close

Вход

Забыли?

вход по аккаунту

?

6.1996-1354

код для вставкиСкачать
Copyright ©1996, American Institute of Aeronautics and Astronautics, Inc.
AIAA Meeting Papers on Disc, 1996, pp. 331-338
A9626833, NSF CDR-88-03017, N00014-90-J-1666, AIAA Paper 96-1354
Fracture criterion for notched thin composite laminates
Rajesh S. Vaidya
Purdue Univ., West Lafayette, IN
C. T. Sun
Downloaded by UNIVERSITY OF FLORIDA on October 25, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1996-1354
Purdue Univ., West Lafayette, IN
IN:AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials
Conference and Exhibit, 37th, Salt Lake City, UT, Apr. 15-17, 1996, Technical Papers. Pt. 1
(A96-26801 06-39), Reston, VA, American Institute of Aeronautics and Astronautics, 1996,
p. 331-338
The fracture behavior of center-notched AS4/3501-6 graphite-epoxy laminates is investigated. Nine laminate
configurations are tested to study crack tip damage mechanisms, failure modes, and the effect of crack size on laminate
notched strength. Results indicate that a constant value of fracture toughness (K sub Q) is a laminate material property.
A lay-up independent failure criterion is proposed which relates laminate fracture toughness to the fracture toughness
K sub Q exp 0 of the principal load bearing ply; this characterizes the fracture toughness of a notched 0 layer in the
presence of fiber breakage. Once its value is established from preliminary tests, it can be used to predict fracture
toughness of other laminates of the same material system. Model predictions are shown to agree well with experimental
results for different laminate configurations. The model is extended to predict residual strength of quasi-isotropic
laminates with inclined cracks (mixed-mode loading). (Author)
Page 1
96-1354
A96-26833
AIAA-96-1354-CP
FRACTURE CRITERION FOR NOTCHED THIN COMPOSITE
LAMINATES
Downloaded by UNIVERSITY OF FLORIDA on October 25, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1996-1354
Rajesh S. Vaidya'and C. T. Sun1
Purdue University, West Lafayette, IN 47907-1282
Abstract
Fracture behavior of center-notched AS4/3501-6
graphite-epoxy laminates is investigated in this study.
Nine laminate configurations are tested to study crack
tip damage mechanisms, failure modes, and the effect
of crack size on laminate notched strength. Results
indicate that a constant value of fracture toughness
(Kg) is a laminate material property. A lay-up
independent failure criterion is proposed which relates
laminate fracture toughness to the fracture toughness
Kg of the principal load bearing ply; KQ characterizes
the fracture toughness of a notched 0° layer in the
presence of fiber breakage. Once its value is
established from preliminary tests, it can be used to
predict fracture toughness of other laminates of the
same material system. Model predictions are shown to
agree well with experimental results for different
laminate configurations. The model is extended to
predict residual strength of quasi-isotropic laminates
with inclined cracks (mixed-mode loading). For this
case, the projection of the crack normal to the applied
load governs laminate residual strength and can be
considered as the 'equivalent crack' in the model.
Introduction
/^OMPOSITE materials are notch sensitive. The
V_y presence of cracks in structural components
drastically reduces their load carrying capacity. For
this reason, the issue of predicting composite residual
strength in the presence of stress raisers such as cracks
has been an important research problem in the
composites community.
Graduate Student, School of Aeronautics and
Astronautics.
Professor, School of Aeronautics and Astronautics.
Fellow AIAA.
Copyright © 1996 by the American Institute of
Aeronautics and Astronautics, Inc. All rights reserved.
A vast amount of experimental literature is available
on the notched strength behavior of different composite
systems.
Several strength-based and fracture
mechanics-based models have been proposed in the last
two decades. Most of the existing models, e.g., those by
Whitney and Nuismer1, Waddoups2 et. al., Pipes3 et.
al., Karlak4, etc., are based on a 'characteristic
distance' concept. Herein, the damage events are
assumed to occur in a region aa ahead of the crack tip.
The value for a0 is then chosen so as to fit the
experimental data. The limitation of such an approach
is that a0 is not a material constant and depends on
factors such as notch size and laminate orientation5. As
such, results obtained from tests on one laminate
configuration cannot be extrapolated to predict the
fracture toughness of other laminates of the same
material system. A comprehensive review of such
fracture models has been done by Awerbuch and
Madhukar5.
