

u=v= z =

CLAMPED

u’=v’=w’= 0

 x ’= y ’= z ’=

Z

X

Y

Z’

X’

Y’ Z

X

Y

Solid

Element

Region

Shell

Element

Region

Z

X

Y

Z

X

Y

Z

X

Y

Solid

Element

Region

Shell

Element

Region

CLAMPED

(u=v=w=

 x = y = z =0)

u=v= z =

CLAMPED

u’=v’=w’= 0

 x ’= y ’= z ’=

Z

X

Y

Z’

X’

Y’

CLAMPED

(u=v=w=

 x = y = z =0)

u=v= z =

CLAMPED

u’=v’=w’= 0

 x ’= y ’= z ’=

Z

X

Y

Z

X

Y

Z’

X’

Y’

Z’

X’

Y’

(a) Finite Element Model (b) Boundary Conditions

Figure 4. 1985-Certification Test Model of X2/2 Specimen (colors are for visualization purposes only).

D. 2003 - Subcomponent Test Model

As part of the investigation, a subcomponent test was conducted during 2003 on a left rear lug made of the same

material as the accident aircraft. A left rear lug was used because this was the only rear lug (with the same material

as the accident aircraft) that was available at the time of the test. Airbus modeled this left rear lug (see Figure 5a)

including the support structure and supplied the model to the lug analysis team. This Airbus model then became

part of the solid-shell series of models. The boundary conditions for this model are shown in Figure 5b. When this

model is used to represent the right rear lug , the loads and boundary conditions are mirrored about the global xz -

plane; i.e. the sign of F Y

, M

X

, M

Z

, v ,  X

, and  Z

are reversed.

IV. Solid Element Models

A. Material Modeling

The right rear lug consists of two pre-cured fitting-halves, the vertical tail plane (VTP) skin and several

compensation layers. The inner fitting-half, skin, and outer fitting-half are made from T300/913C in the form of

±45° fabric, 90°/0° fabric, and 0° tape and are approximately 55 mm thick in the vicinity of the pin.

Table 1 shows the elastic, strength, and toughness

parameters for T300/913C from the recent World Wide

Failure Exercise (WWFE, Soden and Hinton, 1998a and

Soden and Hinton, 1998b). The subscripts 1, 2, and 3

denote the fiber direction, in-plane transverse direction, and

out-of-planedirection,respectively,and thesubscript“c”

denotes a compressive property. Also, X T

, X

C

, Y

T

, and Y C

denote the fiber-direction tensile strength, fiber-direction

compressive strength, transverse-direction tensile strength,

and transverse-direction compressive strength, respectively.

Finally, G IC

is the mode-I interlaminar fracture toughness.

1. Homogenization of Material Properties

The right rear lug contains numerous plies of T300/913C

in the form of tape and fabric. Although a finite element

model that explicitly modeled each of the plies and each of

the numerous curvilinear ply drops within the lug could be

developed, doing so would have required a finite element

model with millions of elements. Such a detailed finite

element model would be too cumbersome to use in progressive failure analyses. To maintain a reasonable number

of elements and yet accurately account for failures in each of the plies, a two-level procedure is followed. In the

first level, within each finite element, the material properties of the plies are homogenized. In the second level,

within the progressive failure analysis, the stress and failure state of each ply is evaluated. The details of this

procedure are described below.

CLAMPED

(u=v=w=

 x = y = z =0)

Z

X

Y

Z

X

Y

CLAMPED

(u=v=w=

 x = y = z =0)

Z

X

Y

CLAMPED

(u=v=w=

 x = y = z =0)

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

(a) Finite Element Model (b) Boundary Conditions (prescribed along

the red edges and the red region)

Figure 5. 2003 - Subcomponent Test Model.

Table 1. Material Properties for T300/913C Tape.

Property

WWFE

[Hinton and Soden 1998]

E

1 (GPa) 138

E

1 C (GPa) --

E

2 (GPa) 11

E

2 C (GPa) --

12

23

12

(GPa) 5.

X

T (MPa) 1500

X

C (MPa) 900

Y

T (MPa) 27

Y

C (MPa) 200

S

xy (MPa) 80

G

IC

(KJ/m

2

) 220

reacted by the pin because the y - force can only react on the contact surface, and Y-MPC #1 effectively treated the y -

force as reacting around 360° of the hole. In order to improve the simulation, another MPC equation, Y-MPC #2,

was developed.

