experimental study on tensile behavior of carbon fiber.pdf
TRANSCRIPT
-
7/29/2019 Experimental Study on Tensile Behavior of Carbon Fiber.pdf
1/15
Experimental Study on Tensile Behavior of Carbon Fiber
and Carbon Fiber Reinforced Aluminum at DifferentStrain Rate
Yuanxin Zhou & Ying Wang & Shaik Jeelani &
Yuanming Xia
Received: 28 June 2006 / Accepted: 8 November 2006 /
Published online: 4 January 2007# Springer Science + Business Media B.V. 2007
Abstract In this study, dynamic and quasi-static tensile behaviors of carbon fiber and
unidirectional carbon fiber reinforced aluminum composite have been investigated. The
complete stressstrain curves of fiber bundles and the composite at different strain rates
were obtained. The experimental results show that carbon fiber is a strain rate insensitive
material, but the tensile strength and critical strain of the Cf/Al composite increased with
increasing of strain rate because of the strain rate strengthening effect of aluminum matrix.
Based on experimental results, a fiber bundles model has been combined with Weibullstrength distribution function to establish a one-dimensional damage constitutive equation
for the Cf/Al composite.
Key words carbon fiber. metal matrix composite . tensile properties
1 Introduction
Fiber reinforced metal-matrix composites (FRMMC) consist of a ductile, usually low-
strength matrix reinforced with elastic, brittle and strong fibers. The fibers impart high
strength and excellent damage tolerance properties in the fiber direction. The metal matrix
allows the composite to be formed and machined with traditional techniques used for
conventional metals, and provides the composites with excellent environmental protection
and impact resistance which are qualities generally lacking in polyermic composite
materials. Additionally, fiber reinforced metal-matrix composites (FRMMC) have the
potential to provide desirable mechanical properties, including high specific stiffness, lower
density, high strength and creep resistance and good oxidation and corrosion resistance.
This suite of properties makes FRMMC attractive for a wide range of applications not only
Appl Compos Mater (2007) 14:1731
DOI 10.1007/s10443-006-9028-5
Y. Zhou (*) : Y. Wang : S. JeelaniCenter for Advanced Material, University of Tuskegee, Tuskegee, AL 36088, USA
e-mail: [email protected]
Y. Xia
Department of Modern Mechanics, University of Science & Technology of China, Hefei,
Anhui 230027, Peoples Republic of China
-
7/29/2019 Experimental Study on Tensile Behavior of Carbon Fiber.pdf
2/15
in weight sensitive aerospace industry, but also in marine, armor, automobile, railways, civil
engineering structures, sport goods etc. [13]
The mechanical response (deformation, strength and failure) of metal matrix composites,
like many other metal materials, depends on the rate of deformation. The knowledge of
mechanical behavior of FRMMC under high strain rate is required if a component made of theFRMMC is subjected to possible high-velocity impact loading, such as the impact of a bird on
the turbine blades of a flying airplane or a space station impacted by various flying space
debris. Guden and Hall [4] have reported the high strain rate deformation of -Al2O3 fiber
reinforced Al composites. Cady and Gray [5] have studied the influence of strain rate on the
deformation and fracture response of a continuous Al2O3 fiber reinforced aluminum. Galvez
et al. [6] have investigated the dynamic tensile behavior of a SiC/Ti-6Al-4V composite.
It also has been found that the strength of a metalmatrix composite (MMC) reinforced by
unidirectional fibers does not reach the strength predicted by the rule of mixtures (ROM) [7].
