DAMAGE TOLERANCE OF COMPOSITE HONEYCOMB SANDWICH PANELS
UNDER QUASI-STATIC BENDING AND CYCLIC COMPRESSION
by
MATTHEW CLAIRE TAYLOR
M.S., University of Southern California
(1986)
B.S., University of Minnesota
(1980)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS OF THE
DEGREE OF
MASTER OF SCIENCE
IN AERONAUTICAL AND ASTRONAUTICAL ENGINEERING
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 1989
Copyright
Matthew C. Taylor
1989
The author hereby grants to M.I.T. permission to reproduce and
distribute copies of this thesis document in whole or in part.
Signature of Author
Z-
W-vw
LOW,,----
--
.
Department of Aeronauticg and Astronaueics
Certified by
Professor James W. Mar, Thesis Supervisor
D Wtment 4,earonauticsjand Astronautics, M.I.T.
Accepted by_
-
_
W;
k~
MV-40
~~ -
-
-
-
----
--
IN lr~fofessor Harold Y. Wachman
A1t
par tment
Committee
JUN 07/ 1989
UBRARIM
WITHDRAW
M.I.T.
L1BRA4RI6
ABSTRACT
DAMAGE TOLERANCE OF COMPOSITE HONEYCOMB SANDWICH PANELS
UNDER QUASI-STATIC BENDING AND CYCLIC COMPRESSION
by
Matthew Claire Taylor
Submitted to the Department of Aeronautics and Astronautics
on May 19, 1989 in partial fulfillment of the requirements
for the Degree of Master of Science
The damage resistance and damage tolerance of minimum
gauge face sheet sandwich panels subjected to quasi-static
four point
bending and cyclic column
compression, was
experimentally investigated for a graphite/epoxy plain weave
fabric and Nomex honeycomb core. Face sheets with [0/901,
[+-45],
[0/901s, and
[+-45]s layups were constructed from
AW193PW/3501-6
prepreg graphite/epoxy
fabric and
three
thicknesses of Nomex honeycomb, 1.0", .687" and .375". Four
point bending specimens
(2.75" x 14") were constructed with
three core thicknesses. Undamaged specimens were constructed
with a 2" Nomex test section bounded by aluminum honeycomb
core for load point reinforcement.
Damage was inflicted with
a spring propelled rod (.5" diameter hemispherical tup; .105
slug) at five levels of kinetic energy.
Visual and x-ray
inspection
measurements
were made
to
assess
damage.
Quasi-static four point loading provided failure moment, face
sheet buckling stress and specimen deflection data. Damaged
and undamaged column specimens (3.25" x 14") with reinforced
grip
sections
were
tested
for
fatigue
life
under
compression-compression cyclic loading
(R =.1).
Results
indicate that damage resistance increases with face sheet
thickness and panel thinness. Residual strength of the 2 ply
face sheet is dramatically reduced (0/90, 50 %; +-45, 30 %).
The Nomex core limits ultimate bending moment in undamaged 2
ply specimens and all 4 ply specimens, with or without damage.
Limited fatigue tests indicate a tremendous high load bearing
longevity for undamaged 0/90 specimens. Notch sensitivity of
the damaged 0/90 specimen cuts its load capability by at least
half. Notch insensitivity of the damaged +-45 specimen allows
for 60% of critical load to be carried to .5 million cycles.
Thesis Supervisor:
James W. Mar
J.C. Hunsaker Professor of
Aerospace Education
AKNOWLEDGEMENTS
I would like to thank all those people who have made
this work possible. Captain Robert W. Sherer and Commander
James G. Ward gave me moral and financial support for this
extracurricular study over the last three years. My thanks
to Carl Varnin and Simon Lie who got me started in the TELAC
lab and made me feel welcome. I extend my special gratitude
to Al Supple who has lead me through many a trying day in
the lab, fixed the computer for me and brought me back "on
line" as well. Al was there always willing to help in every
way.
A very warm and heartfelt thankyou is extended to
Professor James Mar who got me interested in composites two
years ago and offered an avenue of study that is closed to
most part time students. Professor Mar's friendliness and
helpful instruction will always represent M.I.T. to me.
Aknowledgements
would never
be complete
without
mentioning the "worker bees" - The UROPers. I was lucky to
be stuck with such a fine group. All hand selected so they
had to call me "Sir". My thanks to Dave Wright who stepped
in to help when I needed it down the stretch.
My warmest
appreciation and gratitude is extended to Chantal Moore who
helped me break over a hundred specimens and slugged through
hundreds of computer files, always producing a polished
result.
My eternal appreciation and gratitude has been
earned by Teri Centner and Cristina Villella who upon
hearing Paul Lagace match their names with me, said "Oh no..
we'll have to call him Sir ". They didn't have to say the
"Sir" word in the lab, as long as they worked.
And they
did! Teri and Cristina constructed specimens through the
summer while I was called away to summer training. They did
everything that could have been asked for the last 13
months.
I couldn't have finished without the dedication
demonstrated by these four fine young people.
I am lucky to have three young ladies at home that have
earned this degree through as much or more sacrifice as I.
My lovely daughters, Autumn and Madeline have never known
their father when he hasn't had a book in his hand. They
tried so hard to leave me alone to study, but often it
wasn't enough and I barked at them.
This is the price I
wish I hadn't paid for this degree.
I can only claim part
ownership to this degree. My wife April has put in as much
sweat, work and frustration as I have. She has raised the
girls and kept up the house without me. She has consoled
me, kicked me in the pants and even used child psychology to
keep me going. She has typed 99%
of this thesis to help me
end my ego experience.
I hope someday I can repay her.
Until then, April you have my eternal loving gratitude and
respect.
FOREWARD
This work
for
Advanced
was conducted
Composites
at the
(TELAC)
Aeronautics and Astronautics at
of Technology.
under
in the
department
of
the Massachusetts Institute
The work was sponsored by Boeing Helicopters
purchase order
Steve Llorente.
Technology Laboratory
TT 70935.
The
project monitor
was
TABLE OF CONTENTS
CHAPTER
Page
LIST OF FIGURES........................................ 8
· · · ·
.10
· · · ·
.11
· · ·
.14
LIST OF TABLES.........
· ·
NOMENCLATURE ..........
· · ·
1
INTRODUCTION .....
· ·
2
PREVIOUS WORK............................
3
4
· ·
·
· ·
·
.17
........
.17
2.1
Backgound...........................
2.2
Impact Damage and Residual Strength Studies. .17
2.3
Impact Damage Effect on Longevity...
e......e
.21
2.4
The Investigation....................
........
.23
........
ANALYTICAL MODELS........... ....................................
24
3.1
Introduction........... ....................................
24
3.2
Stress-Strain Relations in an Orthotropic
Laminate....................... . .......
.24--
3.3
Stress-Strain Relation for Arbritrary Lami
.27
3.4
The Woven Lamina .....................
.32
3.5
Stress-Strain Variations Within a Lamina..
.33
3.6
Beam Deflection Under Transverse Loading..
.38
3.7
Four Point Beam Bending Deflection........
.42
3.8
Flexural Stiffness of the Sandwich Panel..
.43
3.9
Local Buckling of Face Sheet and Core .....
.47
3.10 Residual Strength Model....................
.51
EXPERIMENTAL PROCEDURES ............
.59
"QOO'O'O0""
4.1
0 9
0·
Experimental P.arameters......
.59
"'OOOO''''"
...........
4.2
0 0
Test Program................
o
.60
4.3
Specimen Description ........................... 63
4.4
Manufacturing Procedures........................66
4.4.1
Layup ............................ ...........66
4.4.2
Laminate Cure ........................... 67
4.4.3
Post-Cure.................................69
4.4.4
Trimming .................................. 69
4.4.5
Core Assembly..............................70
4.4.6
Bond Cure................................... 70
4.4.7
Load Tab Cure..............................71
4.4.8
Panel Machining ........................... 72
4.4.9
Coupon Machining..........................72
4.4.10 Strain Gauging............................73
4.5
5
Testing Procedure and Data Acquisition......... 75
4.5.1
Impact Results ............................. 75
4.5.2
Damage Assessment.........................78
4.5.3
Four Point Bending........................ 79
4.5.4
Static Panel Compression...................83
4.5.5
Core Compression and Indentation .......... 84
4.5.6
Panel Fatigue..............................86
EXPERIMENTAL RESULTS ................................. 88
5.1
Impact Test Results ............................ 88
5.1.1
Impact Velocity and Energy ................ 88
5.1.2
Impact Force .............................. 89
5.1.3
Impact Energy............................. 93
5.2
Damage Assessment .............................. 95
5.3
Quasi Static Four Point Bending ............... 102
5.3.1
Failure Modes...... · · · · · · · · · · · · · · · · · · · · ~·103
5.3.2
Panel Deflection Under Load. ............. 107
5.3.3
Failure Stresses
Panel
5.5
Core Compression Results.....
5.6
* aa
· · ·
·
............. 109
· · ·
·
..............114
............. 114
Core Indentation Results ,··~
Panel Fatigue Results .......
· · ·
·
............. 115
CONCLUSIONS ...............................
.117
6.1
.117
6.2
6.3
7
Compression Results.
............. 108
StrAin U~··V
5.4
5.5.1
6
AndA
u
&&·u
Impact Results .......................
6.1.1
Impact Force.....................
.117
6.1.2
Force - Time History.............
.118
6.1.3
Impact Energy and Damage Assessme
.119
6.1.4
Damage ...........................
.120
Residual Strength.....................
.122
6.2.1
Analytical Comparisons...........
.122
6.2.2
Failure Stress and Impact Energy.
.123
6.2.3
Damage Propagation...............
.125
6.2.4
Mar - Lin Relation...............
.128
Panel Longevity.......................
.130
CONCLUSIONS AND RECOMMENDATIONS.
.132
7.1
Conclusions................
.132
7.2
Recommendations ............
.133
REFERENCES.
•..•.......•.•.•....oee.
.135
APPENDIX A: Experimental Results; Tables and Figures. .137
APPENDIX B: Sub-Lamina Geometry of the Wo ven Ply.....
.177
APPENDIX C: Panel Deflection Graphs
.181
LIST OF FIGURES
Figure 3.1
Global Coordinate System ..................... 25
Figure 3.2
Ply Orientation With Respect to
Loading Axes............................
27
Figure 3.3
Fabric Tow Geometry Within a Lamina .......... 32
Figure 3.4
Coordinate and Displacement Orientation......34
Figure 3.5
Geometry of Deformation in the z-x Plane.....34
Figure 3.6
Anticlastic Curvature Under Pure Bending.....40
Figure 3.7
Four Point Beam Loading......................42
Figure 3.8
Panel Side View...............................46
Figure 3.9
Honeycomb Core Bending and Loading
(a) Panel Element Bending.....................47
(b) Face Element Loading and Curvature.......47
Figure 3.10 Core Deformation.............................48
Figure 3.11 Cross Sectional View of a Dimpled Face
Sheet Under Compressive Loading ........... 50
Figure 3.12 A [0/901 Panel With Arbitrary
Face Sheet Damage Under Compression ....... 52
Figure 3.13 Mar - Lin Relation with Corrections... ....... 58
Figure 4.1
Basic Sandwich Panel .................. ....... 64
Figure 4.2
Reinforced Sandwich Panel......... .....
Figure 4.3
Static Compression Sandwich Panel.
Figure 4.4
Fatigue Sandwich Panel........... ............ 65
Figure 4.5
Laminate Cure Layup............... ............ 68
Figure 4.6
Laminate Cure Cycle............... ............ 69
Figure 4.7
Panel Bend Cure Layup ............. ............ 71
Figure 4.8
Static Core Compression and Indent ation Coupon73
Figure 4.9
Strain Gauge Configurations....... ............ 74
..... 64
Figure 4.10 Specimen Holding Jig .......................... 76
.
Figure 4.11 FRED's Striking Unit................. ......... 77
Figure 4.12 FRED; Impacting Rod Mechanism........ ......... 77
Figure 4.13 Four Point Bending Installation ...... ......... 81
Figure 4.14 Face Sheet Damage Photography........ ......... 83
Figure 4.15 Panel Compression Test............... ......... 84
Figure 4.16 Core Compression Test................ ......... 85
Figure 4.17 Core Indentation Test................. ......... 86
Figure 5.1 Impact Velocity/Energy vs. Spring Disp lacement.89
Figure 5.2 Force-Time History:
Impact Spectrum. ......... 91
Figure 5.3a Impact Spectrum - Damage............. ......... 92
Figure 5.3 Force-Time History:
Damaging Impacts ......... 94
Figure 5.4 Cross Sectional Damage Projection.... ......... 96
Figure 5.5 Damage Diameter vs. Impact Energy ............. 98
Figure 5.6 Damage Area vs. Impact Energy........ ......... 99
Figure 5.7 Damage Diameter vs. Impact Energy, 1" Panels..100
Figure 5.8 Damage Area vs. Impact Energy, 1" Panels.....101
Figure 5.9 Compressive Fracture Modes for Damaged
Face Sheet................................104
Figure 5.10 Core Failure Modes ........................... 107
Figure
5.11
Failure Stress vs. Impact Energy.............110
Figure 5.12 Failure Stress vs. Impact Energy, 1"Panel.....111
Figure 5.13 Failure Stress vs. Damage Cross Sectional....112
Figure 5.14 Failure Stress vs. Damaged Cross Section ..... 113
Figure 6.1 Longitudinal Section of Dimple Indentation...127
Figure 6.2
Mar - Lin Residual Strength; +-45............ 129
Figure 6.3
Mar - Lin Residual Strength; 0/90............ 129
Figure B.1 The "Imaginary Bi-Ply" ....................... 177
Figure B. 2
Tow Deflection Angle Within Weave............17•)
LIST OF TABLES
Table 3.1
Material Properties of AW 193PW/3501-6 .........29
Table 3.2
Reduced Stiffnesses ........................... 29
Table 3.3
Invariant Values for AW 193PW/3501-6 .......... 33
Table 3.4 Reduced Stiffnesses Based on Orientation......33
Table 3.5
Stiffnesses for Orthotropic Plain Weave
Laminates...............................................38
Table 4.1
Four Point Bending Residual Strength
Test Matrix ...................... ......... 61
Table 4.2
Undamaged Panel Strength Test Matrix. ......... 62
Table 4.3
Panel Longevity Test Matrix................... 66
Table 5.1
Maximum
Table 5.2
Maximum Impact Forces................ ......... 90
Table 5.3
Dimple Lengths at Fracture Load ...... ......... 105
Table 5.4
Mean Face Sheet Failure Stresses ..... ........ 109
Table 5.5
Core Indentation Results by Cell
Row Direction...................... .........114
Table 5.6
Residual Strength Estimates..........
Table B.1
Tow Bending Within Fabric............
Impact Energy............... ......... 89
........ 115
·
· ··
·
rl.·
NOMENCLATURE
47
stress
o
£
Y
C
S
shear stress
strain
shear strain
stiffness matrix
compliance matrix
V
Poisson's ratio
E
Q0
G
T
Ui
8
t, t,y
a
x,y,z
u,v,w
K
Nf,Nx
M,
f
h
W,b
Aii
B6
Dq
r,R
I
s
P
I
L
Young's modulus
reduced stiffnesses matrix
shear modulus
transformation matrix
invariant constants
ply orientation
lamina thickness
deformation angle
cartesian coordinates
cartesian displacements
curvature
force/unit width in face sheet
moment/unit width
face sheet thickness
panel thickness
panel width
extensional stiffnesses
coupling stiffnesses
bending stiffnesses
radius of curvature
moment of inertia
curved path coordinate
transverse load
moment arm
panel deflection section
8SrA
panel deflection (outboard) angles
q
d
D
load / unit length
rupture diameter
dimple axis length
y,,y, bending region coordinates
Ic
U
Wet
TT
Hc
S
n
N
R
modal amplitude of generalized displacement
core modulus (in z direction)
potential energy
external work
total energy
fracture parameter
standard deviation of a sample
population
fatigue cycles
fatigue ratio
11
Super-scripts:
dz/dx z
neutral plane or axis
Sub-scripts:
Ixx;
f
cr
d
x,y,z
1,2,3
0
,yy
dz/dx z ; dz/dyz
face sheet
critical
deformed
direction of action with respect to specimen
direction of action with respect to material
undamaged, control value
Intentionally left blank for notes:
13
CHAPTER ONE
INTRODUCTION
The sandwich structure has been studied intensively for
the past fifty
years in order to understand
strain mechanics; its
from
cardboard
surfaces.
simple design is used
boxes
The
to
supersonic
sandwich structure
virtually any material in order
The three
face
in-plane loads
sheets.
maintaining
The
core
the load
and a
bearing
faces.
The
constructed from
are two
face sheets
core bonded
between the
structural stability
face
separation distance, along with
the
control
to satisfy its desired use.
provides
parallel to the faces and
for everything
aircraft
can be
components for construction
which carry
its stress and
sheets at
a
by
constant
maintaining shear stiffness
normal stiffness perpendicular to
face sheets
carry
the
compression
and
construction,
the
tension loads that resist panel bending.
Beyond
the
beauty
of its
simple
sandwich panel's reason for being
to weight
ratio and bending
lies in its high strength
stiffness.
Thus
the sandwich
structure has been applied to aircraft construction wherever
possible and
feasible.
in whatever
Face
fiberglass, and
sheet
combination of
materials
metals.
The
materials thought
have
core has
included
consisted of
wood,
balsa
wood, pine, glue pulp, polymen foam and light weight metals.
The need
to reduce weight led
to the invention
of another
structural form - the honeycomb core.
With
the
advent
of
advanced
14
filamentary
composite
materials
which
advantage
and
possess
the
honeycomb cores; it
weight efficient
for
exceptional
development
durability.
phenolic
composite honeycomb
The honeycomb
Nomex
stiffness, and
and
Nomex
construct extremely
core sandwich
Laminate
specific loading
or
aluminum
is now possible to
aerospace application.
tailored for
of
strength-to-weight
face
panels
sheets can
orientations, strengths
core can be made
material.
It
shearing resistance
be
and
from aluminum,
provides
through its
flexural
thickness,
shear modulus, and density, respectively.
Because honeycomb
core
for part
of
the
surface, the durability aspect
of
HCP
panels
(HCPs) are
aircraft's external
design is
now on a par
typically
used
with strength, stiffness
and light
weight.
"Durability" is the combination of structural longevity
and economics of construction
and repair.
The filiamentary
composite fabric facilitates simplified constuction and thus
economic production.
Structural longevity
refers to damage
resistance, damage tolerance, and fatigue life.
composites have
exceptional undamaged
their
heterogeneous
their
failure
composition and
criteria
Filamentary
characteristics, but
brittle
complicated and
nature
specific
to
make
the
structure and its accumulated damage.
This study examines the damage resistance and tolerance
of a
specific graphite epoxy/honeycomb core
under
fatigue
quasi-static
loading.
bending
The
and
objective
sandwich panel
compression-compression
is
to
determine
the
characteristics of
with
its maximum
the panel's resistance to
capabilities
for
construction and load orientation.
damage, along
various parameters
of
CHAPTER TWO
PREVIOUS WORK
2.1 BACKGROUND
A great effort has been made
to
determine
filamentary
that tend
the
fracture
composites.
in the last fifteen years
principles
Work
and
has focused
to degrade composite
mechanics
of
on the
factors
laminate structure
and the
composite material structures.
Composites have some
unique problems in that
susceptible to damage at low
as
might happen
Further,
this
detectable.
levels of imparted energy such
from runway
damage
Often
composite panel
from
the
they are
debris, tool
impact
damage
is below the
may
drops or
not
inflicted
to
hail.
be
visually
a
sandwich
surface between plies
and at
the laminate core interface.
2.2 IMPACT DAMAGE AND RESIDUAL STRENGTH STUDIES
Many
tests
on
infliction
investigators
composite
at
have conducted
sandwich panels
prescribed
energy
to
controlled
impact
determine
damage
levels.
Oplinger
and
Slepetz [11 impacted graphite and S-glass epoxy HCP's with a
2 inch diameter steel ball.
was
very brittle
strain
to fracture
S-glass).
They found that graphite epoxy
compared to
(less than
The Nomex was found
S-glass because
1%
for G/E,
of its
about 3%
low
for
crushed under the impact due
to the graphite face rupturing, while the S-glass face sheet
bridged the crushed core's indentation
absorb
some
of
the
impact.
The
to remain intact and
graphite
face
sheets
absorbed energy by progressive fracture along planes defined
by the
laminate fiber
capability
orientations due
relative to
the indentor
point out the need for a
graphite to be
core
to the
radius.
weight penalty.
sheet of graphite
The
authors
larger strain to failure level for
damage resistant and suggest
(more dense)
low strain
will prevent
Oplinger et al
that a tougher
large impact
damage at
a
also suggests a hybrid face
and S-glass to improve
resiliency at the
cost of ultimate strength.
Rhodes [2]
also recommended a
means of raising the damage
structures.
be more
susceptible to
indentation
(crushing)
panels under
epoxy to Kevlar-491 epoxy
Once again
breaking.
during
stresses in the face, which
impacted
as a
threshold for graphite sandwich
He compared graphite
under projectile impacts.
hybrid face sheet
graphite was found to
Rhodes
impact
found that
causes
high
precipitates buckling.
compression and
was
able to
core
local
He also
cause
buckling at impact energy levels well below that required to
initiate visible damage.
Rhodes suggests
did Oplinger and Slepetz, as well
reduce the "bearly visible
Rhodes
maintains that
a stiffer core as
as thicker face sheets to
impact damage" (BVID) threshold.
a visual
inspection
for damage
is
inadequate.
The
work of
recommendation.
Adsit and
Waszezak
After performing
[31 supports
impacts
Rhodes
with stones,
a
.63cm tip radius and 2.54cm tip
radius, Adsit et. al. found
a panel strength reduction of up
visible impact damage) level.
decreased
as impact
impactor head.
(88kg
Compressive residual strength
energy
was
increased, regardless
The Heat Resistant Phenolic
per cubic
resulted
to 50% at the BVID (barely
meter)
in core
was
crushing
not impact
and
honeycomb core
resistant,
face sheet
of
which
delaminations.
Both forms of damage cause a localized loss of stability and
make face wrinkling more possible.
that distributing the
(ie:
Adsit et. al. also found
impact energy over a
broader surface
.63cm to 2.54cm impactor radius) will add approximately
25% to the compressive residual strength.
that impact
with no
energy with the wide
increase in panel
Data also implies
blunt tip can
damage or reduction
be doubled
in residual
strength.
Gwynn
and
Halpin (5]
O'Brien
[41 and
each arrived at
Husman,
the same
Whitney
conclusion regarding
impact energy's effect on compressive failure stress.
is a minimum
plateau of residual strength
where greater impact energy will
Husman et.
al. [5]
higher, the residual
hole of similar
thick
laminates
laminates, after
laminate
size.
have
face sheet
at penetration and
failure stress approximates that
Gwynn et. al.
each is
thickness.
(minimum stress)
less than
For velocities
higher
of a
[4] demonstrates that
failure
impacted at
Thicker
There
not create further damage.
predicts this at
penetration velocities.
and
strains
the same
laminates
than
thin
energy per
dissipate
impact
matrix cracking
energy through
stretching
of
Delaminations
fibers
because
within the
peanut shaped
direction in
impact
resistance of
AS4/3501-6
materials;
Nomex
and
and
while
stiffness.
Bernard
laminates
and debonds
aluminum honeycomb.
They
1 Joule
The
in
energy;
and confirmed
amounts of debonding
between
reduction
of impact
core
Panels with stiff cores
also implanted
stiffness
Overall, the buckling
core
Nomex debonding
panels.