In this study, a new approach to predicting fracture
strength of a class of laminates is presented. An
experimental study was conducted to examine the
fracture behavior of nine different laminate
configurations. The aim of the present research was the
following :
1) Study crack tip damage mechanisms and failure
modes in center cracked composite laminates.
2) Determine if fracture mechanics concepts such as
critical stress intensity factor and fracture toughness
could be used to describe the fracture behavior of
these composites.
3) Develop a lay-up independent failure model for
predicting laminate fracture.
Experimental Procedure
The material system chosen for the study was
AS4/3501-6 graphite epoxy manufactured by Hercules,
Inc. The material is available in the form of a
unidirectional prepreg tape with a nominal thickness of
0.127 mm. The unidirectional material properties are
reported in Table 1.
The laminates were made using the hand lay-up
331
American Institute of Aeronautics and Astronautics
Downloaded by UNIVERSITY OF FLORIDA on October 25, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1996-1354
technique and cured in an autoclave. Nine different
laminate configurations (Table 2) were chosen such
that they had at least some 0° plies, i.e., plies with
fibers aligned along the loading direction.
Test specimens were cut from 30.5 cm by 30.5 cm
panels on a FLOW™ waterjet system. The test
configuration was that of a center crack oriented
perpendicular to the loading direction. The specimen
dimensions were 25.4 cm x 3.81 cm with 3.81 cm
long end tabs. To make the cracks, a starter hole was
first drilled in the laminate to minimize any
delamination caused by the waterjet. The crack was
then made by a waterjet cut and further extended with
a 0.2 mm thick jeweler's saw blade.
The quasi-static experiments were conducted in a
servo-hydraulically driven MTS machine with an
Instron 8500 controller under position control at a
head displacement rate of 0.254 mm/min. The load and
head displacement histories were recorded using
LABVIEW software.
Figure 1: [0 / 90 / ±45] laminate at 99 % of failure load
Damage Mechanisms and Failure Modes
An important objective of the experiments was to
monitor the growth of damage ahead of the crack tip.
The test specimens were examined prior to testing to
ensure that no significant damage occurred during
their preparation. Damage evolution was studied by
diiodobutane (DIB) enhanced X-ray examination at
different load levels. The fractured specimens were
also examined to determine the failure mode of the
individual plies.
Figure 1 shows typical crack tip damage in a
[0/90/±45] s quasi-isotropic laminate. The damage
zone in such laminates is characterized by matrix
cracks in off-axis plies, axial splits (matrix cracks
along the fiber direction of the 0° ply) and some
delamination. The matrix cracks are observed as dark
lines in the figures. (The dark region in the center part
of the crack is cutting tool induced damage and not
load induced and, hence, should be disregarded. It does
not appear to affect the notched strength of the
laminate). Radiographs of
[±45/0/±45] s and
[±45 2 /0/±45] laminates (Figures 2 and 3) reveal
similar matrix cracks in the off-axis plies along with
some delamination. Radiographs revealed that visible
damage initiated at high values of the applied load (7580% of the failure load). Post failure inspection
revealed that the off-axis plies failed along matrix
cracks extending from the crack tip to the specimen
edge while the 0° plies failed by fiber breakage.
Figure 2: [±45/0/±45] s laminate at 95% of failure load
Figure 3: fL ±45, / 0 / ±45]J s laminate at 97% of failure
L
332
American Institute of Aeronautics and Astronautics
load
Downloaded by UNIVERSITY OF FLORIDA on October 25, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1996-1354
Figure 4: [0/15/-15]s laminate at 92% of failure load
Figure 7: [0/90]2s laminate at 85% of failure load
The [0/±6] s laminates (Figures 4-6) show matrix
Figure 5: [0/30/-30], laminate at 99% of failure load
Figure 6: [0/45/-45]s laminate at 99% of failure load
cracks in the off-axis plies, delamination at the
[±6] interface and axial splits in the 0° plies. The 0°
plies in these laminates exhibited fiber breakage while
the other plies failed along matrix cracks.