Although these results can be influenced by the method of calculation, the most common
explanation has been that the strength of the fiber has been degraded by high-temperature
processing [8]. For fiber-reinforced composite materials, the fibers are the main load-bearing
elements and it is therefore important to be able to measure and characterize the actual strength
properties of fiber at different strain rates. Friler et al. [9] have removed matrix from composite
and performed single filament test on the survived carbon fiber. Results showed that the Pitch-
55 fibers are damaged to some degree as a result of composite sample preparation. However,
owning to technical difficulties in tests, it is impossible to obtain the dynamic properties of a
single fiber directly at present. Chi et al. [10] proposed a procedure for determining the static
properties of single fiber by measuring those of fiber bundles. Xia et al. [11] extended the
method to the dynamic state and first successfully performed tensile impact tests on fiberbundles. Their testing strain rate was up to 1,100 1/s.
In the present paper, static and dynamic tensile tests were conducted on an unidirectional
carbon fiber reinforced aluminum matrix composite (Cf/Al), carbon fiber bundles and
aluminum matrix at different strain rate. Strain rate dependent behavior of carbon fiber,
aluminum matrix and composite were discussed.
2 Experimental
The high-rate tensile tests were carried out using the bar-bar tensile impact apparatus
(BTIA), which is schematically illustrated in Fig. 1. The BTIA includes a rotating disk
loading system, an impact block, a prefixed metal bar, impact hammers, an input bar, an
output bar and a data acquisition system. Also the top view of the impact block, prefixed
bar, impact hammers, connector and input bar is shown in Fig. 1. The loading stress pulse is
initiated by the impact of the hammer fixed on the high-speed rotating disk on the impact
block, which causes the prefixed metal bar (made of Ly12cz aluminum alloy, strain-rate
insensitive material) connected to the block and the input bar by the screw to deform until
fracture. The amplitude of the stress pulse is determined by the diameterdp of the prefixed
metal bar. The rise time and duration of the stress pulse is controlled by the impact velocity
and the length lp of the prefixed metal bar. Therefore, the strain rate for any particular test
can be altered by varying the diameter of the prefixed metal bar.
The incident stress wave travels down the input bar, is partially reflected at the input bar/
specimen interface, and then is partially transmitted to the specimen and the output bar. The
incident strain i(t), reflected strain r(t) and transmitted strain t(t) are recorded as functions
18 Appl Compos Mater (2007) 14:1731
-
7/29/2019 Experimental Study on Tensile Behavior of Carbon Fiber.pdf
3/15
of time t using strain gages on the input/output bars, respectively. From these strain gage
measurements and based on one-dimensional elastic wave propagation theory, the stress, strain
and strain rate in the specimen can be calculated as follows:
ss t EA
As"t t 1
"s t
Zt
0
"i t "t t dt 2
"
s t 2C0
ls"i t "t t 3
where C0 (ffiffiffiffiffiffiffiffiE=r
p, E and are the Youngs modulus and density of the input/output bar,
respectively.) is the longitudinal wave velocity of the bar. A is the cross-sectional area of the
input/output bar. As and ls are the cross-sectional areas and gage length of the specimen,
respectively.The MMCs in the present paper was M40J fiber reinforced aluminum, composite which are
produced by the ultrasonic liquid infiltration method [10]. The matrix is an industrial pure
aluminum (>99.6 wt.% purity). The diameter of the composite wire is about 0.5 mm, and the
volume fraction of the fiber in composite is about 50%. The specimen and its connection are
shown in Fig. 2. First, the lining blocks (1) were glued on the supplement plate (2)
perpendicularly, 10 composite wires (3) were put into the slot of the lining blocks parallel,
then wires were glued with blocks by a high shear strength adhesive (SA103) and covered
with a thick metal plate by SA103. To extract the fibers from the composites, the aluminum
matrix was dissolved in a 5% by weight solution of NaOH which does not degrade the fibers.
Then the 10 composite wires have been change into 10 bundles of in situ fibers. Finally, the
blocks with the slots in the ends of input bar (4) and output bar (5) were connected using
high shear strength adhesive. The supplement plate was taken off before testing.
