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Raju2007-RightRearLug-AA587.pdf
Structural Analysis of the Right Rear Lug of American
Airlines Flight 587
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 Board’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. The moment, Mx (moment about the fuselage longitudinal
axis), has significant effect on the failure load of the lugs. Higher absolute values of Mx give
lower failure loads. The predicted load, mode, and location of the failure of the 1985certification 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.
O
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. [NTSB, 2004]
Several teams at the NASA Langley Research Center were assembled to help the National Transportation Safety
Board with this investigation. The internal NASA teams were 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.
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. Next, a brief
discussion of an alternative modeling approach, layered-shell modeling, is presented. Fifth, the global-local
*
Structures Discipline Expert, NASA Engineering and Safety Center, MS 188E, AIAA Fellow.
Aerospace Engineer, Durability, Damage Tolerance, and Reliability Branch, MS 188E, AIAA Associate Fellow.
‡
Aerospace Engineer, Durability, Damage Tolerance, and Reliability Branch, MS 188E, AIAA Senior Member.
†
1
American Institute of Aeronautics and Astronautics
connection processes used to virtually embed the local lug model within a global model of the VTP are described.
Sixth, the results of these 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 aircraft 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 1(a) to 1(d)). Six yokes
(not shown in figures) also connect the VTP to the fuselage and react some of the lateral loads. The aerodynamic
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
aerodynamic 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 1(d)) 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 it experienced during
the accident.
The lug analysis team considered the right rear lug region shown in Figure 1(d). The lug is a continuation of the
skin of the vertical tail with two pre-cured fitting halves bonded to either side of the skin at its lower extremity (the
fitting extends to rib 4, as shown in Figure 1(d)). 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 1(d) using threedimensional (3D) elements in the region of the two pre-cured fitting halves of the lug and shell elements for the
remainder 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 1(d) 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 that behave as multi-point constraints in this analysis. 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.
Fin
Rudder
Lugs
(b) Major Components of Vertical
Tail Plane (VTP)
(a) A300-600R Empennage
Rib 5
6
Stringers
1
Rib 4
Pin and
Bushing
Clevises mounted on
the fuselage
Yoke connection at
rear spar
(c) VTP-Fuselage Connections
Rear
Spar
Rib 1
Lug
(d) Construction of Fin near
Right Rear Lug
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
developed. These models are the
1985-certification test model and the
2003-subcomponent (SC) test model.
Figure 2 presents a summary of all the
models used in the analyses – N373
and W375 denote different loading
conditions; X2/1 and X2/2 represent
two different specimens that were
tested as part of an Airbus
certification test conducted in 1985
(the 1985-certification test).
Figure 1. Vertical Tail Plane Mounted on the Fuselage.
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American Institute of Aeronautics and Astronautics
In
the
NASAdeveloped models, the
clevises, the elastic pin,
Solid-Shell Models
Layered-Shell Models
and the bushing were not
modeled. Rather, the pin
is represented as a rigid
Coarse 3D Model 1985-Certification Test Model
2003-Subcomponent Test Model
analytical cylinder with a
(N373, W375)
(SC Test)
(X2/1, X2/2)
diameter equal to the
diameter of the lug hole.
Figure 2. Various Finite Element Models Used.
This analytical cylinder
is rigidly connected to a FE node at the location of the center of the pin. In the models, the pin is loaded by applying
displacements or tractions to this single node. The pin loads are assumed to be reacted in the contact region between
the lug hole and the pin.
The solid-shell and layered-shell analyses were performed using the commercial finite element code, ABAQUS
[ABAQUS, 2000]. The code was chosen because it allows the user to implement specialized elements and material
constitutive relationships while taking advantage of the features of a general-purpose code.
The progressive failure algorithms used to predict failure within the solid-shell and layered-shell models were
defined as user defined material (UMAT) and user field (USFLD) algorithms, respectively. In the implementation
of the UMAT and USFLD routines, material properties are degraded to small but nonzero values either in a single
step or in several steps in each damaged element. To maintain stability of the system of equations, the values cannot
be degraded to zero-values. Further, although some specialized codes allow failed elements to be removed from a
model (element extinction), this capability is not available in ABAQUS v6.1. In the present implementation, the
small stiffness contributions that remain in the degraded elements after failure allow a very small amount of load
transfer across the damaged region. Therefore, in the present implementation of failure, complete separation of the
lug is not possible.
Finite Element Models Used in Study
A. Coarse 3D Model
A coarse 3D model (part of the solid-shell series of models) of the lug was developed using thickness contours
extracted from the reference Airbus model. The coarse 3D model, shown in Figure 3(a), has 25931 nodes and
21519 elements. The axial (x-) coordinate is along the fuselage axis and is directed toward the rear of the airplane.
The y-axis is parallel to the axis of the pin in the lug hole, and the z-axis is normal to the x- and y-axes. The lug
fittings and skin are modeled with up to 14 layers of solid (8-node hexahedral, C3D8) elements with 10 layers of
elements in the vicinity of the hole. The thickness of each of the layers of solid elements was adjusted in order to
match the volume of the lug fittings in the Airbus model. All other regions of the model were converted to shell
elements. Multi-point constraint (MPC) equations were used at the solid-to-shell transition locations to ensure
compatible translations and rotations along the interface.
B. Layered Shell Model
A layered-shell model of the lug was constructed using the same thickness contours as the coarse 3D model.
The pin assembly was modeled as a rigid surface with a diameter equal to that of the lug hole. Frictionless contact
equations were prescribed between the edge of the layered-shell elements around the bolt hole and the rigid surface.
