Cunningham, T. G.

Fahmy, A. A.

English

NASA Technical Reports Server

238111·
Progress Report
Jpvestigation of Thermal Fatigue
in Fiber Composite Materials
NGR 34-002-180
for
National Aeronautics and Space Administration
Thomas G. Cunningham'
25 July 1974
by
Abdel A. Fah~. Professor
and
Department of Materials Engineering
North Carolina State University
Raleigh, North Carolina
- -_.- --.
~ ---
/OLa.SA-CR-1 J.0541) INvr STIGATION OF THERMAL
?ATIGU7 IN r!B~n COHPOSIT' HAT~RIALS
,pr~gr2ss rapo=t (~orth Carolina state
"Jniv.) ~ p
\\ :2..5 ~ 00/99
N74-7
6861
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48543
https://ntrs.nasa.gov/search.jsp?R=19740078922 2020-03-23T02:18:38+00:00Z
INTRODUCTION
The object of this research program is to provide information on
the capabilities and limitations of graphite fiber-epoxy materials to
serve under thermal fatigue conditions and to make possible the production
of improved fiber composites through a better understanding of the
influence of fiber orientation and lamination sequence on their thermal
fatigue performance.
The initial time was spent procuring equipment, fabricating a
suitable sample mold, and preparing samples. Subsequently, the
composite specimens were tested in the as fabricated condition for
elastic modulus, tensile strength, and thermal expansion coefficients.
Presently, two different pieces of equipment are being developed
to thermally cycle the samples.
8
/
FABRICATION
Samples were made from epoxy preimpregnated graphite sheets obtained
from Monsanto. These sheets consisted of Monsanto resin type 4617/mPDA
with a 55 w/o fiber. The sheets, originally 2' x 4', were cut into 6"
squares. The squares were cut so that the fiber axis was at 0' or 90'
with the edge of the square for the unidirectional and the -45°, +450
samples and at 0, 30 ° , and 600 for the 00, 300, 600, 90° sample.
Twelve layer samples were made for each of the following orientation
sequences:
Layer Number 1 2 3 4 5 6 7 8 9 10 11 12
I 0 0 0 0 0 0 0 0 0 0 0 0
w II +45 -45 +45 -45 +45 -45 +45 -45 +45 -45 +45 -45
SIII 0 30 60 90 -60 -30 -30 -60 90 60 30 0
The layers were then placed in a mold fitted with a die and punch. The
mold was then placed between the platens of the hot press where a pressure
of 50 psi and a temperature of 800 C were applied (Figure 1). At the end
of two hours the pressure was increased to 100 psi and the temperature was
increased to 150 0 C. The samples were then cured an additional two hours.
After the samples were properly cured the hot press was turned off and
the samples were cooled to room temperature by water flowing through the
platens.
Once the samples were removed from the mold, they were checked for
any visible flaws and the thickness was measured. The final sample
measured 6" x 6" x 0.080".
Hot Press
Figure 1
-2-
MICROSCOPIC EXAMINATION
To prevent time being wasted by testing poor samples, each sample
was examined microscopically. Two cross sections of each samples, cut
at right angles to one another, were examined under the microscope. The
purpose of the examination was to ascertain the fiber orientation in each
layer, to check thickness, and parallelism of the individual layers as
well as the uniformity of fiber distribution and general integrity of
the composite.
-3-
MODULUS OF ELASTICITY
The proposed work in this area consisted of measuring the elastic
modulus in the 0' direction of the three different composite configurations.
Later it was decided that a complete characterization of the material
was.needed. This characterization required measuring the longitudinal
modulus (EL), the transverse modulus (ET), the shear modulus (GLT), and
Possion's ratio (vLT) of the unidirectional sample. From these values
EL9 ET, GLT' vLT the elastic modulus of any composite with any
construction can be calculated and compared to experimental results.
Specimens, approximately 0.5" x 3.0" x 0.08", were cut from the
samples. To insure that an even load was applied to the specimens and
that the specimens were not damaged by the jaws of the testing machine,
aluminum strips were glued to each side of the sample with epoxy at both ends.
All samples were loaded in tension with the load and strain being
recorded. The accumulated strains were recorded by the use of SR-4
strain gages and a strain gage recorder, both produced by BLH Electronics.
The strain gages were attached to the unidirectional specimens so that
the gage was at 00 with the fiber axis to measure 6L and at 900 to
measure rT. Two measurements were taken on the -450, +450, one with the
strain gage oriented in either the -45, or +450 direction and the
other along the 00 axis. The applied load was read directly from the
Tinus-Olsen Testing Machine.
Due to the small loads required to break the unidirectional 900
specimens, the modulus of elasticity was obtained from a four point
flexure test. The strain was obtained from strain gages and the applied
load from loads placed on the testing apparatus.
