Availableonlineatwww.sciencedirect.com DIRECTO CARBON ELSEVIER Carbon42(2004)1275-1278 ww. elsevier. com/locate/carbon Mechanical properties of high-strength carbon fibres Validation of an end-effect model for describing experimental data M.A. Montes- Moran .w. gauthier. A. Martinez-Alonso J.M.D. Tascon Instituto Nacional del Carbon, CSIC, Apartado 73, 33080 Oviedo, Spain Received 10 July 2003; accepted 28 December 2003 Available online 13 February 2004 The present contribution deals with the use of different models accounting for the mechanical response of high-strength (hT) carbon fibres. In particular, analytical models based on Weibull type of statistical distributions will be employed to analyse the dependence of the strength of carbon fibres on length. This dependence is relevant for interpreting the results of conventional agmentation tests, which are traditionally performed to characterise the level of fibre/matrix adhesion in fibre reinforced com- posites. The objective of this work is to compare alternative models, such as the so-called"end-effect" model, for determining the tensile strength of HT carbon fibres at small gauge lengths. To validate these models, tensile tests were performed with five different HT, ex-PAN carbon fibres: a fresh, untreated sample, and four samples which were prepared after submitting the previous one to various surface treatments. Specifically, plasma oxidation was carried out under three different conditions of power and/or time of exposure. A sample oxidized by the manufacturer, presumably using an electrochemical treatment, was also included. Results showed that the end-effect model represents well the behaviour of the untreated and plasma treated under the mildest conditions carbon fibres. Overall, all treatments tend to decrease the tensile strength of the fibres with the commercial treatment being the most damaging when compared to any of the plasma treatments carried out C 2004 Elsevier Ltd. All rights reserved Keywords: A. Carbon fibres, Carbon composites; B. Surface treatment; D. Mechanical properties; Interfacial properties 1. Introduction strength of polyacrylonitrile(PAN)-based carbon fibres Several statistical models will be used to ascertain gauge Carbon fibres combine exceptional mechanical prop- length dependence of the tensile strength. The theoreti erties and low weight, making them ideal reinforcements cal bases on which every model stands are given in detail for composite materials to be employed in aerospace and elsewhere [3-5] sport applications. An important amount of scientific and technological work has been done to improve the mechanical properties of carbon fibres and carbon fibre 2. Experimental composites Surface treatments have been developed in close connection to the latter. as it has been demon- Fresh (untreated and unsized high-strength, PAN- strated that the interfacial properties of carbon fibre based carbon fibres (CF sample)were selected as start opposites are enhanced after increasin ing material, with typical values of 230 GPa and 3. 3 GPa activity"of the reinforcement [1,2]. An obvious re for the Youngs modulus and tensile strength, respec- quirement of any surface treatment is not to damage the tively. Plasma treatments were carried out in a Technics mechanical properties of the fibres it has been applied t Plasma 200-G reactor where oxygen(99.999% pure)at The objective of the present work is to analyse the 1.00+0.0l mbar of pressure was excited using micro- effect of different surface treatments on the tensile wave energy(2.45 GHz). The microwave power and the sample exposure time were varied in order to prepare Corresponding author. Tel. +34-985-119090: fax: +34-985- samples oxidized to various extents. Three different 297662 plasma treatments were carried out, namely 75 W/3 min E-mail address. miguelaincar M.A. Montes-Moran) (CFPI sample), 75 W/10 min(CFP2)and 150 W/3 min 6223/S- see front matter 2004 Elsevier Ltd. All rights reserved
Mechanical properties of high-strength carbon fibres. Validation of an end-effect model for describing experimental data M.A. Montes-Moran *, W. Gauthier, A. Martınez-Alonso, J.M.D. Tascon Instituto Nacional del Carbon, CSIC, Apartado 73, 33080 Oviedo, Spain Received 10 July 2003; accepted 28 December 2003 Available online 13 February 2004 Abstract The present contribution deals with the use of different models accounting for the mechanical response of high-strength (HT) carbon fibres. In particular, analytical models based on Weibull type of statistical distributions will be employed to analyse the dependence of the strength of carbon fibres on length. This dependence is relevant for interpreting the results of conventional fragmentation tests, which are traditionally performed to characterise the level of fibre/matrix adhesion in fibre reinforced composites. The objective of this work is to compare alternative models, such as the so-called ‘‘end-effect’’ model, for determining the tensile strength of HT carbon fibres at small gauge lengths. To validate these models, tensile tests were performed with five different HT, ex-PAN carbon fibres: a fresh, untreated sample, and four samples which were prepared after submitting the previous one to various surface treatments. Specifically, plasma oxidation was carried out under three different conditions of power and/or time of exposure. A sample oxidized by the manufacturer, presumably using an electrochemical treatment, was also included. Results showed that the end-effect model represents well the behaviour of the untreated and plasma treated under the mildest conditions carbon fibres. Overall, all treatments tend to decrease the tensile strength of the fibres, with the commercial treatment being the most damaging when compared to any of the plasma treatments carried out. 2004 Elsevier Ltd. All rights reserved. Keywords: A. Carbon fibres, Carbon composites; B. Surface treatment; D. Mechanical properties; Interfacial properties 1. Introduction Carbon fibres combine exceptional mechanical properties and low weight, making them ideal reinforcements for composite materials to be