Introduction

Carbon fibers are widely used as reinforcements in composite materials because of their high specific strength and modulus. Such composites have become a dominant material in the aerospace, automotive, and sporting goods industries [1]. Current trends toward the development of carbon fibers have been driven in two directions; ultrahigh tensile strength fiber with a fairly high strain to failure (~2 %), and ultrahigh modulus fiber with high thermal conductivity. Today, a number of ultrahigh tensile strength PAN-based (more than 6 GPa), and ultrahigh modulus pitch-based (more than 900 GPa) carbon fibers have been commercially available. Naito et al. [2, 3] characterized the tensile, flexural properties and Weibull modulus of ultrahigh strength PAN-based, ultrahigh modulus pitch-based and high ductility pitch-based single carbon fibers.

In contrast, carbon nanotube (CNT) with the extremely high tensile strength (~150 GPa) [4] has attracted attention as reinforcements, but they cannot grow as long, continuous fibers. Although it is possible to obtain twisted CNT yam that are continuous fibers, this strength is exceedingly low compared to the carbon fibers [5, 6]. An interesting technique to modify the carbon fiber is CNT grafting on the carbon fiber surface. The grafting of CNT on carbon fibers has been reported in the literature [7–9]. CNT can be grown on the carbon fibers by chemical vapor deposition (CVD) [7, 8], electrodeposition [9], etc. CNT-grafted carbon fibers offer the opportunity to add the potential benefits of nanoscale reinforcement to well-established fibrous composites to create micro-nano multiscale hybrid composites [9–11]. However, the effect of CNT grafting on the mechanical properties of carbon fiber has not been fully evaluated. Naito et al. [12] reported that the grafting of CNT improves the tensile strength and Weibull modulus of ultrahigh strength PAN- and ultrahigh modulus pitch-based carbon fibers. The growth of the dense networks of CNT on carbon fibers may lead to reduction of the strength-limiting defects, which in turn, improves the tensile strength and Weibull modulus [12].

To evaluate the effect of gauge length on the tensile strength is essentially important for understanding the mechanical properties of the carbon fibers that contribute to failure. The effects of gauge length on tensile properties of carbon fibers have been reported in the literature [13–15]. Naito et al. also reported that the effect of gauge length on tensile strength and Weibull modulus of PAN- and pitch-based carbon fibers, and concluded that the Weibull modulus and the average tensile strength increased with decreasing gauge length, a linear relation between the Weibull modulus, the average tensile strength, and the gauge length was established on log–log scale [16]. These results also clearly showed that for PAN- and pitch-based carbon fibers, there was a linear relation between the Weibull modulus and the average tensile strength on log–log scale [16].

In the present study, the tensile tests of single filaments at several gauge length for CNT-grafted ultrahigh strength PAN- and ultrahigh modulus pitch-based carbon fibers were performed. The effect of gauge length on tensile strength and Weibull modulus of CNT-grafted PAN- and pitch-based carbon fibers were evaluated.

Experimental procedure

Materials

The carbon fibers used in this study were ultrahigh tensile strength T1000GB PAN- and ultrahigh modulus K13D pitch-based carbon fibers.Footnote 1 The T1000GB PAN-based carbon fiber was supplied from Toray Industries, Inc. The K13D pitch-based carbon fiber was supplied from Mitsubishi Plastics, Inc.

The physical properties of PAN- and pitch-based carbon fibers are listed in Table 1. Both as-received fibers had been subjected to commercial surface treatments and sizing (epoxy compatible sizing).

Table 1 Mechanical and physical properties of ultrahigh strength T1000GB PAN- and ultrahigh modulus K13D pitch-based carbon fibers
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To grow CNT on the carbon fibers, a Fe(C5H5)2 (ferrocene) catalyst was applied to the T1000GB and K13D fiber bundles using thermal CVD in vacuum. Experimental details on the synthesis technique of CNT can be found elsewhere [7, 8]. Prior to the application of the catalyst, the carbon fiber bundles were heat-treated at 750 °C for an hour in vacuum to remove the sizing. The growth temperature and time for the deposition of CNT were selected as 750 °C (T1000GB) and 700 °C (K13D) for 900 s.