A discussion of the approximations caused by using a rigid frictionless pin can be found in Camanho and Matthews
[Camanho and Matthews, 1999]. The lug fittings were modeled with 14 layers of shell elements that were
connected with 3D decohesion elements [Dávila et al., 2001a]. All other regions of the model were modeled with a
single layer of shell elements. In addition, the model is used for progressive failure analyses in which the matrix and
fiber damage is simulated by degrading the material properties. The analyses used for modeling the progressive
delamination and intra-ply damage were developed within ABAQUS with user defined element (UEL) and user
defined field (USFLD) user-written subroutines, respectively. This model, shown in Figure 3(b), has 20886 nodes
with 34524 elements.
The ability of the coarse 3D and layered-shell models to predict the same displacements as the original Airbus
model was verified. Both the magnitude and spatial distributions of the displacement components predicted using
the two NASA models were in very close agreement with those predicted using the Airbus model.
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American Institute of Aeronautics and Astronautics
z, w,
(FZ)
θ Z,
(MZ)
θY,
(MY)
θX,
(MX)
Z
x, u,
(FX)
X
Y
y, v, (FY)
(a) Solid-Shell Model
(b) Layered Shell Model
CLAMPED
(u=v=w=0
θx=θy=θz=0)
HARD SIMPLE SUPPORT
v’=w’=0
θx’=θy’=θz’=0
PINNED
(u=v=w=0)
Z’
Y’
u=0
X’
Z
X
Y
v=θx=0
(c) Initial Airbus Boundary Conditions
Figure 3. Finite Element Models of Right Rear Lug (colors are for visualization purposes only).
Solid
Element
Region
Shell
Element
Region
CLAMPED
u’=v’=w’=0
θx’=θy’=θz’=0
Z’
Z
CLAMPED
(u=v=w=0
θx=θy=θz=0)
Y’
Z
X
X
X’
Y
Y
Z
u=v=θz=0
(a) Finite Element Model
X
Y
(b) Boundary Conditions
Figure 4. 1985-Certification Test Model of X2/2 Specimen (colors are for visualization purposes only).
C. 1985-Certification Test Model
Two test specimens (called X2/2 and X2/1) were tested by Airbus in 1985. One solid-shell 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 4(a). This model had 23216 nodes and 19149 elements. The boundary conditions used with this model are
shown in Figure 4(b).
D. 2003-Subcomponent Test Model
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American Institute of Aeronautics and Astronautics
As part of the NTSB 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 5(a)) 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 5(b).
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 FY, MX, MZ, v, θX, and θZ are reversed.
CLAMPED
(u=v=w=0
θx=θy=θz=0)
X
Z
Y
X
(a) Finite Element Model
Z
Y
(b) Boundary Conditions (prescribed along
the red edges and the red region)
Figure 5. 2003- Subcomponent Test Model.
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 added to increase the thickness of the lug to match the clevis. 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 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-ofTable 1. Material Properties for T300/913C Tape.
plane direction, respectively, and the subscript “c” denotes a
WWFE
compressive property. Also, XT, XC, YT, YC, and Sxy denote
Property
[Hinton
and
Soden 1998]
the fiber-direction tensile strength, fiber-direction
E
(GPa)
138
1
compressive strength, transverse-direction tensile strength,
E1C (GPa)
-transverse-direction compressive strength, and shear
E
(GPa)
11
2
strength, respectively.
Finally, GIC is the mode-I
E2C (GPa)
-interlaminar fracture toughness.
ν12
0.28
1. Homogenization of Material Properties
ν23
0.4
The right rear lug contains numerous plies of T300/913C
µ12 (GPa)
5.5
in the form of tape and fabric. Although a finite element
XT (MPa)
1500
model that explicitly modeled each of the plies and each of
XC (MPa)
900
the numerous curvilinear ply drops within the lug could be
YT (MPa)
27
developed, doing so would have required a finite element
YC (MPa)
200
model with millions of elements. Such a detailed finite
element model would be too cumbersome to use in
Sxy (MPa)
80
2
progressive failure analyses. To maintain a reasonable
GIC (KJ/m )
220
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 next.
5
American Institute of Aeronautics and Astronautics
Elements of classical lamination theory (CLT) were used to construct and deconstruct the homogenized material
properties and to evaluate ply-level values in a manner that is suitable for the PFA, but its use for this problem
requires several assumptions:
1) Nominal percentages and uniform spatial distribution of 0°, ±45°, and 90°/0° plies at every quadrature
point in each element of the model
2) No non-zero coupling (i.e., the 16, 26, and B-matrix) terms after ply failure
3) Bending deformations that are inherent in the CLT are not explicitly modeled. Rather, the deformations
are modeled using solid elements
4) Independent material properties at each quadrature point in the element that can be degraded
independently
5) Woven fabric can be treated as 2 plies of tape
Plies of each of the orientations are distributed nearly uniformly thoughout the lug adding credibility to the
assumption of a uniform spatial distribution of plies. Additionally, the large number of plies in the lug tends to
reduce the effect of the coupling terms. The assumption of piecewise constant bending is reasonable given the
number of integration points through the thickness of the lug and the relatively low bending gradient. Additionally,
the assumption of independence of properties at each quadrature point has been explored extensively for PFA
analyses [Averill, 1992].
Prediction of failure within textile-based composite materials has been a topic of considerable attention for more
than two decades [Poe and Harris, 1995; Glaessgen et al., 1996]. However, there is no accurate method for
predicting the micromechanical details of damage progression in textile-based composites that has the computational
efficiency needed to predict failure in structural models of the size used in this accident investigation. This
deficiency in the state-of-the-art led to the approximation of the 8-harness satin weave material as plies of
“equivalent” tape as shown in Figure 6. Hashin’s failure criteria was used to predict failure of both the tape lamina
and the “equivalent” tape lamina [Hashin, 1980].
Figure 6. Eight-Harness Satin Weave and Tape Approximation.
V.