For equation Y-MPC #2, two 120° arcs (±60° relative to the load vector) were used instead of the 360° rings, as

shown in Figure 7b. The average displacement of these two arcs is represented by the displacement ( v M

) at Point M.

The displacement at Point M is related to the pin displacement ( v P

) by an equation that includes the global x - and z -

rotations of the pin, as shown in Figure 7b. All lug results generated before the 2003-subcomponent test used Y-

MPC #1; all later analyses used Y-MPC #2.

A. Progressive Failure Analysis (PFA)

1. Background to Failure Theories

Strength-based approaches for the prediction of initial and progressive failure in polymeric matrix composites

are founded on a continuum representation of ply-level failure mechanisms. The comparative simplicity of applying

strength-based criteria for the prediction of failure events within common analysis frameworks such as finite

element procedures has led to this approach becoming increasingly accepted as a method for predicting the onset

and development of material failure in composite structures.

Active research is directed towards representing micromechanical-level damage mechanisms in macroscopic,

continuum-based failure criteria. These investigations have commonly elicited controversial discussions regarding

the theoretical validity of developed failure criteria [Soden and Hinton, 1998a and b]. At issue is the difficulty of

simulating the complexity of underlying failure mechanisms in terms of a discrete set of fixed strength parameters

and the validity of using these parameters determined for individual lamina in the elastically constrained

environment of an assembled laminate. The need to develop computationally efficient methodology to avoid

detailed micromechanical analyses is aptly expressed by a passage by Hashin [Hashin, 1980]:“Themicrostructural

aspects of failure are of such complexity that there is little hope of resolution of this problem on the basis of

micromechanics methods. Such methods would require analytical detection of successive microfailures in terms of

microstress analysis and microfailure criteria and prediction of the coalescence of some of them to form

macrofailures which is an intractable task.”

A large number of continuum-based criteria have been derived to relate internal stresses and experimental

measures of material strength to the onset of failure [Rowlands, 1984; Nahas, 1986]. However, the use of any of

these criteria for predicting failure beyond initiation may become theoretically invalid due to the underlying physics

of interacting failure mechanisms that are implicitly neglected in the experimental determination of critical strength

parameters.

2. Failure Theory Used in the PFA

Intheanalysisoftherightrearcompositelug,theHashincriterion[Hashin, 1980 ]waschosen. Hashin’s

criterion assumes that the stress components associated with the plane of fracture control the failure. This

consideration leads to the following equations expressing fiber and matrix failure written for general three-

dimensional states of stress.

Tensile fiber mode

  1

2

13

2

12 2

2

11

   

xy T

S

X

or

T

  X

11 (2)

Compressive fiber mode

C

  X

11 (3)

Tensile matrix mode ( 22

33

      1

2

13

2

12 2

22 33

2

23 2

2

22 33 2

T T xy

Y S

Compressive matrix mode ( 22

33

        1

2

13

2

12 2

22 33

2

23 2

2

22 33 2

22 33

2

T T xy T

c

c

S

Y

Y

In equations 1 to 5, the strength values ( X T

, X

C

, Y

T

, Y

C

, and S xy

) are defined in Table 1. Note that both the normal

stress in the fiber-direction,  11 , and the shear stress components parallel to the fiber direction,  12 and  13 , are

considered in equation 1. In equations 1-5,  T

is the transverse shear strength corresponding to the  23

stress

component, while S xy

is the shear strength corresponding to the  13

and  12

components.

3. Internal State Variable Approach

Once failures are detected at a quadrature point, the material properties are degraded using an internal state

variable approach. This approach degrades the properties from their original values to very small but non-zero

values in a pre-determined sequence over several load steps. Material properties are degraded according to the

particular active failure mode as determined by the Hashin criterion. For example, a compressive matrix mode

failure requires that the matrix-dependent properties be degraded, but that the fiber-dependent properties, e.g. E 11

remain unchanged. In these analyses, the strength values presented in Table 1 are used.

4. Progressive Failure Analysis Algorithm

Figure 8 shows the algorithm that is implemented as a user defined material (UMAT) subroutine within

ABAQUS. Note that this algorithm consists of a preprocessing phase in which ply-level stresses are computed, an

evaluation phase in which failures are determined, a material degradation phase in which ply level properties are

degraded, and a post-processing phase in which updated laminate properties are computed. This algorithm is called

for every quadrature point of every hexahedral element within the model, and updated material properties are

evaluated at the quadrature points when the ply failure criteria are satisfied.