- 4 -
Possion's ratio was calculated using a dual strain gage that
was attached to the unidirectional specimens. The shear modulus was
measured using the method of torque applied to a rectangular bar.
-5-
DETERMINATION OF THERMAL EXPANSION
The coefficient of thermal expansion was determined for each panel
with different construction. One specimen was cut from the -45,
+450 and the 00, 300, 600, 900 panels since the thermal expansion should
be the same in all directions in these two panels. 3  The specimens
from the unidirectional samples were taken such that the following
angles were made with the unidirectional axis:
Angle in Degrees 0, 15, 30, 45, 60, 75, and 90
The ends of the specimens were ground flat, parallel and
perpendicular to the specimen axis.
Each specimen was slowly heated in a dialatometer, Figure 2, from
room temperature to 180 0C at the approximate rate of l1C/minute. The
specimens were then cooled to room temperature by cutting off the heating
current. While the first heating and cooling curves showed hysteresis,
further heating followed very closely the cooling curve and the behavior
became essentially reversible. The thermal expansion coefficient was
determined from the cooling cycle and was measured between 500 C and 150 0 C.
-6 -
Figure 2
-7-
ULTIMATE TENSILE STRENGTH
Samples used to calculate elastic modulus were loaded until
fracture to obtain the ultimate tensile strength.
-8 -
RESULTS AND DISCUSSION
Microscopic Examination
Figures 3, 4, and 5 show the photomicrographs of the fiber
composites.
Figure 3 is the unidirectional sample. The top micrograph was
taken at 900 to the fiber axis. Four fiber layers are distinguishable
even though there is good bonding between and good fiber distribution
in the layers. The second two micrographs were taken at 00 to the
fiber direction. The fibers are essentially parallel.
Figure 4 is a micrograph of the -450, +450 sample. There is good
bonding between layers and little or no transverse cracking.
Figure 5 is of the 0, 30, 600, 90* sample. The top micrograph
shows seven layers starting with the 00 direction and ending with two
300 directions. The six layers on top represent one-half of the
thickness (the mid plane is marked on the photomicrograph by a dark
line. The construction of the bottom half is identical to that of the
upper half). The other two micrographs taken at higher magnification
show the fiber cross sections in different layers. Good bonding with
practically no cracking was observed for this configuration.
Modulus of Elasticity
a) Theoretical Considerations2
For a single ply fiber composite, the modulus of elasticity,
E, when the uniaxial tensile axis is along the fiber direction is given
by the equation:
EL = EfVf + Em(l-Vf) (
- 9 -
I 
P1 -lp
I 
(A
)ld
:~1
~%
BA
l
I 
11
~ i4
Figure 4
- 11 -
Figure 5
- 12 -
and when the uniaxial tensile axis is normal to the fiber direction,
E is given by:
EE
E =mf
T Ef(l-Vf) + EmVf (2)
Where:
EL  = longitudinal modulus
ET  = transverse modulus
V = volume fraction fiber
Vm = volume fraction matrix
If then a value of the shear modulus (GLT) and Possion's ratio
(vLT) is obtained by experimental results, the composite can be fully
characterized.
The shear modulus (GLT) is obtained from the torque equation for
a rectangular bar:
G = Mt
K LT l(2a)3(2b) (3)
Where:
M = (load)(distance) i.e. twisting moment
0 = (angle of twist) - (length of sample)
a - 0.5 thickness of sample
K = constant obtained from b/a
Possion's ratio can be calculated from the results obtained when
strain, e, is measured in both the longitudinal and transverse directions
for the uniaxial composite.
V : €tVLT
LLT (4)
- 13 -
It also holds that:
STL ET (5)
LT EL
In deriving stress-strain relationships for a single layer of a
laminated composite, it is assumed that the stress normal to the layer
is negligible. Thus it results in a plane stress state.
The stress-strain relationship for a lamina in the matrix form is:
a LQ 11Q 120 cL] [ 11  2 L
LT = L12 ~22 06 LT (6)
.TL ( 0 Q66 LT
Where the components of the stiffness matrix, Q, are:
:- EL
11l = 1VEL
1 ~LT TL
22 = ET
1 -VLTVTL
Q12 = VLTEL (7)
1-V LTv TL
Q66 =  GLT
Q16  Q26  = 0
When the stresses are in an arbitrary coordinate system (x, y, z),
the following matrix is obtained:
lX 11 Q12 0 X
Y [ 1 2 22 0 y (8)
LTX 0o 0 ~6 ~xY
- 14 -
Where the components of the stiffness matrix, Q, which are now referred
to an arbitrary set of axes, are given by:
Qll = Qllcos4e + 2(Q12 + Q66 )sin 2 ecos 2e + Q22sin 4e
Q22  = s in40  + 2(Q12 + Q66 )sin 2 cos2 e + 22c s4 (9)
2 4 (9)
QI2  = (QII + Q22 - 4Q66 )sin2 8 cos E+ Q12 (sin 4+ cas4e)
-66 =  (Q11 +22 - 2Q12 - 2Q66 )sin 2ecos e + Q66 (sin e + cos 4e )Q66 1)s+nQ22os2 66 6)
From these equations it is possible to calculate Qij for each layer of the
composite.
The laminate constitutive equations are then used to determine the
elastic modulus of a multilayer composite.
N A A A (10)
NY 12 A22  26  Y (0)