(+-45/0]s
different
buckling.
against impacted
and a
three
at .4 Joules;
aluminum had equal
damage
panels utilizing
level at
crushing to be cell wall
sheet
filament
examined the
damage threshold
like the
with the
Bernard and Lagace [6]
epoxy
the BVID
The delaminations are
of localized
Rohacell, Nomex
established
associated
again, a source
sandwich
graphite
and
displacement.
were also
(long axis)
once
buckling instability.
impact
cracking.
and oriented
each ply.
of
face sheet
with impact induced matrix
local bending
and not
increases
and face
with
delaminations
face
and core
result was
to
a loss
buckling stress
load dropped by 8 to
in
core
the
compare
in local
threshold.
19% for damaged
panels and was found to be independent of the core material.
This result may simply be a coincidence, because it violates
Lie's
panel;
[71 analytical
which
calls
(Young's modulus
buckling
for
the
equation
flexural
times the beam's
for an
rigidity
moment of
undamaged
term
EI
inertia).
If
the cores were the same thickness this could be explained by
negligible core density and stiffness compared to the face
20
laminates.
measured the
dynamic strains
levels and
three energy
performed impacts at
Lie [7]
of the
panel during
impact.
With this data he compared it against an analytical computer
model derived from Hertzian
contact theory.
of
Nomex
various thickness
residual strength
afore mentioned
(all
The
and compared
and fail
with the
face sheets
at constant
[0/901 laminates were
for
the Mar-Lin
He found the [+-451
failure ocurred at stress levels
stress.
tested
critical buckling equation and
notch insensitive
stress.
cores) were
under compression
residual strength relation.
to be
Damaged panels
net-section
notch sensitive
and so
lower than the net-section
Lie's impact tests found ,7 ft-lbs to be the damage
threshold
where core
crushing begins,
followed by
matrix
cracks, delamination and fiber rupture at 1.5 ft-lbs.
2.3 IMPACT DAMAGE EFFECT ON LONGEVITY
Ramkumar
impacts
on
[8)
examined
laminate
columns
the
effect
of 42
of
and
48
low
velocity
plies.
His
conclusions are:
-Tension provides less threat to impact damaged
laminates.
-Delaminations propagate to cause early failure in
compression-compression fatigue loading.
provides the lowest strain
R =
failures.
This also
(Fatigue test
oo ).
- Recommends ultrasonic imspections to
detect
delamination propagation.
Componeschi et. al.
an indicator of
[9]
studied stiffness reduction as
fatigue damage.
He concludes
that [0,901s
laminates don't experience a loss of longitudinal stiffness.
The stiffness is degraded when the 90 degree ply is damaged.
Camponeschi et.
laminates
al. concludes
reduces
to
significant damage
that
the major
an
that Ex
in quasi-isotropic
equilibrium
occurs until
degradation
failure.
in
state
They
where
no
also claim
shearing stiffness
occurs
early in the panel's fatigue life.
"Sudden - Death"
proposed by Chou
and "Degradation" fatigue models were
et. al.
[101 to
predict residual strength
throughout the laminate's fatigue life.
the "Sudden -
Death" model where residual
degrade, provides
majority
describes
of
a good model
on-axis uni-plies.
increasing
fatigue life.
Tests indicate that
strength
It predicts
strength doesn't
for laminates with
The
a large
"Degredation"
reductions
model
throughout
residual strength
the
for off-axis
uni-ply laminates.
Finally,
Reifsnider,
Schulte and
Duke
[111
propose
three regions of damage: a stage of adjustment; coupling and
growth; and final damage to
failure.
Fatigue failure modes
and damage development is described for each.
Asit [31
with a necked
that
performed fatigue testing on
test section.
oscillated at
sections.
1 Hz.
He used a 4
to fatigue
sandwich panels
point bending jig
impacted panel
test
Results indicate that increases in impact energy
shorten the specimen fatigue life,
and ruptured fibers from
impact have a greater effect on life than delaminations from
a blunt impact.
2.4 THE INVESTIGATION
This investigation follows
In
order
to
maintain a
the work of Simon
consistent
data
base,
Lie [7].
similar
materials, dimensions, impact and test methods are employed.
Residual strength will
used by Adsit
follow-on
Similar
fatigued
[3].
study
under
measured.
Lie's
will
be
static
strength
impacted,
compression-compression
various peak loads.
bending test as
However, the fatigue portion
to
specimens
be tested through a
will be a
experiments.
examined
and
(c-c)
loading
then
at
Damage propagation will be observed and
CHAPTER THREE
ANALYTICAL MODELS
3.1
INTRODUCTION
This chapter
examines the properties and
orthotropic symmetric laminates and
sheets of
their influence as face
a honeycomb sandwich panel.
will be
based on previous
plate theory.
Material properties
tests and
The characteristics of
in this investigation will be
mechanics of
classical lamination
the woven lamina used
discussed.
Stress and strain
relations within the laminate will be developed and extended
to
the
panel
under
pure
homogeneous beam bending
bending.
panel
derivation
A residual strength
damage propagation under compression
bending will
be discussed.
And
of
the four -
and its application to
point bending problem will be reviewed.
face sheet
The
because of
finally, a
global
buckling model for one face sheet will be proposed.
3.2
STRESS - STRAIN RELATIONS IN AN ORTHOTROPIC LAMINATE
Principle material directions will be oriented to the
three dimensional global coordinate system x, y and z,
defined by test specimen geometry, illustrated in Figure
3.1, Global Coordinate System.
Specimen axes will be
parallel or coincident to an orthogonal coordinate axis as
follows:
x y z -
Principle
longitudinal
transverse
normal (to panel face)
material
directions
24
or axes
will
be
assigned
numbers
1, 2,
and
3.
The
direction
of
filaments in
a
uni-ply or the "fill" filament direction in a woven ply will
be
refered
to
as
the principal
perpendicular axis to
be axis 2.
material
1 which lies in the
axis
1.
The
ply's plane will
The "right hand rule" will define the third axis
which is normal to the reference ply.
notation using
x, y, z
and 1, 2,
used throughout this report to
Tensor and contracted
3 as subscripts
will be
define directions and states
of stress - strain.
Ar-
Figure 3.1 Global Coordinate System
Jones [121 provides a discussion of background material
on
this
subject.
assuming that
0,= 0,
reasonable for
allows
for
A
a thin
the
constants from the
plane stress
Tz.= 0,
T,= 0.
laminate.
reduction
state
of
An
27
This
- = C ij
defined
by
assumption is
orthotropic material
independent
stiffness matrix Cij.
case (anisotropic material).
is
for
stiffness
the general
Where;
i,j = 1,...6
(3.2.1)
r
0'g
C1 CIt C,5
C2 , Czz Cz
2
crt
Cst, Czz C 33
0
0
0
(T
r,
14&
be
can
=
the
with
further
reduced
0
0
0
0
0
0
0
0
0
0
0
o
0
0
0
C,,, 0
CSr
0
0
C
0
plan e
£0
(
(3.2.2)
stress
state
assumptions.
I 0
CitC C,
,
0
C,
C2 c, 0
O;r
Lo= C7
Tt
0
Note:
0
EI
'
(3.2.3)
C&
,
C,, = C,, due to orthotropic symmetry.
The above relation can also be expressed in the compliance
form.
c,
= S(j
Sq ~
t
S,,
=
S,
0
S-
S
S,
0
Where:
/E,So==
Where: S,, = 1/E
/E,
SIZ = - 2I/EI = -,/E
l
z
S,= 1/E
S6S=
Ez z
I
S6& 1/G
1
orthotropic plane stress state
The stiffness matrix for the
from the reduced stiffnesses
be determined more easily
can
(3.2.4)
Cr
form.
0"?
0,,
=i
IL, 0t2
0
a,
0
O
E
0
Eza
Q
(3.2.5)
Where the reduced stiffnesses are:
Q,1 = -SIZ /(S S -sL, )
Set/S
Q,
Qt == SZ.
/ ( S,,1set--s,:,
S-St ))
QIM27
Sit
/(Suit
5
Q, = i/s,
f2S.~
(3.2.6)
In terms of engineering constants
Q,, = E,/(1 -~'~,
Qz
E2/1(I - Vt•
,)
,I
~.
Q
E ( EV/(1
=
=
VZ2,)E / (I
)
(3.2.7)
G,
Thus four independent material properties,
/
E, Ez,
V,2
and G
will determine the
stress - strain relations
orthotropic lamina".
and 2
in a "special
That is, the principle material axes 1
are aligned with the
natural body loading axes x and
y.
3.3
STRESS - STRAIN RELATION FOR ARBRITRARY LAMINA
3.3.1
Orientation
A stress - strain relation must be developed for lamina
constructed from orthotropic plies
with
respect
directions.
to
In this
facesheets will
in
the
the
of arbitrary orientation
geometrically
natural
experimental work, 2 and
be subjected to compressive
direction
of
the
specimen's
Individual ply orientation can range from
coordinate
4 ply lamina
loads oriented
longitudinal
-90
to +90
axis.
with
respect to the longitudinal or loading axis, x.
01
0X
X
Figure 3.2
Ply Orientation With Respect to Loading Axes
Stress and strain transformations express the
stresses
and strains of an x-y
system.
coordinate system in a 1-2 coordinate
The transformations are commonly written as
(TY = IT]
(T,
where
= IT]
E
wcos
IT]
sin28
cos z8
e
sin
=
Ez
(3.3.1)
2sinecose
-2sin6cos0
-sin9cos8
sinScosO
cos 6
sin'I
-2sinecos8
sin 8
cos 2 8-sin z
and the inverse
T
TI
=
sinGcos8
cos2
-sinecos
2sinecos8
cos
j
?8-sin
The reduced stiffness matrix for any ply orientation 8 can
be found through matrix multiplication.
[i] =
where
[TI "T
TIT]-' [Q
(3.3.2)
Qij : transformed reduced stiffnesses
inverse transpose of IT]
(TITT:
The orthotropic lamina becomes generally orthotropic after
transformation.
cry
1
0
Ey
(3.3.3)
The stiffness constants are simplified by Tsai and Pagano
[13].
Q,,
= U, + U z cos 28 + U7
Off = U, - U3
cos 46
cos 40
Qzz= U, - U2 cos 28 + U~
cos 48
Qr, = (1/2)U 2 sin 26
+ U3 sin 48
Ott= (1/2)U z sin 28
- U3 sin 40
Q&= U. - U3 cos 4e
28
(3.3.4)
in which
U, = [3Q,, + 3Q0
Uz
=
[Q,, -
U
= [Q",, + Q22 -
Q0/
+ 2Q,
2
20,, -4Q64]/
UY =
IQ,, + Qu +
6
Q,z -
=
[Q,, + Qzz -
2
Q,
U-
8
(3.3.5)
4Q64]/
8
+ 4QC]/
8
the Q..are composed
Note that
8
+ 4Q4]/
of invariant terms U;
, which
are independent of ply orientation and dependent on material
stiffnesses, only.
Using material constants
determined for AW193PW/3501-6
graphite epoxy fabric, within
TELAC and Boeing Helicopters,
[Q] can be determined.
TABLE 3.1
Material Properties of AW193PW/3501-6 Graphite/Epoxy
EE
E,
TELAC
Boeing
so
2
8.72 Msi
9.30 Msi
9.09 Msi
9.36 Msi
Recall that
V1.E(9_qS)
.087
.050
2
2.99 Msi
3.00 Msi
.083
.050
,,E,z= 2)•1 E,
(8.72/9.09) .087 = .083 =
z,=
Et/E,
or
(9.30/9.36) .05 =
•r,
TELAC
B.H.
.050 = Vz,
TABLE 3.2
Reduced Stiffnesses
TELAC Values:
Q,, =
Q2z =
Qz =
9.09/(1-(083).087) = 9.16 Msi
8.72/(1-(.083).087) = 8.78 Msi
.087 (8.78) = .764 Msi
Boeing Values:
Q,, =
Q,,=
Q,a =
9.36/ (1- .05 ) = 9.38 Msi
9.30/ (1- .052) = 9.32 Msi
.05 (9.32) = .466 Msi
By
substituting
the
engineering
constants
into
the
compliance matrix and performing
transformation for a given
ply orientation with respect to the loading axis, we find:
- 22•,/E,)sin zcos 6 + 1/Esin 6
+ (1/G,
1/E,
= 1/E,cos 8
7 ,y=
Ex[VIz/E,(sin 9 + cos ~) - (1/E,
1/E
= 1/E, sin28 + (1/G,i
+ 2/E
1/Gxy= 2(2/E,
+1/Ez-i/G,)sinz6cos28]
- 2v,/E, )sin2 8cos 8 + 1/Ezcosv8
+ 4,1/E, - 1/G,f)sinz8cos 8
z
(3.3.6)
+ 1/G z(siny6 + cosvB)
did not measure G,, with a specific
Since this investigator
shear
(such
test
the
as
Shear
Rail
used to indirectly determine
relations will be
+-45 compression tests.
the
test),
above
G,, from the
was found to average 3.0 Msi by
E
Lie [71 and Boeing Helicopters.
By
substituting 8 = 45°and
Ex = 3.0 Msi, we have the following
1/E, = (1/E,
- 2jz/E,
+ 1/G,z + 1/Ez)/4
= 1/Ey
(3.3.7)
where G,z is the only unknown.
Solving for G,z
-I
GI = [4/E
x
- 1/E, - 1/E
z
+ 2Azf/E,]
(3.3.8)
and substituting:
TELAC values
Boeing values
Similarly, Gyp can
be found for any orientation
[2/E, + 2/E z + 4Vz1/E,
GVy= 4.10 Msi
TELAC
Since QG
now that G
For 8 = + 45ý:
is known.
1/GV ,=
G,1 = .887 Msi
G,
1 = .885 Msi
=
G,z
, all
- 1/G,I ]/
Boeing
2
+ 1/2 G,2
(3.3.9)
Gxy= 4.44 Msi
of the material constants, orientation
transformation equations and
stress
- strain relations are
available to calculate the stresses and strains within a ply
at any
given orientation
applied load.
invariant
respect to
This is facilitated
reduced
Substituting
8, with
of
with the Tsai
& Pagano
equations
(3.2.5).
stiffnesses
engineering
the axes
material
constants
into
the
invariant relations produces the following invariant values.
TABLE 3.3
Invariant Values for AW193PW/3501-6
U,
7.36
7.57
TELAC
Boeing
The
Uz
.19
.03
reduced stiffnesses
U3
1.61
1.78
Uq
2.37
2.24
calculated
UV (Msi)
2.50
2.66
from equation
(3.3.4)
using TELAC values are:
0,, =
=
z=
=,,
=
Q,&=
7.36 + .19 cos 28 + 1.61 cos 46
2.37 - 1.61 cos 48
7.36 - .19 cos 20 + 1.61 cos 48
(.19/2) sin 28 + 1.61 sin 48
(.19/27 sin 28 -ý 1.61 sin 46
2.5 - 1.61 cos 46
Reduced stiffnesses
(Msi units)
are calculated using TELAC
values, for
given orientations.
TABLE 3.4
Reduced Stiffnesses Based On Orientation
8
=
00
100
200
300
400
450
5,,
9.16
8.77
7.79
6.65
5.88
5.75
2,z
.76
1.14
2.09
3.18
3.88
3.98
12
8.78
8.41
7.49
6.46
5.81
5.75
0
1.07
-1.00
1.27
1.65
-1.52
2.22
1.48
-1.31
3.31
.64
-.46
4.01
.095
.095
4.11
Ots
OQ,
QO6
0
.89
Values are in Msi or 10' psi.
31
3.4 THE WOVEN LAMINA
Typical laminates are composed
stacked at various
principal axis
weave
lamina
"bi-ply".
of multiple "uni-plies"
orientations with respect to
for the laminate.
used
in this
The
the chosen
graphite/epoxy plain
research
is an
orthotropic
That is, each ply has two principle directions of
fiber orientation, which are approximately perpendicular and
have
center of
their
filament tows
fashion as
mass
in each
within
direction are
over and
they pass
in figure 3.3(a).
of graphite/epoxy
is woven
tows, each
populated
with load
As long
tightly with
cross-section of
as the fabric
will be
Note from
Sub-lamina geometry is discussed in Appendix B.
L
tow width +
:-::.-•
. .
..
\
':.:'
-...
:"::'
i
(a)
Figure 3.3
or gaps
well
figure
filaments are divided by the
central ply plane throughout the fabric.
central
plane
The
woven filament
no holes
a ply
bearing filaments.
3.3(b) that these load bearing
plane.
bent in a sinusoidal
under cross
tows, as depicted
between
the same
(b)
Fabric Tow Geometry Within A Lamina
3.5 STRESS - STRAIN VARIATIONS WITHIN A LAMINATE
For
will
it
thin laminates,
that
be assumed
lines
originally straight and perpendicular to the central surface
of the laminate, will remain straight and perpendicular when
the laminate is
extended, compressed or bent.
Kirchoff hypothesis for
classical
laminated
assumption is
that
the
plate
theory.
that shearing
central
laminates.)
plates and the basic
strains are
surface
rxz =
Thus,
The
will
be
= 0
yz
a
This is the
assumption of
result
of
neglected.
plane
and normals
this
(Note
for
flat
in the
direction are assumed to maintain constant length, so
Z
0.
0£=
The Kirchoff-Love hypothesis for thin shells introduces
laminate displacements u, v, and w for coordinate axes x, y,
and z,
The laminate
respectively.
occupies the
and undergoes deformations as illustrated
reproduced in
Figure 3.4 and
3.5.
x-y-plane
in Jones [12] and
From the
figure, line
ABCK remains straight under deformation (by definition).
Uc =
Subscript 0 indicates
Uo - Zec
(3.5.1)
a point on the
middle surface.
Line
ABCD also remains perpendicular to the middle surface, which
leads to
S=
Then,
the
wo/
displacement, u,
ax
at
(3.5.2)
any
point z
through
the
laminate thickness is
u
=
uo - z aw./ ax
By similar reasoning, v = v, - z bw,/ by
(3.5.3)
t zw
Figure 3.4 Coordinate and Displacement Orientation
--
#1
-[d
Z
1
undeformed cross section
Figure 3.5
deformed cross section
Geometry of Deformation in the z-x Plane
Non zero strains are defined in terms of displacements.
av/ by
Ey=
EX = bu/ bx
Placing the results
cy= au/3y + Zv/bx
of equations (3.5.3) into
(3.5.4)
(3.5.4), the
strains become:
EC= au o /?x - z( bwo/bxZ )
Ey=
v./by - z( awo/ay1 )
-
+ 6Vo /bx
J.= au o /ay
(3.5.5)
2z(a w./ax y)
Re-writing in matrix form, the strain variation equation is
-
5Ey=
Ky
Z
(3.5.6)
where the middle surface strains are
EY
Žuo/?x
=
v,/ay
(3.5.7)
and the middle surface curvatures are
=
Ky
Kry
By
2ý
substituting
variation
(3.5.8)
wa/'y
w,/axby
the
equation (3.5.6)
through
the
into the
thickness
strain
orthotropic stress
-
strain relation, equation (3.3.3); the stresses in any ply k
can be determined.
=
Since
Q*j
can
variations may
Z
;KY
LQ
be
different
not be
0
(3.5.9)
for
each
linear through
though the strain variation is linear.
ply,
the
the thickness,
stress
even
The force and moment per
on a laminate
unit length (or width) acting
is found through integration
of the stresses
in each layer or lamina through the laminate thickness.
f/2
N =1
fN f/2
Mx
=
0, dz
f f/2
0, zdz
-f/2
where Nx and M. are the force
and
My
are the
intergration of
through
force
the laminate
and moment per unit length. Ny
and
Ty through
for
(3.5.10)
moment
per unit
the thickness,
0y , and
T.,
width,
f.
1Ty
with
Integrating
(substituting
equation (3.5.9) into (3.5.10)), for both force and moment.
4
Nx
NY
Ny
zk
K
z*
f s.j
dz +
z
Ky zdz
z
K35
(
11)
(3.5.11)
M =
MY
1
k=l
E
zk
SJzdz
Ki
Ky
yI + fz IK
zk.,
k•
z
NMY
zk
zzdz
Kxy
(3.5.12)
where
the laminate
has m
middle surface strains
layers or
lamina.
and curvatures are not
Recall
functions of
z, but values which can be removed from the summation.
equations (3.5.11) and (3.5.12)
that
can be written as
Thus
E.
Nx
A,l
A,,
Ny
AMt
A ? I
NXY
AN
A6, I
B
But
B,1
(
BN
K1
KX
B
K J
B,
B,,
B tj
B,&
(3.5.13)
MX
B,
My
Bi
My
B&
B,
D12
IV
Y0+
B4
D24&
Kr
DIG
K
DZ
K
D
( KW)
(3.5.14)
where
m
Ai
'.1
(Qj )k
k=l
k=1
(zk - zkI)
m
= 1/2
zk-z
(z-
:
k=1
m
Agj
(Qci
)k
= 1/3
D..IJ
(zk3
-
(3.5.15)
z•k-
k=1
, B.j
and
D,'
are the extensional, coupling and bending
stiffnesses, respectively.
Equations (3.5.13
layups, [81s or
[91z 3,
AW193PW/3501-6 makes
symmetric
also.
construction.
[45]z,V
.
and the
surface.
These
....
for symmetric
The perpendicular
[+-
would
45],
not
be
weave of
and [+-
[0/90]s
true
lay-ups are equivalent
for each
summation is
are simplified
(0/901,
This
Thus Q•-
All
- 15)
for
45]s
uni-ply
to (0 1
,,y and
ply in the laminate is the same
over the distance
coupling terms
Bij
,
z from
are zero
the middle
because
symmetric lamina orientation about the middle surface.
of
Table 3.5
Stiffnesses for Orthotropic Plain Weave Laminates
Extensional
Coupling
A*
Bending
B
D*i
[0/90],1+-45]
2 Qg& tply
0
2/3 Q.- t I
[0/901s,[+-451
4 Qj tpir
0
16/3 Qi t,
Using
the nominal
ply
reduced stiffnesses
1;
=
thickness, t,,
from Table
.0076 inch
and
3.4, one .can calculate
the extentional and bending stiffnesses for use in equations
(3.5.13)
and
(3.5.14).
Measurement
of
strains
and
curvatures will permit the calculation of extentional forces
(Nr,
Ny ),
in-plane shearing forces
(N,y), moments (M, ,My)
and torsion (My.).
3.6 BEAM DEFLECTION UNDER TRANSVERSE LOADING
To
this
point,
the plane
considered as a perfectly bonded
with
special
characteristics
weave
laminate
has
been
stack of orthotropic plies
because
of
it's
symmetric lay-up and material axis orientation.
weave,
In order to
study the interaction of plain weave laminate facesheets and
honeycomb
cores
under
bending,
the
global
model
of
a
homogeneous thin beam or panel under transverse loading will
be examined.
for
This loading method was the experimental means
determining
characteristics.
panel
capabilities
and
failure
Timoshenko
supported by two
homogeneous beam
loads or
transverse
bending
that the beam has a thin
neutral axis
the
[14] described
deflection
of a
thin
fixed pivot points under
moments.
assumed
Timoshenko
rectangular cross section and
its
lies in the middle surface.
Neglecting the small effect of shearing force, the curvature
at any point
depends only on the magnitude of
the moment M
at that point.
The resulting relation for pure bending:
1/r = M/EIy
(3.6.1)
where: r is the radius of curvature
M is the moment of external forces
E is Young's Modulus for a homogeneous beam
I,= f
2
(3.6.2)
dA
is the moment of inertia for the cross section with
I
respect to the neutral axis.