There are two adjustable parameters in this algorithm: the degradation schedule and the load (or displacement)

increment. Studies undertaken by the authors have shown that a degradation factor of 0.7 (instead of 1.0 or 100%)

appears to be ideal for the stability of the algorithm. Rather than incrementing the loads, the current PFA increments

Pass i-

st (converged) material state, i-

st (converged) strain

vector, i

th strain increment and i

th state variables into routine

Degrade ply moduli

corresponding to

failure mode

i

th (converged) material state is i

th material state at equilibrium

Ply Failure?

Evaluate

0 °,+45°, -45° and 90 °

plies

Recompute Q ij

and Q ij

from updated ply moduli

Compute failure modes corresponding to

chosen failure criterion

Compute C ij

and  kl

and return

Compute laminate A ,  i

and G i

from updated ply moduli

Yes

No

From

ABAQUS

To

ABAQUS

Compute stresses in each ply

Transform ply stresses into principal material directions

Figure 8. PFA Algorithm Used as a UMAT Subroutine in ABAQUS (Note: Stop is executed in

ABAQUS and hence is not shown in this figure).

where a potential for damage growth is

anticipated, are constructed of four superposed

layers of shell elements that share the same

nodes. No centroidal offset is applied to any of

the elements. Each layer of elements represents

one ply orientation (0 or 45 or - 45 or 90

degrees), and each element spans the entire thickness of the laminate as shown in Figure 10. It is implied that the

plies for each orientation are uniformly distributed and can be smeared over the thickness of the laminate. The

elements used in the analyses consist of the ABAQUS four-node reduced-integration shear deformable S4R element

[ABAQUS, 2000].

To model the appropriate stiffnesses corresponding to a given damage state, reduced engineering properties are

applied to each layer. A reduced material property for a given orientation is simply the product of the engineering

property and the sum of the thicknesses of all the plies in that orientation divided by the total laminate thickness.

Reduced material properties are denoted by the notation [] R , as illustrated in Figure 10. Bending effects are taken

into account by the use of five integration points through-the-thickness of the laminate.

B. Progressive Failure Analysis for the Layered-Shell Model

A progressive damage model for notched laminates under tension was first proposed by Chang et al. [Chang and

Chang., 1987] and accounts for all of the possible failure modes in each ply except delamination. Chang and

Lessard [Chang and Lessard, 1991] later investigated the damage tolerance of composite materials subjected to

compressive loads. The present analysis, which also deals with compression loads, is largely based on the work by

Chang and Lessard. However, thepresentanalysisextendsChang’smethodfrom two-dimensional membrane

effects to a shell-based analysis that includes bending.

The failure criteria applied in the present analysis are those for unidirectional fiber composites as proposed by

Hashin [Hashin and Rotem, 1973], with the elastic stiffness degradation models developed for compression by

Chang and Lessard [Chang and Lessard, 1991]. Unidirectional failure criteria are used, and the stresses are

computed in the principal directions for each ply orientation. The failure criteria included in the present analysis are

summarized below. In each, failure occurs when the failure index exceeds unity.

Matrix failure in tension and compression occurs due to a combination of transverse stress  22

and shear stress

12

. The failure index e m can be defined in terms of these stresses and the strength parameters Y T / C and the shear

allowable S xy

. The matrix allowable Y T / C takes the values of Y T in tension and Y C in compression. Failure occurs

when the index exceeds unity. Assuming linear elastic response, the failure index has the form:

2

12

2

22

TC xy

m

Y S

e

Fiber buckling/tension failure occurs when the maximum compressive stress in the fiber direction exceeds the

fiber tension or buckling strength X T / C

, independently of the other stress components. The failure index for this

mechanism has the form:

T C

b

X

e

/

11

Fiber-matrix shearing failure occurs due to a combination of fiber compression and matrix shearing. The failure

index has the form:

2

12

2

/

11

TC xy

f

X S

e

The finite element implementation of this failure analysis was developed in ABAQUS using the USFLD user-

written subroutine. The program calls this routine at all material points of elements that have material properties

=

t

[45/-45/0/90] s

[45] R

[-45] R

[0] R

[90] R

Figure 10. The Thick Laminate Modeled With Four Layers

of Superposed Shell Elements.

defined in terms of the field variables. The routine provides access points to a number of variables such as stresses,

strains, material orientation, current load step, and material name, all of which can be used to compute the field

variables. Stresses and strains are calculated at each incremental load step and evaluated by the failure criteria to

determine the occurrence of failure and the mode of failure.

