Appl Compos Mater (2007) 14:17–31 DOI 10.1007/s10443-006-9028-5
Experimental Study on Tensile Behavior of Carbon Fiber and Carbon Fiber Reinforced Aluminum at Different Strain 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 stress–strain 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 Weibull strength 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 lowstrength 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 Y. Zhou (*) : Y. Wang : S. Jeelani Center 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, People’s 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. [1–3] 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 the FRMMC 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 α-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 metal–matrix 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 Pitch55 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 fiber bundles. 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 diameter dp 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 ɛi(t), reflected strain ɛr(t) and transmitted strain ɛt(t) are recorded as functions
Appl Compos Mater (2007) 14:17–31
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Fig. 1 Schematic diagram of the bar–bar tensile impact apparatus
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: s s ðt Þ ¼ Z "s ðt Þ ¼
t
EA "t ðtÞ As
ð1Þ
½"i ðtÞ "t ðtÞdt
ð2Þ
2C0 ½"i ðt Þ "t ðtÞ ls
ð3Þ
0
"s ð t Þ ¼
pffiffiffiffiffiffiffiffi where C0 (¼ E=r, E and ρ are the Young’s 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 s−1) of tensile impact tests were conducted. Typical signal in the inputbar and output-bar were shown in Fig. 3. In addition, quasi-static tensile experiments were
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Appl Compos Mater (2007) 14:17–31
Fig. 2 Specimen and its connection
performed on the MTS-810 testing machine to compare with the above tensile impact results. The strain rate was 0.001 s−1. The average experimental values at different strain rates are listed in Table 1. Figure 4 shows the complete stress–strain 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 σb, the critical strain ɛb and lg " are shown in Fig. 5. Their relationship with strain rate can be formulated as:
sb ¼ s0
" þ "T
ð4Þ
"0
"b ¼ "0
!n
" þ "T
!m ð5Þ
"0
where, ", "0 , σ0 and ɛ0 are strain rate , reference strain rate, reference stress and reference strain, 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.
" þ 61 s b ¼ 1:43 100
!0:036 ðGPaÞ
ð6Þ
Appl Compos Mater (2007) 14:17–31
21
1500
800
600
Input Wave
1000
ε i (t):2.15E-6
400
500 200
0
Digital Signal in Output Bar
Digital Signal in Input Bar
Output Wave ε t (t):6.02E-7
0 0
200
400
600
800
Time (μs) Fig. 3 Strain signal in the input-bar and output bar
" þ 47 "b ¼ 0:97 100
!0:012 ð%Þ
ð7Þ
The solid lines in Fig. 5 are simulated results, which fit the experimental points well. Figure 6 show the stress–strain curves of carbon fiber bundles at strain rate 0.001, 100 and 1,300 s−1. From these curves, it can be concluded that reinforced fiber is a strain rate insensitive material [12]. On the other hand, the tensile stress–strain curves of the aluminum matrix (Fig. 7) at strain rates 0.001, 200, 500 and 1,300 s−1, 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. Table 1 Mechanical properties of composite
" (1/s)
E (GPa)
ɛb (%)
σb (GPa)
0.001 100 500 1,300
180 179 180 180
0.94 0.96 0.97 0.98
1.41 1.45 1.52 1.59
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1.60
Stress (GPa)
1.20
0.80
Strain Rate 1300 500
0.40
100 0.001 Simulated Results
0.00 0.0
0.4
0.8
Strain (%)
1.2
1.6
Fig. 4 Stress–strain curves of carbon fiber reinforced aluminum at different strain rate
From stress–strain 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 be explained 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 2.0×10−5/°C). So, the residual thermal stress and residual thermal strain will certainly exist in matrix and fiber during the high temperature manufacturing process. N σR 3 σr σRAl þ αAl $T ð8Þ "Al ¼ Al þ EAl 7 EAl σr
"Al ¼
σRCF þ αCF $T ECF
ð9Þ
Equation 8 is based on Ramberg–Osgood model for metal material without apparent yield point. σr is the reference stress, and N is stress exponent. Besides, αAl and αCF are thermal
Appl Compos Mater (2007) 14:17–31
23 1.1
1.6 1.0
Failure Strain
1.5
0.9 1.4
Failure Strain (%)
Tensile Strength (MPa)
1.7
Tensile Strength
1.3
0.8 -4
-2
0
.