A study of cross-ply [0/90] 2s laminates shows long
axial splits emerging from the crack tips of the 0° plies
(Figure 7). Transverse matrix cracks were also
observed in the 90° plies and the'se grew in density
with the applied load. Similar damage modes for crossply laminates have previously been reported in the
literature6'7. The visible damage initiated at lower load
levels compared to that in the other laminates.
Ultimate failure of these laminates was caused by fiber
failure in the 0° plies.
To broadly
summarize
the
experimental
observations, when a specimen containing a crack is
subjected to increasing tensile loads, the following
sequence of events is observed:
1) At very low loads the specimen deforms
elastically with no damage.
2) At a threshold value of load, sub-cracks form
parallel to the fibers of each ply at the crack tip.
3) As the load increases above the threshold value,
the sub-cracks extend, and some region of
delamination may form between plies.
4) At some critical maximum load the fibers in the
0° plies of the laminate fail causing the specimen to
fail.
The laminate failure processes observed in this study
can be separated into two relatively distinct categories.
The first is general stress relaxation. Damage
formation ahead of the crack tip in the form of matrix
cracks relieves some portion of the high stress
concentrated at the crack tip. Axial splits in the 0° plies
are particularly effective in this regard, because they
333
American Institute of Aeronautics and Astronautics
Downloaded by UNIVERSITY OF FLORIDA on October 25, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1996-1354
have the effect of separating the 0° ply into a strip
containing a crack and two outer strips without a
crack. Laminates with more extensive damage zones
achieve more stress relaxation and are, therefore, less
notch sensitive. McGarry8 et. al. have reported that
these matrix cracks grow in length proportional to K2
(stress intensity factor). The second category is
ultimate failure caused by fiber failure of the principal
load carrying plies (0° plies). The post-failure
examination revealed that these were the only plies
that exhibited fiber breakage, while the off-axis plies
failed along matrix cracks. Since fiber strength is
significantly higher than matrix strength, it is surmised
that fiber breakage in the 0° ply governs the notched
strength of the laminate.
••:
40 -
it!
e «
H fe
30 20 -
£
6
8
10
half crack length a (mm)
Figure 8: Effect of varying crack length on KQ for a
[90/0/45/-45]5 laminate
Determination of Laminate Fracture
Toughness
Laminate fracture toughness (KQ) is defined as the
value of the linear elastic stress intensity factor at the
maximum test load. (This corresponds to catastrophic
failure of the center-cracked tension specimens).
Fracture toughness of the laminate KQ (or critical stress
intensity factor) is calculated as
KQ =
Fracture Criterion
(1)
where af is the remote applied stress at failure, a is
half the crack length and Y is the correction factor to
account for the finite width of the specimen, given by
(2a}
laminate fracture toughness calculated using (1). The
results for a [90/0/45/-45], laminate are shown in
Figure 8. The results clearly indicate that K^ is
independent of crack length and can be considered a
laminate material property. Similar results are
observed for all the other laminates as well. The
measured KQ values for the nine laminates are
presented in Table 2.
(2aV
Y = 1 + 0.1282 —1-0.2881—
f2aV
+1.5254—
(2)
vwJ
vwJ
vw/
It should be noted that this is the correction factor
originally developed for isotropic materials. However,
researchers have reported5'7 that it can be used for
orthotropic materials with little loss of accuracy.
Effect of Crack Length on Kn
The experimental results indicate that while matrix
Notched strength in metals is characterized by a
'critical stress intensity factor' or a 'critical strain
energy release rate'. These are material parameters
which uniquely characterize the fracture resistance of
metals in the presence of cracks and are independent of
the size of the crack. If a similar parameter exists for
composite laminates, it should be independent of the
crack length. With this objective in mind, the effect of
crack length on laminate fracture toughness is studied
in the experiments. The crack lengths were varied
approximately from 10-20 mm and the corresponding
As discussed in the previous section, the fracture
resistance for any laminate can be characterized by a
unique fracture toughness parameter KQ. Its value, of
course, depends on laminate configuration. Most of the
existing models'"4 estimate Kg by adjusting the damage
zone size a0 to determine the 'equivalent crack
length'. This is a major limitation, since experimental
data for each laminate configuration is required to
determine its damage zone size. The present research
objective is to establish a more general parameter that
is independent of laminate configuration.
cracks provide local stress relaxation, final fracture of
the laminate is controlled by fiber breakage in the 0°
plies. The entire laminate fails when the 0° plies within
it fail. Fiber breakage of these plies can thus be
considered as the principal failure mechanism. This
seems quite logical considering that fiber strength for
composites is significantly higher than matrix strength.