VII. Global-Local Analysis

A. Global-Local Connection Procedure

The aerodynamic loads on the vertical tail at failure (during the accident) were computed by Airbus and provided

to NASA. This load case, referred to as W375, was directly applied only to the global model. The local region of

the global NASTRAN (MSC/NASTRAN, 1997) model is shown in Figure 11a. Because the global model is a

MSC/NASTRAN model and the local lug model (the coarse 3D model) is an ABAQUS model, it was not possible

to embed the local model in the global model.

Conversion of the NASTRAN model to ABAQUS

was not feasible due to time constraints.

Additionally, the version of NASTRAN used for

the global model was not capable of modeling

contact. The details of the global model and

global analysis are discussed by Young et al.

[Young et al ., 2005].

Along the interfaces between the global and

local models, the continuity of the displacements

and the reciprocity of tractions need to be

satisfied. An iterative process was developed to

ensure satisfaction of these requirements. This

process is illustrated in Figure 12 and is

implemented as follows:

  1. Perform the global analysis using the global model and evaluate the displacements at all the nodes in the

global model. Let { u G

} represent the displacements of the global nodes along the global-local boundary

and { u L } represent the displacements of the local nodes along the global-local boundary. Evaluate the

tractions at the global nodes, { F G

}, from the elements that are entirely in the global region. That is,

evaluate the tractions that do not include the elements that occupy the local region of the global model.

  1. Establish a transformation matrix, [ T ], between { u G

} and { u L

}, and use this matrix to compute { u L

} using

    L G

uT u

  1. Solve the local model with { u L } as prescribed displacements.

  2. Because of the prescribed displacements, reactions at the interface nodes in the local model { R L

} are

produced.

  1. Local reactions are mapped back to the global nodes using

    L

T

G

R  T R (10)

Equation 10 is obtained by requiring that the work done on the global-local boundaries in the local model

(½)·({ u L

T

·{ R L

}) and the global model (½)·({ u G

T

·{ R G

}) are identical. The { R G

} reactions represent the

stiffness of the local model in the global model.

  1. The global tractions { F G

}, in general, will not be identical to the reactions mapped from the local model,

{ R

G }, as the reciprocity of tractions is not imposed. Thus, a residual, {r}, is left on the global-local

boundary:

     G G

rFR

  1. Evaluate a norm r for the residual {r} using

(a) Local Region in (b) Local Model with

Global Model Transition Mesh

Figure 11. Models of Region Near Right Rear Lug.

VIII. Results

The PFA results are compared with available experimental results for the 1985-certification test (X2/1 and X2/

specimens) and the 2003-subcomponent (SC) test. In addition, the load case corresponding to W375 is analyzed

using the coarse 3D model. Table 2 presents various load cases analyzed and the corresponding models used in the

analysis. Note that all of the PFA analyses shown in Table 2 were performed considering both geometric non-

linearity and pin-lug contact.

A. 1985 - Certification Test (X2/2 Specimen)

1. Configuration

As part of the certification process for the composite lugs on the A300-600R aircraft, Airbus developed the

certification test configuration shown in Figure 15. In this configuration, a hydraulic piston and lever were used to

apply an in-plane load to the lug as

shown in Figure 15a. The test specimen

was fixed around the perimeter of the

skin as shown in Figure 15b, and the

constraint due to rib 1 was simulated

using the transverse girder shown in

Figure 15c. Because all of the loading

was in the plane of the specimen, the M X

at the lug in this test was entirely due to

the combination of F X

, F

Z

, and the

eccentricity. A boundary condition of

X =0 at the pin is hypothesized and is

used in the analysis.

The instrumentation on the X2/2 test

specimen consisted of 16 strain gauges as

shown in Figure 16. There are two sets

of back-to-back rosettes on the tapered

portion of the lug immediately above rib

0 1 2 3 4 5 6

Iteration

Normalized Reaction Forces at Pin

Global - Fx Global - Fy Global - Fz

Local - Fx Local - Fy Local - Fz

0 1 2 3 4 5 6

Iteration

Global - Mx Global - Mz

Local - Mx Local - Mz

Normalized Reaction Moments at Pin

(a) Convergence of Pin Forces (b) Convergence of Pin Moments

Figure 14. Convergence in Global-Local Analysis (Load Case W375).