lg ε
2
4
Fig. 5 Relationship between tensile strength, failure strain and strain rate
expansion coefficients of aluminum matrix and carbon fiber, ΔT is the temperature change. ɛAl, ɛCF, s RAl and s RCF are strain and residual thermal stress of matrix and fiber, which must be self-consistent as follows: s RAl VAl þ s RCF VCF ¼ 0
ð10Þ
"Al ¼ "CF
ð11Þ
In the present paper, ΔT=700°C, the residual stress can be calculated from Eqs. 8, 9, 10 and 11. s RAl ¼ s RCF ¼ 97MPa
ð12Þ
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
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Appl Compos Mater (2007) 14:17–31
4
Stress (MPa)
3
2
M40J 0.001 1/s 1
100 1/s 1300 1/s Simulated Curve
0 0.0
0.4
0.8
1.2
1.6
2.0
Strain (%) Fig. 6 Stress–strain curves of carbon fiber bundles at different strain rate
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
Appl Compos Mater (2007) 14:17–31
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0.16
Stress (GPa)
0.12
0.08
Strain Rate 1/s 1300 500 200
0.04
0.02 0.001 Simulated Results
0.00 0.00
0.10
0.20
0.30
0.40
0.50
Strain Fig. 7 Stress–strain curves of aluminum at different strain rates
single carbon fiber or coated carbon fiber (a single fiber surrounded by aluminum matrix). The assumptions for the fiber bundles model are: 1. The stress–strain curve of each filament is linear until the fiber breaks.
s ¼ E"
ð13Þ
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 n s ¼ E" 1 N
ð14Þ
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Appl Compos Mater (2007) 14:17–31
4.00 M40J (original) M40J (actural) M40J/Al
Stress (GPa)
3.00
2.00
1.00
0.00 0.0
0.5
1.0
1.5
2.0
Strain (%) Fig. 8 Stress–strain curves of carbon fiber bundles before and after processing
3. The strength of each filament is not a constant, and they flows either a unimodal Weibull function or a bimodal Weibull function [12]: " # s b ðunimodal WeibullÞ ð15Þ ϖ ¼ H ðs Þ ¼ 1 exp s0 " b 2 # s b1 s ðBimodal WeibullÞ ϖ ¼ H ðs Þ ¼ 1 exp s 01 s 02
ð16Þ
where H is the cumulative probability of failure, σ0 is the Weibull scale parameter, β is the Weibull shape parameter, and σ is the stress applied on the material. Substituting Eqs. 15 and 16 into Eq. 14, one can obtain the following stress–strain relationship. (a)
Unimodal Weibull: b 1 E" s ¼ E" exp s0
ð17Þ
Appl Compos Mater (2007) 14:17–31
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Fig. 9 Fracture surface of aluminum (a) and carbon fiber reinforced aluminum (b)
(b)
Bimodal Weibull: " b 2 # E" b1 E" s ¼ E" exp s 01 s 02
ð18Þ
By taking double logarithms on both sides of Eq. 17, one can obtain: ln ½ln ðE"=s Þ ¼ b ln ðE"Þ b ln ðs 0 Þ
ð19Þ
Equation 19 represents the equation of a straight line when plotted on a Weibull coordinate system. β and σ0 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 " b 2 # E" E" b1 E" ¼ ln ð20Þ ln ln s s 01 s 02 The parameters σ01, σ02, β1 and β2 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 been changed by high temperature manufacturing processing. According to these Weibull plots, one can obtain the Weibull distribution parameters of fibers. Before the processing b1 ¼ 3:74
b2 ¼ 10:4
s 01 ¼ 6:45ðGPaÞ s 02 ¼ 3:74ðGPaÞ
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Appl Compos Mater (2007) 14:17–31
Fig. 10 Fiber bundles model
σ
σ
4
LnLn( E ε /σ )
Actural Fiber in Composite 0
Original Fiber -4
-8 0.40
0.80
1.20
Ln (E ε )
Fig. 11 Weibull plots of carbon fiber before and after processing
1.60
2.00
Appl Compos Mater (2007) 14:17–31
29
1.0
Strain Rate 1/s 1300 500
0.0
LnLn(E ε /σ )
100 0.001 Simulated Results
-1.0
-2.0
-3.0 0.30
0.50
Ln(Eε)
0.70
0.90
Fig. 12 Weibull plots of CF/Al at different strain rate
After the processing b ¼ 10:2 s 0 ¼ 3:75ðGPaÞ 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, σ0 , is a measure of nominal strength, and the average strength will increase with increasing the value of σ0. Weibull shape parameter, β, is a measure of scatter. Scatter of strength will decrease with increasing the value of β. 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 Weibull shape 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. !0:037 " þ 68 ðGPaÞ b ¼ 9:76 s 0 ¼ 2:01 100
30
Appl Compos Mater (2007) 14:17–31 30
2.2 20
σ
2.0
10
β
1.8
1.6
Weibull Shape Parameter
Weibull Scale Parameter (GPa)
2.4
0 -4
-2
0
.
lg ε
2
4
Fig. 13 Effect of strain rate on Weibull scale parameter and Weibull shape parameter
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 loading condition. 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 stress–strain 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
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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 stress–strain relationship of the composite at different strain rates. The simulated stress–strain 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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