Contact
Although most of the load transfer between the pin and the lug is normal to the interface (initially, the global xzplane), only friction prevents the pin from sliding (rigidly translating) in the global y-direction. Because of the
proximity of the location of the material failures to the location of the pin-lug interface, considerable effort was
taken to accurately model the details of the load transfer between the pin and the lug.
Although the ABAQUS code correctly models the normal contact between the pin and the lug, the modeling of
friction along the pin-lug contact region was not straightforward. The lug analysis team did not have access to
friction data about the lug, so the following
Outer ring of nodes
Outer ring of nodes
approach was developed. A multi-point constraint
(MPC) equation was generated to prevent sliding
Point O
of the pin. In the MPC equation, the displacement
Point O
of the pin in the global y-direction (vP) is set equal
Point P
to the average of the global y-displacements of all
vP
dX
vP
of the nodes in the two rings on the lug hole (vI and
Z
vO for average displacements of the inner and outer
Point I
rings, respectively) shown in Figure 7. This MPC
Point I
equation, referred to as Y-MPC #1, was used for all
Inner ring of nodes
analyses prior to the 2003-subcomponent test.
Inner ring of nodes
Differences were found between the global-local
v M = 0.5 ⋅ (v O + v I )
vP is the Y-Displacement at P
moments computed by NASA using Y-MPC #1
v
=
v P − dZ ⋅θ X + d X ⋅θZ
v P = 0.5 ⋅ (v O + v I )
M
and the moments computed by Airbus using their
(a) Y-MPC #1
(b) Y-MPC #2
global-local analysis process. The NASA lug team
re-evaluated the MPC equation and concluded that
Figure 7. Multi-Point Constraint Formulation.
it was not accurately simulating the global y-force
Point P
Point M
d
6
American Institute of Aeronautics and Astronautics
reacted by the pin because the y-force can only react on the contact surface, and Y-MPC #1 effectively treated the yforce 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 applied xz-load vector) were used instead of the
360° rings, as shown in Figure 7(b). The average displacement of these two arcs is represented by the displacement
(vM) at Point M. The displacement at Point M is related to the pin displacement (vP) by an equation that includes the
global x- and z-rotations of the pin, as shown in Figure 7(b). All lug results generated before the 2003subcomponent 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]: “The microstructural
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.” This “intractable task” will continue to be an active area of research for
many years to come. Nevertheless, at the time at which this analysis was conducted, it was an impractical one.
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
In the analysis of the right rear composite lug, the Hashin criterion [Hashin, 1980] was incorporated. 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 threedimensional states of stress.
Tensile fiber mode
2
' !11 $
1
2
2
%%
"" +
!12
+ !13
=1
2
X
S xy
& T #
(1a)
!11 = X T
(1b)
!11 = X C
(2)
(
)
or
Compressive fiber mode
Tensile matrix mode (σ22 + σ33) > 0
7
American Institute of Aeronautics and Astronautics
1
YT2
(" 22 + " 33 )2 +
1
$T2
("
2
23
)
# " 22 " 33 +
1
2
S xy
("
2
12
)
2
+ "13
!1
(4)
Compressive matrix mode (σ22 + σ33) < 0
1
Yc
*0 Y
(. c
(./ 2$T
)
2
'
1
++ # 1% (" 22 + " 33 )+
(" 22 + " 33 )2 + 12 " 223 # " 22 " 33 + 12 "122 + "132 ! 1
2
%
4$ T
$T
S xy
,
&
(
)
(
)
(5)
In equations 1 to 4, the strength values (XT, XC, YT, YC, and S xy) are defined in Table 1. Note that both the normal
stress in the fiber-direction, σ11, and the shear stress components parallel to the fiber direction, σ12 and σ13, are
considered in equation 1a. In equations 1–4, τT is the transverse shear strength corresponding to the σ23 stress
component, while Sxy is the shear strength corresponding to the σ13 and σ12 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. E11,
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. Once failure is determined, the degradation factor is applied
From
ABAQUS
Pass i-1st (converged) material state, i-1st (converged) strain
vector, ith strain increment and ith state variables into routine
Compute stresses in each ply
Transform ply stresses into principal material directions
Compute failure modes corresponding to
chosen failure criterion
Evaluate
0°,+45°, -45° and 90°
plies
Ply Failure?
Yes
Degrade ply moduli
corresponding to
failure mode
No
Recompute Qij and Qij from updated ply moduli
Compute laminate A, "i3 and Gi3 from updated ply moduli
To
ABAQUS
!
ith
Compute Cij and ! kl and return
(converged) material state is ith material state at equilibrium
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).
8
American Institute of Aeronautics and Astronautics
upon each load increment until a near-zero value of the moduli is achieved. Rather than incrementing the loads, the
current PFA increments the displacements and hence simulates displacement-controlled tests. This approach
simplifies the process of simulating unloading past the peak load as discussed in the following section.
5. “Load-Increment in the PFA”
Displacement control is used in the current implementation of the progressive failure analysis to ensure that both
the loading and unloading are traced by the algorithm. A load control procedure will encounter convergence
difficulties after damage occurs because the monotonically increasing load applied to the damaged structure will
cause abrupt failure. In contrast, a displacement-controlled procedure has fewer convergence difficulties after
damage initiates because the load can decrease as damage forms, and the material becomes more compliant.
In cases where the maximum linear load, Pmax,
Pmax
carried by the specimen is known, the corresponding
maximum linear displacement, dmax, is calculated from a
linear analysis. If Pmax is unknown, a projected value is
assumed and the corresponding maximum linear
Pfailure
displacement, d max, is also calculated from a linear
analysis. The displacements are incremented using the P
dmax as a guide and are termed here as load factor
(d/dmax). A schematic of the load vs. load factor curve is
shown in Figure 9. The solid line with symbols and
dashed line represent a hypothetical PFA loaddisplacement curve and a linear load-displacement
curve, respectively. Note that the load factor of unity
will intersect the dashed line at Pmax, the maximum linear
load, and corresponds to the maximum linear
displacement, dmax (i.e. at load factor equal to unity).