By controlling the height of input impulse, three groups (corresponding to strain rate of
100, 500 and 1,300 s1) of tensile impact tests were conducted. Typical signal in the input-
bar and output-bar were shown in Fig. 3. In addition, quasi-static tensile experiments were
Fig. 1 Schematic diagram of the barbar tensile impact apparatus
Appl Compos Mater (2007) 14:1731 19
-
7/29/2019 Experimental Study on Tensile Behavior of Carbon Fiber.pdf
4/15
performed on the MTS-810 testing machine to compare with the above tensile impact
results. The strain rate was 0.001 s1. The average experimental values at different strain
rates are listed in Table 1.
Figure 4 shows the complete stressstrain curves of the composite at different strain
rates. The curves show considerable non-linear deformation, and no obvious yield point can
be observed. The specimens failed gradually after reaching the maximum stress. From
Table 1 and Fig. 4, it is clear that the composite is a strain rate sensitive material and
exhibits significant ductility even under high strain rate tensile impact. The higher the strain
rate, the larger is the critical strain at the maximum stress. The correlation between the
ultimate stress b, the critical strain b and lg "
are shown in Fig. 5. Their relationship with
strain rate can be formulated as:
sb s0" " T
"
0
!n4
"b "0"
"T
"
0
!m5
where, "
, "
0, 0 and0 are strain rate , reference strain rate, reference stress and referencestrain, respectively. n and m are strain rate sensitivity coefficients and "
T is a transition
strain rate. The following equation fit the data listed in Table 1.
sb 1:43"
61
100
!0:036GPa 6
Fig. 2 Specimen and its connection
20 Appl Compos Mater (2007) 14:1731
-
7/29/2019 Experimental Study on Tensile Behavior of Carbon Fiber.pdf
5/15
"b 0:97"
47
100
!0:012% 7
The solid lines in Fig. 5 are simulated results, which fit the experimental points well.
Figure 6 show the stressstrain curves of carbon fiber bundles at strain rate 0.001, 100
and 1,300 s1. From these curves, it can be concluded that reinforced fiber is a strain rate
insensitive material [12]. On the other hand, the tensile stressstrain curves of the
aluminum matrix (Fig. 7) at strain rates 0.001, 200, 500 and 1,300 s1, show that it is a
strain rate sensitive material. Therefore, the strain rate sensitivity of the Cf/Al composite
was mainly caused by the aluminum matrix.
0 200 400 600 800
Time ( s)
0
500
1000
1500
DigitalSignalinInputBar
(t):2.15E-6 i
(t):6.02E-7 t
Input Wave
Output Wave
0
200
400
600
800
DigitalSignalinOutputBar
Fig. 3 Strain signal in the input-bar and output bar
Table 1 Mechanical properties of composite
"
(1/s) E (GPa) b (%) b (GPa)
0.001 180 0.94 1.41
100 179 0.96 1.45
500 180 0.97 1.52
1,300 180 0.98 1.59
Appl Compos Mater (2007) 14:1731 21
-
7/29/2019 Experimental Study on Tensile Behavior of Carbon Fiber.pdf
6/15
From stressstrain curves of aluminum matrix, obvious yield point can be found at the
strain of 0.2%. But in the composite, yield point disappeared. This phenomenon can beexplained by the thermal residual stress in carbon fiber and aluminum matrix. In the
composite wires, the aluminum matrix and carbon fiber have very different thermal
properties (the thermal expand coefficient of M40J fiber is nearly zero, while the thermal
expand coefficient of aluminum is about 2.0105/C). So, the residual thermal stress and
residual thermal strain will certainly exist in matrix and fiber during the high temperature
manufacturing process.
"Al RAlEAl
3
7
r
EAl
RAlr
N
Al$T 8
"Al RCFECF
CF$T 9
Equation 8 is based on RambergOsgood model for metal material without apparent yield
point. r is the reference stress, and N is stress exponent. Besides, Al and CF are thermal
0.0 0.4 0.8 1.2 1.6
Strain (%)
0.00
0.40
0.80
1.20
1.60
Stress(GPa)
Strain Rate
1300
500
100
0.001
Simulated Results
Fig. 4 Stressstrain curves of carbon fiber reinforced aluminum at different strain rate
22 Appl Compos Mater (2007) 14:1731
-
7/29/2019 Experimental Study on Tensile Behavior of Carbon Fiber.pdf
7/15
expansion coefficients of aluminum matrix and carbon fiber, T is the temperature change.