Previous researchers6'7 studying cross-ply laminates
have also shown that the 0° ply governs laminate
notched strength.
334
American Institute of Aeronautics and Astronautics
Model Verification
Downloaded by UNIVERSITY OF FLORIDA on October 25, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1996-1354
According to the failure criterion (equation 6) the
Figure 9: Fracture toughness KQ corresponding to
fiber breakage in the 0° ply
It is proposed that the fracture toughness of the 0°
ply (defined as KQ) is a constant at failure; i.e., the
laminate fails whenever the load in the 0° plies
reaches the critical value KQ. The existence of such a
parameter for cross-ply laminates was first postulated
by Kageyama7, who estimated its value by three
dimensional finite element analysis. This value
corresponds to the toughness of the 0° ply when there
is fiber breakage (Figure 9). Unfortunately, this failure
mode is not exhibited by unidirectional laminates
which fail due to axial splitting (matrix cracks parallel
to fiber direction). Thus, KQ cannot be directly
determined
from
experiments
on
notched
unidirectional laminates. However, we can estimate its
value by simple stress analysis using lamination theory
to calculate the portion of the applied load that is
carried by the 0° plies in the laminate. Such an analysis
is approximate, since it does not take into account any
stress redistribution caused by local damage in the
form of matrix cracks, etc. The effect of any stress
relaxation is absorbed in the parameter K Q . We define,
crf =-naf
laminate fails when the load carried by its 0° plies
reaches the critical value K Q . It is a material constant
and thus should be independent of the laminate
orientation. To verify this hypothesis, the value of K Q
within the different laminate configurations is
calculated using (6) and plotted in Figure 10 (see Table
2). The results indicate that the value of K° is
approximately the same in all the laminates and does
not deviate by more than 10 % from the mean value of
110 MPa-m1/2. (The K° value for the [±45/0/±45] s
and [±452 / 0 / ±45] laminates is slightly higher because
they were manufactured from a different batch of
material.) Using the mean value for KQ in the model,
the predictions are compared with the experimental
results in Figure 11. Good agreement is observed
between the experiments and predictions. The
agreement would be even better if K Q were estimated
separately for each batch of material.
We can thus use a single parameter model to
characterize the fracture behavior of these laminates.
Preliminary tests are required for a single laminate
configuration to determine K Q . Once its value is
determined, the fracture toughness of other laminates
can be predicted by this simple model.
• [0/90/45/-45]s
• [45/-45/90/OJS
A [90/0/45/-45JS
X[0/15/-15]s
X [0/30/-30JS
• [0/45/-45JS
+ [0/90]2s
• [45/-45/0/45/-45]s
• [45/-45/45/-45/0/45/-45]s
(3)
where of is the laminate applied stress at failure, a? is
the remote (far-field) stress in the 0° ply and n is the
factor relating the two stresses, (n depends on the
laminate configuration and material elastic constants
and can be calculated using classical lamination
theory).
Using (1) in (3), we get
K0
°° =1177^=
150
125 100 -
W
or,
1
1.5
We denote the l.h.s. of (5) as K°. Thus,
(6)
2
2.5
3
3.5
stress ratio r\
(5)
Figure 10: Value of parameter KQ in different
laminates
335
American Institute of Aeronautics and Astronautics
4
•
•
A
projected crack lengths. It is clear from the figure that
the results for different crack orientations collapse onto
[0/15/-15]s
[0/30/-30JS
[0/90]2s
a single curve corresponding to the residual strength
vs. crack length curve for a normal crack (9 = 0). This
'master curve' can be predicted by the model (equation
(6)) discussed in the previous sections. The failure
stress for any orientation of the center crack in the
[0/90/145] laminate is thus given by
X [0/45/-45]s
X [0/90/45/-45]s
• [90/0/45/-45]s
+ [45/-45/90/0]s
• [45/-45/0/45/-45]s
_ [45/-45/45/-45/0/45/-45]s
predicted curve
100
WO
so
(7)
Downloaded by UNIVERSITY OF FLORIDA on October 25, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1996-1354
"g 60
2
u.