Once damage is determined and the corresponding
material properties are degraded, the actual loaddisplacement curve will begin to deviate from the linear
curve. The load continues to increase monotonically
1.0
Load Factor (d/dmax)
until a peak value, the failure load, Pfailure, is reached.
Then, P decreases until a zero-value of load is reached or Figure 9. Schematic of Load vs. Load Factor Curve.
the analysis can no longer converge.
Note that in the PFA implementation, large displacement increments are chosen to start the algorithm, and
shortly before damage initiates, the increment size is scaled down. As the damage accumulates, near the failure
load, the increment size is scaled down further. The determination of the load factor increments is an art and
requires the insight of an experienced analyst.
VI.
Layered-Shell Model
In addition to the coarse 3D element analyses of the right rear lug described in the previous section, an analysis
based on a layered-shell model was developed. The layered-shell analyses were developed as an alternate means of
predicting the failure of the lug. The term layered-shell signifies that the thickness of the lug is modeled by several
layers of shell elements rather than a number of layers of solid elements. The layered-shell analyses lend themselves
to the evaluation of delamination initiation or propagation through the addition of decohesion elements between the
shell layers. The analysis was developed in ABAQUS, and UEL and USFLD user-written subroutines were used for
modeling the progressive delamination and intra-ply damage, respectively.
As with the solid-shell models, the layered-shell model was developed by modifying the original Airbus model
of the right rear lug. The original Airbus model used 3D solid elements in the lug region and solid and shell
elements in the remainder of the model. To develop the ABAQUS model, the faces of the solid elements in the xzplane were converted into quadrilateral shell elements, and then the solid elements were converted into decohesion
elements. The layered-shell model had approximately 21000 nodes.
A. Material Modeling
1. Modeling Damage with Superimposed Shell Elements
The layered-shell models use a computationally efficient element superposition technique that separates the
failure modes for each ply orientation and does not rely on the computation of the ([A],[B], and[D]) matrices [Dávila
9
American Institute of Aeronautics and Astronautics
et al., 2000]. The modeling is performed such
=
+
+
+
that the elements in the region around the bolt t
hole, where a potential for damage growth is
[45] R
[-45] R
[0] R
[90] R
[45/-45/0/90] s
anticipated, are constructed of four superposed
layers of shell elements that share the same Figure 10. The Thick Laminate Modeled With Four Layers
nodes. No centroidal offset is applied to any of of Superposed Shell Elements.
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 the 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, the present analysis extends Chang’s method from 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 σ22 and shear stress
σ12. The failure index em can be defined in terms of these stresses and the strength parameters YT/C and the shear
allowable Sxy. The matrix allowable YT/C takes the values of YT in tension and YC in compression. Failure occurs
when the index exceeds unity. Assuming linear elastic response, the failure index has the form:
2
&'
em = $ 22
$ YT C
%
•
2
(6)
Fiber buckling/tension failure occurs when the maximum compressive stress in the fiber direction exceeds the
fiber tension or buckling strength XT/C, independently of the other stress components. The failure index for this
mechanism has the form:
eb =
•
# & '12 #
! +$
!
! $ S xy !
"
" %
!11
(7)
XT /C
Fiber-matrix shearing failure occurs due to a combination of fiber compression and matrix shearing. The failure
index has the form:
& '
e f = $$ 11
% XT /C
2
# &$ '12 #!
!! +
" $% S xy !"
2
(8)
The finite element implementation of this failure analysis was developed in ABAQUS using the USFLD userwritten subroutine. The program calls this routine at all material points of elements that have material properties
10
American Institute of Aeronautics and Astronautics
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 11(a). 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
(a) Local Region in
(b) Local Model with
satisfied. An iterative process was developed to
Global
Model
Transition Mesh
ensure satisfaction of these requirements. This
process is illustrated in Figure 12 and is
Figure 11. Models of Region Near Right Rear Lug.
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 {uG} represent the displacements of the global nodes along the global-local boundary
and {uL} represent the displacements of the local nodes along the global-local boundary. Evaluate the
tractions at the global nodes, {FG}, from the elements that are entirely in the global region (i.e., traction
evaluation does not include the elements that occupy the local region of the global model).
2) Establish a transformation matrix, [T], between {u G} and {uL}, and use this matrix to compute {uL} using
{u L }= [T ]{uG }
(9)
3) Analyze the local model with {uL} as prescribed displacements.
4) Because of the prescribed displacements, reactions at the interface nodes in the local model {RL} are
produced.
5) Local reactions are mapped back to the global nodes using
{RG }= [T ]T {RL }
(10)
Equation 10 is obtained by requiring that the work done on the global-local boundaries in the local model
(½)·({uL}T·{RL}) and the global model (½)·({uG} T·{RG}) are equivalent. The {RG} reactions represent the
stiffness of the local model in the global model.
6) The global tractions {FG}, in general, will not be identical to the reactions mapped from the local model,
{RG}, as the reciprocity of tractions is not imposed. Thus, a residual, {r}, is left on the global-local
boundary:
{}
r = {FG }! {RG }
7) Evaluate a norm r for the residual {r} using
11
American Institute of Aeronautics and Astronautics
(11)
5
6
{uL}=[T] {uG}
Solve the local
model with {uL} as
prescribed
Perform global analysis
8
4
Reanalyze global
model with {r}! as
additional loads:
{F}!+1={F}!+{r}!
{uL}!+1=[T] {uG}!+1
9
No
7
Yes
Evaluate
reactions {RL}
at these nodes
{RG}=[T]T
1
||r||! < TOL
Iterate
Calculate residual
{FG} - {RG}={r}
on global / local
interface
{RL}
!
r
#
=
!