Combining equations (3.6.1) and (3.6.2) yields
Mr
EI /r
=
E/r
f
z dA
=
J
E/r ZadA
(3.6.3)
where EIy: flexual rigidity
Thus the
radius
bending moment
of curvature
by
is inversely
proportional to
a factor
the beam's
of
the
flexural
rigidity, a constant for a given material cross section.
Any beam or panel which is not constrained on its edges
will exhibit anticlastic curvature through lateral extension
and longitudinal
contraction in
the surfaces
of the
beam
which lie on the concave side of the neutral surface, during
bending.
The
opposite is true for
neutral surface.
The
neutral surface as its
does not contract or extend in
directions.
anticlastic
curvature in a thick
Figure
3.6
the
beam
is
in
a
longitudinal contraction.
The
state
name implies,
illustrates
homogeneous
curves in orthogonal directions due
mass and material density.
of the
any direction as it bends in
orthogonal
of
the convex side
beam as
it
to conservation of beam
top surface or concave side
of
lateral
extension
and
That is, Ey is positive and Ex is
negative.
r
1
Figure 3.6
the
\\
Anticlastic Curvature Under Pure Bending
40
Surface strains
within an
element of
related by Poisson's ratio.
intact material
are
unit strain in the lateral
The
direction is
7
where z
is the
-'x
distance from
surface and r is the
considered.
Due
-2t
E,
(3.6.4)
z/r
the neutral
surface to
the
radius of longitudinal curvature being
to the distortion,
cross section originally
material lines
in the
parallel to the y
axis will curve
and remain normal to the sides of the beam.
Their radius of
curvature R will be larger than r by the same proportion
as 6E is
to Ey . A more useful form is
R
=
r/z.
(3.6.5)
where R : the lateral radius of curvature.
This lateral bending
of a beam under
moment becomes quite apparent for
an axial bending
thin sandwich beams under
large bending distortion.
The incremental
distance ds
along a
deflected beam's
neutral surface can be written as
ds = rde
(3.6.6)
using the small angle assumption,
and
for sign convention
Assuming flat deflections
1/r =
de/ds
(3.6.7)
8 - tan 8 = dz/dx
ds - dx,
and placing approximate values into equation (3.6.7)
1/r =
Equation
(3.6.1)
becomes
d z z/dxz
the
differential
(3.6.8)
equation
of
deflection.
EI dZz/dxz =
M
(3.6.9)
Large curves prevent the small angle approximation and
require a more accurate value for 8:
1/r = (de/ds) =
d(arctan (dz/dx))/dx
1/r =
dx/ds
(3.6.10)
(d z/dxz)/[1l + (dz/dx)] 3/z
where 6 = arctan (dz/dx).
So equation (3.6.9) becomes
EIy
(d z/dx z ) /
[1 + (dz/dx)Z
]F
(3.6.11)
= M
3.7 FOUR POINT BEAM BENDING DEFLECTION
Defining the moment equations from equation (3.6.9) for
a four point symmetrically loaded beam.
0
M =
EI,
i x
I - x - (L-1)
(dlw/dxz) =
P(L-x)
;
(L -P)I
(3.7.1)
x - L
P
z
-
'~~
-"
M
f
A
Figure 3.7
Integrating
the
moment
x
•
L-
L
Four Point Beam Loading
equations twice
and
solving
for
associated boundary conditions
and compatibility conditions
leads to the well known solution.
(P/El)
w(x)
[x/6
- Ax(L - j)/21
+ tV/61
(Pl/EIy)([x/2 - Lx/2
=
x
;0
- 1
; 1 - x
_ (L-B)
(P/EIl,) [ -x 3 /6 + Lxz/2 - x(L - LA + tz)/2
+ L(L
-
3LI + 31 )/61
;(L-.)
x e L
(3.7.2)
Maximum Deflection
occurs when dz/dx
= 0
and x =
L/2, by
symmetry
= (Pl/EIy)[ tZ/
(w)MA
6
- L2 /8 i
(3.7.3)
The angle on either end of this symmetrically deflected beam
is:
08
= (dz/dx),,
80
= (dz/dx), & =
= -(P/2EI,)(-
(P/2EIy)(1 - IL)
Equations (3.7.3) and (3.7.4) will
flexural rigid-ity
upon measured
1L)
be used to calculate the
of damaged and undamaged
values of load,
(3.7.4)
68 and
specimens based
mid-beam deflection.
The idealized homogeneous beam model must now be examined as
a sandwich
beam/panel with its
3 dimensional
stresses and
multiple component parts.
3.8 FLEXURAL STIFFNESS OF THE SANDWICH PANEL
Extending the Kirchoff assumption
allows
equation
(3.5.15) to be
to a sandwich panel
written in its
with the following defined panel dimensions as:
basic form
h: panel thickness
f: face sheet thickness
c: core thickness
and
h/2
Aij
= J-h/2
B.
B
=
Q i dz
h/2
(3.8.1)
Qi. zdz
J
-h/2
h/2
D =
DJ
-
f-h/2
z dz
..z
(3.8.2)
h = c + 2f
where
= one ply
t or tp
for A,-
The values
to
doubled
for
account
found
Bij
and
face
2
are simply
in Table 3.6
sheet
laminates
and
a
negligible core stiffness in the x - y plane.
[+-45]:
[0/90],
10/901s,
Ai;
[+-45]s: Aij
f
Bij = 0
= 4Qij f
Bij = 0
= 4Q.; tp1 y = 25il
= 8Qij tpr,
(3.8.3)
The bending stiffness becomes (3.8.4)
z
Di) =1/3
h/2
ij[
/-h/2
-c/2
3
+ Z
c/2
Since Q..
S=
2/3
D..
+ 1/3
C'
3
we
+c
/ 2
-h/2
is negligible it can be removed to leave
(h/8
-
c/8)
2/3 d (h/8- c /8)
=
1/12
(h-
)
3_ C)
1/12 5 (h
(3.8.5)
(3.8.5)
This
bending
stiffness
symmetric sandwich
equation
panels with
is
applicable
negligibly stiff
to
all
cores and
face sheets with constant orientation for every ply.
Equations
(3.5.13)
simplified
(3.5.14) can
now
be
written
in
matrix form for these specific panels.
(N} = 2f [Qij
(M} = (h3
and
-
{ •}
c 3 )/12
(3.8.6)
[QWi;]
MK{
For a sandwich panel under
(3.8.7)
pure bending, the mid-plane
will experience no extension, only bending curvature.
{W1}
= 0 and
into
(3.5.5)
{N} = 0.
and
If we substitute
assume
no
Hence
equation (3.5.8)
mid-plane
extension
(or
contraction), equation (3.5.5) becomes
Ex(z) = -zK
Ey(z)
= -zKy
= -zKX
'(z)
where the curvatures
Kirchoff
(3.8.8)
are constant through the
assumption.
Rearranging
equation
panel by the
(3.6.9)
into
matrix form, we have the curvature relation
K
3y
: -;/z
(3.8.9)
Measured face sheet strains Ex, E' and •Y can be placed into
equation (3.8. 9) along
curvatures.
(3.8.7).
(M)
can
with z = h/2, to
then
be
provide the panel
calculated
from
equation
Note: Sign convention
Curvatures are positive
the positive x,y,
when the concave normal
or z direction.
Positive
positive curvatures.
jr
(ros.)
-I3
.f
f
_
(a) General Panel
t
x
(b) Top Face of 2 Ply Panel
Figure 3.8 Panel Side View
is in
moments create
3.9 LOCAL BUCKLING OF FACESHEET AND CORE
If a
that the
sandwich panel
is bent and
bending moment is carried
the face sheets only, then an
deflection angle
force Nf w"
and
by the axial
forces in
3.9 (a).
The left hand and
in the face sheets are
rotated through a
of w" dx with
is compressed in
core element
been assumed
element in its deformed state
is loaded as depicted in Figure
right hand forces
it has
per unit run
respect to each
other, the
the vertical direction
as illustrated in Figure
by a
3.9 (b)
expressed as
q dx = N; (d2w/dxZ)
dx
(3.9.1)
This force compresses the core and c is reduced.
ds
r
r
NT
-dx
qWx
(a)
Panel Element Bending
Figure 3.9
(b)
Face Element Loading Curvature
Honeycomb Core Loading
Concentrated loading in the vertical (z direction) causes an
As
compression.
additional
reduces
c
thickness
core
under a constant moment.
in-plane face sheet loads increase
increase the normal load on
Increased face sheet loads will
the core once again.
deformation until its buckling load
crush.
is approached; at which
crimp and
buckle,
finally
Figure 3.10 is a typical honeycomb core load diagram
to failure.
until 0
start to
walls
the cell
time
vertical
to
resistance
provides
core
honeycomb
A
approaches
can be
loading deformation
The core
ignored
cell buckling
the core's wrinkling and
stress.
L o•d
•W"
Tkicksess
Figure 3.10 Core Deformation Load Diagram
Researchers working
face sheet
with thin
wrinkling and dimpling
panels
subjected to
dimple
appears
face sheets
to occur
critical in-plane
within
the
confines
with honeycomb
loading; where
of
the
Dimpling is essentially a localized buckling
the face
element over
edges of
the cell.
relation between
a cell,
Weikel and
the critical
have found
core
cell.
phenomenon of
which is supported at
Kobayashi [151
stress and
the
all
proposed a
a characteristic
dimension f/d.
where d
is the length
of a square cell
and f is the face
sheet thickness.
= 2.5.E (f/d)2
O.
The 2.5
factor assumes a Poisson
sheet.
Compressive
loads
(3.9.2)
value of .3 for
were parallel
to
the face
the
square
cell's diagonal.
the
For hexagonal
cell sandwiches,
test
of
results
Norris/Kommers
[51-17], and found that the
dimension f/d, was
Plantema [16] compared
[50-51
and
Kuenzi
exponent for the characteristic
1.7 and 2.4, respectively.
By settling
for the compromise value of 2 and simpler formula:
"cr= 3Er(f/d)2
Plantema found
(3.9.3)
a +-8% deviation from
Kuenzi's experimental
results.
The
normal
panel
loading
qdx
applied
to
an
undamaged core during sandwich panel bending is NFw" dx from
equation 3.9.1.
In
most cases w"dxwill be
c/f is greater than 10)
applied to
the core.
and so
panel
perfectly flat
sheet running
sheet plane
face sheet indentation.
and undeformed,
and susceptible
fibers
increases beneath the facial indentation.
face
the face
under compressive
is bent with
compression, localized normal
cross
With the
of the
are out of
to buckling
When the panel
loading q
the length-wise
through the indentation
in-plane loading.
face under
will the normal
Now consider
section of a panel with a
quite small (if
the dented
loading/unit area
Where wj "
indentation.
is
wj "
a
is
function of position
within the
'~X)in their deformed condition, one
continue to carry N; (or
from equation
sheet
If the tows
3.11(b).
indentation, as illustrated in Figure
can see
the face
curvature within
the local
(3.9.4) that
(Ois larger than
the
undamaged core load, O~ = Nfw"/dx by a factor of (w"+ wd'2w").
X
(a)
Side View
w'/x
Alf
(b) Tow Deflection
r
D --
?
y
(c) Cross Sectional View
D: Dimple axis length
Figure 3.11 Cross Sectional View of a Dimpled Face Sheet
Under Compression
3.10 RESIDUAL STRENGTH MODEL
Once the
damage has been
growth forecast,
a practical
predict panel buckling
assessed and
regional damage
global model
is required
loads and modes.
The
to
buckling load
for the undamaged panel is the first step.
A sandwich
illustrated in
panel loaded
between the two
described in section 3.7.
be
as
elastic foundation.
points, as
= Pl/(c+f)W,
force N,
restrained
by
a
and
stiff
The film adhesive embedded in the Nomex
considerable stiffness to the
foundation adds
pure bending
interior load
orthotropic plate
an
as
The. top laminate face sheet will
a compressive
subjected to
modeled
point bending
Figure 3.7, is subjected to a
= P1,
moment Mc
under four
laminate and
thus must be considered in the model.
It is assumed that
panel
bending
bending
stiffness
test section.
supported
at x
= a,
The
curvature.
the Nomex
are
constant
In addition,
o and
to face
through
the
approximation
final
curvature, is
the
panel is
displays minimal
simplification is that the face
due
foundation modulus
and
pure
simply
anticlastic
neccessary
for
sheet bending moment
M;x,
insignificant
compared to
the
bending moment of the sandwich panel.
In order to simplify the plate-mode calculations, a new
coordinate system parallel to the existing x-y-z system will
be defined as ) , P, ý7, respectively.
bound two
panel and
sides of
'
the pure
will be the
The
bending test
3 and e axes will
section of
face sheet deflection
the
parallel to
the z
3.1^
axis, from the
for
an
~-
e
datum plane.
illustration
of
the
Refer
to Figure
coordinate
systems
positioning.
W
X
y
Figure 3.12
Bending Region Coordinate System
bending region
The
has the
coordinate system
following
relations:
e=
y - W/2
where:
(3.10.1)
W = b
from the
and
= y - b/2
deflection equation
(3.7.7)
for the
entire
panel
w = -(Pl/EI,)[xl/2 - Lx/2 +
1/61 ;
Lx!(L-1)
(3.10.2)
we gain the deflection relation
ý = w(x) + P12/EI [(2/3f - L/2 ]
and assuring a small anticlastic
(3.10.3)
curvature we can shift the
deflection relation to y = -W/2, the edge of the panel.
deflection
function
errors become
more
critical
7 is defined by position ( , ).
The bending region has dimensions:
a = L - 21
b = W = width
52
as the
Now
defection
= -P1/EIr[
(ý)
-
= Pl/
i)
2
EIy[
(3.10.4)
]1
Y
,,occurs at x = L/2 or
As expected,
~(L/2
Z/2 + (t-L/2)
LZ/4 -
=(L/2) - i
+ 2z]
Li
(3.10.5)
The boundary conditions for the bending region are:
S= 0,a;
0;
'=
Mx
= -D,,~ x -D IL•
by the assumption of insignificance
0
compared to the panel's
moment.
P=
0,b;
0 because
0p=
the
plate
is in
a
curved
equilibrium state;
(f) = -Pl/2EI,(
Mn = -D, DS
and
z-
=0
ay )
(3.10.6)
for specially orthotropic
plates.
The Rayleigh-Ritz method of assumed
to
predict
critical
displacements
'
( T,
( 7
()
loads
failure
modes.
The
are modeled as:
fl
sin--h\,
and
modes will be used
51I
Sb
sin
(3.10.7)
where: m and n are the total munber of modes,
q
is the modal amplitude (the generalized
displacements),
3 is
the coordinate along the panel's edge
(parallel to x the loading axis),
C is the lateral coordinate (parallel to the y
axis), and constants K' is the modulus of the core.
Nx is the effective end load.
a and b are the length and width of the bending
Boundary conditions are satisfied in that
state of
= 0
variational equilibrium
the plate is
along all
in a
sides,
prior to buckling.
The total potential energy of the sy stem is given by:
1r7 = Ubehjn + U priýiS
TT = 1/2
EI(
a
z
Id
fro,
+ 1/2
K zdj
Substituting the
+
E
(
-
dP
-
)
1/2f
Wext
d deP
dY•
N)(
) d
assumed deflection function
(3.10.8) and carrying out integration
(3.10.8)
d
(3.10.7) into
over the test region,
we find a simplified form due to orthogonality of modes.
TT
=Z>
Applying
MCI
lizI
the
M
+(±Ir) EI,
Principle
of
+
(3.10.9)
NX q
ri
Stationary
Potential
Energy
requires that
bTT/
i=
(3.10.10)
0
(3.10. 11)
where the Kronecker Delta
S
The summation terms
one
non-trivial term
1 , if m = n
0, if m = n
can be discarded as there
per
choice of
m
will be only
and n.
equation (3.10.11) and dropping non-zero factors.
Rewriting
=
I
N] q = 0
-).
+ J
(3.10.12)
This equation is of the form
- N ) q
( Br
where B
=
(•-EI
= 0
+ (--)'EIr
+
(3.10.13)
]
-()
and can be written in matrix form as
[BA - Nx1( q] = 0)
(3.10.14)
For each selection of m there exists a diagonal matrix in n
-
(B
NX )
0
0
(B
0
0.
...
Lq-NX)
q
= (0}
0
0
...
Bj-
(3.10.15)
f
NX
which provides a non-trivial solution if and only if the
determinant of the diagonal matrix is zero.
(Bb,
- Nx)(Br,~-
Nx)...(B,~-
Hence,
(3.10.16)
Nx ) = 0
From equation (3.10.16) one can see tha t the term which
equals zero at
the lowest value of B
buckling load for
will
the selected mode value
(3.10.14-16) can be used for each
be the critical
of m.
Equations
iteration of m, m+1, m+2,
etc. until a complete matrix has been calculated.
Ncr= min
where NCr
Notice
rigidity
)EI,
EI
+
(3.10.17)
is the buckling or face sheet wrinkling load.
that the
in
+
two
buckling load
directions,
depends
test
on panel
section
flexural
dimensions,
foundation stiffness modulus and modal combinations.
The failure load for damaged
panels will be estimated,
based upon the critical load of undamaged panels, calculated
from equation (3.10.17)
This undamaged failure load N
55
will
be converted to
be used
an equivilent stress (,.
to approximate the
Two methods will
residual strength of
a damaged
panel:
1) Constant net-section stress (upper bound)
2) Mar - Lin relation [171
Lie
[71
describe
this
(lower bound)
bounding
method
for
predicting
residual strength.
For
panels
which
are
insensitive
net-section on both sides of the
to
notches,
the
damage is assumed to carry
a constant stress:
(3.10.18)
cr, = (OT (b-d)/d
where:
aO, is the failure stress of the damaged panel,
(To is the failure stress of an undamaged panel,
If the
b
is the panel width, and
d
is the ruptured face sheet diameter.
panel is notch-sensitive, then
the Mar-Lin[171
relation is used to predict the failure stress:
(r,
where:
(3.10.19)
= Hc (d)'.
Hc is the experimentally determined composite
"fracture parameter".
Equation (3.10.19)
is based
on two
is an empirically derived
material properties
formula which
and the
dimension of
cross sectional
damage.
The fracture toughness
depends on
laminate lay-up
, ratio
of matrix
elasticity
moduli,
yielding
discontinuity, d.
Lin denotes as
stress,
and
to laminate
original
length
of
the
However, the exponential value -.28 which
-m represents the order of
56
singularity of a
crack within
a matrix.
constituent properties
Lin requires
of the
that m depend
filament and
on the
matrix.
Lin's
study provided values of -.28 and -.30 for Hercules graphite
filaments and epoxy
matrix 3501-6.
Hence, the
value for m
the order of singularity, is used in equation (3.10.19), but
fracture parameter Hc, is left to experimental derivation.
Lie [71
technique
uses Federson's
to
impractical
approaches
bound
result
3.13 illustrates
Net
- Stress
depicted
and
provide
domain
from
0, O~,r
approaches b, O~r
the
[18] tangent
where
equation
increases
tangent
upper
d/b
without
bound;
corrections.
bounds
an
(ie:
As
d
and
as
d
zero value).
Relation with
and lower
provides
(3.10.19),
does not approach a
the Mar-Lin
line correction
Figure
Lie's Constant
The
two
for
methods
predicting
residual strength of damaged laminates in compression, for a
given damage-to-width
ratio.
The failure stress
bending failure will be compared
compression predictions.
for panel
with these in-plane column
Mar-Lin Relation
with Tangent Corrections
0.0
Figure
3.13
0.1
0.4
0.3
Damage Width (d/w)
0.2
0.5
Mar - Lin Relation with corrections
CHAPTER FOUR
EXPERIMENTAL PROCEDURE
4.1 EXPERIMENTAL PARAMETERS
The objectives of the residual strength experimentation
was
to isolate
and
examine
parameters
to
(honeycomb
core
panel).
parameters
were
fixed
the
experimental task.
the contribution
residual
strength
Both
to
of
material
reduce
the
a
and
of
various
damaged
HCP
experimental
enormity
of
the
The fixed parameters were:
- specimen width and length
- face sheet material
- core material and density
- impactor mass, shape and size
- bonding epoxy
- age within specimen's life
- temperature and humidity (normal room temperature and
humidity)
- dual cantilever clamping during impact
The
parameters which
were
isolated,
measured and
varied
were:
- core thickness
- impact energy
- face sheet thickness
- face
sheet orientation
(relative to
load application
and core ribbon direction)
- strain measurement positions
The
method of
testing
was
tailored to
isolate
and
characteristics of the HCP.
evaluate certain parameters and
Four
curvature, anticlastic
and
deflection
rigidity,
maximum
curvature,
failure
flexual
evaluated
bending
point
moment, damage/dimple propagation, and failure modes.
compression tests
The
ultimate face
extent of
edge effects.
of
final series
specimens
were performed to evaluate
in compression and
sheet strength
tests examined
various
with
Panel
compression-compression
of
states
loading,
fatigue life
the
of
damage,
under
panel
because
of
the
impracticality of fatigue bending.
4.2 TEST PROGRAM
The test program called for the fabrication of HCP's of
layup, core
(ie: face sheet
various "types"
thickness and
core composition) for impact testing, four point bending and
column compression -under
quasi-static
and cyclic
loading.
Table 4.1 describes the four point bending residual strength
test
matrix.
speeds to
The
tests
simulate static
some undamaged
aluminum and
performed under
were
strength conditions.
specimens were
fabricated with
Nomex core, so that
under the loading
the core would
the impact energy
for each specimen and
of the impact test matrix.
ramp
Note that
a composite
not crush
section could be
tabs and the Nomex test
brought to its ultimate bending moment.
slow
Table 4.1 specifies
thus contains part
The remaining impact test matrix
is included within the fatigue test matrix.
60
TABLE 4.1
FOUR POINT BENDING RESIDUAL STRENGTH TEST MATRIX
FOUR POINT BENDING; Damaged Laminate Under Compression
Layup
Core Thickness
(in)
Impact Energy
(ft-lb)
(N/A)
+-45
+-45
.375
.375
.375
.375
.375
0.0
0.0
1.0
1.2
2.0
+-45
+-45
+-45
.687
.687
.687
(N/A)
0.0
1.0
2.0
+-45
+-45
+-45
+-45
+-45
1.00
(N/A)
+-45
+-45
+-45
1.00
1.00
1.00
1.00
[+-45]s
[+-45]s
[+-451s
1.00
1.00
1.00
0/90
0/90
0/90
0/90
.375
2.0
2.5
3.15
(N/A)
.375
0/90
0/90
0/90
0/90
0/90
.687
.687
.687
.687
(N/A)
1.00
(N/A)
0/90
0/90
1.00
1.00
1.00
[0/901s
[0/90]s
(0/901s
1.00
1.00
1.00
0.0
0.0
1.0
1.2
.375
.375
.375
0/90
0/90
# of Specimen
2.0
0.0
0.0
1.2
2.0
0.0
1.0
1.2
2.0
2.0
2.5
3.15
Total
126
Note: (N/A) indicates a reinforced Nomex/aluminum core
The
employed
Panel Compression
Test Matrix
to
ultimate
evaluate
failure load
for the
thick core of
premature
width;
face sheets
in-plane
at two
also
through greater
contribute
was
compression
orientations.
light weight aluminum honeycomb
buckling
and
the
in Table 4.2
normal
may
prevent
stiffness
negligibly
to
A
and
longitudinal
stiffness.