Al, CF, sRAl and s
RCF are strain and residual thermal stress of matrix and fiber, which must
be self-consistent as follows:
sR
AlVAl sR
CFVCF 0 10
"Al "CF 11
In the present paper, T=700C, the residual stress can be calculated from Eqs. 8, 9, 10
and 11.
sRAl sR
CF 97MPa 12
The quasi-static yield strength of matrix is about 80 MPa, residual stress tensile matrix to
plastic deformation.
After the aluminum matrix was dissolved in a 5% by weight solution of NaOH, high strain
rate tensile tests were performed on carbon fiber bundles. These are actual mechanical
performance of carbon fiber in MMCs after high temperature processing. Figure 8 shows stress
strain curves of original carbon fiber, carbon fiber after processing and carbon/aluminum
composite. 4.5% decrease in modulus and 17% decrease in tensile strength were observed.
Figure 9a shows the fracture of aluminum at strain rate 1,300 1/s. A large amount of
dimples indicate its excellent plastic deformation capability. But for the composite (as
-4 -2 0 2 4
lg
1.3
1.4
1.5
1.6
1.7
TensileStrength(MPa)
0.8
0.9
1.0
1.1
Fa
ilureStrain(%)
.
Tensile Strength
Failure Strain
Fig. 5 Relationship between tensile strength, failure strain and strain rate
Appl Compos Mater (2007) 14:1731 23
-
7/29/2019 Experimental Study on Tensile Behavior of Carbon Fiber.pdf
8/15
shown in Fig. 9b, the fracture surface is nearly planar and no dimples formed in the matrix.
Little fiber is pulled out and no interface breaking is observed. All of these phenomenons
indicate a strong fiber/matrix interface. Usually, the initial failure of composite is formed at
the weakest chain of one fiber. Then strong interface make the stress redistribute in the
specimen, and redistribution of stress caused stress concentration in the neighborhood of the
broken section. The stress concentration may propagate transversely through the specimen
and then make the specimen failure.
3 Statistical Analysis on the Strength of Carbon Fiber and Carbon
Fiber Reinforced Aluminum
The fiber bundles model is shown in Fig. 10. In this model, the N parallel filaments of same
length, L, cross sectional area, A, are rigidly fixed between two ends. The filament can be
0.0 0.4 0.8 1.2 1.6 2.0
Strain (%)
0
1
2
3
4
Stress(MPa)
M40J
0.001 1/s
100 1/s
1300 1/s
Simulated Curve
Fig. 6 Stressstrain curves of carbon fiber bundles at different strain rate
24 Appl Compos Mater (2007) 14:1731
-
7/29/2019 Experimental Study on Tensile Behavior of Carbon Fiber.pdf
9/15
single carbon fiber or coated carbon fiber (a single fiber surrounded by aluminum matrix).
The assumptions for the fiber bundles model are:
1. The stressstrain curve of each filament is linear until the fiber breaks.
s E" 13
2. The interaction between filaments is neglected. As n fibers break, the load they carried
before are instantaneously distributed equally among the surviving N-n fibers, and
stress can be described as
s E" 1 n
N
14
0.00 0.10 0.20 0.30 0.40 0.50
Strain
0.00
0.04
0.08
0.12
0.16
Stre
ss(GPa)
Strain Rate 1/s
1300
500
200
0.02
0.001
Simulated Results
Fig. 7 Stressstrain curves of aluminum at different strain rates
Appl Compos Mater (2007) 14:1731 25
-
7/29/2019 Experimental Study on Tensile Behavior of Carbon Fiber.pdf
10/15
3. The strength of each filament is not a constant, and they flows either a unimodal
Weibull function or a bimodal Weibull function [12]:
H s 1 exp s
s0
b" #unimodal Weibull 15
H s 1 exp s
s01
b1
s
s02
b2" #Bimodal Weibull 16
where H is the cumulative probability of failure, 0 is the Weibull scale parameter, is the
Weibull shape parameter, and is the stress applied on the material. Substituting Eqs. 15
and 16 into Eq. 14, one can obtain the following stressstrain relationship.