3
Evaluate
||r||!
Figure 12. Global-Local Iterative Analysis Process.
Boundary
s
2
Figure 13. Interfaces Between the
Global and Local Models.
(FGi )# [(uGi )# " (uGi )#"1 ]
(FGi )Initial (uGi )Initial
(12)
Boundary
where α is the current iteration number in the convergence process and the
!
Boundary
implies accumulation
at all nodes on the global-local boundary.
8) If the normalized residual is less than a prescribed tolerance, then this procedure is stopped, and the
system has converged. If the normalized residual is higher than the prescribed tolerance, then the residual
vector is added as an initial load set in the global model and the global analysis is executed again (i.e.
return to step 1).
The interfaces between the global and local model are defined on 9 edges (shown as red and blue lines in Figure
13) and at 17 discrete locations (shown as red dots in Figure 13). The coarse 3D model was modified so that the
local edge nodes matched the global edge nodes exactly as shown in Figure 11(b). Therefore, the mapping from the
global and local models can be accomplished with a unit [T] matrix.
To maintain symmetry of the global model, the stiffness of both the right rear and left rear lugs was updated by
the global-local process. Thus, during the global-local process, two local analyses were performed during each
iteration. Instead of creating another FEM, one local FEM was used for both the right rear and left rear lug. For the
left rear lug, the loads and boundary conditions were mirrored about the global xz-plane (i.e. the sign of FY, MX, MZ,
v, θX, and θZ are reversed). A similar algorithm to that described above was presented in the literature [Whitcomb
and Woo, 1993]
B. Global-Local Analysis and PFA
The global-local process described in the previous section assumes that the stiffness of the local model does not
change in the iterative procedure. Similarly, the PFA assumes that the boundary conditions on the local model do
not change as the PFA continues. The most rigorous analysis of the VTP requires that damage determined in the
local model be returned to the global model. That is, at step 2 of the global-local process, the PFA needs to be
performed to determine the current damage state of the lug. After convergence is obtained (and equilibrium is
established), the global-local process is continued with step 3.
Such a rigorous procedure involving both the global model and the local model and with the current large degree
of freedom model is impractical. Therefore, the global-local procedure is performed first to determine the boundary
conditions on the global-local interfaces and the loads at the pin. With these boundary conditions and loading, the
PFA is performed on the local model. The verification of this decoupling assumption is provided in the Results
section.
Convergence of the forces and moments in the right rear lug for the W375 load case are plotted in Figures 14(a)
and 14(b), respectively. In these figures, the reactions are normalized by the average of the global and local results
12
American Institute of Aeronautics and Astronautics
1.5
1.4
Global - Fx
Global - Fy
Global - Fz
1.3
Local - Fx
Local - Fy
Local - Fz
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0
1
2
3
Iteration
4
5
6
Normalized Reaction Moments at Pin
Normalized Reaction Forces at Pin
1.5
1.4
Global - Mx
Global - Mz
1.3
Local - Mx
Local - Mz
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
(a) Convergence of Pin Forces
0
1
2
3
Iteration
4
5
6
(b) Convergence of Pin Moments
Figure 14. Convergence in Global-Local Analysis (Load Case W375).
at the end of the sixth iteration. At the sixth iteration, the difference between the global and local forces is less than
1 kN, and the difference between the corresponding moments is approximately 0.03 kN-m.
VIII.
Results
The PFA results are compared with available experimental results for the 1985-certification test (X2/1 and X2/2
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 nonlinearity and pin-lug contact.
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
Coarse 3D Model
X
Solid-Shell Model
1985 Test Model
X
SC Test Model
X
Layered-Shell Model
X
X
X
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
Hydraulic
Piston
certification test configuration shown in
Figure 15.
In this configuration, a
hydraulic piston and lever were used to
Lever
apply an in-plane load to the lug as
shown in Figure 15(a).
The test
specimen was fixed around the perimeter
of the skin as shown in Figure 15(b), and
the constraint due to rib 1 was simulated
using the transverse girder shown in
Figure 15(c). Because all of the loading
was in the plane of the specimen, the MX
at the lug in this test was entirely due to
the combination of FX, FZ, and the
eccentricity. A boundary condition of
(a) Test Apparatus
W375
X
Rib 1
Specimen
Constraint
Fixture
Transverse
Girder
(b) Test Specimen
Specimen
(c) Transverse Girder
Figure 15. 1985-Certification Test Configuration.
13
American Institute of Aeronautics and Astronautics
CLAMPED
θX=0 at the pin is hypothesized and is used in the
9
3
(u=v=w=0
7
1
analysis.
θx=θy=θz=0)
The instrumentation on the X2/2 test
8
specimen consisted of 16 strain gauges as shown
2
Outboard
Side
Outboard
in Figure 16. There are two sets of back-to-back
12
Side
10
rosettes on the tapered portion of the lug
6
4
immediately above rib 1 (gauges 1-12) and four
uniaxial gauges along the profile of the lug
11
16
13
5
(gauges 13-16). During the test, all 16 gauges Stringer Side
Z
Stringer Side
15
were monitored. The load vs. strain data from
u=v=θz= 0
14
Y
all these 16 gauges was available and was used
X
0
in the PFA validation.
Figure 16. Strain Gauges on X2/2 Test Specimen.
2. Results
Figure 17 shows the strain gauge results obtained from Airbus as open red circle symbols and NASA’s finite
element predictions made 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
1250
1250
1250 Gauge 04
1250
Gauge 02
Gauge 01
Gauge 03
changes in stiffness, they are not
1000
1000
1000
1000
shown in Figure 17. In general, the
predicted values agree very well
750
750
750
750
with the strain gauge results, except
500
500
500
500
strains from gauges 3 and 10. The
reason for these two deviations is
250
250
250
250
unknown.