Tensile test

Single carbon filament specimens were prepared on the stage with the help of a stereoscope. A single filament was selected from carbon fiber bundles and cut perpendicular to the fiber axis by a razor blade. The diameter of the single as-received carbon fiber, d f was measured using a laser scanning microscope (Lasertec Corp., 1LM15 W) before testing and a high resolution scanning electron microscope (JEOL, JSM-6500F) during the fractured surface observation. No difference was observed between two techniques. The diameter of the single CNT-grafted carbon fiber without CNT, d f was measured using a high resolution scanning electron microscope (JEOL, JSM-6500F) during the fractured surface observation. The measured fiber diameters, d f are shown in Table 1 (average diameters and standard deviations are obtained from the same kind of all carbon fibers at various gauge lengths). All specimens were stored in a desiccator at 20 ± 3 °C and at 10 ± 5 % relative humidity prior to testing.

Tensile tests of single carbon fibers were performed using a universal testing machine (Shimadzu, Table top type tester EZ-Test) with a load cell of 10 N. The tensile specimen was prepared by fixing the filament on a paper holder with an instant high viscosity type cyanoacrylate adhesive, as reported elsewhere [17, 18]. The specimen was set up to the testing machine using active gripping systems. To allow for ease of severing of the paper holder and to avoid the fracture during gripping of the shorter length samples (L = 1 and 5 mm), a scalpel was used to widen the slot [14]. The holder was cut into two parts, before testing. Plastic films were set on both sides of the carbon fiber filament, and water was filled between them to avoid secondary damage of the carbon fiber. The gauge length, L of 1, 5, and 25 mm, and crosshead speed of 0.5 mm/min were applied. All tests were conducted under the laboratory environment at room temperature (at 23 ± 3 °C and 50 ± 5 % relative humidity). Twenty specimens were tested for all carbon fibers. The fracture surfaces of these carbon fibers were examined using a high resolution scanning electron microscope (JEOL, JSM-6500F) at an operating voltage of 5 kV.

Results

For all the carbon fibers, the stress applied to the specimen was linearly proportional to the strain until failure. The tensile fracture surfaces of the CNT-grafted and as-received T1000GB PAN- and K13D pitch-based carbon fibers at gauge length of 25 mm were showed in our previous report [2, 12] and the fracture surfaces of the CNT-grafted and as-received T1000GB PAN- and K13D pitch-based carbon fibers at gauge lengths of 1 and 5 mm were also observed in this study. Figures 1 and 2 show the scanning electron microscope (SEM) micrographs of transverse cross-sectional views for the tensile fractured surfaces of the CNT-grafted and as-received T1000GB PAN-based and K13D pitch-based carbon fibers at gauge lengths of 1, 5 and 25 mm. The failure initiation sites were clearly observed for the CNT-grafted and as-received T1000GB fibers and the some of CNT were lost for the CNT-grafted T1000GB fibers due to impact of fracture of fiber. However, for the K13D carbon fiber, the failure initiation sites were obscured for the CNT-grafted and as-received K13D fibers and the almost CNT were remained for the CNT-grafted K13D fiber. Morimoto et al. indicated the gauge length dependence on the Weibull parameters of the silicon carbide (SiC: Tyranno ZMI Si–Zr–C–O) fiber provided biased estimation and classified the fracture surfaces into the characteristic fracture patterns [19]. In this study, however, the fracture pattern differences among the all gauge lengths for PAN- and pitch-based carbon fibers were not observed and it was difficult to classify the fracture surfaces of all carbon fibers into the characteristic patterns.

Fig. 1
figure 1

SEM micrographs of the tensile fractured surfaces showing the transverse cross-section views of CNT-grafted and as-received T1000GB PAN-based carbon fibers at gauge lengths of 1, 5 and 25 mm. a CNT-grafted fiber at gauge length of 1 mm, b CNT-grafted fiber at gauge length of 1 mm (high magnification), c CNT-grafted fiber at gauge length of 5 mm, d CNT-grafted fiber at gauge length of 5 mm (high magnification), e CNT-grafted fiber at gauge length of 25 mm [12], f CNT-grafted fiber at gauge length of 25 mm (high magnification), g as-received fiber at gauge length of 1 mm [16], h as-received fiber at gauge length of 5 mm [16], and i as-received fiber at gauge length of 25 mm [2, 12, 16]