Table 2. Various Load Cases Analyzed and Finite Element Models Used.

Load Cases Analyzed

Finite Element Models

X2/1 X2/2 PFA Studies SC Test W

Coarse 3D Model X X

1985 Test Model X Solid-Shell Model

SC Test Model X

Layered-Shell Model X X X

Hydraulic

Piston

Lever Transverse

Girder

Specimen

(b) Test Specimen

Rib 1

Constraint

Fixture

Specimen

(a) Test Apparatus (c) Transverse Girder

Hydraulic

Piston

Lever Transverse

Girder

Specimen

Hydraulic

Piston

Lever Transverse

Girder

Specimen

(b) Test Specimen

Rib 1

Constraint

Fixture

Specimen

(b) Test Specimen

Rib 1

Constraint

Fixture

Specimen

(a) Test Apparatus (c) Transverse Girder

Figure 15. 1985-Certification Test Configuration.

1 (gauges 1-12) and four uniaxial gauges along

the profile of the lug (gauges 13-16). During the

test, all 16 gauges were monitored. The load vs.

strain data from all these 16 gauges was

available and was used in the PFA validation.

2. Results

Figure 17 shows the strain gauge results

obtained from Airbus as open red circle symbols

and NASA’sfiniteelementpredictionsmade

using the solid-shell model as solid blue lines.

Applied load is shown in kN on the ordinate,

and measured or predicted strain is shown (in

thousands of microstrain) on the abscissa.

Because gauges 13 and 16 are located near large changes in stiffness, they are not shown in Figure 17. In general,

the predicted values agree very well with the strain gauge results. However, the predicted values do not agree well

with strains from gauges 3 and 10. The reason for these two deviations is unknown. Also, because the location of

gauges 14 and 15 through-the-

thickness was not known, finite

element predictions of strain on the

outboard side and stringer side of

the lug are shown. These

predictions bound the strain gauge

results. From this figure, it was

concluded that the present PFA

represents accurately the behavior

of the lug over the complete loading

range.

The computed values of F Res

(resultant of F X

, F

Y

, and F Z

force

components) and M X

vs. load factor

are shown in Figure 18. In Figure

18, the load factor is a non-

dimensional scaling factor that is

applied to the displacements during

the PFA analysis. A load factor of

1.0 corresponds to the

displacements produced from a

linear analysis. The curve for

resultant force ( F Res ) vs. load factor

is shown as a solid blue line with

open circle symbols and the curve

of M X

vs. load factor is shown as a

solid red line with open square

symbols. The linearly projected

values of M X and F Res are shown as

closed diamonds. The failure load

from the X2/2 test specimen is

shown as a thick horizontal red line.

Peak values of M X

and F Res

are

shown on the graph and in the

tabular insert as points A and B,

respectively. The load factor for the

linear case and points A and B are

shown with vertical dashed lines.

The F Res

at the maximum moment

(Point A) agrees extremely well

CLAMPED

(u=v=w=

 x = y = z =0)

u=v= z =

0

15

14

16 13

6

4

5

Stringer Side

12

10

11

Stringer Side

9

7

8

Outboard

3 1

2

Outboard

0

Z

X Y

CLAMPED

(u=v=w=

 x = y = z =0)

u=v= z =

0

15

14

16 13

6

4

5

Stringer Side

12

10

11

Stringer Side

9

7

8

Outboard

3 1

2

Outboard

0

CLAMPED

(u=v=w=

 x = y = z =0)

u=v= z =

0

15

14

16 13

6

4

5

Stringer Side

12

10

11

Stringer Side

9

7

8

Outboard

3 1

2

Outboard

0

Z

X Y

Z

X Y

Figure 16. Strain Gauges on X2/2 Test Specimen.