Also, because the
0
0
0
0
location of gauges 14 and 15
through-the-thickness
was
not -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3
1250 Gauge 07
known, finite element predictions of
1250 Gauge 08
1250 Gauge 06
Gauge 05
strain on the outboard side and
1000
1000
1000
1000
stringer side of the lug are shown.
750
750
750
750
These predictions bound the strain
gauge results. From this figure, it
500
500
500
500
was concluded that the present PFA
250
250
250
250
represents accurately the behavior
of the lug over the complete loading
0
0
0
0
range.
-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3
The computed values of FRes
1250 Gauge 09
1250 Gauge12
1250 Gauge 10
1250 Gauge 11
(resultant of FX, FY, and FZ force
components) and MX vs. load factor
1000
1000
1000
1000
are shown in Figure 18. In Figure
750
750
750
750
18, the load factor is a non500
500
dimensional scaling factor that is
500
500
applied to the displacements during
250
250
250
250
the PFA analysis. A load factor of
0
0
0
0
1.0
corresponds
to
the
displacements produced from a -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3
linear analysis.
The curve for
1250 Gauge 14
1250
Gauge 15
Stringer
resultant force (FRes) vs. load factor
15
side
Stringer
is shown as a solid blue curve with
14
1000
1000
side
open circle symbols and the curve
750
750
of MX vs. load factor is shown as a
Test
Test
data
data
500
solid red curve with open square
500
symbols. The linearly projected
Outboard
Outboard
250
250
side
side
values of MX and FRes are shown as
0
closed diamonds. The failure load
0
-3 -2 -1 0 1 2 3
from the X2/2 test specimen is
-1 0 1 2 3 4 5
shown as a thick horizontal red line.
Figure 17. Strain Gauge and Finite Element Results.
0
14
American Institute of Aeronautics and Astronautics
Peak FRes
A)
1077 kN
B)
1120 kN
1200
MX
3.486 kN-m
3.267 kN-m
B
A
1100
11.0
Failure Load
(Test)
900
800
9.0
8.0
FRes
MX
700
600
7.0
Linear FRes
(Non-PFA)
500
6.0
5.0
Linear MX
(Non-PFA)
400
3.0
200
2.0
100
1.0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Elements with Predicted Damage
(a) View normal to the hole
4.0
300
0.0
MX (kN-m)
10.0
1000
FRes (kN)
12.0
1.0
1.1
1.2
0.0
1.3
(b) View through the hole
Unsymmetric Damage
Due to Configuration and
Applied Moments
Load Factor
Figure 18. Load and Moment vs. Load Factor for 1985Certification Test.
Peak values of MX and FRes are shown on the graph and in the
tabular insert as points A and B, respectively. The load factor
(c) View through the outer thickness of the lug
for the linear case and points A and B are shown with vertical Figure 19. Damage Prediction from PFA for
dashed lines. The FRes at the maximum moment (Point A) 1985-Certification Test.
agrees extremely well with the experimentally determined
value for this configuration. The extent of the damage predicted by the PFA in Figure 19 agrees well with that
Figure 20. X2/2 Test Specimen – Observed Failure.
observed during the 1985-certification test shown in Figure 20. Note that Figure 19 is based on superposition of all
active failure modes within all ply types at each Gauss point in the model.
B. 2003-Subcomponent Test
As part of the AA 587 accident investigation, Airbus developed a new certification test configuration to more
accurately simulate the load introduction and boundary conditions near the lug. The 2003-subcomponent (SC) test
model and the PFA algorithm shown in Figure 8 were used to predict the response of the 2003-subcomponent test
specimen with boundary conditions shown in Figure 5(b). Because the exact value of the MX to be applied was
unknown prior to the test, several values were considered as shown in Table 3. Note that in Table 3, because the SC
test model is a left rear lug, the loads and moments are mirrored from their corresponding right rear lug load cases
(i.e. the sign of FY, MX, MZ, v, θX, and θZ are reversed). The pin forces in all cases in Table 3 correspond to the
global-local analysis with Y-MPC #1 (with FY reversed). Case (C) was analyzed before the 2003-subcomponent test
and corresponds to an MX value of of 6.537 kN-m. Cases (D) and (E) were analyzed after the subcomponent test.
Cases (D) and (E) correspond to the actual θX value of 0.51° applied in the test with 360° friction contact (Y-MPC
#1) and 120° friction contact (Y-MPC #2), respectively. Post-test linear analyses gave the MX values of 6.67 and
6.27 kN-m for cases (D) and (E), respectively.
Table 3. Pin Moments and Rotations for Subcomponent Test Model (left rear lug).
Loading Case
MX (kN m)
MZ (kN m)
θ X (deg)
θ Y (deg)
SC Test W375 (C)
+6.537
-1.000
0.487
0.000
SC Test W375 (D)
+6.670
-0.379
0.510
0.000
SC Test W375 (E)
+6.270
-0.508
0.510
0.000
15
American Institute of Aeronautics and Astronautics
θ Z (deg)
-0.065
0.000
0.000
FRes (kN)
MX (kN-m)
Because the PFA is implemented as a
Peak FRes
MX
Linear FRes
A)
900 kN
5.933 kN-m
displacement- (translation and rotation) controlled
(Non-PFA)
B)
983 kN
3.721 kN-m
12.0
1200
process, a linearly projected target value of MX based
11.0
1100
B
Failure Load = 907 kN
A
on an assumed linear relationship between applied
(Test)
10.0
1000
rotation and the resulting moment was used. Note
9.0
900
that as damage develops, the specimen loses its
Linear MX
8.0
800
(Non-PFA)
F
Res
stiffness and hence will not carry the moment that is
7.0
700
MX
predicted by the linear relationship.