&
40 -
^——'
20
0
I
1
1.5
2
2.5
3
3.5
Laminate stress ratio n
where,
af = applied stress at failure
KQ = fracture toughness of the 0° ply
r| = stress ratio for the laminate
a eff = effective crack length = acosG
Y = Y(2aefl/W) = finite width correction factor
Figure 11: Comparison of experimental results with
model predictions.
Residual Strength of Laminates with
Inclined Cracks
In most real world situations, a crack is oriented at
an angle to the applied load (Figure 12). This problem
is investigated to determine if the present model can
predict residual strength of laminates with inclined
cracks. [0 / 90 /+45] s quasi-isotropic laminates are used
in the experimental study, with attention restricted to
the case where the loading is along the 0° fiber
direction (i.e. the material axis coincides with the
loading axis). Center cracks were cut in the test panels
at 0°, 30°, 45° and 60° angles w.r.t. the horizontal axis
(0° angle corresponds to the normal crack orientation
discussed in the previous section).
A radiograph of the crack tip damage in an inclined
crack is shown in Figure 13. The damage pattern in the
form of axial splitting and matrix cracking is similar to
that in a normal (d = 0°) crack in the same laminate.
The eventual failure mode of the laminate for the two
cases is also similar, with the off-axis plies failing
along matrix cracks and the 0° plies failing by fiber
fracture. The failure is controlled by the stress
concentration in the 0° ply near the crack tip. The
relevant crack length parameter seems to be the
projected length (2acos#) normal to the applied load
(see Figure 12).
The test results (Figure 14) support this hypothesis.
The residual strength of the laminates with different
crack orientations 6 are plotted against their respective
Figure 12: Inclined crack configuration
Figure 13: Damage growth in a [O/ 90/ ±45]s laminate
with a crack at a 45° angle
336
American Institute of Aeronautics and Astronautics
Manufacturing Systems at Purdue University and in
part by the Office of Naval Research through grant
N00014-90-J-1666.
• theta = 0 deg
•
500
£
theta = 30 deg
A theta = 45 deg
X theta = 60 deg
Model Prediction
400 -
References
•j 300 W5
•2
Downloaded by UNIVERSITY OF FLORIDA on October 25, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1996-1354
«
200 100-1
9
12
15
18
21
Projected crack length 2a*cos6 (mm)
Figure 14: Failure stress for inclined crack in
[0/90/±45] s laminates
The problem of predicting residual strength of
laminates with inclined cracks thus reduces to the
problem of a normal crack with effective crack length
equal to the projection of the crack perpendicular to the
applied load.
Conclusions
A new failure criterion was proposed to predict the
strength of composite laminates containing cracks. The
criterion was based on the experimental observation
that the 0° plies in a laminate govern its strength. The
fracture toughness of such 0° plies in the presence of
fiber breakage was introduced as the material
parameter K°. The parameter was shown to be
independent of stacking sequence and was used to
predict the fracture toughness of laminates containing
some 0° plies. Comparisons with experimental data
indicate that the model provides a good estimate of
laminate
fracture
toughness
for different
configurations.
The model was also extended to predict notched
strength of quasi-isotropic laminates with arbitrary
crack orientations. For this problem, the projected
length of the crack normal to the applied load was
determined to be the governing parameter and was
used as the 'effective crack length' in the model. The
authors believe that similar results would be observed
for other laminate orientations as well.
'Whitney, J. M., and Nuismer, R. J., "Stress Fracture
Criteria for Laminated Composites Containing
Stress Concentrations," Journal of Composite
Materials, Vol. 8, pp. 253-265 (1974).
2
Waddoups, M.E., Eisenmann, J. R., and Kaminski, B.
E., "Macroscopic Fracture Mechanics of Advanced
Composite Materials," Journal of Composite
Materials, Vol. 9, pp. 446-454 (1971).
3
Pipes, R. B., Wetherhold, R. C, and Gillespie, J. W.,
Jr., "Notched Strength of Composite Materials,"
Journal of Composite Materials, Vol. 12, No. 16,
pp. 1151-1155(1979).