TABLE 4.2
UNDAMAGED PANEL STRENGTH TEST MATRIX
PANEL COMPRESSION; Laminate Compression Limits
Layup
Core Thickness
Core Material
# of Specimens
+-45
1.00
Low Density
Aluminum Core
4
0/90
1.00
Low Density
Aluminum Core
4
The
fatigue test
variables
because
investigation.
were
tested
practical
As
limited in
enormity
sinusoidal
substitute
four point
the
was
of
for four
cyclic
point
bending stroke would
loads at
scope
and
multi-variable
panel
specimens
compression
bending
The specimen's deflection
beam specimen would
a
mentioned previously,
under
deflections.
greater
of
program
as
a
oscillatory
amplitude under the
be too large.
A shorter
have a smaller deflection,
but require
the loading
points to
meet the
desired
maximum moment for cyclic bending and cause premature if not
immediate localized
The result of
core crushing
under the
loading tabs.
panel fatigue testing is that the longevity
of
considered.
not
described in
program as
panel fatigue test
However, this
is
fatigue
bending
under
core
the
Table 4.3, is implicitely applicable to the longevity of the
sheet
face
compression
HCP
and
bending
under
In fact this
applicable to in-plane compression of the HCP.
longevity
as
intended
was
study
a
to
continuance
the
[ 7 1,
of Lie
compression investigation
quasi-static panel
directly
using similar panels and impact damage.
4.3 SPECIMEN DESCRIPTION
constructed
this investigation;
for
basic
sandwich,
and fatigue
The face sheet for each specimen consisted of two or
plies of
four
the
static compression panel,
reinforced sandwich,
panel.
specimens were
of sandwich honeycomb panel
Four types
an AS4
Face sheet orientation
graphite epoxy
sheets were bonded
fabric.
by the
and thickness was prescribed
a given core material
test matrix for
plain weave
to a homogeneous or
and thickness.
Face
composite honeycomb
core:
CORE MATERIAL
SPECIMEN TYPE
Basic
Reinforced
Static Panel
Fatigue Panel
Both types of
Nomex Honeycomb
Nomex/Aluminum honeycomb composite
Aluminum honeycomb composite
Nomex honeycomb composite
panel specimens have Scotch
bonded to both face sheets at
aluminum honeycomb core
ply loading tabs
either end and a high density
between
the loading tabs.
4.1,2,3 and 4 illustrate the specimen configuration.
63
Figures
Nomex core
-bb
1-
laminate
facesheet
-
film adhesive
6.
14"
2.75"
I
Figure 4.1 Basic Sandwich Panel
film
adhesive
7
*b.
laminate
facesheet
6"
_1
Nomex
honeycomb
high density
aluminum
honeycomb
2"
1`
6"
T
Figure 4.-
14"
'r(
Reinforced Sandwich Panel
2.75"
d
2.75"
Scotchply
3"
)p
_I_
film adhe,
laminate
facesheet
light wei;
aluminum
honeycomb
14"
high dens:
aluminum
honeycomb
2.75"
2.75"
3"
31±
Figure 4.2
Static Compression Sandwich Panel
2.75"
Scotchply
3"
_i_
film adhesive
laminate
facesheet
14"
3.54"
I
Nomex honeycomb -
14"
high density
aluminum
honeycomb
2.75"
4-
Figure 4.,'
Fatigue Sandwich Panel
TABLE 4.3
PANEL LONGEVITY TEST MATRIX
Test: Panel Compression - Compression Oscillation
Face sheet
Layup
# of Specimens
Impact
Energy
(ft-lb)
Panel
Thickness
(in)
2.0
1
.687
0.0
2
.687
.687
1.0
2.0
3
3
1.00
1.00
1.00
0.0
1.0
2.0
2 (P:1)
2
1
0/90
.375
2.0
1
0/90
0/90
0/90
.687
.687
.687
0.0
1.0
2.0
3
3
2
0/90
1.00
0.0
1 (P)
+-45
.375
+-45
+-45
+-45
+-45
+-45
+-45
TOTAL
24
(P):Specimen o f width 70mm and non-standardized
fabrication of grip reinforcement.
4.4 MANUFACTURING PROCEDURES
The fabrication of the test
as
nine separate
cure,
operations:
trimming, core
assembly,
specimens involved as many
layup,
laminate cure,
sandwich
panel bond,
post
tab
bond, machining, and strain gauge application.
4.4.1
Layup
All face sheets
plain
weave fabric
are made from a
impregnated
with
pre-preg is a net-resin system with
66
AS4 graphite filament
3501-6 epoxy.
This
a 34% resin content, by
volumn.
The
pre-preg fabric
Fiberite and known as
is supplied
AW193PW/3501-6.
contains red and yellow tracer
uses white tracer fibers.
and
The Hercules product
fibers.
Both
by Hercules
The Fiberite fabric
materials have very similar
properties.
The pre-preg fabric is removed from its freezer storage
30
minutes before
room temperature
with
cutting.
Once
the material
it can be removed
minimal
condensation
approaches
from its air
formation.
tight bag
Normal
temperature makes
the fabric tacky
humidity and room
temperature makes the pre-preg
and easy to
room
cut.
High
too tacky
and troublesome to layup.
A 12 by
14 inch aluminum plate
covered with non-stick
tape provides the template for cutting pre-preg plies with a
Stanley
utility knife.
desired
angles with
tracer
fibers
The template
respect to
with
pre-cut
experiment required only
to cut
the four layups
[+-45]s.
A
can
be oriented
the fabric's
angular
degree
used: [0/901; [+-451;
sheet of Teflon
longitudinal
templates.
the 0/90 and 45
at
This
templates
[0/901s; and
FEP flourocarbon film
is then
applied to each face of the pre-preg layup.
4.4.2
Laminate Cure
The cure layup
is depicted in Figure
of the aluminum cure base
work
of
aluminum
T
4.5 and consists
plate, non-porous Teflon, a frame
dams and
cork,
the
pre-preg
layup
surrounded by the FEP flourocarbon film, a second layer of
Vacuum Bag
Fiberglass Air
Breather
Aluminum
Top Plate
- -Non-porous Teflon
o
Laminate --
-
Laminate
•
- FEP Peel Ply
-.
Cork--Aluminum
Alum um
T-Dam4
s
-
- - -4 *
-
Non-porous Teflon
S-4--
Vacuum tape
Aluminum Cure Plate
non-porous
Figure 4.5
Laminate Cure Layup
Teflon and
an
aluminum
bleeder plies are required.
paper
It is recommended that the
Teflon be wrapped tightly around the
to prevent resin bleed.
No
top plate.
edges of the top plate
The entire assembly is covered with
a fiberglass cloth and then enclosed under a vacuum film bag
secured at the
edge of the cure base plate
by vacuum tape,
for an air tight seal.
The
laminates
are
cured under
a
135
psi
pressure
differential (15 psi vacuum and 120 psig autoclave pressure)
using a two step process.
The first stage is the resin flow
throughout the fabric at 225 "F
stage cures
for 60 minutes.
the resin at 350 o F for 2
hours.
The second
Temperature
increases and reductions are conducted at 5 OF per minute to
avoid thermal shock.
in Figure 4.6
A cure cycle time history is presented
Laminate Cure Cycle.
AUTOCLAVE
C)
350
225
150
RT
-70
0
TIME
Figure 4.6
4.4.3
(mins)
Laminate Cure Cycle
Post-Cure
The post-cure procedure
non-pressurized oven
at 350OF
is to cure the
laminate in a
for 8 hours.
This extended
cure maximizes the epoxy matrix capabilities.
4.4.4
Trimming
Following the
post-cure, the
laminate is
trimmed and
squared on all four edges with
a diamond grit cutting wheel
mounted on
The
a milling machine.
wheel is cooled
with a
low velocity stream of water, which also carries away debris
during the cutting.
the cutting
minute.
The 5 inch wheel rotates at 1100 rpm as
table advances
the laminate
at 11
inches per
4.4.5
Core Assembly
The core
simply the
assembly for the
basic sandwich
cutting of an oversized
Nomex honeycomb, with a nominal
specimen is
12 by 14 inch
piece of
density of 3.0 pcf.
Excess
core material is trimmed following panel bonding.
The
reinforced
honeycomb on
section, as
sandwich
both sides
of a
specimen
requires
mid beam
2 inch
illustrated in Figure
with a density of 22.0 pcf
4.2.
The
aluminum
Nomex test
aluminum core
will not wrinkle and crush under
the loading tabs as does the Nomex.
The
static compression
column is composed
of a
low
density (3 pcf) aluminum honeycomb core test section bounded
by two inch high density
to Figure 4.3).
aluminum honeycomb sections (refer
The fatigue
compression column has similar
end sections bounding
a Nomex honeycomb test
high density aluminum
end sections are neccessary- to 'ith-
section.
The
stand the test machine grip pressure.
All
of the
Hysol Clear
composite core
Epoxy-Patch with
joints
the aid
are cemented
of an
with
assembly jig.
The epoxy cures in 8 hours at room temperature.
4.4.6 Bond Cure
The face sheets
are bonded to the
cores with American
Cyanimid's
FM-123-2 film
adhesive (density:
Non-porous
Teflon sheets
cover the
Steel
top plates
followed
are
by fiberglass
then placed
panel
on
air-breather.
top
An
.06 lb/ft
).
on both
sides.
of the
Teflon
aluminum bar
is
placed
along the
order to protect
vacuum bag.
side of
exposed Nomex
core material
it from the 40 psi crushing
The panel
bond cure
in
effect of the
arrangement is shown in
Figure 4.7.
Vacuum Bag
Fiberglass Air
Breather
Steel
Top PlatesAluminum•Edge Bar
*
L•,iiii.I~III •
"
'
TlNon-pooous
Assembled •
.Panel
'
,,.
-,,-,,m,,,
,~,,,,i,,,/,
4-
l
-
Vacuum ta-e
Aluminum Cure Plate
Figure 4.7
The
dog-eared
atmosphere as
Panel Bond Cure Layup
vacuum
is
autoclave pressure is
the temperature reaches
for 2 hours.
bag
Note that a
225 OF.
left
vented
brought to 40
This single
to
the
psi and
stage is held
vacuum drawn under the vacuum bag
would cause a pressure diffential between the
and the atmospheric pressure trapped
internal bag
within each core cell.
This differential has been known to cause core damage.
4.4.7
Load Tab Cure
Pre-cured fiberglass crossply loading
distribute test machine grip pressure
grip induced damage.
Type 1002
evenly and thus avoid
These tabs are cut
Crossply material.
tabs are used to
The tabs
from 3M Scotchply
are 7
plies thick
with a nominal thickness of .07
inches.
They are bonded to
the panels with the same adhesive and procedure used to bond
the face sheets to the cores.
4.4.8 Panel Machining
After the
into four
bond cure,
the panels
2.75 inch (70mm) or
are cut
length wise
three 3.54 inch
(90mm) wide
beams for bending and panel tests, respectively.
diamond grit wheel rotating at 700
feed rate
of 5 inches per
An 11 inch
rpm, cuts the panel at a
minute.
The cut
specimens have
nominal dimensions of:
2.75 by 14 inches;
basic and reinforced panels, and
and static compression column
3.54 by 14 inches;
fatigue column
The
disassembled
4.4,3,3
specimens
are
illustrated
in
Figures
and 4.
4.4.9 Coupon Machining
Twelve static
panel coupons
cut with the 11 inch wheel,
from each
of the three
and .375") were
interface
2.75 inches
square, were
from spare panels.
core thickness types
then cut through the top face
of the laminate/core bond.
Two coupons
(1.0", .687",
sheet to the
A second parallel cut
and removal of debris results in a slit between 2.0 and 3.5
mm in
width.
One
slit is
core's ribbon direction.
cut parallel
Figure
4.8
to the
honeycomb
illustrates the three
types of static compression and indentation coupons.
Af
72
Core Compression
Coupon
X
Parallel Slit
Figure 4.8
4.4.10
Perpendicular Slit
Static Core Compression and Indentation Coupons
Strain Gauging
The
final step
application
of
in the
manufacturing
strain gauges.
Since
deals with post-impact damage and
not necessary to mount strain
event.
This procedure
process is
this
the
investigation
residual strength, it was
gauges until after the impact
saved undue
wear and
tear on
the
delicate gauges.
Micro-Measurements
EA-06-125TM-120 strain
sheets
with
a
type
EA-06-125AD-120
gauges are mounted to
cyanoacrylate
manufacturer's instructions.
adhesive
The
for six test configurations, as
and
specimen face
according
to
the
gauge locations specified
shown in Figure 4.: . Each
strain guage configuration is labeled with a Roman numeral
and
each
gauge
is
assigned
a
number
within
the
II
I
w
r,
fa
II
I
3"
''I
4
I
1/4"
1/4"
8
r
III
8
|
Iv
Z•
I
IP
I
"
1.5"
!
V
VI
I
I
3"
I
Figure 4.9
Strain Gauge Configurations
74
longitudinal
Static compression
transverse direction.
with two strain
are mounted
both
face sheets.
only
on the
column specimens
gauges (configuration
III) on
have gauges
mounted
Bending specimens
specimens
Fatigue column
face.
compression
mounted in the
numbers are
Even
direction.
specimen's
in the
gauges mounted
5) to
(1,3 and
numbers
require no strain gauges.
4.5 TESTING PROCEDURE AND DATA ACQUISITION
Five
bending,
static
types
static
were
tests
of
column
and
indentation
compression,
core
and
compression,
column
were first subjected to
for residual strength or longevity,
damage
measurement,
impact
Specimens that were to be tested
compression fatigue tests.
a prescribed
beam
static
performed:
impact and damage assessment
assessment consisted
inspection.
visual measurements
of
magnification and x-ray photography.
The
under
One specimen from each
test type and damage level was dissected to measure core and
bond damage.
tested
Specimens with and
for ultimate
and
residual
without damage
were then
strength, or
longevity
under compression-compression cyclic loading.
4.5.1 Impact Tests
Specimens to be
which
is designed
impacted are mounted in
to provide
a holding jig
clamped boundary
conditions
along the short edges and leave the long edges free.
75
Figure
4.1C
depicts the
aluminum bars to
holding
jig.
The
Jig
uses
clamp the specimen.
The
jig is supported
4 sets
of
by a rigid steel frame.
6.00
8.50
Front View
are
3ar (8)
Top View
---.
Figure 4.10
A1 Plate
Specimen Holding Jig
The impactor mechanism is a spring driven 26 inch steel
rod mounted
on linear
bearings so
striking
may have
free
The rod has a mass of ;.105 slugs.-
travel along its axis.
The main spring
that it
of the striker unit is compressed when the
mechanism's
end
plate is coupled
to
activated
electromagnets and the magnet mechanism is drawn back with a
hand
winch.
Figure
Figure
4.11
4.12 illustrates
illustrates
the impacting
entire device is known as
the striking
rod mehanism.
unit.
The
FRED within the TELAC laboratory.
The name has no significance other than identification.
The striking unit
any net
deflection of
can be drawn back with
the main spring
at any
the winch to
time.
Thus
impacts are repeatable based on spring compression distance.
TUI
Figure 4.11
FRED's Striking Unit
Magnet
b
Figure 4.12
The
striking
electromagnets are
then driven forward
FRED; Impacting Rod Mechanism
unit
is
in
set
The
de-energized.
target specimen in the holding
jig.
a CENCO Model 31709 photo electric
start and
timing flag.
stop a digital timer
The
when
striking surface
by the compressed main
strikes the impactor rod, which in
rubber "doughnut"
motion
the
is
spring until it
turn is propelled at the
The impactor rod trips
timing gate with a 13 mm
photo-electric sensors
as the flag
interrupts the
beam of
into
light.
The photo-electric
the flag
and
at 12.5mm,
cells trigger
resulting
in an
at .5mm
effective
timing flag of 12mm.
The
impacting
anti-rebound
rod
lever
mechanism
which
is equipped
prevents
the
with
impactor
an
from
rebounding and striking the specimen and passing through the
light gate a second time.
Attached
to the impacting rod is
a PCB Model 208A05 force transducer
hemispherical stainless
The transducer
and a 1/2 inch diameter
steel impact head
measures force
during the
known as
a tup.
impact with
the
specimen.
Data is collected by
equipped with
a Data
a DEC
Micro PDP-11/23
Translation DT-3382-G-32DI
digital converter.
The signal from
sampled at
of 25 kHz
a rate
later analysis.
computer
analog to
the force transducer is
and this
data is stored for
Data collection is triggered by the falling
edge of the signal from the CENCO timing unit.
Impact velocity
filed for
and force over
each specimen impact.
examined for
time are
recorded and
The specimen must
damage and quantified
relative to
now be
the impact
history.
4.5.2 Damage Assessment
Impacted specimens are inspected visually under 15 to 1
magnification
ruptured
An
to
measure
the
cross
sectional
width
of
fibers and is also subjected to x-ray photography.
x-ray opaque
dye, 1,4-Dilodobutane
78
is applied to
the
perimeter of the
drop
at
a time.
laminate's
hours.
damage with a hypodermic
The
dye
deepest cracks
is
allowed to
penetrate
through capillary
After the absorbtion period,
damaged face down
needle, one tiny
the
action for
2
the specimen is placed
on a sheet of Polaroid Type
52 Polapan 4
5 Instant Film inside a Scanray Torrex 150D X-Ray Inspection
System cabinet.
is set
The x-ray machine operates at 50 kVolts and
to expose the film
control.
the "TIMERAD"
After exposure, the film is processes according to
the manufacturer's
instructions.
white photograph displays
area.
to 240 mrad using
The
resulting black
a full size image
The photograph can be
and
of the damaged
measured to provide dimensions
and area of the delamination.
Specimen
dissection
milling procedure as
sectioned
through
is
accomplished
used in fabrication.
the
center
of
the
with
The
the
same
specimen is
impact
site,
and
specimens and
the
inspected for debonding and core indentation.
4.5.3 Four Point Bending
The
residual strength
of
ultimate strength
of undamaged
bending
provided
by
mounted
in
MTS-810
installation
aluminum I
the
a
The upper I beam has a grip
specimens are
four-point
illustrated in
beams with two
damaged
uniaxial
bending
test
Figure 4.12,
tested under
installation
machine.
consists of
loading roller cradles
The
two
on each.
block bolted to it, which holds
the I beam in place when the MTS-810's upper gripping Jaws
are pressurized.
for any
The loading point cradles
loading point
placement.
Four
are adjustable
one inch
diameter
cold roll steel rollers are placed in the loading cradles to
act as non-fixed loading points.
Loading tabs 5/8 inch wide
are mounted
to each specimen's
faced tape.
The loading points can vary throughout the test
loading points
series, but symmetry about the
with double
specimen mid-point should be
maintained.
The bending specimen
is loaded for testing
by placing
the beam on the bottom two rollers and aligning the specimen
edge with the I beam with the
assures
that
the
loading
perpendicular to
inch
use of a straight edge.
rollers
lead
strain box terminals
wires are
then
then calibrated for a 40,000
An angular deflection
one end
zero degree
and I
mark
The
and pivot
point of
a
The lower I
the starting position
manual stroke control, the
between cradle and loading tab.
faced tape.
indicator is
beam cradle.
is then raised to
beams aligned, and the
to the top
wood, Nomex and toothpicks,
protractor mounted to the lower I
with the MTS-810
with double
each specimen thickness.
beam with specimen
as data
The strain gauges are
indicator is now attached
of the specimen,
with the
the
micro-strain range and zeroed.
The indicator, constructed from
aligned
are
The 15
connected to
which send strain measurement
to the DIGITAL 1134 digital computer.
is tailored for
lines)
the specimen's longitudinal axis.
strain gauge
face of
(loading
This
top two rollers
loading points
are inserted
arm
loading
tabs
Figure
4.13
Four Point Bending Installation
from the indicator
is of interest)
and the
and protractor (the net
and the distance between the
specimen's mid-point center
A digital indicator connected
terminal
on
the
placed
in
at 1.0
stroke
between .00125
specimen
MTS-810,
control
and
with
ramp
manual
MTS-810 and. DIGITAL 1134
constant
half inch.
and .00250 inches
stiffness
to a stroke output
provides
volt per
bottom I beam
line is measured with
calipers.
displacement
change in angle
stroke
The MTS-810
compression
is
speeds
per second,
depending on
measurement
speed.
are started
The
simultaneously.
The
MTS-810 providing constant stroke displacement and load from
two
digital
average
of
indicators
3 data
and
samples
the
computer
every
recording
second for
gauges, and load and stroke transducers.
all
the
strain
Specimen mid-point
and angular deflection at the end loading point are measured
and recorded along with the
stroke
intervals
Photographs of
(typically
.0625
the damaged face
bending with a 2
beam and
applied load, at pre-determined
or
.125
sheet can be
taken during
inch wide mirror strip taped to
hung down at
inches).
the top I
approximately 45 degrees.
A tripod
mounted 35mm camera with ASA 400 film is then focused on the
image in the mirror.
propagation can
eye.
also be made with
Measurements
failure.
Length measurements of damage
a thin ruler and
and observations can be
a keen
continued until
rbeam
-
-=f
-
Spec im e
Figure 4.14 Face Sheet Damage Photography
Failure
is defined
as a
substantial
drop
in
load
bearing capacity and is caused by:
- core crushing, wrinkling, or shearing
- debonding between face sheet and core
- face sheet folding or buckling
4.5.4
Static Panel Compression
Two groups
cores
were
of panel specimens with
tested
under compression
aluminum honeycomb
to
determine
ultimate buckling load and face sheet stresses.
their
The testing
procedure is the following.
The panel
are loaded
in the
MTS-810 by
aligning the
panel in the upper grip with a square so that the specimen's
axis is parallel to
grip is
then activated and the
flat grips
then
the machine's
under 500 psi
procedure.
column is held
pressure.
connected, calibrated
loading axis.
The strain
and zeroed
With stroke control selected,
raised and clamped to the lower
After checking that
as
The top
by textured
gauges are
in the
bending
the lower grip is
grip section of the column.
the applied load is zero, the computer
and test machine are started.
Again, the stroke rate can be
selected between .00125
and .00250 inches per
second.
The
procedure is to place
the
test is terminated upon column buckling.
Figure 4.15
4.5.5
Panel Compression Test
Core Compression and Indentation
The core
compression test
test coupon on
a steel plate, which lies on
mount of the MTS-810 test machine.
is then placed on
An identical steel plate
top of the coupon and the
stack are
raised to the
control.
Once again
lower grip and
starting position with
the computer
started simultaneously, with a stroke
As the 2.75 X 2.75 inch
the lower grip
and
the stroke
test machine
are
rate of .0025 in/sec.
coupon core is compressed, the load
cell and stroke
transducers provide continuous data
computer, which
samples and
averages 3
times per
to the
second.
Significant core wrinkling is observed and identified during
the
test by
a mark
placed in
the test
data history.
A
second mark is made when significant crushing is determined.
84
Both
marks are
observer.
subjective judgements
The test
is terminated
on the
part of
the
core crushing
when
is
pronounced and the load has dropped significantly.
panel coupon
flat steel plates
Figure 4.16 Core Compression Test
The
core indentation
across one face
test
using
coupons with
sheet laminate is designed
slits
to simulate the
impinging core crushing pressure of a face sheet indentation
(dimple) as
it propagates laterally
compressive loading
axis. The slit
width to provide an incident
honeycomb cell axis.
from the
face sheet's
is cut to
a prescribed
angle between the indentor and
The slit
also prevents the face sheet
from providing z axis support to the core through tension.
The core indentation test begins
the
test
coupon
compression test.
inches
slit.
on
Next,
in diameter,
The
the steel
plate
a 4 inch long
is laid
lower grip
with the placement of
used
in the
control, until the cylinder
upper grip housing
face.
work in concert
Once again the
at the
core
coupon's
configuration is then
raised with stroke
machine
the
steel cylinder, 1.5
length wise
and specimen
in
usual
touches the
computer and test
stroke rate.
