Experimental Study on Tensile Behavior of Carbon Fiber.pdf

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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


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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


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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


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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



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"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



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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



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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



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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



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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



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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



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(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)



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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



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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



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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



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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.

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Experimental Study on Tensile Behavior of Carbon Fiber.pdf