4
Karlak, R. F., "Hole Effects in a Related Series of
Symmetrical Laminates," Proceedings of Failure
Modes in Composites, IV, The Metallurgical Society
of AIME, Chicago, pp. 105-117 (1977).
5
Awerbuch, J., and Madhukar, M. S., "Notched
Strength of Composite Laminates: Predictions and
Experiments - A Review," Journal of Reinforced
Plastics and Composites, Vol. 4, pp. 3-159 (1985).
6
Kortschot, M. T., and Beaumont, P. W. R., "Damage
Mechanics of Composite Materials: II - A DamageBased Notched Strength Model," Composites Science
and Technology, Vol. 39, pp. 303-326 (1990).
'Kageyama, K., "Fracture Mechanics of Notched
Composite Laminates," Application of Fracture
Mechanics to Composite Materials, Elsevier Science
Publishers B.V., pp. 327-396 (1989).
8
Mandell, J. F., Wang, S. S., and McGarry, F. J., "The
Extension of Crack Tip Damage Zones in Fiber
Reinforced Composite Laminates," Journal of
Composite Materials, Vol. 9, pp. 266-287 (1975).
Acknowledgment
This work was supported in part by the National
Science Foundation through grant CDR 8803017 to the
Engineering Research Center for Intelligent
337
American Institute of Aeronautics and Astronautics
Downloaded by UNIVERSITY OF FLORIDA on October 25, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1996-1354
Table 1: Material properties of unidirectional AS4/3501-6 graphite epo.xy
E,
E2
G12
G, 3
G23
(GPa)
(GPa)
(GPa)
(GPa)
(GPa)
138
9.65
5.24
5.24
3.24
V, 2
V[3
v':3
0.3
0.3
0.49
Table 2: Fracture toughness of AS4/3501-6 graphite epoxy laminates
Fracture Toughness
Laminate
Stress ratio
KQ
n
Configuration
(MPaVm)
Fracture Toughness of
o° ply
K° (MPaVm)
[0/90/±45] s
44.83 ± 3.05
2.58
115.66
[±45/90/0] s
40.28 + 1.87
2.58
104.43
[90/0/+45] s
41.25 + 1.46
2.58
106.43
[0/±15] s
90.82 ± 4.01
1.12
101.81
[0/±30],
60.84 ± 3.14
1.66
101
[0/±45] s
45.83 ± 2.17
2.32
106.32
58.3l± 5.30
1.87
109.04
37.48 ± 0.43
3.2
119.81
32.42± 0.6
3.82
123.64
[0/90] 2s
[+45/0 / ±45]s
[±45,
/0/±45l-U
I
*
338
American Institute of Aeronautics and Astronautics
Downloaded by UNIVERSITY OF FLORIDA on October 25, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1996-1354
Copyright ©1996, American Institute of Aeronautics and Astronautics, Inc.
Downloaded by UNIVERSITY OF FLORIDA on October 25, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1996-1354
Copyright ©1996, American Institute of Aeronautics and Astronautics, Inc.
Downloaded by UNIVERSITY OF FLORIDA on October 25, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1996-1354
Copyright ©1996, American Institute of Aeronautics and Astronautics, Inc.
Downloaded by UNIVERSITY OF FLORIDA on October 25, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1996-1354
Copyright ©1996, American Institute of Aeronautics and Astronautics, Inc.
Downloaded by UNIVERSITY OF FLORIDA on October 25, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1996-1354
Copyright ©1996, American Institute of Aeronautics and Astronautics, Inc.
Downloaded by UNIVERSITY OF FLORIDA on October 25, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1996-1354
Copyright ©1996, American Institute of Aeronautics and Astronautics, Inc.
Downloaded by UNIVERSITY OF FLORIDA on October 25, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1996-1354
Copyright ©1996, American Institute of Aeronautics and Astronautics, Inc.
Downloaded by UNIVERSITY OF FLORIDA on October 25, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1996-1354
Copyright ©1996, American Institute of Aeronautics and Astronautics, Inc.
Документ
Категория
Без категории
Просмотров
2
Размер файла
7 339 Кб
Теги
1354, 1996
1/--страниц
Пожаловаться на содержимое документа