The
observer monitors the propagation of the point of face sheet
deflection.
recorded
Marks are
when the
place in the data
deflection
history and loads
propagation
along the
face
sheet reaches pre-determined distances from the slit center.
The
test
is
terminated
when
the
propation
reaches
a
specified distance.
ller
C
steel p
Figure 4.*.
4.5.6
Panel Fatigue
Damaged and
the
MTS-810
undamaged panel specimens are
grips
compression panel.
in
with
same
can be
as
the
static
are not
The MTS-810 is placed in load control
tuned to ten percent
amplitude with the "Set
read directly
"DC" selected.
amplitude and
manner
placed into
gauges and the computer
loading force is fine
desired compression
The load
the
Strain
needed for this test.
and the
Core Indentation Test
the 10%
from the
The difference
set point
86
Control" dial.
digital indicator
between the
is then
of the
selected
dialed into
the
"SPAN
1"
control.
oscillatory
mode,
"INVERT" are
The
machine
is
"REMOTE" selected
depressed.
The final
then
and
set
to
the
"HAVERSINE"
and
preparation step
is to
reset the cycle counters to zero.
Damage
test.
A
dimensions
damage width
with no load,
at
the
measurement using
can
of
be
the
fatigue
taken
oscillation speed to .1 Hz
quite
throughout
a ruler
the
was made
the amplitude load,
test.
easily
The
by
amplitude
setting
the
and adjusting the amplitude load
with "SPAN 1i", while "PEAK READ"
indicator.
monitored
the "Set Point" load and
beginning
measurement
must be
is selected in the digital
If the damaged indentation does
not propagate,
the cycle frequency
can be increased incrementally
load amplitude fine
tuned with "SPAN 1i".
and the
A high intensity
photographic lamp will aid in measuring the dimple length of
the damaged
region as well
and cycle
number are
specimen.
The test
as photography.
recorded throughout
terminates when
longer carry the selected load.
the
Dimple length
the life
of the
specimen can
no
The MTS-810 can be set with
stroke limits which automatically disconnect hydraulic power
when the limit is reached.
A
quarter inch of stroke travel
is the recommended limit for these columns.
CHAPTER FIVE
EXPERIMENTAL RESULTS
5.1 IMPACT TEST RESULTS
Impact
core
events were
thicknesses, 4
impact
energy
conducted for
different face
levels.
cantilever clamping
A
8.5"
specimens of
sheet
test
three
layups using
section
5
between
arrangement as depicted in
a
Figure 4.10
allowed for dynamic response to impact. The damage inflicted
had
generally
the
same characteristics
impact energy level.
within
the
same
The impact tests and damage assessment
is reported for individual specimens in Appendix A.
5.1.1 Impact Velocity and Energy
The
spring
driven
impact test
machine
(FRED),
was
employed at five different spring displacements; 40, 43, 50,
55, and 60mm.
impact
Figure
FRED propelled the
velocities between
5.1,
Impact
Displacement, displays
4.4
.105 slug impactor rod at
and
8.7 feet
Velocity/Energy
the impact
per
second.
versus
Spring
energies and
velocities
recorded
during
setting.
Table 5.1, Mean Impact Energy, reports the average
testing
for
each
spring
displacement
impact energy, sample size and standard deviation within the
sample.
Standard deviations for
samples will be calculated
throughout this report using
S =
(-
)/(n
-1)
(5.1.1)
where n is the number of elements in the sample and x is the
sample mean.
r
-5
6-
-4
+
4-
Velocity
.. --....-
-3
Energy
'i
-2
2-1
0J
0
I
'
i
'
-o
t
20
40
60
Spring Displacement (mm)
80
Figure 5.1 Impact Velocity/Energy vs. Spring Displacement
TABLE 5.1
Spring Displacement Versus Kinetic Energy
Spring displacement: 40mm
43mm
50mm
55mm
60mm
Mean (ft-lb):
1.14
1.94
2.47
3.17
.99
Std. devation(ft-lb): .17
Sample size:
41
.29
.42
.11
.14
16
46
5
7
5.1.2 Impact Force
The force transducer in the tup provided force values
throughout
the impact
Forces, displays
the
tup force
event.
the average
transducer for
Table
5.2, Maximum
peak forces
specific
energy level (spring displacement).
Impact
recorded through
specimen type
and
TABLE 5.2
Maximum Impact Forces
.375 inch
.687 inch
1 inch
[+-453
40mm
43mm
50mm
140 [11] (6)
145
(1)
144 [25] (4)
148 [121 (7)
(0/901
40mm
43mm
50mm
122 [341 (3)
120 [12] (4)
283 [31] (3)
126 [12] (7)
[0/90]s
50mm
55mm
60mm
155 [15] (3)
280 (.7] (2)
282 [20] (3)
Notes:
130 [2.91 (4)
151 [8.41 (3)
154 [10]
(4)
157 [18] (7)
(4)
(4)
(5)
124 [33]
137 [16]
148 [22]
152 [26] (4)
- Maximum force in lbs.
- [ i Standard deviation
within sample in lbs.
- ( ) Population of sample
- skewed data are not
[+-45]s
50mm
55mm
60mm
Force
versus
computer during
History:
included
144 [24] (4)
239 [641 (2)
255 11.6] (5)
Impact
time
histories
event.
the impact
three [+-451 1
31) impacted
at 2.12, 1.31
Their peak forces
recorded
the
force-time
inch specimens, (#29,
and 1.10
the--
by
5.2, Force-Time
Figure
illustrates
Spectrum,
histories of
were
30, and
ft-lbs, respectively.
were all about the same, 131
to 145 lbs.
The plateau of force oscillations following the maximum peak
evident in #29 is reduced in #30 and bearly evident in #31.
The impactor
graph's
contact time
base was
as denoted by
.030 seconds
seconds for specimen #'s
the width
for specimen
30 and 31.
#29 and
of the
.025
Most low energy impacts
only dented the face sheet and did not break many fibers.
FORCE-TIME HISTORY FOR
HIGH, MEDIUM AND LOW ENERGY DYNAMIC IMPACTS
E8
Spec. # 29
2.12 ft-lb Impact
r
.w8
L
1.88
d/W = .186
i
Area .270 sq. in.
37-29 Z.-d!
r
0 9.98
R
C
-
IE
.8
-,?..
9.98
2.98
4.W
I
6.w
8.8
Spec. # 30
1.31 ft-lb Impact
d/W = .043
Area .130 sq. in.
-30 [,+-451
1.9
F
-10.8
I t ,
I
II
II
i, ,
I
I
I
-2.80
8.8
2.98
4.08
6.98
8.98
Spec. # 31
1.10 ft-lb Impact
d/W = .057
Area .136 sq. in.
2.800
37-31 C.d5
1.80
0
9.0
-1.98
-2.M8
8.8M
2.88
4.08
6.08
8.98
Figure 5.2 Force-Time History: Impact Spectrum
91
30
.4
Nu
Specimen # 30;
Delamination Area =
.13 sq. in.
3/
.......
-r
z<
-i
/!
i
'
f
,f
t
1
1
1
-
r.
!
'
I
t
"
X%
-
.
.
'*.
",
'
K
"'~
N'
"
"
>\ \'\,.
K
Specimen # 31;
Figure 5.3a
Delamination Area = .136 sq. in.
Impact Spectrum
92
-
Damage
The force oscillation "plateau" can be
used as a measure of
the level of damage being inflicted.
Figure
5.3
"plateau"
Damaging
effect
Impacts,
associated
illustrates
with
the
ruptured
force
fibers
and
delamination area as found to occur in the 2 and 4 ply face
sheets
and for
impacts
different
which did
not
panel
rupture the
specimen # 204 and 301), leaving
have
force-time graphs.
parabola.
of impact
"plateau" width decreases
face
Low
energy
sheet (refer
to
only a dent, were found to
Similar in shape
Specimen numbers
varying degrees
thicknesses.
29, 212 and 309
damage as
to a
each sustained
denoted by
with d/W until the
negative
d/W.
The
shape of #309
approaches the parabolic shape associated with minimal fiber
rupture.
5.1.3 Impact Energy
Impact energy was calculated
measured
during
presented
the
in Tables
impact
A.1-8
testing.
in
specimens and plotted against
in Figures
5.5-9.
from each impact velocity
Impact
Appendix A
for
evergy
is
individual
inflicted damage measurements
These results
Chapter 6.
93
will
be
discussed
in
FORCE-TIME HISTORY
.375 in. Specimens
[0/901
Spec. # 212
1.93 ft-lb Imp.
d/W = .143
Area = .174 sq.
(0/901
Spec. # 204
.98 ft-lb Imp.
d/W = .014
Area = .013 sq. in.
in.
EO
2.080
-
p9-20
1.00
F
0 e.0088
R
C
E
HB-212 [o8/8
, II
ýý, , I , , I ,
-2.088
0.80
2.880
4.88
6.80
!
6.88
E -?
1.0 in. Specimens
[+-45]s
Spec. # 309
3.01 ft-lb Imp.
d/W =
[+-45]s
Spec. # 301
2.12 ft-lb Imp.
d/W = .014
Area = .197 sq.
.086
Area = .234 sq. in.
in.
E88
4.880
301; [+-4532
2.88
a,~....l.
0.00
-2.88
I
I I
I I
I I I
....
I
Figure 5.3 Force-Time History - Damaging Impacts
I I I
I I
5.2 DAMAGE ASSESSMENT
Following the impact event, each specimen was x-rayed
and inspected visually
as described in section
4.5.2.
The
x-ray photographs provided excellent resolution of inter-ply
delaminations.
gray lines
Cracks and delamination
or shaded areas.
regions appeared as
Dye accumulation
cells was quite evident in some photographs.
around core
Core and face
debonding was not evident from these photographs.
The area of
damage defined by gray
(delamination) was determined by
mesh over the
that
placing a transparent grid
photograph and counting 2mm
contained
reported by
cracks and shading
damage.
specimen
The
in
resulting
Appendix A,
x
2mm
damage
squares
area
Tables A.1
is
through
A.8.
The
cross-sectional rupture
under 15 to 1 magnification and
the specimen's nominal width, W.
ratio d/W is reported by specimen
diameter
d was
measured
is reported as a ratio over
The cross-sectional damage
in the tables of Appendix
A.
Both damage
evaluation
on the
cracks within the
unit square
measurement techniques
part
of
the investigator.
laminate were assigned a
area that they
displayed signs of
require subjective
occupied.
Individual
fraction of the
Filament
tows which
partial or complete breakage
beneath an
obscurring tow were assigned as a complete or partial break.
It was
found that tows
fracture from center
outward.
The
measurement of d simply involved choosing the rupture limits
95
which were furthest from the
on each side of the inclusion,
and projecting
specimen's centerline
transverse mid-line of the specimen.
the
d on
a distance
Figure 5.4 illustrates
this projection technique.
wI
Wd
Figure 5.4 Cross-Sectional Damage Projection
of impact
ft-lbs
approximately
1.0
hemispherical
impactor.
impact.
Actual
ply
Four
minimum .05 square inches of
ft-lb
ply
2
for
rupture
Fiber
laminates
for
face
at
begins
inch
half
this
sheets exhibit
a
delamination area after a 1.93
surface filament
rupture
was
not
observed until 2.42 ft-lb of impact for the 4 ply laminates.
Specimens with a d/W
center of the
impact site.
dye for sub-lamina
The
.5mm hole
value of .014 have a .5mm
was
The hole was
x-ray inspection
unimportant
hole in the
drilled to inject
of intact face sheets.
to damage
propagation
or
residual strength.
The fiber rupture threshold proposed by Lie [7], of 1.4
ft-lbs
is
high because he
timing flag unaware
measured velocity using
that a 1mm error
a 13mm
existed in triggering
the
timing
light
gate.
"effective" timing flag
This
investigator
is
using
an
of 12 mm, which
reduces comparable
speeds by 8% and impact energies by 15%.
This leaves just a
.19 ft-lbs
difference between
Lie's threshold
estimate of
1.19 ft-lbs and 1.0 ft-lbs proposed here.
This differential
is within
and
subjective visual
inspection
experimental
error.
Core indentation
honeycomb cells
delamination,
Sectioned
was found to
at
impact
indentation
debonding.
in the form
depth
of wrinkled
occur with the
approximately
specimens
and
the
The measurements
.70
were
and buckled
initiation of
ft-lbs
measured
diameter
of
of
impact.
for
core
core/face
sheet
are provided in Table
A.9
of
Appendix A.
Specimen 29 listed
in Table A.9, suffered
damage due to face sheet penetration.
and had
a 12mm core/face
had a rupture diameter of
The core indented 3mm
debond diameter.
13mm.
severe core
The
face sheet
Other specimens had larger
core debonds than face sheet ruptures.
The typical indentation from a
2.0 ft-lb impact upon a
2 ply face sheet is between 1.2 and 3 mm( ie: specimens 29 &
55).
2.0 ft-lbs represents the 2 ply face sheet penetration
threshold.
If the face
less than 1.2mm.
4 ply face
sheet holds,
is
Core indentation is reduced further by the
sheet, as evidenced by a
impacts of 3.01 and 3.26 ft-lbs,
respectively.
core indentation
.8mm indentation umder
for specimens 321 and 307,
Damage Diameter vs. Impact Energy
[0/90] Panels
U.0
I
x
x
x
0.5 -
x
oxx
0.4 -
o3 .375"
xK x
0
0.3 OX
0
.675"
x
1"
0.2 X
0.1 -
0
K
Impact
(ft-Ib)
Energy
Damage Diameter vs. Impact Energy
[±45] Panels
I.U
I
0.8 -
0.6
-
x
x
0.4
-
x x
o3
x
0.2
x
o
X
Xa~lKo[
I•
0.0 -1
0]
·
Impact
Figure 5.5
o
x
Energy
(ft-Ib)
Damage Diameter vs Impact Energy
o
.375"
o
.675"
x
1"
x
Damage Area vs. Impact Energy
0.4
[0/90]
I
Panels
o
0.3x
xo
0.2-
o0
x
0
.375"
o
.675"
x
1"
0
.375"
o
.675"
x
1"
0
0
0.1 -
0
x0 x
xo
xoa x
0
0
[]
0.0
I
1
Impact
Energy
2
(ft-lb)
Damage Area vs. Impact Energy
[±45] Panels
0.4
0.3
0.2
0.1
0
1
Impact
Figure 5.6
Energy
2
(ft-Ib)
Damage Area vs Impact Energy
3
0.6
Damage Diameter vs. Impact Energy
[0/90] and [0/90]s 1" Panels
0.5
0.4
* (0/90]s
o [0/90]
0.3
0.2
0.1
2
Energy
1
0
Impact
3
4
(ft-Ib)
Damage Diameter vs. Impact Energy
[±45] and [±45]s 1" Panels
1.0u
1
0
0.8
-
0.6-
0
0
0
0
0.4
-
.0a
00
* [±45]s
* [±45]
o*0
0.2
0*
_
0
|
2
Impact
Figure 5.7
Energy
(ft-Ib)
Damage Diameter vs Impact Energy: 2 and 4 ply, 1" Panels
100
Damage Area vs. Impact Energy
U,.
[0/90] and [0/90]s 1" Panels
Energy
Impact
Damage Area vs.
[0/90] and [0/90]s 1" Panels
0.4C*
0.3-
0
0%o
a
00
S 0.2-
0
o [0/90]
[0/90]
*
o
c
E
o
oo
0 0
0.1-
0.0
0
I
LII
Impact
Energy
4
3
2
1
0
(ft-lb)
Damage Area vs. Impact Energy
[±45] and [±45]s 1" Panels
0.8
.E
S
0.6
0.4
0.4 -
[45]s
*
[±45]
0
E
0.2 *
*
0.0
0
1
Impact
Figure 5.8
2
Energy
3
4
(ft-Ib)
Damage Area vs Impact Energy: 2 and 4 ply, 1" Panels
101
A
of
sample
within
delamination
x-ray
photographs
damaged
face sheets
Appendix A.
Figures A.1,2,3,4, and 5 of
not provide
any information
debonding.
But they
is
provided
in
The photographs do
indentation or
regarding core
do show
the
depicting
honeycomb
of the
the shape
cells under and around the inclusion.
5.3 QUASI STATIC FOUR POINT BENDING
Nomex sandwich
were
tested to
through
panels and
the inclusion
the
on
panels
Undamaged
expected.
Damaged
failure.
loading
experienced face
test section.
points.
The 4 ply
aluminum
as
core
and crushing under the
in the
undamaged
2 inch
panels
Nomex core
despite moderate face sheet
The specimens which failed
face sheet debonding
sheet
face sheet panel s typically failed
with core buckling or shearing,
damage.
no
with
Reinforced
sheet buckling
buckled
panels usually
compression face
reinforcement suffered core buckling
interior
panels
reinforced sandwich
due to core crushing or
are reported with t:he
failed through the damage site.
specimens which
The sandwich panel is only
as strong as its weakest element, which justifies the report
of core and bond failure.
Tables
A.1
through
A.8 in Appendix
A
report
four
catergories of information about each test specimen:
1.) degree of impact - velocity and energy of the impact
2.) degree
of damage
- delamination
cross-section
102
size and
ruptured
3.) parameters at failure - moment, stress and strain
4.)
mode of
-
failure
laminate buckling
failure
was
predominant and can be assumed unless actual failure mode is
stated.
5.3.1 Failure Modes
Two typical modes of fracture were observed for the two
ply
damaged
The
panels.
0/90
face
fractured
sheets
laterally through the damage site with in-plane splicing and
between
"brooming"
fractured through
run parallel to
the damage, but
included
"turn
the
0/90)
is the
where
the core.
fractlre
sheet
Combinations
and
core
of these
following
modes
illustrated in Figure 5.9.
103
were
sheet
also
line would
fine toothed zigzag
to 1 inch in
length.
the
Other
laminate
Lateral stair step
along.. tow
predominantly in the lateral direction.
face
face
the fracture
down" buckling
fractures and bends down into
(for
+-45
tows (+45 or -45) in a
in large splits up
fashion or
modes
The
plies.
boundaries
Delamination of the
fracture
also
also observed
occured.
and
are
-.100*
debonding
splicing; 0/90
brooming; +-45
rr #I|I
Irrrr
stair step &
zig-zag
line fractures
fractures
turn down buckling fracture
Figure 5.9 Compressive Fracture Modes for Damaged Face Sheet
An
indentation
elliptical
or
the damage site of 2
become visible around
would
dimple
usually
ply face sheets
as the in-plane compressive load reached 75% of its critical
load.
The dimple expanded laterally
Figures A.6,7,8, & 9 contain photographs of
load increased.
Specimen # 235 at four
Dimple length increases with
loads.
Dimple length was measured
stress.
across the specimen as
visually at the instant
of specimen fracture for a number of specimens.
The longest
dimples recorded were 38mm measured from three [0/90] .375in
specimens
dimple
and
one
among the
specimen.
The
(0/901 .687in
+-45 face
average
specimen.
sheets
dimple
recorded in Table 5.3.
104
was 30mm
lengths
at
The
in a
longest
.375in
fracture
are
TABLE 5.3
Dimple Lengths at Fracture Load
1 "
Core Thickness:
.687 "
.375 "
0/90
18(2)
31(2)
32(8)
+-45
23(4)
24(4)
27(8)
lengths in millimeters
( ) number in sample
No
dimples were
observed
in any
four
ply laminate
face
sheets.
the dimple prescribed the
In some cases,
pattern.
failure mode
Specimens which developed long dimple indentations
often fractured
with "turn down"
occupied by the
dimple and in-plane straight
the length
line fracture
This result is not surprising
at either side.
face sheet is
buckling over
turned down into the core
in that the
by the indentation
prior to fracture.
The
typical
reinforced
mode
specimen
of
was
fracture
face
the
undamaged
fracture
(buckling
for
sheet
presumed) within the 2 inch Nomex test section.
illustrates a test section buckling
61 at
55.45 Ksi.
Some failures
Figure A.10
fracture for Specimen #
occured on or next
to the
Nomex/aluminum core joint.
Tables A.1 - 6 contain undamaged
specimen
moments,
failure
failure mode.
face
sheet
bending
Specimen # 117
debonding.
specimens
(Table A.5:
deflected
enough
to
strains
and
failed prematurely because of
The
[+-45]
#'s 230,
gain
stresses
231
fracture.
105
.375
in. reinforced
& 233)
Figure
could not
A.11
is
be
a
photograph of
deflections of
their maximum
are recorded for
and strains
assembly at
The stresses
excessive deflection.
because of
either end
impinging on the
Specimen # 232
38mm and 21 degrees at the outboard support.
specimens ( 300 series in
The damaged 4 ply face sheet
undamaged 2 ply face sheet specimens
Table A.7 & 8) and the
A.1-6)
(Tables
shearing,
the 4
Only three of
323)
322, &
301,
great shearing
under
was placed
core
to
through a
laminate fracture
because of
core
(#'s
series specimens
300
due
the combination of both.
crushing or
ply
failed
typically
failed
The
damage site.
stress
in the
300
were twice as stiff in
series tests because the face sheets
compression, eight times stiffer in bending and the core was
Shearing strain of the
one inch thick.
by compressive buckling and crushing
in the x axis followed
of
the
core's
core was observed
cells,
for all
of
the
300
series
core
Figures A.12-14 depict core ripping, crushing and
failures.
shearing failures.
The undamaged
failed
buckling
with
core
under
buckling under
fracture or
one
2 ply
face sheet
shearing
of the
and
inner
these loading
continued into
specimens typically
crushing
or
loading
points either
further core
sheet
points.
Core
initiated face
crushing.
5.10 illustrates observed core failure modes
106
face
Figure
±
IUUE~
~P
core shearing and
buckling failure
core shearing (rip)
and debonding failure
core crushing
failure
Figure 5.10 Core Failure Modes
5.3.2 Panel Deflection Under Load
Mid-point
deflection
deflection
and angular
at
the
outboard loading point were measured and recorded throughout
the quasi-static
deflection
load
for
each type
reported in Appendix C.
for these
plotted versus
89 are
deflection angle,
and
The mid-point
bending test.
of
specimen
deflection,
the
applied
tested,
and
The curves are provided as raw data
specific specimens
From Figure 3.7 Four Point
and loading
point placement.
Beam Loading, the loading points
are:
2 ply face sheet specimens - I = 110mm
L = 320mm
moment arm
4 ply face sheet specimens - 1 = 130mm
L = 330mm
moment arm
Taking P to equal half of
the applied experimental load and
placing experimental data for deflection w,,, and deflection
angle 8s
into equations
(3.7.3) and
107
(3.7.4) respectively,
will
produce the
small
angle
specimen's flexural
rigidity
EIy.
the
accuracy
of
limits
assumption
The
these
equations for anything but small deflections.
5.3.3 Failure Stresses and Strains
compression
were
at failure
Stresses
face
sheet
calculated
using
the
in
for Cr
following
the
point
four
symmetric bending equation.
0, = PI /{2fW[h-fl}
far field
The
(5.3.1)
recorded in Appendix A
stress values
Local failure stress is the
directly from equaiton (5.3.1).
far
field
stress
times
a
come
net
cross-section
correction
factor.
[1/(1 - d/W)]
Cr
The
average failure
stresses
fracture are presented in Table 5.4.
through other modes have been
a
basis for
energy effects
sheet
residual strength
for
(5.3.2)
actual face
Specimens which failed
excluded.
Table 5.4 provides
comparisons between
and specimen parameters, thickness
orientation.
