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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:
- 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.
- Establish a transformation matrix, [ T ], between { u G
} and { u L
}, and use this matrix to compute { u L
} using
L G
u T u
Solve the local model with { u L } as prescribed displacements.
Because of the prescribed displacements, reactions at the interface nodes in the local model { R L
} are
produced.
- 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.
- 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
r F R
- 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
Gauge 03
0
250
500
750
1000
1250
Gauge 02
0
250
500
750
1000
1250
Gauge 04
0
250
500
750
1000
1250
Gauge 01
0
250
500
750
1000
1250
Gauge 03
0
250
500
750
1000
1250
Gauge 02
0
250
500
750
1000
1250
Gauge 04
0
250
500
750
1000
1250
Gauge 05
0
250
500
750
1000
Gauge 0 6
0
250
500
750
1000
1250
Gauge 07
0
250
500
750
1000
1250
Gauge 08
0
250
500
750
1000
1250
Gauge 05
0
250
500
750
1000
Gauge 0 6
0
250
500
750
1000
1250
Gauge 07
0
250
500
750
1000
1250
Gauge 08
0
250
500
750
1000
1250
Gauge 09
0
250
500
750
1000
1250
Gauge 10
0
250
500
750
1000
1250
Gauge 11
0
250
500
750
1000
1250
Gauge 12
0
250
500
750
1000
1250
Gauge 09
0
250
500
750
1000
1250
Gauge 10
0
250
500
750
1000
1250
Gauge 11
0
250
500
750
1000
1250
Gauge 12
0
250
500
750
1000
1250
Gauge 14
0
250
500
750
1000
1250
Gauge 15
0
250
500
750
1000
1250
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.
References
ABAQUS User's Manual, Vol. III, Version 6.1, Hibbitt, Karlsson & Sorensen, Pawtucket, RI, 2000.
Averill, R.C., Non-linear Analysis of Laminated Composite Shells Using a Micromechanics-Based Progressive Damage
Model, Ph.D. Thesis, Virginia Polytechnic Institute and State University, 1992.
Camanho,P.P.,and Matthews,F.L.,“A Progressive Damage Model for Mechanically Fastened Joints in Composite
Laminates,”Journal of Composite Materials, Vol. 33, No. 24, 1999, pp. 2248-2280.
Chang, F.-K., and Chang,K.Y.,“A Progressive Damage Model for Laminated Composites Containing Stress
Concentrations,”Journal of Composite Materials, Vol. 21, 1987, pp. 834-855.
Chang, F.-K., and Lessard, L.B., “Damage Tolerance of Laminated Composites Containing an Open Hole and Subjected to
Compressive Loadings: Part I-Analysis,”Journal of Composite Materials, Vol. 25, 1991, pp. 2-43.
Dávila, C.G., Ambur, D.R., and McGowan, D.M., “Analytical Prediction of Damage Growth in Notched Composite Panels
Loaded in Compression,”Journal of Aircraft, Vol. 37, No. 5, 2000, pp. 898-905.
Dávila, C.G., Camanho, P.P., and de Moura, M.F.S.F., “Mixed-Mode Decohesion Elements for Analyses of Progressive
Delamination,”Proceedings of the 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials
Conference, Seattle, Washington, April 16-19, 2001(a).
Glaessgen, E.H., Pastore, C.M., Griffin,O.H.,Jr.andBirger,A.,“Geometrical and Finite Element Modeling of Textile
Composites,”Composites Part B, Vol. 27B, No. 1, 1996, pp. 43-50.
Hashin, Z., and Rotem, A., “A Fatigue Criterion for Fiber-Reinforced Materials,”Journal of Composite Materials, Vol. 7,
1973, pp. 448-464.
Hashin,Z.,“Failure Criteria for Unidirectional Fiber Composites,”J. Appl. Mech., Vol. 47, 1980, pp. 329-334.
Hilgers,R.andWinkler,E.,“AAL 58 7InvestigationLugSubComponentTest# 1 – ResultsTest/FEAComparisons,”TN-
ESGC – 1014/03, November 2003.