Gauge 01

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 03

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 02

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 04

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 01

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 03

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 02

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 04

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 05

0

250

500

750

1000

  • 3 - 2 - 1 0 1 2 3

Gauge 0 6

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 07

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 08

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 05

0

250

500

750

1000

  • 3 - 2 - 1 0 1 2 3

Gauge 0 6

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 07

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 08

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 09

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 10

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 11

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 12

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 09

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 10

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 11

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 12

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 14

0

250

500

750

1000

1250

  • 3 - 2 - 1 0 1 2 3

Gauge 15

0

250

500

750

1000

1250

  • 1 0 1 2 3 4 5

15

14 Stringer

side

Outboard

side

Stringer

side

Outboard

side

Test

data

Test

data

Figure 17. Strain Gauge and Finite Element Results.

moment was used. Note that as damage develops, the

specimen loses its stiffness and hence will not carry

the moment that is predicted by the linear

relationship.

The computed values of F Res

and M X

vs. load

factor are shown for load cases SC (C), SC (D), and

SC (E) in Figures 21a to 21c, respectively, for applied

rotations resulting from linearly projected load and

moment values as given in Table 3. The curves for

resultant force ( F Res

) vs. load factor are shown as solid

lines with open circles, and the curves of M X

vs. load

factor are shown as solid lines with open square

symbols. The linearly projected values of M X

and F Res

are shown as closed diamonds. The failure load

observed during the test is shown as a thick horizontal

red line in Figures 21a to 21c. Peak values of M X

and

F

Res

are shown on the graph and in the tabular insert

as points A and B, respectively. The load factor for

the linear case and points A and B are shown with

vertical dashed lines.

Two entirely different loading sequences are

represented by the sets SC (C) (Figure 21a) and SC

(D) and (E) (Figures 21b and 21c). In load case SC

(C), the translations and rotations were applied

simultaneously and proportionally starting from zero

values to develop the F Res and M X shown in the

figures. For load cases SC (D) and (E),  X was

applied initially until the desired initial rotation ( X

was reached, and then the translations and rotations

were increased proportionally. These later cases (D

and E) represent more accurately the loading

sequence during the 2003-subcomponent test.

While the curves in Figures 21a to 21c show the

same general trends, increased values of M X

result in

lower values of F Res at failure. Also, larger values of

M

X decrease the difference between F Res at peak

moment (point A) and maximum F Res

(point B). The

difference between the values of points A and B is

largest for load case SC (E) in which an initial value

of  X is applied, and then is held constant. The

constant rotation contributes to an artificial stiffening

of the lug in load case SC (E) and results in higher

peak F Res

than for load case SC (C).

The damage predictions for the lug under load

case SC (C) at peak moment and peak force are

shown in Figures 22a and 22b, respectively. The

mode of damage (cleavage type failure) is the same as

seen previously in the 1985-certification test. The

extent of the damage predicted by the PFA (Figures

22a and 22b) also agrees well with that observed

during the SC test shown in Figure 23. These damage

surfaces are consistent with the damage surfaces seen

in the other cases.

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.

Load Factor

F

Res

(kN)

A B

Linear M X

(Non-PFA)

Linear F Res

(Non-PFA)

F Res

M X

Failure Load = 907 kN

(Test)

M

X

(

kN

-

m)

Peak F Res

M X

A) 900 kN 5.933 kN-m

B) 983 kN 3.721 kN-m

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.

Load Factor

F

Res

(kN)

A B

Linear M X

(Non-PFA)

Linear F Res

(Non-PFA)

F Res

M X

F Res

M X

Failure Load = 907 kN

(Test)

M

X

(

kN

-

m)

M

X

(

kN

-

m)

Peak F Res

M X

A) 900 kN 5.933 kN-m

B) 983 kN 3.721 kN-m

(a) SC (C) Load Case

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.

Load Factor

F

Res

(kN)

M

X

(

kN

-

m)

Peak F Res M X

A) 903 kN 6.257 kN-m

B) 975 kN 3.573 kN-m

A B

Linear M X

(Non-PFA)

Linear F Res

(Non-PFA)

F Res

M X

Failure Load = 907 kN

(Test)

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.

Load Factor

F

Res

(kN)

M

X

(

kN

-

m)

M

X

(

kN

-

m)

Peak F Res M X

A) 903 kN 6.257 kN-m

B) 975 kN 3.573 kN-m

A B

Linear M X

(Non-PFA)

Linear F Res

(Non-PFA)

F Res

M X

F Res

M X

Failure Load = 907 kN

(Test)

(b) SC (D) Load Case

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.