Far-field
sheet
failure
stress
impact
and face
is plotted
versus impact energy and cross-sectional damage for all test
specimens, in Figures 5.11,12,13 and 14.
108
TABLE
5.4
Mean Face Sheet Failure Stresses
.687 in.
.375 in.
64.39 (4)
58.11 (4)
67.09 (4)
0/90
high
21.52 (6)
(28.76] (6)
31.28 (3)
[37.86] (3)
0/90
Med.
25.16 (4)
(28.761 (4)
0/90
Low
31.07 (3)
(34.871 (3)
37.32 (5)
[38.62] (5)
31.76 (5)
[32.601 (5)
+-45
Zero
35.97 (4)
36.58 (3)
50.00+ (3)
+-45
High
25.66 (3)
(33.52] (3)
23.28 (2)
[25.88] (2)
(22.06] (4)
+-45
Med
25.79 (2)
(30.101 (2)
+-45
Low
26.53 (5)
[29.171 (4)
1 in.
Damage
Level
0/90
zero
29.76 (3)
(34.93] (3)
35.44 (5)
[32.60] (5)
20.85 (4)
24.27 (2)
(24.521 (2)
23.70 (3)
24.23 (3)
[24.70] (3)
(23.87] (3)
All stresses are in Ksi units.
[ ] local stresses
( ) number in sample
5.4
PANEL COMPRESSION RESULTS
The
aluminum
fabrication
flaws
honeycomb
which caused
results of Lie's (7] Nomex
panel
test
premature
specimens
failures.
had
The
panel compression tests are more
suitable for determining face sheet failure loads.
109
Failure Stress vs. Impact Energy
[0/90] Panels
0
1
Impact
2
Energy
o
.375"
o
.675"
x
1"
a
.375"
o
.675"
x
1"
3
(ft-Ib)
Failure Stress vs. Impact Energy
[±45] Panels
0
Figure 5.11
1
Impact
Energy
2
(ft-Ib)
Failure Stress vs Impact Energy
110
3
Failure Stress vs. Impact Energy
[0/90] and [0/90]s 1" Panels
70 1
60
-
I
50 -
* [0/90]s
o [0/90]
40 o
0
30 -
0 e%0
o
20
-
_
_I
Impact
Energy
·
·
(ft-lb)
Failure Stress vs. Impact Energy
[±45] and [±45]s 1" Panels
0 [±45]s
o
0
1
Impact
Figure 5.12
2
Energy
3
[+45]
4
(ft-lb)
Failure Stress vs Impact Energy: 2 and 4 ply, 1" Panels
111
Failure Stress vs. Damage Cross Section
[0/90] Panels
70
6C
5C
4C
o
.375" FS
o
.675" FS-FF
x
1" FS-FF
3C
2C
1C
0.0
0.1
0.3
0.2
Damage Diameter / Specimen Width
Failure Stress vs. Damage Cross Section
[+45] Panels
a .375" FS
0.0
0.1
0.2
0.3
Damage Diameter / Specimen Width
Figure 5.13
Failure Stress vs Damage Cross Section
112
0.4
o
.675" FS
x
1"FS
Failure Stress vs. Damage Cross Section
[0/90] and [0/90]s 1" Panels
* [0/90]s
o [0/90]
0.0
0.1
0.3
0.2
Damage Diameter / Specimen Width
,,
Failure Stress vs. Damage Cross Section
[±45] and [±45]s 1" Panels
40
S
40'
-
S*
* [±45]s
30
-
*
0*
*0 *
o
o
o
o
0
20O
-
·
0.0
Figure 5.14
0
I
0
0.1
0.2
0.3
Damage Diameter / Specimen Width
Failure Stress vs Damaged Cross Section:
2 and 4 ply, 1 inch Panels
113
0.4
[±45]
5.5 CORE COMPRESSION RESULTS
Six Nomex coupons with 2
tested
buckling
for core
was
buckling
determined
ply laminate face sheets were
threshold.
The onset
by noticable
sectioned honeycomb cell walls.
waves
of
core
through
the
The average buckling stress
(from two samples) for each Nomex thickness is:
The
1.0 inch
218 psi
.687 inch
221 psi
.375 inch
205 psi
critical
load
for
Nomex
buckling
appears
to
be
independent of thickness and approximately 210psi
5.5.1 Core Indentation Results
Six
Nomex
sandwich
indentation resistance.
coupons
The objective
load/unit area required to buckle
cells at
an impinging
steel cylinder
were
load angle
38.04mm in diameter
tested
for
core
was to determine the
a single row of honeycomb
of 8
to 12
acted as
degrees.
A
the indentor.
The results are summarized below in Table 5.5.
TABLE 5.5
Core Indentation Impinging Loads
Perpendicular to Ribbon
Impinging Angle:
3 - 8 degrees
With Ribbon
3.5 - 10.4 degrees
1 inch core
210psi
262psi
.687 inch core
210psi
222psi
.375 inch core
214psi
2.08psi
114
the normal load/unit area for the
The data is very close to
core as determined with the core compression test.
5.6 PANEL FATIGUE RESULTS
An introductory series of
specimens
panel
fatigue life
of twenty
and
A.11
dimensions
tested
were
twenty eight Nomex honeycomb
for
damaged
under cyclic compression (R=.1).
four specimen tests
A.
of Appendix
listed
are
are reported in
impact energy
The
by specimen
number.
compression stress amplitude is reported
undamaged
and
The results
Tables A.10
and
The
damage
maximum
as a percentage of
the undamaged critical stress as determined by Lie [19], for
each
damage state.
Table
summarizes Lie's
5.6
residual
strength estimates.,
TABLE 5.6
Residual Strength Estimates (Ksi)
Layup
Core
Thickness
Damage Level
medium
low
zero
high
+-45
.687 in.
.687 in.
45.05
29.37
35.67
26.92
32.99
26.22
24.95
24.12
0/90
+-45
1.00 in.
1.00 in.
48.81
30.31
38.46
27.25
35.50
26.38
26.62
23.75
0/90
.375 in.
.375 in.
44.86
27.76
35.08
25.29
32.37
24.58
23.88
22.46
0/90
+-45
The undamaged strength estimates are
in Tables A.10 and A.11.
115
provided as foot notes
The
specimens
maximum
during
stress
their
amplitude was
fatigue life
inflicted immediately as with specimen
altered
because
damage
amplitude is recorded in
Stress Amplitude column
of Tables A.10 and 11.
the cycles at each stress amplitude
Cycles column.
116
some
was
260, or the specimen
was continuing past reasonable life expectations.
each specific stress
for
Cycles at
the Cycles @
The sum of
is recorded in the Life
CHAPTER SIX
DISCUSSION
6.1
IMPACT RESULTS
6.1.1 Impact Force
Refering
energy
level
thicknesses.
to Table
5.2,
for all
energy.
However, the
The
constant
ply
two
force level that remains
Impact
4
force increases
face sheets
and
with
specimen
ply specimens exhibit
a high
constant through escalating impact
impact forces listed
across specimen
in Table 5.2
thicknesses
for
are fairly
a given
impact
energy level.
A
comparison
between specimens
of
constant
impact
energy and core thickness suggests that 10 to 20 more pounds
is exerted on the +-45 specimen
to medium energy level.
are
exactly the
The flexural
orientation
that
phenomena may
and the clamped
stiffness of the
and core
occurs in
as rupture.
bending
stiffness.
stiffness parameters
Table
by
The answer
The
D =
0/90
face sheet
5.2 data
suggests
panel thickness.
with only
lie in
orientation
2.68 in-lb
and D
indentation as
the face
has
= 2.57
These bending stiffness parameters do not support the
117
Fiber
effect because it
a slight
may
face
either end.
panel depends on
does not explain the
face sheets
depend on
boundary at
thickness.
force is not influenced
rupture or breakage
well
Since the 0/90 and +-45 face sheets
same, this
sheet orientation
for every thickness and low
sheet
bending
in-lb.
phenomena.
One
conclusion is clear.
Thicker
face sheets
provide a greater resisting force to impact.
Force versus
Lie's [7]
time histories
of impact
explaination of sudden
rupture at
critical strains
within the face sheet.
as penetration
or fiber
force drops due
and the
Impacts
events support
on set
to fiber
of vibrations
which result in damage such
rupture have
with a steep peak followed by a
force-time history's
slight drop to a plateau of
force oscillations, which then dampens to zero.
6.1.2 Force - Time History
Specimens
histories
with
without
parabolically
oscillations
shaped
force
typically
have
-
time
limited
filament breakage.
The large impact energies exerted on the 4 ply laminate
face sheets (Figure 5.3) can be seen in the force vibrations
following the peak.
These vibrations
by the strain energy released
just
occured
during
vibration phenomenon
by the delaminations that had
impact.
is the
may be caused in part
The
second
part
natural vibration
of
the
modes of
a
plate on an elastic foundation.
The highly damaged
306 and
308 have
4 ply face sheets
significant filament
of specimens #'s
damage.
They
also
have characteristic plateaus and
slow dampening curves with
oscillations.
delamination
plate vibrations
It
appears that
and
contribute to force oscillations
filament fracture causes a plateau
118
of constant
natural
and that
oscillation
followed by slow dampening to zero.
Lie 171 made the same
conclusion.
6.1.3 Impact Energy and Damage Assessment
The data
insight
plotted in Figures
into the
damage to thin
relationship
5.5 and 5.6
between
face sheet panels.
provide some
impact energy
Increased
and
impact energy
will usually cause more delamination, fiber rupture and core
damage.
The
data
variance
indicates
predictions will be subject to
that
theoretical
large deviations.
A band of
values may be an appropriate empirical estimation.
It is evident from both damage plots that the .375 inch
panel and
the .687
inch panel,
resists fiber
delamination better than thicker panels.
thin panel's
flex
reduced flexural rigidity
and absorb
the
impact
This is due to the
which allows
through a
distance (in the impactor's
rupture and
larger
direction of
energy through global strains
localized failure
strains.
more
damage
resistant than
stiffness argument.
deflection
force) and
absorb the impact
The
0/90
thus
instead of
+-45 orientation
the
it to
layup by
would be
the
same
This face
sheet flexibility is evident
in the data plots for the .375
in. and the .687 in. panels.
The
1 in. panel is not influenced
significantly by
face
sheet bending compliance, because of its stiffness.
The 4 ply
surface
face sheet has a much
filament
rupture,than
illustrated in Figure 5.7.
the
greater resistance to
2
ply
laminate,
The delamination area for the
119
as
4 ply
converges with the delamination
the 2
the 1.8 ft-lb threshold is
ply face sheet (Fig. 5.8), after
energy for filament rupture
The threshold impact
attained.
area plot for
is almost 3 times greater for the 4 ply, and 2 times greater
for
diameters which
for
dye
Note:
of delamination.
the initiation
and
injection
should
be
damage
artificially induced
.1 are
are less than
4 ply
ignored
for
damage
assessment.
Face sheet thickness is
and penetration.
core from indentation
a 2 ply face
will rupture
penetrate a
instrumental in protecting the
sheet.
2 ply face sheet
A 2.0
ft-lb impact
impact will
A 3.0 ft-lb
will only
into the core, but
make a small .8mm dent in a 4 ply face sheet.
6.1.4 Damage
occurs in an increasing
Face sheet damage
sequence of
damage levels as follows:
core indentation
delaminations and
damage may hide small
1) No external
may be hidden
under an
unmarked laminate
surface.
2) External matrix
dimple indicate
cracks between
tows
some delamination, slight
and a
slight
core indentation
and debonding.
3) A significant
individual
filament
dimple with matrix cracks
beakage, and
will
may contain
certainly
contain
delamination and core indentation on the order of .8mm.
120
Ruptured tows
4)
will be
accompanied
by many
matrix
cracks in the dimple and core indentation depth of 1mm.
5)
Face
sheet
rupture
will
be
evidenced
by
four
triangular flaps bending down into the dimple.
6) Face sheet
greater
than
penetration will have a
1.5mm
and significant
shoulder of the dimple.
cracking
around
the
The core may be visible.
66 and 29
provided in
3 of Appendix A, display damage
levels 2, 4
X-ray photographs
Figure A.1, 2,
core indentation
of specimens 208,
and 6, respectively.
Figures A.4
of 4 ply specimens 303 and
& 5 are x-ray photographs
321, which display damage levels
3 and 5, respectively.
All
of
these
x-ray photographs
rupture
in
through
an accumulation
tows.
Figure
A.3)
This shows up as
display
of
Figure
delaminations
axis.
A.2
face
for
sheet
delamination
parallel to
These delaminations
Note that
the
ends
66
also
of each
at damage level 4
displays
central
are caused by
tows bending excessively at the shoulder of the dimple.
delamination relieves
filament strain and
rupture as in damage level 6, penetration.
121
the
to +-45 and the others to
containing specimen
perpendicular to
severe
orientation
dark perpendicular axes.
specimens 29 and 303 are oriented
0/90.
(except
The
prevents further
6.2
RESIDUAL STRENGTH
6.2.1 Analytical Comparisons
The basis for residual strength predictions lies in the
ability to accurately calculate
from predicted
establish
or measured
confidence
in
loads, moments and stresses
failure strains.
the
analytical
In order
method,
a
to
few
calculations will be discussed.
Equation (3.8.7)
was used
with the
TELAC and
BOEING
reduced stiffnesses matrices to calculate the bending moment
Mx , for
the (0/901 1"
failure were used
the fracture
was
then
specimens.
Strain
gauge values at
to calculate the far field
site) bending moments.
compared
to
the
determine the differential.
The
measured
and local (at
analytical moment
failure
moment
to
The results are:
TELAC
BOEING
-.86%
1.64%
8.76%
9.95%
16
18
6.65%
10.99%
std. deviation
12.46%
13.64%
sample size
13
13
Mx far field differential
std deviation
o
sample size
M. local field differential
The local
errors in Mx
specimens
are failing
gauges would indicate.
of
6.65 and 11% indicate
at a
lower load
than their
that the
strain
The thin face sheet laminate becomes
alastic - plastic very quickly which would account for this
122
loss
of load
bearing
per unit
of
strain.
greatest
The
plastic stretching occurs in the local failure cross section
either side of the inclusion.
The stress-strain relation {OM)
and TELAC Qgj
using experimental strains
1"
panel
groups
and
= [Qij]{(;} was calculat-
the
values,
.687"
(0/90]
for both
specimens.
The
deviation results from experimental stresses are:
Core
Percent Difference
0. (far field)
",y
(local)
Face sheet
1 in.
0/90
1.3 [9.91 (17)
-.59 [5.8] (9)
1 in.
+-45
-2.6 [191 (10)
121.0 [521 N/A
.687 in.
0/90
-4.9 (9.6] (8)
3.5 [17.7] (8)
[ I Sample standard deviation in percent
( ) Sample size
The +-45 panel
to
its 121%
stress.
has a very non-linear
error between
gauge
local region refering
computations and
actual
The large standard deviations in strain measurement
on the +-45 face sheet is probably due to gauge orientation
diagonally
on
the
laminate's
weave
where
slight
shear
strains become large extensional strains.
6.2.2 Failure Stress and Impact Energy
Figure
5.11
shows
a pattern
stress as impact energy increases.
core
thickness
of
decreasing
The data indicates that
is significant in determining
123
failure
far
field
failure stress
for the
0/90 panels, but
panels. The +-45 data points
not for
the +-45
in Figure 5.11 are practically
independent of thickness and marginally influenced by impact
energy.
Figure 5.13
independent of
data indicates that the
damage diameter.
conclusion that +-45 laminates
This leads
+-45 panel is
to Lie's
are notch insensitive.
[7]
That
is, loads are easily carried around damaged areas.
The
+-45
orientation
of
tows
effectively around damage sites as
intact.
When the matrix starts
the tows cannot carry load
which
further damages
the
nature is the key to the
can
transfer
loads
long as the matrix stays
to crack at large stresses,
without inducing shearing strain
matrix.
The matrix
+-45 panels damage
dependent
tolerance and
also its limit on strength.
The
0/90 panel's
susceptability
0/90 panel
threshold
stiffness contributes
and reduced
residual
1 in. thick loses
impact of
A
damage
damaged
its strength
Thinner
damage resistant but still loose
their strength
strength.
50% of
.9 ft-lbs.
to its
from a
panels are
more
approximately 40 to 50% of
from a threshold impact.
Notch sensitivity
is demonstrated by the huge drop in residual strength due to
a damage diameter of any size.
Doubling
the face
sheet
thickness
makes both
orientations more damage resistant and damage tolerant.
10/901s laminate is more tolerant of surface
than the 2
ply version.
The [+-45]s has
of elasticity .(determined through
124
linear
layup
The
fiber rupture
a greater modulus
regression
of
data)
stress-strain
the
are
improvements
the
2
of
result
by
provided
stiffness
than
laminate.
ply
extra
the
and
more matrix
Both
and
support
fabric.
filament
Buckling instability and matrix cracking are reduced through
greater stiffness.
Damage Propagation
6.2.3
Face dimpling was observed during testing, but only for
face sheets with
cell's size
of a
axis)
and the
stiff through
characteristic
face
The graphite/epoxy
were observed.
is too
sheet used
on the order
No dimples
observed damage.
its thickness
dimension
(in the
f/d described
z
by
Weikel et. al. [15] is too large for any 1/8 inch dimples to
appear before global buckling takes place.
that
appear were
did
indentation in
supported
by
the core (typically
The indentations
the perimeter
1/2 inch
of
an
in diameter).
Experiments demonstrated that a small indentation or rupture
in
the
face sheet
elliptical dimple
bending
and
elliptical
due
to
an
impact, propagates
transverse to
column
the loading
compression
dimple reaches
a
tests,
critical
as
axis in
[7].
Once
length, face
an
both
the
sheet
buckling occurs.
The
following hypothesis
experimental observations.
loading because of
edges of a
damage
is offered
Damage
to explain
propagates transverse to
maximum principle stress at
damage inclusion.
inclusion over
Local buckling
a weakened
125
the
core,
the lateral
occurs in the
which causes
the
plate
to
deflect
resistance).
into
Because
the
third
the
dimension
panel
is
compressed plate will deflect (locally)
greater radius of
As the
in the
bending,
transverse direction,
of the expanding dimple deflection.
the honeycomb core are buckled at
the
honeycomb core).
down and slightly from the side
the
by the tip
The thin cell walls of
the tip of the elliptical
damage propagation.
The
cells can no longer
stresses
the
core face
normal to
least
in the direction of
curvature (ie: into the
dimple elongates
core is crushed
in
(of
support local
(parallel
to the
cell
axis), and the sandwich panel cannot transfer loads properly
in the dimple
indentation.
The face sheet
finally buckles
due to the loss of effective load bearing cross-section.
The dimple
Figure
6.1,
in the direction
Longitudinal Section
illustrates the
tows which
does not expand
unloaded and
pass through
of
Dimple
Indentation,
loaded condition
the damage
dimple.
of load.
of filament'
The
core has
pre-existing damage from the impact event which produced the
indentation.
indentation are
Core cells
beneath
crushed further
an
unloaded face
during bending
sheet
by greater
face fiber deflection and localized load/unit area, Oz.
The
localized load/unit area on the crushed core will decrease
when
the
deflected tow's
load
Cr,
is reduced.
Thus
equilibrium between the core's damage resistance threshold
126
an
ox=0
z
W-J
(Wx
wJx
=0
undeflede
daIte
line
11
z X4
z
=0
before loading
Figure 6.1
during loading
Longitudinal Section of Dimple Indentation
(Czto buckle) and the crushing load/unit area T7 = O~(w"+ w
caused
by
deflected
propagation
of
the
face
sheet
tows,
deflection in
the
arrests
direction
further
of
the
fiber/tow axis.
The load carried by a tow fibers which passes through a
face
sheet
indentation
That
deformation.
adjacent
tows.
graphite/epoxy
longitudinal
will
excess
The
loads can
reduced
because
load
must
be
of
load
transmission
means
laminate
be
is
the
be shared
127
epoxy
through
of
transmitted
in
to
a
matrix.
If
the matrix,
it
follows
that
adjacent tows
out of
plane
of 0'z
addition
loads
to the
and
transmitted
to
The woven
this experiment makes the lateral
loads
The
tow and
tows
through warp
possible
matrix.
ultimate
can be
loading face plane.
still in the
face sheet fabric used in
transmission
loads
lateral transmission
face
buckling
in
of
C.'
with
differs
loading orientation.
6.2.4 Mar - Lin Relation
failure stresses for the
Damage diameter and localized
1 inch, 2
taken from Tables
ply face sheet specimens, were
equation (3.10.19), the Mar-Lin (171
A.1 and 2, and used in
relation.
Solving
for
Hc, the
parameter,
fracture
the
following values were attained:
Mean Hc
Std. Deviation
Sample Size
0/90, 1i" panel
22.55
3.0
12
+-45, 1" panel
23.18
4.2
10
fracture parameter units are 10
The
fracture
indicating
parameters
that
Hc
is
are
lb./cu. in.
within
dependent
3%
on
of
each
material
other,
and
not
using
the
orientation (17].
Figures
6.2
and
6.3
have
been
calculated fracture parameter, equation
lines as did Lie (7].
plotted
3.10.19 and tangent
Data points have also been plotted to
illustrate the accuracy of the approximation.
128
-^
50
40
30
20
10
0
0.0
0.1
0.2
0.3
0.4
0.5
Damage Width (d/W)
Figure 6.2 Mar-Lin Residual Strength; +-45, 1" Panels
0.0
0.1
0.2
0.3
0.4
0.5
Damage Width (d/W)
Figure 6.3 Mar-Lin Residual Strength; 0/90, 1" Panels
129
6.3 PANEL LONGEVITY
Undamaged 0/90
669,000 cycles at
above 90% appear
panels have
a longevity
loads as high as 90%
in excess
of buckling.
to weaken the matrix
of
Loads
after 40,000 cycles,
leading to eventual buckling.
The +-45
panels have
a reduced
life at
much smaller
loads, because damage
accumulates in the matrix
or
The
stress
cracks.
longitudinal compression
large
of the
lateral
as fatigue
extension
face sheet
as it
and
cycles,
induces matrix cracking.
To attain a 100,000 cycle life for a 0/90 panel damaged
by a
threshold impact
must
be
50%
orientation
or
less of
the
buckling
inability
load amplitude
load.
The
to transfer
not lasting more than 210 cycles
0/90
loads
at 50% 0
with a damage diameter of 15mm.
Threshold
impacts of
specimens
are tolerated
cycles at
69% and
buckling load.
those
ft-lbs., the
demonstrates its
around damage by
critical,
of 1.1
carried
1.1 ft-lbs
well with
211,320 cycles
These loads are
by
the 0/90
because of the +-45 panel's
on
almost
at 73%
+-45 face
half a
of the
at
47%.
million
critical
approximately the
columns
sheet
same as
Therefore,
ability to transfer load around
ruptured fibers, it can carry moderate loads longer than the
0/90 panels with damage.
Three
series
of
provided in Appendix A.
fatigue
Figure
specimen
photographs
are
A.15 illustrates the growth
of a dimple in Specimen # 166 (0/90), maximum load amplitude
130
2878 lbs (R=.1).
measured just
specimen (#
series
The 40mm dimple in the last photograph was
before failure.
156) at fracture.
of photographs
Specimen #
Figure
Figure A.17 is
and dimple
164, a 0/90 face
A.16 depicts
sheet.
unique in that it propagated in
an extended
length measurements
This failure
for
mode was
only one direction and then
continued to carry the load with one face fractured.