6.0
600
The computed values of FRes and MX vs. load
5.0
500
4.0
400
factor are shown for load cases SC (C), SC (D), and
3.0
300
SC (E) in Figures 21(a) to 21(c), respectively, for
2.0
200
applied rotations resulting from linearly projected
100
1.0
load and moment values as given in Table 3. The
0
0.0
curves for resultant force (FRes) vs. load factor are
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 1.3
shown as solid lines with open circles, and the curves
Load Factor
of MX vs. load factor are shown as solid lines with
(a) SC (C) Load Case
open square symbols. The linearly projected values
of MX and FRes are shown as closed diamonds. The
Peak F
M
Linear F
failure load observed during the test is shown as a
A)
903 kN
6.257 kN-m
(Non-PFA)
B)
975 kN
3.573 kN-m
12.0
thick horizontal red line in Figures 21(a) to 21(c).
1200
11.0
Failure Load = 907 kN
1100
Peak values of MX and FRes are shown on the graph
A
B
(Test)
10.0
1000
and in the tabular insert as points A and B,
9.0
900
respectively. The load factor for the linear case and
8.0
800
F
points A and B are shown with vertical dashed lines.
7.0
700
Linear M
M
Two entirely different loading sequences are
6.0
(Non-PFA)
600
represented by the sets SC (C) (Figure 21(a)) and SC
5.0
500
4.0
(D) and (E) (Figures 21(b) and 21(c)). In load case
400
3.0
300
SC (C), the translations and rotations were applied
2.0
200
simultaneously and proportionally starting from zero
100
1.0
values to develop the FRes and MX shown in the
0
0.0
figures. For load cases SC (D) and (E), θX was
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 1.3
applied initially until the desired initial rotation (θX)
Load Factor
was reached, and then the translations and rotations
(b) SC (D) Load Case
were increased proportionally. Recall that Case D has
360o friction contact (Y-MPC#1) while Case E has
Peak FRes
MX
Linear FRes
A)
896 kN
5.036 kN-m
120o friction contact (Y-MPC#2). All these cases
(Non-PFA)
B)
1009 kN 3.089 kN-m
12.0
1200
predict nearly the same failure loads. These later
B
11.0
Failure
Load
=
907
kN
1100
A
cases (D and E) represent more accurately the loading
(Test)
10.0
1000
sequence during the 2003-subcomponent test.
9.0
900
While the curves in Figures 21(a) to 21(c) show
8.0
Linear MX
800
FRes
the same general trends, increased values of MX result
(Non-PFA)
7.0
700
MX
in lower values of FRes at failure. Also, larger values
6.0
600
of MX decrease the difference between FRes at peak
5.0
500
4.0
400
moment (point A) and maximum FRes (point B). The
3.0
300
difference between the values of points A and B is
2.0
200
largest for load case SC (E) in which an initial value
100
1.0
of θX is applied, and then is held constant. The
0
0.0
constant rotation contributes to an artificial stiffening
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 1.3
of the lug in load case SC (E) and results in higher
Load Factor
peak FRes than for load case SC (C).
(c) SC (E) Load Case
The damage predictions (superposition of all
Figure 21. Load and Moment vs. Load Factor.
failures) for the lug under load case SC (C) at peak
moment and peak force are shown in Figures 22(a)
and 22(b), respectively. The mode of damage (cleavage type failure) is the same as seen previously in the 1985certification test. The extent of the damage predicted by the PFA (Figures 22(a) and 22(b)) also agrees well with
Res
X
16
American Institute of Aeronautics and Astronautics
X
MX (kN-m)
Res
MX (kN-m)
X
FRes (kN)
FRes (kN)
Res
(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).
that observed during the SC test shown in Figure 23. This damage is consistent with the damage seen in the other
cases.
MX (kN-m)
FRes (kN)
C. W375 Accident Case PFA Analysis
The forces and moments at the pin and the boundary conditions on Table 4. Pin Rotations for Load Case
the global-local interfaces for W375 accident case were obtained from W375 in Accident Model (RHS).
the global-local analysis. The corresponding pin rotations predicted
CASE
θ X (deg) θ Z (deg)
from global-local analysis are given in Table 4 and are 48% higher than
Accident W375
0.756
0.286
those
Peak FRes
MX
Non-linear FRes
A)
925 kN
5.406 kN-m
used in the Airbus 2003-subcomponent test because
(Non-PFA)
B)
1100 kN 4.459 kN-m
12.0
B
1200
they represent global rotations and include the effect
11.0
1100
of the rotation of the fuselage; the boundary
10.0
1000
conditions during the test did not consider the
A
900
Non-linear MX 9.0
deformation of the fuselage and corresponded to a
(Non-PFA)
8.0
800
FRes
fixed condition at the base of the VTP.
7.0
700
MX
The computed values of FRes and MX vs. load
6.0
600
factor are shown for the W375 accident case in
5.0
500
Figure 24, using applied translations and rotations
4.0
400
resulting from linearly projected load and moment
3.0
300
2.0
200
values. The curve for resultant force (FRes) vs. load
100
1.0
factor is shown as a solid blue line with open circle
0
0.0
symbols, and the curve of MX vs. load factor is
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 1.3
shown as a solid red line with open square symbols.
Load Factor
The linearly projected values of MX and FRes are
Figure 24. Load and Moment vs. Load Factor for W375
shown as closed diamonds. Peak values of MX and
Load Case.
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Elements with Predicted Damage
(a) View normal to the hole
FRes 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.
IX.
(b) View through the outer thickness of the lug
Unsymmetric Damage
Due to Configuration and
Applied Moments
Discussion
This section discusses the results and
lessons learned during the course of the
analysis of the failure of the AA 587 right
rear lug.