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Fig. 2
figure 2

SEM micrographs of the tensile fractured surfaces showing the transverse cross-section views of CNT-grafted and as-received K13D pitch-based carbon fibers at gauge lengths of 1, 5 and 25 mm. a CNT-grafted fiber at gauge length of 1 mm, b CNT-grafted fiber at gauge length of 1 mm (high magnification), c CNT-grafted fiber at gauge length of 5 mm, d CNT-grafted fiber at gauge length of 5 mm (high magnification), e CNT-grafted fiber at gauge length of 25 mm [12], f CNT-grafted fiber at gauge length of 25 mm (high magnification), g as-received fiber at gauge length of 1 mm [16], h as-received fiber at gauge length of 5 mm [16], and i as-received fiber at gauge length of 25 mm [2, 12, 16]

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The tensile strength, σ f was calculated using:

$$ \sigma_{\text{f}} = \frac{{P_{\max } }}{{\left( {\frac{{\pi d_{\text{f}}^{2} }}{4}} \right)}}, $$
(1)

where P max is the maximum fracture load.

The average tensile strengths (σf.ave) at various gauge length are summarized in Table 1 and the relation between the enhancing ratio, ((σf.ave (CNT-grafted) − σf.ave (as-received))/σf.ave (as-received)*100) and the gauge length, L ranging from 1 to 25 mm was shown in Fig. 3. These results show that the average tensile strength of CNT grown on ultrahigh strength T1000GB fiber at gauge length of 1, 5, and 25 mm is 8.97 ± 0.80, 8.23 ± 0.84, and 6.73 ± 1.01 GPa [12], which is 0, 7, and 18 % higher than that in the as-received state (8.98 ± 0.80, 7.71 ± 0.88, and 5.69 ± 1.02 GPa [2, 12, 16]). The average tensile strength of CNT grown on K13D fiber at gauge length of 1, 5, and 25 mm is 5.16 ± 0.87, 4.65 ± 0.84, and 4.09 ± 0.85 GPa [12], which is 1, 16, and 27 % higher than that in the as-received state (5.12 ± 0.85, 4.00 ± 0.82, and 3.21 ± 0.81 GPa [2, 12, 16]). Evidently, the grafting of CNT improved the average tensile strength of PAN- and pitch-based carbon fibers at gauge lengths of 5 and 25 mm. However, the average tensile strength of CNT-grafted PAN- and pitch-based carbon fibers at gauge length of 1 mm is almost identical to that in the as-received state.

Fig. 3
figure 3

Relation between the enhancing ratio and the gauge length for T1000GB PAN- and K13D pitch-based carbon fibers

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The results shown in Table 1 clearly indicate that there is an appreciable scattering of tensile strength for these carbon fibers. The statistical distribution of fiber strengths is usually described by means of the Weibull equation [20]. The two-parameter Weibull distribution is given by

$$ P_{\text{F}} = 1 - \exp \left[ { - \frac{L}{{L_{0} }}\left( {\frac{{\sigma_{\text{f}} }}{{\sigma_{0} }}} \right)^{{m_{\text{f}} }} } \right], $$
(2)

where P F is the cumulative probability of failure of a carbon fiber of length L at applied tensile strength σf, m f is the Weibull modulus (Weibull shape parameter) of the carbon fiber, σ0 a Weibull scale parameter (characteristic stress), and L 0 a reference gauge length. The cumulative probability of failure, P F, under a particular stress is given by

$$ P_{\text{F}} = \frac{i}{n + 1}, $$
(3)

where i is the number of fibers that have broken at or below a stress level and n is the total number of fibers tested. Rearrangement of the two-parameter Weibull statistical distribution expression (Eq. 2) gives the following:

$$ \ln \left( {\ln \left[ {\frac{1}{{1 - P_{\text{F}} }}} \right]} \right) = m_{f} \ln \left( {\sigma_{f} } \right) - m_{f} \ln \left( {\sigma_{0} \left( {\frac{{L_{0} }}{L}} \right)^{{\frac{1}{{m_{f} }}}} } \right). $$
(4)

Hence the Weibull modulus, m f can be obtained by linear regression from a Weibull plot of Eq. (4).

Figure 4 shows the Weibull plots of CNT grown on ultrahigh tensile strength T1000GB PAN- and ultrahigh tensile modulus K13D pitch-based carbon fibers. A threshold of the tensile strength was observed. The influence of threshold stress on the estimation of the Weibull statistics was discussed by Lu et al. [21, 22]. It was concluded that the two-parameter Weibull distribution is still a preferred choice, if test specimens are limited in number and threshold stress is not too large. As a result, the two-parameter Weibull distribution was applied in this study.