131
a +-45
CHAPTER SEVEN
CONCLUSIONS AND RECOMMENDATIONS
7.1 CONCLUSIONS
impact
determining
A
explored.
and
limitations
panel
identified
longevity
damage tolerance
investigation
preliminary
effect of
The
modes.
on damage resistance and
panel parameters
was
and failure
bending moment
under a
strength
residual
dimensions,
damage
of
goals
its
accomplished
investigation
This
panel
of
for
areas
expanded research.
observations support the
Test results and experimental
minimum
about
conclusions
following
gauge
sheet
face
graphite/epoxy plain weave
sandwich panels constructed from
fabric and Nomex honeycomb cores of various thickness:
-
Increased
face
sheet
thickness
increases
damage
resistance for both the face sheet and core.
- A
reduction in
core thickness
leads to
more impact
damage resistant due to greater bending flexibility.
- Impact
sheet
increases with
force amplitude
thickness
because
of
its
inherent
increased face
plate
bending
stiffness.
-
The
+-45 face
sheet
has
some damage
quasi-static loading because it can
damaged area.
- The
tolerance
for
transfer loads around a
Failure loads depend on matrix strength.
0/90 face sheet
has limited damage
tolerance for
quasi-static loading because it cannot transfer loads around
132
a damaged area.
- The Nomex core was the failing component for most 4 ply
and
panels
undamaged
face
two-ply
sheet
not
panels
reinforced with an aluminum core.
relation provides a good
- The Mar-Lin
approximation of
residual strength for a given damage cross section ratio.
- Face sheet
dimple indentation length is
a function of
load and existing laminate and core damage.
-
To attain
by
damaged
a
100,000 cycle
a threshold
impact
life
of
for
a 0/90
1.1 ft-lbs,
the
panel
load
amplitude must be less than 50% of the buckling load.
-
The ability
of +-45
face sheets
to transfer
loads
compression loads of 60%
around damaged areas allows cyclic
critical, to reach half a million cycles.
- Face
laminate
sheet dimple growth can
at
cyclic
critical and in
be observed in
compression
loads
+-45 laminates at cyclic
greater
the 0/90
than
50%
compression loads
greater than 60% critical.
- The undamaged 0/90 panel has a
fatigue life of 669,000
cycles at 90 to 95% critical load.
7.2
RECOMMENDATIONS
The
sandwich
growth of
panel made
fatigue loading,
damage in
a minimum
from AW193PW/3501-6
merits further
gauge face
under static
investigation. Areas
sheet
and
that
need further exploration include:
- Properties of panels with
133
different layups and loading
orientations.
- Strength properties of other core materials.
- Impact
effects on panels
subjected to
in-plane loads
and/or bending moments.
- Development
of an
analytical model
which describes
dimple formation and propagation to global failure.
- Fatigue life of damaged panels at low loads.
- Fatigue
life of damaged
panels under
compression, tension-tension and
compression -
compression-tension cyclic
loading.
-
Damage
fatigue life,
delamination,
development
within
a
panel
as measured by reduced
crack
length,
crack
throughout
its
stiffnesses, expanded
population,
broken
filaments and residual strength.
- Damage
resistance and tolerance
at various
stages of
panel life.
- Residual strength and fatigue
life of panels subjected
to high humidity and water ingestion.
- Damage resistance
and/or
of hybrid panels with
modified epoxies
at
various
multiple material lamina.
134
buffer strips
volume fractions
and
REFERENCES
[11
Oplinger, D.W. and Slepetz, J.M., "Impact Damage
Tolerance of Graphite/Epoxy Sandwich Panels", Foreign
Object Impact Damage ta Composites, ASTM STP 568x
American Society for Testing and Materials, 1975, pp.
30-48.
[21
Rhodes, M.D., "Impact Fracture of Composite Sandwich
Structures", AIAA Paper No. 75-748, 16th Structures,
Structural Dynamics and Materials Conference., Denver,
CO, May 1975.
[3]
Adsit, N.R. and Waszczak, J.P., "Effect of Near-Visual
Damage on the Properties of Graphite/Epoxy,"Composite
Materials: Testina and Design (Fifth Conference), ASTM
TPE 674, pp. 101-117.
[4]
Guynn, E.G. and O'Brien, T.K., "The Influence of
Lay-Up and Thickness on Composite Impact Damage and
Compression Strength", AIAA Paper No. 85-0646
[5]
Husman, G.E., Whitney, J.M. and Halpin, J.C.,
"Residual Strength Characterization of Laminated
Composites Subjected to Impact Loading", ForeiQgn
Object Impact Damage to Composites, ASTM STP 568,
American Society for Testing and Materials, 1975,
pp. 92-113
[6]
Bernard, M.L., "Impact Resistence and Damage
Tolerance of Composite Sandwich Plates", S.M. Thesis,
Massachusetts Institute of Technology, May 1987
[71
Lie, S.C., "Damage Resistance and Damage Tolerance of
Thin Composite Facesheet Honeycomb Panels", S.M.
Thesis, Massachusetts Institute of Technology,
March 1989
[8]
Ramkumar, R.L., "Effect of Low-Velocity Impact on the
Fatigue Behavior of Graphite/Epoxy Laminates",
Long-Term Behavior of Composites. ASTM STP 813,
T.K. O'Brien, Ed., American Society for Testing
Materials, Philadelphia, 1983, pp. 116-135
[91
Camponeschi, E. T. and Stinchcomb, W. W., "Stiffness
Reduction as an Indicator of Damage in Graphite/Epoxy
Laminates,"Composite Materials: Testing and Design
(Sixth Conference), ASTM STP 787, I. M. Daniel, Ed.,
American Society for Testing and Materials. 1982, pp.
225-246.
110]
Chou, P.C. and Croman, Robert, "Degradation and
Sudden-Death Models of Fatigue of Graphite/Epoxy
Composites,"Composite Materials: Testing and Design
I
1
(Fifth Conference),. ASTM STP 674 pp. 431-454.
(11]
Reifsnider, K.L., and Duke, J.C., "Long-Term Fatigue
Behavior of Composite Materials", Long-Term Behavior
of Composites, ASTM STP 813, T.K. O'Brien, Ed.,
American Society for Testing and Materials,
Philadelphia, 1983, pp. 136-159
(12]
Jones, R.M., "Mechanics of Composite Materials",
Scripta Book Company, Washington, D.C., 1975
[13]
Tsai, S.W., Halpin, J.C., and Pagano, N.J. (eds.):
"Composite Materials Workshop", Technomic Publishing
Co., Wesport, Conn., 1968
(14]
Timoshenko, S., "Strength of Materials", D. Van
Nostrand Company Inc., New York, N.Y., 1950
[15]
Weikel, R.C. and Kobayashi, A.S., "On the Local
Elastic Stability of Honeycomb Face Plate Subjected
to Uniaxial Compression", J. Aero/Space Sci., 26,10,
Oct. 1959, pp. 672-674
[16]
Plantema, F.J., "Sandwich Construction", John Wiley &
Sons, Inc., New York, N.Y., 1966
(171
Mar, J.W., and Lin, K.Y., "Characterization of
Splitting Process in Graphite/Epoxy Composites",
Journal of Composite Materials, Vol. 13, October 1979
[181
Federson, C.E., "Evaluation and Prediction of Residual
Strength of Center Cracked Tension Panels", Damace
Tolerance in Aircraft Structures, ASTM Special
Technical Publication 486, 1970
[191
Lie,S.C. and Mar, J.W., "Damage Resistance and Damage
Tolerance af Minimum Gauge Honeycomb Structures",
TELAC Report 88-10, Dept. of Aero/Astronautics, MIT
1988
[201
Bhatia, N.M., "Strength and Fracture Characteristics
of Graphite-Glass Intraply Hybrid Composites,
"Composite Materials: Testing and Design (Sixth
Conference), ASTM
=STe 787
L.
i•
Daniel.- Ed.i
American
Society for Testing and Materials, 1982, pp. 183-199.
1211
Williams, J.G. and Rhodes, M.D., "Effect of Resin on
Impact Damage Tolerance of Graphite/Epoxy Laminates,"
Composite Materials: Testing and Design (Sixth
Conference). ASTM STP 787, I. M. Daniel. Ed., American
Society for Testing and Materials, 1982, pp. 450-480.
-0
1%1
APPENDIX A: EXPERIMENTAL RESULTS;
TABLES AND FIGURES
This appendix contains experimental results presented
in tabular form and photographs.
137
TABLE A.1
RESIDUAL STRENGTH TEST RESULTS
Spec.
#
Impact
Vel.
[ft/s]
Impact Damaged
Area
Energy
[ft-lb]
d/W
[sq in]
Failure Failure Failure
Stress Stress
Moment
(far) (local)
[Ksil
[in-lb]
[Ksil
1 Inch Panels; [+-45]
0.206
0.304
0.256
0.242
0.174
0.174
0.205
0.158
0.141
0.201
782
951
1026
857
1195
18.56
28.12
24.22
19.87
24.65
22.
35.
28.
23.
30.
1.13
0.155
*
0.223
0.108
0.129
0.173
1068
1085
1111
25.30
25.61
26.28
28.42
28.75
31.78
0.136
0.143
0.101
0.071
0.028
0.014
1152
1161
1120
1174
1119
1121
27.04
25.97
26.31
27.48
25.78
26.04
31.32
35.24
29.25
1
2
3
@ 4
17
7.35
7.23
6.99
6.01
5.55
2.84
2.74
2.57
1.89
1.61
6
7
8
4.64
5.20
1.42
0.171
9
10
11
12
13
19
4.79
1.21
1.35
1.23
1.21
1.10
0.69
0.140
@
#
@
5.08
4.85
4.79
4.59
3.61
0.155
0.084
0.074
0.076
0.02
@
@
@
14
15
16
1144
1163
1217
26.96
27.30
28.45
J
36
37
38
39
1492
1566
1618
1459
35.37
36.64
37.72
34.15
*
denotes lost data
buckling under loading point
core crushed
fracture over or adjacent to Nomex/aluminum joint
138
29.59
26.52
*
TABLE A.1 (cont.)
RESIDUAL STRENGTH TEST RESULTS
Spec.
Net Strain to Failure
Gage 1
Gage 2
Gage 3
Gage 4
Gage 5
1 Inch Panels; [+-45]
1
2
3
4
17
-0.01686
6
7
8
9
10
11
12
13
19
0.0051
0.0133
0.00781
0.00571
0.01208
-0.0076
-0.0083
-0.00826
-0.00644
-0.01084
0.00513
0.00663
0.00654
-0.01407
-0.01185
-0.01084
0.01137
-0.01107
0.01029
-0.01017
0.01051
-0.01028
0.01027
0.00904
0.00966
-0.01348
-0.01221
-0.01232
-0.01252
0.00994
0.01162
-0.01106
-0.01293
0.00851
0.01011
-0.01181
-0.01289
-0.01092
-0.00968
-0.01101
0.00876
-0.01141
-0.01447
0.01297
-0.01442
0.01091
-0.01215
-0.01123
-0.00728
-0.01369
-0.01231
0.00512
-0.00728
-0.00852
-0.00924
-0.00715
-0.01056
-0.01018
-0.01234
-0.01459
0.01078
*
0.010
14
15
16
-0.01471
-0.01508
-0.01656
0.01221
0.01291
0.01412
36
37.
38
39
-0.02466
-0.02525
-0.02391
-0.02194
0.02164
0.02093
0.01987
0.01641
139
-0.00872
TABLE A.2
RESIDUAL STRENGTH TEST RESULTS
Spec.
#
Impact
Vel.
Impact Damaged
Area
Energy
d/W
[ft/s] [ft-lb] [sq in]
Failure Failure Failure
Stress Stress
Moment
(far) (local)
[Ksi]
[Ksi]
[in-lb]
1 Inch Panels; [0/90]
42
51
52
53
54
65
5.88
6.06
6.25
6.45
6.45
5.47
48
49
50
64
41
43 @
44
45 #
46
4.
3.
4.
3.
4.
920.
930.
993.
898.
803.
994.
21.51
21.67
23.17
20.91
18.76
23.09
25.98
26.59
28.97
25.65
22.84
28.36
0.157
0.071
1067.34
1037.03
1047.86
1152
25.14
24.12
24.41
26.98
29.37
27.66
28.95
29.04
0.101
0.036
0.135
0.007
0.085
1334
1418.07
1513.33
1026.21
1140.95
31.16.
33.03
35.24
24.95
26.81
34.59
34.27
40.74
25.12
29.29
2613.15
2305.72
3056.98
2940.07
61.25
55.45
71.53
69.32
1.811.93
2.05
2.19
2.19
1.57
0.155
0.261
0.279
0.316
0.322
0.192
0.172
1.37
1.37
1.53
1.03
0.155
0.205
0.205
0.105
0.144
.94
0.74
1.03
0.83
1.05
0.074
0.074
0.078
0.099
0.155
buckling under loading point
core crushed
140
0.185
0.201
0.185
0.178
0.186
0.128
TABLE A.2 (cont.)
RESIDUAL STRENGTH TEST RESULTS
Spec.
Net Strain to Failure
Gage 1
1 Inch Panels;
48
49
50
64
60
61
62
63
Gage 2
Gage 3
Gage 4
Gage 5
[0/901
-0.00280
-0.00272
-0.00334
-0.00260
-0.00238
-0.00302
.00012
.00012
.00016
.00006
.00012
.00012
-0.002461
-0.001881
-0.002961
-0.002501
-0.002421
-0.00251
-0.00104
-.00002 -0.001101
.00014 -0.001321
.00008 -0.001261
.000120
-0.00134
-0.00328
-0.00328
-0.00272
.00004
.00006
.00016
.00014
-0.003161
-0.002641
-0.002801
-0.00268
-.00004
.00010
.00008
-0.001501
-0.001461
-0.001401
-0.00718
-0.00400
-0.00316
-0.00236
-0.00358
.00006
.00048
.00063
.00030
-0.00364
-0.003241
-0.003501
-0.002421
-0.003161
.00070
.00035
-0.002581
-0.002121
-0.002201
-0.00711
-0.00639
-0.00845
-0.00760
.00082
.000334
.000485
.00078
-0.007061
.000770
-0.00316
-0.00738
11
1
.00014
TABLE A.3
RESIDUAL STRENGTH TEST RESULTS
Spec. Impact
#
Vel.
(ft/s]
Impact Damaged
Energy Area
(ft-lb]
Failure Failure Failure
Moment Stress Stress
(far)
(local)
[Ksi]
[Ksil
[in-lb]
d/W
[sq in]
.687 Inch Panels; [+-451
121
122
123
5.88
5.97
5.88
1.81
1.87
1.81
0.354
0.381
0.282
0.114
0.156
0.086
730.01
689.01
667.01
23.99
23.28
22.56
27.08
27.58
24.68
113
114
115
116
4.42
4.52
4.63
4.63
1.03
1.07
1.13
1.13
0.078
0.084
0.144
0.21
0.014
0.014
0.028
0.014
719.01
751.01
773.01
697.01
24.35
25.42
26.14
21.13
24.69
25.78
26.89
21.43
0 686.00
0 1026.00
0 1005.00
0 983.00
25.65
38.63
37.81
33.31
117 D
118
119
120 J
*
@
D
J
denotes lost data
buckling under loading point
face sheet debonding failure
fracture over or adjacent to Nomex/aluminum joint
142
TABLE A.3 (cont.)
RESIDUAL STRENGTH TEST RESULTS
Specimen
Number
Net Strain to Failure
Gage 1
Gage 2
Gage 3
Gage 4
Gage 5
.687 Inch Panels; [+-451
121
122
123
-0.011131
-0.012081
-0.012961
.009460
.009320
.011180
-0.011131
-0.009101
-0.009401
.008080
.007880
-0.011641
-0.010421
-0.010361
113
114
115
116
-0.010861
-0.011661
-0.014101
-0.011141
.008720
.010800
.010900
.008600
-0.009261
-0.011071
-0.010741
-0.008981
.008160
.008780
.008140
.007920
-0.010241
-0.011461
-0.001131
-0.011141
117
118
119
120
-0.012541
.007500
-0.003381
-0.022781
.027961
0.020901 -0.015621
143
0.017001
TABLE A.4
RESIDUAL STRENGTH IMPACT RESULTS
Spec.
#
Impact
Vel.
[ft/s]
Impact Damaged
Area
Energy
[ft-lb]
[sq in]
d/W Failure Failure Failure
Stress Stress
Moment
(far) (local)
[Ksi
[Ksil
[in-lb]
.687 Inch Panels; [0/90]
108
109
110
6.45
6.45
6.25
2.18
2.19
2.05
0.194
0.341
0.256
0.171
0.171
0.179
920.01
868.01
983.01
105
106
107
111
112
4.33
4.28
4.19
3.98
5.69
0.98
0.96
0.92
0.124
0.135
0.099
0.062
0.062
0.071
0.064
0.086
0.043
0.029
0
0
0
0
0.83
1.71
126
127
128
129
101 @
37.59
35.46
40.54
1258.01
953.01
1059.01
1024.01
1068.01
42.
32.
37.
37.
36.
45.
34.
39.
36.
37.
1555.00
1724.00
1459.00
1492.00
56.
63.
55.
56.
1195
1228
102 @
@
31.16
29.41
33.28
buckling under loading point
1AA,
40.47
41.54
TABLE A.4
(cont.)
RESIDUAL STRENGTH TEST RESULTS
Specimen
Number
Net Strain to Failure
Gage 1
.687 Inch Panels;
108
109
110
-0.003351
-0.005231
-0.003701
105
106
107
111i
112
-0.004811
-0.004101
Gage 2
Gage 3
Gage 4
Gage 5
.000100
.000080
.000100
-0.001401
.000110
.000780
.000280
-0.002461
[0/901
.000050
-0.003281
.000090
.000100
-0.002871
-0.003331
.000560
-0.003661
-0.003681
-0.004321
.000300
.000480
-0.004741
-0.004421
.000600
.000680
126
127
128
129
-0.011131
.000340
101
102
-0.005241
.000660
-0.006451
-0.006641
.001020
.000580
-0.00472
.000600
-0.00456
.000440
145
-0.004321
-0.003781
-0.004281
-0.005841
-0.001021
-0.001791
-0.002001
-0.002361
-0.002101
-0.002841
-0.00146
TABLE A.5
RESIDUAL STRENGTH TEST RESULTS
Spec
#
Impact
Vel.
Impact Damaged
Energy
Area
d/W
(ft/s] (ft-lb] [sq in]
Failure Failure Failure
Moment
Stress Stress
(far) (local)
[in-lb]
[Ksi]
(Ksi]
.375 Inch Panels; [+-45]
223
239
240
241
5.97
5.97
5.88
6.06
1.87
1.87
1.81
1.93
0.328
0.223
0.308
0.236
.115
.014
.028
.058
237
238
4.58
4.63
1.11
1.13
0.007
0.033
221
234
235
236
3.91
4.14
4.14
4.14
0.81
0.91
0.91
0.91
0.013
0
0.007
0
230
231
233
$
327.
349.
338.
349.
20.01
21.35
20.70
21.35
22.61
21.65
21.30
22.67
0.007
0.014
403.00
392.00
24.59
23.94
24.76
24.28
0.014
0.007
0.007
0.007
370.00
381.00
381.00
925.00
814.00
647.00
discontinued without failure
146
not tested
23.06
23.22
23.70
23.87
24.34
24.51
56.04
49.96
39.59
TABLE A.5 (cont.)
RESIDUAL STRENGTH TEST RESULTS
Spec.
Net Strain to failure
__
Gage 1
Gage 2
Gage 3
Gage 4
Gage 5
.375 Inch Panels; [+-45]
223
239
240
241
-0.003021
-0.009261
-0.008601
-0.009231
.000200
.006681
-0.005521
-0.008281
-0.007481
-0.007731
.000100
.006901
-0.009001
237
238
-0.012841
-0.009301
.009380
-0.009961
-0.008581
.008040
-0.011141
-0.023861
-0.02112
-0.018741
.016900
.015920
.014020
221
234
235
236
230
231
233
1/17
.012770 -0.014541
TABLE A.6
RESIDUAL STRENGTH TEST RESULTS
Spec.
#
Impact
Vel.
Impact Damaged
Energy
Area
(ft/s] ift-lb] [sq in]
.375 Inch Panels;
(0/90]
212
217
218
219
6.06
6.06
6.15
6.15
1.93
1.05
1.99
1.99
0.174
0.181
0.186
0.131
0.143
0.157
0.143
0.143
667.01
518.01
466.01
444.01
209
210
211
5.54
4.86
539
1.61
1.24
1.53
0.155
0.087
0.155
0.065
0.036
0.114
487.01
624.01
645.01
204
205
206
207
208
4.33
4.23
4.1
4.19
4.32
0.98
0.94
0.88
0.92
0.98
0.013
0.039
0.074
0.031
0.056
0.014
0.014
0.014
0.036
0.05
528.01
225
226
227
228
202 @
203 ^
@
d/W Failure Failure Failure
Moment Stress Stress
(far) (local)
(in-lbs]
[Ksil
[Ksil
19.63
31.71
29.76
27.82
39.07
31.51
39.21
44.09
528.01
539.00
528.00
498.01
32.02
32.02
32.66
32.02
30.1
32.48
32.48
33.13
33.22
31.68
1100.00
1068.00
1152.00
1068.00
67.28
65.29
70.46
62.76
589
814
36.03
39.63
29.46
37.79
buckling under loading point
core shear and buckling failure
fracture over or adjacent to Nomex/aluminum joint
148
37.61
34.73
32.46
TABLE A.6 (cont.)
RESIDUAL STRENGTH TEST RESULTS
Spec.
Net Strain to Failure
Gage 1
Gage 3
Gage 2
Gage 4
Gage 5
.375 Inch Panels; [0/901
212
217
218
219
-0.002021
-0.004341
-0.004281
-0.005101
.000141
209
210
211
-0.003861
-0.004591
-0.004971
.000100
.000650
.000110
-0.003461
-0.003871
-0.004361
.000120
.000100
.000090
-0.001761
-0.002211
-0.001731
204
205
206
207
208
-0.007321
-0.004001
-0.004261
-0.004321
-0.00398
.000600
-0.003761
.000260
-0.002521
.000040
-0.004381
-0.003761
-0.003601
.00012
225
226
227
228
-0.007621
-0.006961
-0.007861
-0.006741
.000680
.000440
.000880
.000580
-0.007041
.000320
202
203
-0.00437
-0.00449
.000320
.000380
-0.00398
-0.00452
.000420
.00038
-0.003361
-0.003441
-0.003621
-.003660
149
-0.00206
TABLE A.7
RESIDUAL STRENGTH TEST RESULTS
Spec. Impact
# Velocity
Impact Damaged
Area
Energy
[ft/s] [ft-lb]
d/W
[sq in]
Failure Failure
Stress
Moment
(far)
[Ksil
[in-lb]
Failure
Stress
(local)
[Ksi]
1 Inch Panels; [+-45]s
308 D
309 D
310 D
8.03
7.57
7.87
3.39
3.01
3.26
0.611
0.243
0.394
0.127 994.00
0.086 1487.00
0.086 1451.00
23.00
34.93
34.05
26.38
38.22
37.25
305 ^
306 #
312 D
7.03
8.56
6.79
2.59
3.85
2.42
0.184
0.617
0.025
0.028 1555.00
0.185 1661.00
35.97
38.42
37.58
47.85
0.014
301
302 ^
303 #
311 ^
6.35
6.35
6.25
6.06
2.12
2.12
2.05
1.93
0.197
0.164
0.171
0.056
0.014
0.014
0.014
0.014
*
denotes lost data
D
^
#
face sheet debonding failure
core shear and buckling failure
core crushed
150
*
1533.00
1924.00
1901.00
1152.01
*
35.48
45.12
44.62
26.97
*
36.51
45.83
45.25
27.32
TABLE A.7 (cont.)