A. Effect
of
MX
and
MZ
on
Experimentally Determined Failure Load
As discussed in the Results section, the
moment MX has a significant effect on the
failure loads during the tests.
Larger
absolute values of MX result in lower failure
(c) View through the outer thickness of the lug
loads for the lugs.
For example, an
observed increase in MX of 45 percent from
Figure 25. Damage Prediction for W375 Accident case from PFA.
the 1985-certification test (Figure 18) to the
2003-subcomponent test (Figure 21(c))
FWD
caused a 17 percent decrease in the
predicted failure load. In contrast, the
moment MZ was determined to have a
minimal effect on the failure load.
(c) View through the outer thickness of the lug
B. Failure Modes
The classical failure modes of a bolted
Figure 26. AA 587 Right Rear Lug – Observed Failure.
joint are bearing failure, net tension failure,
and shear-out failure. In addition to these
three classical modes of failure, a failure identified as cleavage failure is also common [Camanho and Matthews,
1999]. The progressive failure analysis showed that the right rear lug failures are very similar to the cleavage type,
but do not show separation of the failed piece from the remainder of the lug. Ideally, the progressive failure analysis
of a lug should reproduce the entire sequence of failure events and should end with an analysis result exhibiting the
same fracture surfaces as those on the failed part. However, several issues in the analysis make the determination of
the fracture sequence difficult. The first issue pertains to the convergence of the numerical solution. Once the
ultimate strength of the lug is exceeded, the lug is no longer in equilibrium and the numerical procedure fails to yield
a converged solution. Secondly, models assume that all the applied loads and boundary displacements are
incremented proportionally to each other during the analysis. The proportionality is a reasonable assumption until
the ultimate strength is exceeded. After the peak force, the stiffness of the lug changes dramatically, and the
assumption of load proportionality is no longer valid. Finally, damage is modeled as a softening of the material
continuum rather than as a stress free surface or crack. Consequently, fracture surfaces that are plainly observable in
the failed part are not as clearly represented in the model.
C. Test and Accident Case Comparisons
Figures 27 and 28 compare the failure loads and MX variation predicting with the solid-shell model and PFA for
the three cases: the 1985-certification test, 2003-subcomponent (SC) test, and the W375 accident condition. The
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American Institute of Aeronautics and Astronautics
W375 Accident
Condition
300
200
100
0
Moment Mx, kN-m
Fres (kN)
stiffnesses of the lug (represented by the slope of the FRes vs. Load Factor curve in Figure 27) for the three cases and
the maximum moment MX (Figure 28) for the SC test and the W375 accident case agree very well.
The failure loads (Figure 29) and the damage regions (Figure 30) obtained using the solid-shell model and PFA
for the three cases are compared in these figures. Table 5 presents the individual load components in the lug at
failure for the 2003-subcomponent test and W375 accident condition. The experimentally determined failure loads
8.0 the present PFA methodology for the lug
agree1200
very well with the PFA predicted values, thus validating
1985 Test
1100
configuration.
Further, all three configurations showed cleavage type failures. The failure load for the lug for the
SC Test
7.0 load (467 kN) [Hilgers
W375
accident condition (925 kN) is greater than 1.98 times the limit
and Winkler, 2003].
1000
W375 Accident Condition
900
6.0
800 Ultimate Load
5.0
700
600
1985 test
4.0
Limit Load
500
SC Test
3.0
400
2.0
1.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Load Factor
Figure 27. FRes vs. Load Factor Variation for 1985Certification Test, 2003-Subcomponent Test, and
W375 Accident Case.
Normalized Failure Load, kN
PFA Analysis Failure Load
PFA Analysis Load at Maximum Moment MX
Test Failure Load
3.0
0.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Load Factor
Figure 28. Bending Moment MX Variation 2003for 1985-Certification Test, Subcomponent Test,
and W375 Accident Case.
W375 Accident Case
2.5
2.0
1.5
SC Test
1.0
0.5
0.0
1985 Test
SC Test
W375
Accident Case
Figure 29. Failure Loads Normalized by Limit Load
for 1985-Certification Test, 2003-Subcomponent
Test, and W375 Accident Case.
1985 Test
Figure 30. Comparison of Damage Predictions
1985-Certification Test, 2003-Subcomponent Test,
and W375 Accident Case.
Table 5. Load Components (Normalized by Limit Load) in the Lug at Failure.
Test Case
FX
FY
FZ
FRes
MX
SC Analysis (PFA)
-374.8
-40.39
-812.7
895.9
-5.04
2003-Subcomponent Test
-381.6
-39.10
-822.5
907.0
Not measured
W375 Analysis (PFA)
-359.9
-40.35
-851.5
925.3
-5.41
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X.
Concluding Remarks
An analysis of the failure of the composite vertical tail of the American Airlines Flight 587 - Airbus A300-600R
was performed as part of the National Transportation Safety Board’s failure investigation of the accident that
occurred on November 12, 2001. Two structural analysis teams, a global analysis team and a 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. The lug analysis team then developed and evaluated a
global-local connection procedure 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, MX (moment about the fuselage longitudinal axis) had significant effect on the failure load of
the lugs. Higher absolute values of MX give lower failure loads. For example, an observed increase in MX 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, MX. 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.
Acknowledgments
The authors would like to take this opportunity to thank Brian Murphy and John Clark of NTSB, Dr. Larry
Ilcewicz of FAA, Dr. Mark Shuart and the Structures and Materials Community at NASA Langley, and Ralf Hilgers
and Erhard Winkler of Airbus for their encouragement, in-depth discussions, and suggestions throughout the course
of this work. Their inspiring faith in our ability to perform this work is greatly appreciated.
Dedication
This report is dedicated to the memory of Dr. James H. Starnes, Jr. Dr. Starnes was our friend and colleague,
who led the NASA Langley AA587 investigation team and passed away before the completion of this report.
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