Fig. 4
figure 4

Weibull plots for T1000GB PAN- and K13D pitch-based carbon fibers at gauge lengths of 1, 5 and 25 mm. Open circle 1-mm gauge length, open triangle 5 mm gauge length, open diamond 25-mm gauge length as-received carbon fibers, and filled circle 1-mm gauge length, filled triangle 5-mm gauge length, filled diamond 25-mm gauge length CNT-grafted carbon fibers. a T1000GB PAN- and b K13D pitch-based carbon fiber

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The Weibull modulus, m f, for the CNT grown on T1000GB and K13D fibers at gauge lengths of 1, 5, and 25 mm were calculated to be 11.92, 10.44, 7.15 [12], and 6.38, 5.75, 5.09 [12], respectively. The Weibull modulus, m f , for the T1000GB and K13D fibers with sizing at gauge lengths of 1, 5 and 25 mm were found to be 11.92, 9.24, 5.86 and 6.38, 5.24, 4.23, respectively [2, 12, 16]. The results clearly show that the grafting of CNT improves the Weibull modulus of PAN- and pitch-based carbon fibers at gauge lengths of 5 and 25 mm. However, the Weibull modulus of CNT-grafted PAN- and pitch-based carbon fibers at gauge length of 1 mm is almost identical to that in the as-received state as well.

The Weibull modulus (m f) of PAN- and pitch-based carbon fibers at various gauge lengths were summarized in Table 2.

Table 2 Weibull modulus of T1000GB PAN-based and K13D pitch-based carbon fibers at various gauge lengths
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Discussion

The grafting of CNT improved the tensile strengths and Weibull modulus of T1000GB PAN- and K13D pitch-based carbon fibers at the gauge length of 5 and 25 mm (longer gauge length). However, the tensile strengths and Weibull modulus of the CNT grafted T1000GB PAN- and K13D pitch-based carbon fibers were almost similar to those in the as-received state at the gauge length of 1 mm (shorter gauge length). It is important to evaluate the “true” improvement of the CNT-grafted PAN- and pitch-based carbon fibers. However, it is difficult to estimate the “true” improvement of the CNT-grafted carbon fibers quantitatively.

It is considered that the characters of PAN- and pitch-based carbon fibers are difficult to change in this CVD process (maximum temperature is 750 °C) because both the carbon fibers are heat-treated at more than 1000 °C during the producing process and are relatively thermal stable materials in an inactive atmosphere. The potential (ideal) strengths of both carbon fibers are not changed. The effect of CNT grafting is observed in the surfaces and flaws (surface and internal) of both carbon fibers which are related to the lower tensile strengths of both fibers. The grafting of CNT helps to reduce the lower strength (the threshold strength) which is observed in the longer gauge length. As a result, the average tensile strengths of both carbon fibers increase and the strength distributions decrease (the Weibull modulus is strongly related to the strength distribution and the Weibull modulus increase). In the shorter gauge length, the almost tensile strengths of both carbon fibers observe in higher stress levels (more than the threshold strengths of both fibers) which are strongly related to the potential (ideal) strengths of both carbon fibers. Therefore, the effect of grafting CNT is disappeared and, the average tensile strengths, the strength distributions (the Weibull modulus) of the CNT grafted on both carbon fibers are almost similar to those in the as-received state.

In our previous investigation [16], it was found that when the gauge length of as-received T1000GB PAN- and K13D pitch-based carbon fibers is less than 100 mm, the Weibull modulus and the average tensile strength increased with decreasing gauge length. Also, there is a linear relation between the Weibull modulus, the average tensile strength and the gauge length on log–log scale. For the CNT-grafted T1000GB PAN- and K13D pitch-based carbon fibers, there is also a linear relation between the Weibull modulus, the average tensile strength and the gauge length on log–log scale. Thus, the Weibull modulus and the average tensile strength is given by

$$ m_{\text{f}} = \left( {\frac{L}{{L_{0} }}} \right)^{\alpha } $$
(5)
$$ \sigma_{{{\text{f}} . {\text{ave}}}} = \sigma_{0} \left( {\frac{{L_{0} }}{L}} \right)^{{\frac{1}{{m^{*}_{\text{f}} }}}} $$
(6)

where, L 0 , α and m *f are the characteristic length, the length factor of Weibull modulus and the Weibull modulus (Weibull shape parameter) obtained from the tensile strength versuss the gauge length relations.