RESIDUAL STRENGTH TEST RESULTS
Spec.
Net Strain to Failure
Gage 1
Gage 2
Gage 3
Gage 4
Gage 5
1 Inch Panels; [+-451s
308
309
310
-0.004221
-0.006501
-0.006601
305
306
312
-0.007341
-0.008601
301
302
303
311
-0.008001
-0.011701
-0.011621
-0.003501
.002970
-0.003461
.005940
-0.007041
-0.007561
.005341
-0.006901
.006010
.009670
.009930
-0.007141
.005400
.011771
.009610
-0.007401
-0.017341
-0.012641
.005300
1 C1
TABLE A.8
RESIDUAL STRENGTH TEST RESULTS
Spec. Impact
# Velocity
Ift/s]
Impact Damaged
Energy
Area
d/W
[ft-lb] [sq in]
Failure Failure Failure
Moment Stress Stress
(far) (local)
[in-lb]
[Ksil
[Ksi
1 Inch Panels; [0/90]s
#
321 #
322
323
7.57
7.72
7.72
3.01
3.13
3.13
0.433
0.459
0.441
0.086 1745.00
0.086 2137.00
0.086 1763.00
40.98
50.20
38.75
44.84
54.92
43.79
319
^
6.67
2.34
0.322
0.043 1903.00
44.71
46.72
316
317
318
^
5.97
6.06
6.06
1.87
1.93
1.93
0.086
0.046
0.221
0.014 1893.00
0.014 2063.00
0.014 2262.00
45.87
47.72
53.11
47.48
49.64
54.24
^
^
core shear and buckling failure
core crushed
152
TABLE A.8 (cont.)
RESIDUAL STRENGTH TEST RESULTS
Spec.
Net Strain to Failure
Gage 1
Gage 2
Gage 3
-0.002661
-0.002981
-0.003001
.000181
.000180
.000180
-0.002401
.000221
-0.0055
.000100
319
-0.00238
.000060
-0.00211
.000060
-0.00182
316
317
318
-0.002241
.000140
-0.002181
.000100
-0.002241
-0.002741
-0.002081
.000120
.000160
.000740
-0.002741
1 Inch Panels;
321'
322
323
Gage 4
Gage 5
[0/901s
153
-0.001421
TABLE A.9
SPECIMEN SECTION RESULTS
Specimen
Number
Layup
Impact
Energy
(ft-lb)
Core/Face
Debond
Dia.
(mm)
Core
Indent.
Depth
(mm)
Rupture
Dia.
d
(mm)
29
+-45
2.12
12
3
13
31
+-45
1.10
7
1
4
47
+-90
1.03
10
1.3
8
55
+-90
2.05
14
1.2
12.5
66
+-90
1.11
9.2
1
10.5
220
+-90
1.93
13.1
2.5
12
224
+-45
1.87
7.5
.5
2
242
+-90
1.07
0
0
1
307
+-45
3.26
9
.8
9
321
+-90
3.01
10
.8
6
154
TABLE A.10
FATIGUE TEST RESULTS
(0/90] Columns:
Spec.
Number
Impact
Energy
[ft-lb]
Damaged
Area
d/W
[sq In]
Stress
Cycles
Amplitude @Stress
'(/0"crit
Amplitude
(%)
(N)
Fl
167
160
0
0
0
0
0
0
161
0
0
166
163
162
1.10
1.16
1.13
.132
.109
.155
.114
.121
.121
59
67
71
164
2.51
.279
.161
42
260
1.87
.100
.078
165
2.34
.270
.167
50 #
47
50
74
90
90 #
95
95
Life
Cycles
(N total)
515000*
669140?
904260*
40770
69640
515000*
23830
100
192
23830
100
192
& load altered
? doubtful fatigue failure
F1 is 1 inch thick and 2.75 inch wide
260 is .375 inch and 3.54 inch wide
1 - 99
101-199
201-299
Core
0 critical (undamaged)
(Ksi)
48.81
45.05
44.86
1 in
.687 in
.375 in
155
945030
69640
30530(1 face fail)
123920*
123920*
(1 cycle-20mm crack)
70100
70100
210
210
(Ist cycle damage)
* discontinued
Specimen Series
669140?
TABLE A.11
FATIGUE TEST RESULTS
[+-45] Columns:
Spec.
Number
Impact
Energy
[ft-lb]
Damaged
Area
d/W
[sq in]
Stress
Cycles
Amplitude @Stress
T/(C crit
Amplitude
(%)
(N)
P2
71
153660
Life
Cycles
(N total)
153660
34580*
150
151
85
90
153
1.01
.124
.089
69 #
157
152
1.13
.80
.147
.019
.144
.011
.83
.75
.050
.050
.086
.014
73
78 #
80
76
80
72
73
155
2.26
.295
.194
62 #
154
156
74
2.42
2.20
1.53
.280
.264
.149
.200
.178
.278
66
70
64 #
78 #
72
.143
.167
250
1.82
#
load altered
*
discontinued
5000
118040
4720
472700*
94600
211320
1189990
671890*
302360
197050
883340
15620
88870
143590
1036120*
171760*
6160*
210
70 series are 1 inch thick and 3.54 inch wide
P2 is 1 inch thick and 2.75 inch wide
250 is .375 inch thick and 3.54 inch wide
Specimen Series
1 - 99
101-199
201-299
Core
(r critical (undamaged)
(Ksi)
30.31
29.37
1 in
.687 in
.375 in
27.76
156
39580
118040
4720
566330
211320
1851880*
302360
197050
898960
88870
143590
(No dimple
growth)
210
~----^
.-
..
-
.
~
•
..
-
Impact .98 ft-lb
d/W = .05
Force 145 lb.
Delam.
Area .056
Figure A.1 Specimen 208 - [0/90]
Impact 1.11 ft.-lb.
d/W = .150
Figure A.2
sq.
in.
.375 Inch Core
Force 129 lb.
Delam. Area .205 sq. in.
Specimen 66 - (0/901 1 Inch Core
157
2?
r,
,r
r
.- r
i,
/r
/I
,,
,r
rr
,.r
rr
.r
.r
ir
,r
,
/I
)· ~
r.
ur
ri
r
//
rr
r·
N
Ir
~
'N
-
tt
,I
; I
;
r
''
Impact 2.12 ft.-lb.
d/W = .186
Figure A.3
Force 131 lb.
Delam. Area .270 sq. in.
Specimen 29 - [+-451 1 Inch Core
158
r00
rI,
rI
Impact 2.05
d/W =
ft.-lb.
Force 259 lb.
.014
Delam.
Figure A.4 Specimen 303 -
-.-
--
Area .171
sq.
in.
[+-45]s 1 Inch Core
,-
,
Impact 3.01
d/W =
ft.-lb.
Force 305 lb.
Delam. Area .433 sq.
. 086
Fi'gure A.5 Specimen 321 -
159
C0/903s 1 Inch Core
in.
I
I'
•J
C) r·-.
4'
".4
u7
i'
r-U
-*i
Q.
uu
i!-Bt:·-·.
1~~
LU
C-,e
7?
N
I~
UI_
ca6
IO
°-I
CA
C
C"
r-4
IC)
OC
4-
i
I
C
)-Q)
a
oen
C')
ur
C/3
¼1
C"
161
C.'
v-
S(••
Figure A.10
Specimen # 61, (0/90); undamaged,
face sheet fracture and debond
Failed at 55.45 Ksi
16I
o
4r-
C-",
k
-I
C-)
o
0
a)
C)
rci·
Cl
E°.
(.
o
I-
CO
a)
C-)
Fx.
4
rAJ
; At
b
o
H
rjj
t
,I
·I
.?
i
0
Lry
n-e
:t· ···
·,
r;·
C)
N31
k
.i4
"f
*H
Figure A.13 Specimen #303; Core Crushing
Figure A.14 Specimen #318; Core Shearing
167
i
-rrr
• .
o .
.
.
.
.
e,"
b
flmi
--,..,,
,....~
,-....,,
· ~~ rr
* 3B
me[
a* aM,
Specimen #166 (0/90),
-
--
r
oil
A..-
,·I
-·
a
.3
Figure A.15
Damage Growth Over Fatigue Life
N = 220, D = 30 mm, 28781bs
rr
r·
::
·
?rai~
AkL~
·----r--r--·
· ~rr·r·r·-·
· rrpar-----~~~CI·~·~·C·
.,~p~-··
r
r
LI-l·
I-~·- ·
--
'
·
rr~-rr
---r·rrr·~
1441111~~11111
Figure A.15 (cont.)
Specimen #166 (0/90); Damage Growth Over Fatigue Life
N = 3000,
D = 32 mm,
1b8
2878 lbs
r--r~rr
rrr-·rd
a-·-·r·(
~-·~-·
,-~
--
rr
j
·*,!~
i
1mAa
-;· ·· I·-·~d~-~
I
irur
t
· ·
rrr----·
r-r· ~
·-
- l .
r-r
ILILar~~:
-
Specime n
Ob
Figure A.15 (cont.)
#166 (0/90); Damage Growth Over Fatigue Life
N = 5000,
P•
-- r
~-rr
r~-··,I-r··~
rr
I-
D = 33 mm, 28781bs
h
-.~-~-.•.-.-.--.--..•
. .
. ""::.':.".,.Li -- .,
-2"
"".
'--l-..-'-...~r
wJ.llr~rrr
,,,
Y.,
WO
AF
lb sm a a
Figure A.15 (cont.)
Specimen #166 (0/90); Damage Growth Fatigue Life
N = 23,830,
D = 40 mm, 2878 lbs
16?
Figure A.16
Specimen #156 (+-45); Damage Growth Over Fatigue Life
N = 120,
D = 20 mm,
A,44AS
-
hbd44
~
h~~~Yt
N~~3C4
c
-s-Ilk1-
.
~
(-4-
~
.
1.-
·
1Y
2210 lbs
.-
LLL
41
LLL
~f~.aOLr
~
-
(4-
-4-.-'
-'~·'
4···
-4"`··'
Figure A.16 (cont.)
Specimen #156 (+-45); Damage Growth Over Fatigue Life
N = 37,000,
D = 22,
1 74'
2210 lbs
li~f~~r"~3~6~~
b1j
II
.1,1~~
~kNN
·i4Q
Figure A.16 (cont.)
Specimen #156 (+-45); Damage Growth Over Fatigue Life
N = 143,590
2210 lbs
1 .':
Figure A.17
Specimen #164 (0/90); Damage Growth Over Fatigue Life
N = 0.0
D = 14.5 mm,
2019 lbs
Figure A.17 (cont.)
Specimen #164 (0/90); Damage Growth Over Fatigue Life
N =
30,
D = 21,
17Z
2019 lbs
I
IlI"II
I Ii' I
1
,
t1
I
I
SII
ill
,I**
I t
lIII I I I I IiII.!Iu'
I I
*
I I
tIii
I
I
·I
i
i
.inI,;o
ii •
t
1
.
.-..
..
.'
I t.
Illlr
I1 I I
il
9? -~~~,
-l(
-'tr
~ir2~~r~-
l
Figure A.17 (cont.)
Specimen #164 (0/90); Damage Growth Over Fatigue Life
N = 130,
D = 22.5,
2019 lbs
Figure A.17 (cont.)
Specimen #164 (0/90); Damage Growth Over Fatigue Life
N =1000,
D = 27,
2019 lbs
r"7.7
i~~
I
~rh~rrrcrmrrrr
•I
_- .....
· CI~
I !
I
i i
0
a a a·,
a iiii
Iiiii a l il !,a
'
::
I"
S
I I
,
t . ,
,
| l ll ,
t iI•
ii a
I I
I 14h I.. I
cJJ
I :;i
1
Specimen #164
,.T
+
+,
.
i
L,'
I
·.,-~
-al-a.~~--
Fig ure A.17 (cont.)
(0/90); Damage Growth Over Fatigue Life
N = 11,700 ,
D = 32 mm,
2019 lbs
't~t:"/
·
,",,
--
I
1-'-
a
I lia-
,,
I ll~
I ICl1
11111
I Ill
II"
ii
,
al
ii
II
,
I
ii
111
11
11
11
,+
jii J
~ila 1"'
aa
a.i
Figure A.17 (cont.)
(0/90); Damage Growth Over Fatigue Life
N = 19, 200
D = 36 mm
2019 lbs
Specimen #164
17 f
Figure A.17 (cont.)
Specimen #164 (0/90); Damage Growth Over Fatigue Life
N = 30,440
D = 45 mm
2019 lbs
Figure A.17 (cont.)
Specimen #164 (0/90); Damage Growth Over Fatigue Life
N = 30,485
D = 50
175
2019 lbs
1
Figure A.17 (cont.)
Specimen #164 (0/90); Damage Growth Over Fatigue Life
2019 lbs
D = 53 mm
N = 30,520
Specimen #164
Figure A.17 (cont.)
(0/90); Damage Growth Over Fatigue Life
N = 30,530
17C
APPENDIX B: SUB-LAMINA GEOMETRY OF THE WOVEN PLY
In order to
the plane
plate
make use of the
weave ply and
theories,
the
"imaginary" bi-ply
axes
acting
apply them to
woven
with two
within the
orthotropic properties of
ply
classical laminated
can
be
viewed
equivilent principle
central
plane
of the
as
an
material
ply.
The
sinusoidal bending of the fiber tows will be ignored for the
"imaginary ply", and
addressed later in this
final assumption is that
effective thickness
is, one
half
half of
of
the
stiffness
the lamina's
in the
its actual
thickness,
principle
both sides of
thickness. That
filaments, which
actually
material
3.2(b) illustrates that fiber tows
principle material
The
the "imaginary" ply's mechanically
is half of
lamina
chapter.
contribute
direction.
to
Figure
of thickness t/2 provide
stiffness in the
the central plane.
occupy one
fill direction
The warp
and on
tows provide no
longitudinal filament stiffness in the paper direction, but
they
do occupy
one
half of
the
ply
thickness, t.
imaginary ply is depicted in figure B.1.
t
-.ý I.,
Figure B.1
--
The "imaginary bi-ply"
177
The
for the woven ply
The assumptions made
the
central plane
equal to
and the
t/2, are
identical.
effective mechanical
possible only if
implies
A large thickness to
bending
buckling.
out-of-plane
to
succeptability
ratio between
sinusoidal
greater
tows are
This determines the
woven width.
shape of the tow's sinusoidal bending.
ratio
thickness
the filament
geometric factor is the
A second
the tow thickness and its
width
acting through
The
and
nominal
dimensions for AW193PW/3501-6 graphite/epoxy fabric are:
ply thickness
.0076" (.193mm)
tow thickness
.0038" (.0965mm)
tow width
.0878" (2.23mm)
thickness/ width ratio = .0433 = 1 to 23.1
Figure
B.2 illustrates
the
deflection, £1 .
angular
deflections and
tow
Greater
tow
bending angles
possible but not
likely, because fibers at the
tow are expected
to form a pointed cross
40 psi
curing pressure
very thin
section
and free
as
the
laminate is
section under the
matrix.
be the likely
compressed
are
edge of the
flowing epoxy
elongated ellipse would
greatest
to
its
A
tow cross
minimum
thickness during the pressurized cure cycle.
If one assumes that X percent of the filament tow width
has a thickness of t/2 (or .0038 inch in this case) and that
only the
outer (100-X)/2
tapered
thickness,
assumption of
then
percent of
.L
(X + 10) percent
can
the tow
be
width has
calculated.
on each tow
An
will obviously
yield a different angular deflection for the tow.
172
a
_
T Ow
Figure B.2
..
·.
I
Il
W|dTI
Tow deflection angle within weave
If one assumes that X percent of the filament tow width
has a thickness of t/2 (or .0038 inch in this case) and that
only the
outer (100-X)/2
tapered
thickness,
then
X1
(X + 10) percent
assumption of
width has
the tow
percent of
be
can
An
calculated.
on each tow
a
will obviously
yield a different angular deflection for the tow.
maximum deflection
Usingqthis- scheme,-the
from the central
X.
assumption,
illustration.
in that it
and laminate
The
ply plane can be approximated
Table
B.1
some
provides
maximum deflection angle
represents a weakness in the
buckling.
It's
makes it unstable and dependent
stability as the
angle SI ,
for a given
values
as
an
is significant
retardation of tow
inherant buckling
mode shape
upon the matrix to maintain
tows carry longitudinal loads
in the fill
direction.
TABLE B.1
Tow Bending Within Fabric
Unaffected Tow Width,
Maximum Deflection Angle,
X % :
(deg.):
75
10.0
80
12.6
85
16.8
90
25.8
Thickness/ width for AW 193PW/3501-6 is 1/23.
This ratio
can be used to calculate other deflection angles for a given
tow cross section with the following formula:
ai
=
arcsin (1/[23(1-X)])
1
(B.1)
APPENDIX C:
PANEL DEFLECTION GRAPHS
This appendix contains mid-panel deflection and angular
deflection curves for specimen type and impact damage level.
1.'I
[±45] Thick Nomex
No Impact
0
100
0
300
200
400
500
Net Deflection
600
Load (Ibs)
[+45] Thick Nomex
No Impact
0
0
Figure C.1
100
200
300
400
500
600
Load (Ibs)
[+-45] 1 inch; Undamaged: Deflection Curves
Theta-B
[±45] Thick Nomex
Low Impact
E
E
C
0
0
0
0
A
Net Deflection
A
Theta-B
0,
z
0
100
200
300
400
500
600
Load (Ibs)
[±45] Thick Nomex
Low Impact
0
Figure C.2
100
200
300
400
500
600
Load (Ibs)
[+-45] 1 inch; Low Damage: Deflection Curves
173
[±45] Medium Nomex
Low Impact
A
0
100
200
300
Net Deflection
400
Load (Ibs)
[±45] Medium Nomex
Low Impact
U,
0
0n
I-
a
0
100
200
300
400
Load (Ibs)
Figure C.3
[+-45]
.687"; Low Damage: Deflection Curves
Theta-B
[±45] Medium Nomex
Medium Impact
Net Deflection
a
0
100
200
Load
300
400
(Ibs)
[±45] Medium Nomex
Medium Impact
0
0
Figure C.4
100
[+-45]
200
300
400
Load (Ibs)
.687"; Medium Damage: Deflection Curves
185S
Theta-B
[+45] Thin Nomex
Low Impact
A
200
100
0
Net Deflection
Load (Ibs)
[+45] Thin Nomex
Low Impact
A Theta-B
0
Figure C.5
100
[+-45]
200
300
Load (Ibs)
.375"; Low Damage: Deflection Curves
I1%
[±45] Thin Nomex
Medium Impact
*
0
100
Net Deflection
200
Load (lbs)
[±45] Thin Nomex
Medium Impact
0
0
100
Theta-B
200
Load (Ibs)
Figure C.6
[+-45]
.375"; Medium Damage: Deflection Curves
127
[±45] Thin Nomex
High Impact
m Net Deflection
100
0
20U
Load (Ibs)
[+45] Thin Nomex
High Impact
a
100
0
200
Load (Ibs)
Figure C.7
[+-45]
.375"; High Damage: Deflection Curves
rs2
Theta-B
[+45]2 Thick Nomex
No Impact
Load
Net Deflection
E
Theta-B
800
600
400
200
0
E
(Ibs)
[±45]2 Thick Nomex
No Impact
I
LIU
piU
Ua
piU
*
U
crU
-
·
U ·
·
·
-4
200
400
600
800
Load (Ibs)
Figure C.8
[+-45]s
1.0 inch; Undamaged: Deflection Curves
[±45]2 Thick Nomex
Low Impact
200
0
400
Load
600
0
Net Deflection
o
Theta-B
800
(Ibs)
[±45]2 Thick Nomex
0
200
400
600
800
Load (Ibs)
Figure C.9
[+-45]s
1.0 inch; Low Damage: Deflection Curves
190
[±45]2 Thick Nomex
Medium Impact
0
600
400
200
+
Net Deflection
+
Theta-B
800
Load (Ibs)
[±45]2 Thick Nomex
Medium Impact
0
200
Figure C.10
[+-45]s
400
600
800
Load (Ibs)
1.0 inch; Medium Impact: Deflection Curves
191
[t45]2 Thick Nomex
High Impact
0
200
400
Load
600
M
net deflection
U
theta-B
800
(Ibs)
[±45]2 Thick Nomex
High Impact
0
200
400
600
800
Load (Ibs)
Figure C.11
[+-45]s
1.0 inch; High Damage: Deflection Curves
192.
[0/90] Thick Nomex
Low Impact
Net Deflection
a
0
600
400
200
800
Load (Ibs)
[0/90] Thick Nomex
Low Impact
A
0
200
400
600
Theta-B
800
Load (Ibs)
Figure C.12 [0/90] 1 inch; Low Damage: Deflection Curves
193
[0/90] Thick Nomex
Medium Impact
o
100
0
200
300
400
Net Deflection
500
Load (Ibs)
[0/90] Thick Nomex
Medium Impact
o
0
Figure C.13
100
Theta-B
200
300
400
500
Load (Ibs)
[0/90] 1 inch; Medium Damage: Deflection Curves
19q
[0/90] Thick Nomex
High Impact
a
0
100
400
300
200
Net Deflection
500
Load (Ibs)
[0/90] Thick Nomex
High Impact
3 Theta-B
0
Figure C.14
100
200
300
400
Load (Ibs)
[0/90] 1 inch; High Damage: Deflection Curves
195
[0/90] Medium Nomex
Low Impact
A
0
500
400
300
200
100
Net Deflection
600
Load (Ibs)
[0/90] Medium Nomex
Low Impact
A Theta-B
0
Figure C.15
100
[0/90]
200
300
400
500
Load (Ibs)
.687"; Low Damage: Deflection Curves
19(
[0/90] Thin Nomex
Low Impact
A
0
100
200
Net Deflection
300
Load (Ibs)
[0/90] Thin Nomex
Low Impact
A Theta-B
0
100
200
300
Load (Ibs)
Figure C.16
[0/90] .375"; Low Impact: Deflection Curves
197
[0/90] Thin Nomex
Medium Impact
200
100
0
o
Net Deflection
o
Theta-B
300
Load (Ibs)
[0/90] Thin Nomex
Medium Impact
0
100
200
300
Load (Ibs)
Figure C.17
[0/90]
.375"; Medium Damage: Deflection Curves
198
[0/90] Thin Nomex
High Impact
a
200
100
0
Net Deflection
300
Load (Ibs)
[0/90] Thin
Nomex
High Impact
3 Theta-B
200
100
0
300
Load (Ibs)
Figure C.18
[0/90]
.375"; High Damage: Deflection Curves
199
[0/90]2 Thick Nomex
Medium Impact
0
200
600
400
Load
800
x
Net Deflection
x
Theta-B
1000
(Ibs)
[0/90]2 Thick Nomex
Medium Impact
0
200
400
600
800
1000
Load (Ibs)
Figure C.19
[0/90]s 1 inch; Medium Damage: Deflection Curves
200
[0/90]2 Thick Nomex
Low Impact
0
200
600
400
Load
[0/90]2
800
*
Net Deflection
*
Theta-B
1000
(Ibs)
Thick Nomex
Low Impact
0
200
400
600
800
1000
Load (Ibs)
Figure C.20
[0/90]s 1 inch; Low Damage: Deflection Curves
20o
[0/90]2 Thick Nomex
High Impact
a
0
200
400
600
800
Net Deflection
1000
Load (lbs)
[0/90]2 Thick Nomex
U
0
0
200
400
Load
Figure C.21
600
800
1000
(Ibs)
[0/90]s 1 inch; High Damage: Deflection Curves
202
Theta-B