Load Factor

F

Res

(kN)

M

X

(

kN

-

m)

Peak F Res

M X

A) 896 kN 5.036 kN-m

B) 1009 kN 3.089 kN-m

A

B

Linear M X

(Non-PFA)

Linear F Res

(Non-PFA)

F Res

M X

Failure Load = 907 kN

(Test)

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.

Load Factor

F

Res

(kN)

M

X

(

kN

-

m)

M

X

(

kN

-

m)

Peak F Res

M X

A) 896 kN 5.036 kN-m

B) 1009 kN 3.089 kN-m

A

B

Linear M X

(Non-PFA)

Linear F Res

(Non-PFA)

F Res

M X

F Res

M X

Failure Load = 907 kN

(Test)

(c) SC (E) Load Case

Figure 21. Load and Moment vs. Load Factor.

C. W375 Accident Case PFA Analysis

The forces and moments at the pin and the boundary conditions on

the global-local interfaces for W375 accident case were obtained from

the global-local analysis. The corresponding pin rotations predicted

from global-local analysis are given in Table 4 and are 48% higher than

those used in the Airbus 2003-subcomponent test because they represent

global rotations and include the effect of the rotation of the fuselage; the boundary conditions during the test did not

consider the deformation of the fuselage and corresponded to a fixed condition at the base of the VTP.

The computed values of F Res

and M X

vs. load factor are shown for the W375 accident case in Figure 24, using

applied translations and rotations resulting from

linearly projected load and moment values. The

curve for resultant force ( F Res ) vs. load factor is

shown as a solid blue line with open circle symbols,

and the curve of M X

vs. load factor is shown as a

solid red line with open square symbols. The

linearly projected values of M X

and F Res

are shown as

closed diamonds. Peak values of M X

and F Res

are

shown on the graph and in the tabular insert as points

A and B, respectively. Further, the extent of the

damage predicted by the PFA for the W375 accident

case (Figure 25), again a cleavage type failure,

generally agrees with the damage seen in a

photograph of the failed AA 587 right rear lug in

Figure 26. These damage predictions are similar to

those obtained for the 1985-certification test and the

2003 - subcomponent test.

(a) Damage Region at Peak Moment (b) Damage Region at Peak Force

Figure 22. Damage Regions for SC (C) Load Case.

Figure 23. 2003-Subcomponent Test – Observed Failure (Red arrows point to the primary fracture path).

Table 4. Pin Rotations for Load Case

W375 in Accident Model (RHS).

CASE 

X

Z

Accident W375 0.756 0.

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.

Load Factor

F

Res

(kN)

A

B

Non-linear M X

(Non-PFA)

Non-linear F Res

(Non-PFA)

F Res

M X

M

X

(

kN

-

m)

Peak F Res

M X

A) 925 kN 5.406 kN-m

B) 1100 kN 4.459 kN-m

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.

Load Factor

F

Res

(kN)

A

B

Non-linear M X

(Non-PFA)

Non-linear F Res

(Non-PFA)

F Res

M X

F Res

M X

M

X

(

kN

-

m)

M

X

(

kN

-

m)

Peak F Res

M X

A) 925 kN 5.406 kN-m

B) 1100 kN 4.459 kN-m

Figure 24. Load and Moment vs. Load Factor for W

Load Case.

for the 2003-subcomponent test and W375 accident condition. The experimentally determined failure loads agree

very well with the PFA predicted values, thus validating the present PFA methodology for the lug configuration.

Further, all three configurations showed cleavage type failures. The failure load for the lug for the W375 accident

condition (925 kN) is greater than 1.98 times the limit load (467 kN) [Hilgers and Winkler, 2003].

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

Load Factor

Fres

kN

1985 test

SC Test

W375 Accident

Condition

Limit Load

Ultimate Load

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

Load Factor

Fres

kN

1985 test

SC Test

W375 Accident

Condition

Limit Load

Ultimate Load

Load Factor

Moment

Mx

kN

m

1985 Test

SC Test

W375 Accident Condition

Load Factor

Moment

Mx

kN

m

1985 Test

SC Test

W375 Accident Condition

1985 Test

SC Test

W375 Accident Condition

Figure 27. F Res vs. Load Factor Variation for 1985- Figure 28. Bending Moment M X Variation 2003 -

Certification Test, 2003-Subcomponent Test, and for 1985-Certification Test, Subcomponent Test,

W375 Accident Case. and W375 Accident Case.