From Eqs. (5) and (6), the Weibull modulus is modified

$$ m_{\text{f}} = \left( {\frac{{\sigma_{{{\text{f}} . {\text{ave}}}} }}{{\sigma_{0} }}} \right)^{{ - \alpha \cdot m^{*}_{\text{f}} }} . $$
(7)

Rearrangement of the Eq. (7) gives the following:

$$ \ln \left( {m_{\text{f}} } \right) = - \alpha \cdot m^{*}_{\text{f}} \ln \left( {\sigma_{{{\text{f}} . {\text{ave}}}} } \right) + \alpha \cdot m^{*}_{\text{f}} \ln \left( {\sigma_{0} } \right). $$
(8)

Hence, there is a linear relation between the Weibull modulus, m f and the average tensile strength, σf.ave on log–log scale and this relation can be obtained from experimental data.

Figure 5 shows the relation between the Weibull modulus, m f and the average tensile strength, σf.ave of the CNT-grafted and as-received T1000GB PAN- and K13D pitch-based carbon fibers. The results clearly show that for both types of carbon fibers, the Weibull modulus increased with increasing the average tensile strength. It is evident that there is a linear relation between the Weibull modulus and the average tensile strength of the CNT-grafted and as-received PAN- and pitch-based carbon fibers on log–log scale.

Fig. 5
figure 5

Relation between the Weibull modulus and the average tensile strength of the CNT-grafted and as-received T1000GB PAN-based and K13D pitch-based carbon fibers. Open square as-received T1000GB PAN-based, open diamond as-received K13D pitch-based carbon fibers, and filled square CNT-grafted T1000GB PAN-based, filled diamond CNT-grafted K13D pitch-based carbon fibers.−α·m *f  = 1.23 (T1000GB) and 0.94 (K13D)

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This means that the high strengths of both carbon fibers cause the narrow strength distributions. It is important to consider this phenomenon. In the longer gauge length, the surfaces (features and modifications) and the flaws (surface and internal) of both carbon fibers strongly depend on the tensile strengths of both carbon fibers. The strength distributions of both carbon fibers are varied from the lower (related to the surfaces and flaws) to the higher stress (related to the potential strength) levels. Therefore, the average tensile strengths and the Weibull modulus of both carbon fibers become lower value. However, in the shorter gauge length, it is difficult to observe the lower tensile strengths of both carbon fibers because the effect of surfaces and flaws on the tensile strengths becomes small. The almost tensile strengths of both carbon fibers observe in the higher stress level and the strength distributions of both carbon fibers become narrow. As a result, the average tensile strengths and the Weibull modulus of both carbon fibers become higher value.

A potential mechanism for enhanced tensile strength at longer gauge length is thought to be the three-dimensional network structures of CNT. Figure 6 shows the schematic model of CNT-grafted carbon fiber filament. The growth of the dense networks of CNT on carbon fibers lead to reduction of the strength-limiting defects. Especially, the grafting of CNT healed the flaws (surface and internal) that relate to lower tensile strength. In addition, it is highly possible that the growth of CNTs on the fibers could change the slippage regions to shorten effective gauge length. These effects were similar to that of gauge length on tensile strength for as-received carbon fibers. The fracture behaviors of CNT-grafted carbon fiber at longer gauge length could be seen as that of as-received (ungrafted) carbon fiber at shorter gauge length, which in turn, improves the tensile strength and Weibull modulus. This result also observed in the tensile strength versus the Weibull modulus relation as shown in Fig. 5.

Fig. 6
figure 6

Schematic model of CNT-grafted carbon fiber filament

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Concluding remarks

The tensile properties of CNT grown on T1000GB PAN- and K13D pitch-based single carbon fibers were performed at gauge lengths of 1, 5 and 25 mm. The results are briefly summarized.

  1. (1)

    The grafting of CNT improves the tensile strength and Weibull modulus of PAN- and pitch-based carbon fibers with longer gauge length (≥5 mm).

  2. (2)

    The Weibull modulus increased with increasing the average tensile strength of CNT-grafted PAN- and pitch-based carbon fibers. There is a linear relation between the Weibull modulus and the average tensile strength of CNT-grafted and as-received PAN- and pitch-based carbon fibers on log–log scale.