N X A A26 A YXLY 26 66i LXY~
Where:
n=x
Aij = hp (Qij)n n=l
hp = thickness of one layer
X = total number of layers
N = force
The modulus of elasticity can be obtained from the equation:
E I A 12Ek=All 
- 12} (11)
h = total thickness of composite
- 15 -
Using the following values, the elastic modulus of the different
fiber orientation was calculated:
E = 26.44 X 106psi
*L
ET = 0.99 X 106 psi
TGLT = 0.46 X 106psi
VLT = 0.33
For the -450, +45' sample:
Along the fiber axis (either -45, +450) E = 13.75 X 106psi
Along the 00 axis E = 1.98 X 106 psi
For the 00 300 - 600 - 90* sample: E = 9.03 X 106psi
b) Experimental Data
The strain and load data taken during the testing was plotted
and a best fit line was drawn. From this the modulus, E, was calculated
using:
load
E area 
(12)
strain
This was done on all specimens except the transverse unidirectional
specimen where four point bending was used. The modulus in this case
is given by the formula:
E 3P
2bhz- (13)
Where:
E = elastic modulus
P = applied load
b = width of specimen
h - thickness of specimen
= : strain
and the distance between knife edges in the four point bending test was 2".
- 16 -
Using formulas (1) and (2) the modulus for the unidirectional
sample was calculated. E was 27.73 X 106 psi and ET was 1.10 X 106 psi.
LT
These values compared very favorably with the EL of 26.44 X 106psi and
ET of 0.99 X 106psi obtained experimentally. The experimental values
were used in the theoretical calculations.
The -45° , +45' specimen had a modulus of 11.32 X 106 psi when
measured at 0O*. These values compared well with the 13.75 X 106psi
and the 1.98'X 106 psi moduli calculated.
The 0', 300, 60, 900 specimen should have the same modulus in
all directions. The modulus measured was 8.3 X 106psi as compared
to the calculated value of 9.03 X 106 psi.
The calculated values were higher than the experimental values
in most cases. This could be due in part to the specimen not being
tested exactly along the designated axis. It is easy to see the
dramatic reduction in modulus in the -45*, +450 specimen when the
tensile axis is moved away from the fiber axis.
- 17 -
THERMAL EXPANSION
The thermal expansion coefficient a of the quasi-isotropic samples
(i.e. -450, +450 and the 0', 30° , 600, 90°) were very close. The
value of this coefficient a for the (-450, +450) sample was 1.6 X 10-6/ C
as compared to 2.2 X 10-6 /OC for the (00, 300, 600, 90') sample. Considering
the values are subject to an experimental error as much as + 0.5 X 10-6 /C,
the values could be considered to be the same. It can be seen that these
values of the coefficients are very small when one considers that a
unidirectioned composite of the same material and proportions yields a
transverse coefficient in the range of 70 X 10- 6 /OC.
The unidirectional sample showed a clear trend for the expansion
coefficient to increase as the angle between the fiber axis and
specimen axis increased from 00 to 900 . This is shown in Figure 6. The
simple formula for a homogeneous orthotropic material is
ac= a0cos 2 0 + 90osine and the experimental results show a good
correlation with this formula.
- 18 -
Coefficient of Thermal Expansion
Unidirection Sample
80
70
60
Coefficient 50
X10-6/oC
40
30
20
10
0 15 30 45 60 75 90
Angle in Degrees
Figure 6
- 19
ULTIMATE TENSILE STRENGTH
The ultimate tensile strength of the unidirectional longitudinal
specimen was 34,000 psi while the transverse specimen was 3,645 psi.
The (-450, +450) sample had a tensile strength of 27,400 psi along the
fiber axis and 15,840 psi at 450 from the fiber axis. The (0O, 300,
600, 90') specimen had a uniform tensile strength of 24,300 psi.
- 20 -
SUMMARY AND CONCLUSIONS
1. The modulus of elasticity of the composites is as follows.
Unidirectional 0O axis 26.44 X 106psi
Unidirectional 900 axis 0.99 X 106psi
-450, +450along fiber axis 13.75 X 106psi
0', 300, 600, 900 9.03 X 106psi
2. Microscopic examination of the composites shows little cracking
after fabrication.
3. The thermal expansion coefficient of the quasi-isotropic samples
were very close. The unidirectional sample follows the expansion
formula = cocos2e + a g 0 sin2e.
C9021
- 21 -
PLAN FOR FUTURE WORK
1. Development of Thermal Cycling Apparatus
2. Thermal Cycling of Material
3. Determination of thermal expansion coefficient, modulus, and
strength of all cycled samples
4. Calculation of thermal stresses developed
5. Examination of fractured surface by the use of a scanning electron
microscope
6. Evaluation of all data obtained
- 22 -
REFERENCES
1. Ashton, J. E., Primer on Composite Materials: Analysis. Technomic
Publication, 1969.
2. Krock, R. H., Modern Composite Materials. Addison-Wesley
Publishing Company, 1967.
3. Fahmy, A. "A Research Analysis Study of the Thermal Expansion and
Thermal Fatigue Behavior of Graphite Fiber Reinforced Composites"
BMI, July 1971.,
- 23 -


Investigation of thermal fatigue in fiber composite materials

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