(a) Unimodal Weibull:
s E" exp E"
s0
b117
0.0 0.5 1.0 1.5 2.0
Strain (%)
0.00
1.00
2.00
3.00
4.00
Str
ess(GPa)
M40J (original)
M40J (actural)
M40J/Al
Fig. 8 Stressstrain curves of carbon fiber bundles before and after processing
26 Appl Compos Mater (2007) 14:1731
-
7/29/2019 Experimental Study on Tensile Behavior of Carbon Fiber.pdf
11/15
(b) Bimodal Weibull:
s E" exp
E"
s01 b1
E"
s02 b2" #
18
By taking double logarithms on both sides of Eq. 17, one can obtain:
ln ln E"=s bln E" bln s0 19
Equation 19 represents the equation of a straight line when plotted on a Weibull coordinate
system. and 0 can be determined from the slope and intercept of the straight line.
Similarly, by taking double logarithms on both sides of Eq. 18, one can obtain
lnln E"s
ln E"
s01
b1 E"
s02
b2" #20
The parameters 01, 02, 1 and 2 can be determined by regression analysis.
Figure 11 shows the Weibull plots of carbon fiber before and after processing. Before the
processing, the Weibull probability plots of the original fiber are nonlinear, that means
strength follows the bimodal Weibull distribution. However, after processing, a Weibull
probability plot is linear, indicating the fiber strength follows the single Weibull
distribution. Both the Weibull shape parameter and Weibull scale parameter have beenchanged by high temperature manufacturing processing. According to these Weibull plots,
one can obtain the Weibull distribution parameters of fibers.
Before the processing
b1 3:74 b2 10:4 s01 6:45 GPa s02 3:74 GPa
Fig. 9 Fracture surface of aluminum (a) and carbon fiber reinforced aluminum (b)
Appl Compos Mater (2007) 14:1731 27
-
7/29/2019 Experimental Study on Tensile Behavior of Carbon Fiber.pdf
12/15
Fig. 10 Fiber bundles model
0.40 0.80 1.20 1.60 2.00
Ln (E )
-8
-4
0
4
LnLn(E
/
)
Actural Fiber in Composite
Original Fiber
Fig. 11 Weibull plots of carbon fiber before and after processing
28 Appl Compos Mater (2007) 14:1731
-
7/29/2019 Experimental Study on Tensile Behavior of Carbon Fiber.pdf
13/15
After the processing
b 10:2 s0 3:75 GPa
Figure 12 exhibits the Weibull plots of carbon fiber reinforced aluminum at different
rate. As this figure show, these plots are linear at all four strain rates, indicating strength of
composite follows single Weibull distribution. Usually, Weibull scale parameter, 0 , is a
measure of nominal strength, and the average strength will increase with increasing the
value of 0. Weibull shape parameter, , is a measure of scatter. Scatter of strength will
decrease with increasing the value of. These linear plots are nearly parallel to each other,
which means test condition has no effect on the scatter of strength.