0.

0.

1.

1.

2.

2.

3.

1985 Test SC Test W

Accident Case

Normalized Failure Load,

kN

PFA Analysis Failure Load

PFA Analysis Load at Maximum Moment M X

Test Failure Load

0.

0.

1.

1.

2.

2.

3.

1985 Test SC Test W

Accident Case

Normalized Failure Load,

kN

PFA Analysis Failure Load

PFA Analysis Load at Maximum Moment M X

Test Failure Load

W375 Accident Case

SC Test

1985 Test

W375 Accident CaseW375 Accident Case

SC TestSC Test

1985 Test1985 Test

W375 Accident Case

SC Test

1985 Test

W375 Accident CaseW375 Accident Case

SC TestSC Test

1985 Test1985 Test

Figure 29. Failure Loads Normalized by Limit Load Figure 30. Comparison of Damage Predictions

for 1985-Certification Test, 2003-Subcomponent 1985 - Certification Test, 2003-Subcomponent Test,

Test, and W375 Accident Case. and W375 Accident Case.

Table 5. Load Components (Normalized by Limit Load) in the Lug at Failure.

Test Case F X

F

Y

F

Z

F

Res

M

X

SC Analysis (PFA) - 374.8 - 40.39 - 812 .7 895.9 - 5.

2003 - Subcomponent Test - 381.6 - 39.10 - 822.5 907.0 Not measured

W375 Analysis (PFA) - 359.9 - 40.35 - 851.5 925.3 - 5.

X. Concluding Remarks

An analysis of the failure of the composite vertical tail of the American Airlines Flight 587 - Airbus A300- 6 00R

wasperformedaspartoftheNationalTransportationSafetyBoard’sfailureinvestigationoftheaccidentthat

occurred on November 12, 2001. Two structural analysis teams, the global analysis team and the detailed lug

analysis team, analyzed the vertical tail. The global analysis team evaluated the loads on each of the six lugs that

attach the tail to the aluminum fuselage and determined that the right rear lug carried the largest loads compared to

the design allowable. The detailed lug analysis team developed and verified user defined material and user field

algorithms within the ABAQUS general-purpose finite element code. The team then performed progressive failure

analyses (PFA) to predict the failure of the right rear composite lug. A global-local connection procedure was

developed and validated to ensure the satisfaction of the continuity of displacements and reciprocity of tractions

across the global-local interfaces and connection regions.

The right rear lug, including the neighboring fin region near the rear spar, was analyzed using two modeling

approaches. In the first approach, solid-shell type modeling was used, and in the second approach, layered-shell

type modeling was used. To validate the models, the solid-shell and the layered-shell modeling approaches were

used in conjunction with the PFA to determine the load, mode, and location of failure in the right rear lug under

loading representative of a certification test conducted by Airbus in 1985 (1985-certification test). Both analyses

were in excellent agreement with each other and with the experimentally determined failure loads, failure mode, and

location of failure. The solid-shell type modeling was then used to analyze a subcomponent test conducted by

Airbus in 2003 as part of the failure investigation (2003-subcomponent test). Excellent agreement was observed

between the PFA analyses and the experimentally determined results from the 2003-subcomponent test. Excellent

agreement was also observed between the analyses of the 2003-subcomponent test and the accident condition_._

From the analyses conducted and presented in this report, the following conclusions were drawn:

 The moment, M X (moment about the fuselage longitudinal axis) had significant effect on the failure load of

the lugs. Higher absolute values of M X

give lower failure loads. For example, an observed increase in M X

of

45 percent from the 1985-certification test to the 2003-subcomponent test caused a 17 percent decrease in

the failure load. Therefore, to properly test a lug under a loading condition that is representative of the flight

loads, it is important to apply to the lug an accurate moment, M X

. The predicted load, mode, and location of

the failure of the 1985-certification test, 2003-subcomponent test and the accident condition were in very

good agreement. This similarity in results suggests that the 1985-certification and 2003-subcomponent tests

represented the accident condition accurately.

 The failure mode of the right rear lug for the 1985-certification test, 2003 - subcomponent test, and the

accident load case was identified as a cleavage-type failure.

 For the accident case, the predicted failure load for the right rear lug from the PFA and solid-shell models

was greater than 1.98 times the limit load of the lugs.

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