According to the slopes and intercepts of these straight lines, the Weibull shape
parameter and Weibull scale parameters can be determined. The Weibull parameters of
composite wires are plotted as functions of strain rate in Fig. 13. It shows that the Weibullshape parameter has no correlation with strain rate over the rate range from 0.001 to
1,300 1/s, but that Weibull scale parameters are increased with increasing strain rate.
b 9:76 s0 2:01"
68
100
!0:037GPa
0.30 0.50 0.70 0.90
Ln(E)
-3.0
-2.0
-1.0
0.0
1.0
LnLn(E
/)
Strain Rate 1/s
1300
500
100
0.001
Simulated Results
Fig. 12 Weibull plots of CF/Al at different strain rate
Appl Compos Mater (2007) 14:1731 29
-
7/29/2019 Experimental Study on Tensile Behavior of Carbon Fiber.pdf
14/15
The above results show that strain rate only affects the strength of the composite wires, and
does not affect the strength dispersion of the composite wires. The degree of strength
dispersion, which is character of the composite wires, is related to the properties of
component and high temperature manufactory process, and is not affected by loadingcondition. It is also testified that the strain rate sensitivity of the composite wires is caused
by the rate sensitivity of aluminum matrix.
By substituting the Weibull parameters into Eqs. 17 and 18, one can obtain the simulated
stressstrain curves. The simulated curves and experimental points are shown in Figs. 4,
6 and 8 and they match well.
4 Conclusion
Quasi-static and high strain rate tensile tests were conducted on carbon fiber, aluminum,
and carbon fiber reinforced aluminum. Based on the analysis of the experimental data, the
following conclusions are reached:
1. Carbon fiber reinforced aluminum is typical strain rate dependent materials. Both
ultimate tensile strength and failure strain increased with increasing of strain rate. The
-4 -2 0 2 4
lg
1.6
1.8
2.0
2.2
2.4
WeibullSc
aleParameter(GPa)
0
10
20
30
WeibullShapeParameter
.
Fig. 13 Effect of strain rate on Weibull scale parameter and Weibull shape parameter
30 Appl Compos Mater (2007) 14:1731
-
7/29/2019 Experimental Study on Tensile Behavior of Carbon Fiber.pdf
15/15
strain rate sensitivity of composite is caused by aluminum matrix, and carbon fiber is a
strain rate insensitive material.
2. Strength loss in carbon fiber was observed in carbon fiber reinforced aluminum. High
temperature processing not only decreased the strength of fiber, but also change scatted
of strength.3. A one-dimensional statistical constitutive equation has been established to describe
tensile stressstrain relationship of the composite at different strain rates. The simulated
stressstrain curves match the experimental results well. The results show that strength
of composite obeys a unimodal Weibull distribute.
Acknowledgements The authors would like to gratefully acknowledge the support of National Science
Foundation through grant no.: HRD-0317741.
Reference
1. Subramanian, S.: J. Reinf. Plast. Compos. 16(8), 676-685 (1997)
2. Ghorbel, E.: Compos. Sci. Technol. 57, 10451056 (1997)
3. Zhou, Y., Xia, Y.: Appl. Compos. Mater. 6, 341352 (1999)
4. Guden, M., Hall, I.W.: Comput. Struct. 76, 139144 (2000)
5. Cady, C.M., Gray III, G.T.: Mater. Sci. Eng. A298, 5662 (2001)
6. Galvez, F., Gonzalez, C., Poza, P., Llorca, J.: Scr. Mater. 44, 26672671 (2001)
7. Zhou, Y.X., Xia, Y.: Appl. Compos. Mater. 6(6), 341352 (1999)
8. Draper, S.L., Brindley, P.K., Nathal, M.V.: Metall. Trans. 23A, 25412548 (1992)
9. Friler, J.B., Argon, A.S., Cornie, J.A.: Mater. Sci. Eng. A162, 143
152 (1993)10. Chi, Z.F., Chou, T.W., Shen, G.: J. Mater. Sci. 19, 3319 (1984)
11. Xia, Y., Yuan, J., Yang, B.: Compos. Sci. Technol. 52, 499504 (1994)
12. Zhou, Y.X., Jiang, D.Z., Xia, Y.: J. Mater. Sci. 36, 919922 (2001)
Appl Compos Mater (2007) 14:1731 31