employed in aerospace and sport applications. An important amount of scientific and technological work has been done to improve the mechanical properties of carbon fibres and carbon fibre composites. Surface treatments have been developed in close connection to the latter, as it has been demonstrated that the interfacial properties of carbon fibre composites are enhanced after increasing the ‘‘surface activity’’ of the reinforcement [1,2]. An obvious requirement of any surface treatment is not to damage the mechanical properties of the fibres it has been applied to. The objective of the present work is to analyse the effect of different surface treatments on the tensile strength of polyacrylonitrile (PAN)-based carbon fibres. Several statistical models will be used to ascertain gauge length dependence of the tensile strength. The theoretical bases on which every model stands are given in detail elsewhere [3–5]. 2. Experimental Fresh (untreated and unsized) high-strength, PANbased carbon fibres (CF sample) were selected as starting material, with typical values of 230 GPa and 3.3 GPa for the Young’s modulus and tensile strength, respectively. Plasma treatments were carried out in a Technics Plasma 200-G reactor where oxygen (99.999% pure) at 1.00 ± 0.01 mbar of pressure was excited using microwave energy (2.45 GHz). The microwave power and the sample exposure time were varied in order to prepare samples oxidized to various extents. Three different plasma treatments were carried out, namely 75 W/3 min (CFP1 sample), 75 W/10 min (CFP2) and 150 W/3 min * Corresponding author. Tel.: +34-985-119090; fax: +34-985- 297662. E-mail address: miguel@incar.csic.es (M.A. Montes-Moran). 0008-6223/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2004.01.019 Carbon 42 (2004) 1275–1278 www.elsevier.com/locate/carbon
M.A. Montes.Moran et al. Carbon 42(2004)1275-1278 (CFP3). A sample of carbon fibres(CF) oxidized(but Table I unsized)following an unknown industrial method was Tensile and dimensional data determined for the carbon fibres under also studied for comparison(CFO sample). According to the literature, it can be assumed that CFO was pre- Diameter (um) pared following the conventional method of electro- chemical oxidation 7.7 2.93 The diameter of the fibres was measured using a laser (0.560) 2.83 diffraction technique. At least three measurements were (0.483) performed in each single filament. The diameter of the 2.79 filament was then estimated from the average of the (0.468) three measurements CFP Single filament tensile tests were performed according (0.61) 0.335) to a method described in the literature, adapted from the ASTM standard [6]. Tensile tests were carried out using an Instron 1 122 universal testing machine equipped with a load beam of 5 N at a typical crosshead speed of 0.5 (0.517) mmmin-l. Three gauge lengths, namely 20, 30 and 40 CFP2 3.32 mm, were tested for each type of fibre; a minimum of 30 (0.48) (0.543) single filaments were tested at each gauge length. (0.652) 3. Results and discussion CFP Table 1 contains some of the results obtained from the single filament tensile tests. As mentioned in the (0.666 experimental section, data of Table I are averaged (0.17) (assuming a normal distribution) from, at least, results obtained from 30 specimens. Thus, in the case of the CFO 20.3 diameter values, at least 90 measurements were per- (0.442) formed for each carbon fibre variety. From these results it can be concluded that the surface treatments do not affect the fibre diameter, except in the case of the long (0.374) time plasma treatment(CFP2 sample), where a statisti- cally significant reduction of the fibre diameter is noticed (t-test, P=0.05). This reduction is, nonetheless, very the parameters of each model the"maximum likeli- small. On the other hand, the normal average of the hood"theory was adopted to find the best fit of the tensile strength of all fibres tested decreases as the gauge experimental data. A maximum likelihood function length increases. The tensile strength of a material is a (MLF) is thus defined and maximised using an iterative property that is statistically controlled at a microscopic routine that was performed computationally. The level. For a given geometry, it depends mainly on the parameters for the simple Weibull distribution were amount and nature of flaws(or defects) present in the determined for all gauge lengths simultaneously. The solid. Thus, for carbon fibres in particular, it is expected results of the parameters estimation and the average that they will become weaker as the length tested in- tensile strength for a gauge length of 20 mm are pre- creases, since it will be statistically more likely to contain sented in Table 2. In this table, a1 and a2 represent the a strength-reducing flaw. This length-dependency of the mean strength resulting from true strength and end-ef- carbon fibres tensile strength is critical when predicting fect related failures, respectively values of ultimate tensile strength at small lengths [7, 8], The determination of the best model for a given set of which is fundamental to estimate the final performance experimental data is performed by direct observation of of a composite material the model fitted to the strength data. the best fit The simple Weibull distribution and the end-effect considered to be the best model. The "log-likelihood model were both used to fit all the tensile strength data. ratio statistic", T derived from the maximum likelihood The first is a two-parameter distribution (ool, m), function(MlF)of the two compared distributions [3]. whereas the latter model includes two additional only used if the model selection cannot be decided parameters (i.e, it is a four parameter distribution, Gol, visually. Figs. I and 2 illustrate the difference between 71, 002, m2), to account for the hypothetical flaw pop- the simple Weibull distribution and the end-effect model ulation that the end-effects would originate. To estimate for the untreated CF fibres, at 20 mm gauge length: the
(CFP3). A sample of carbon fibres (CF) oxidized (but unsized) following an unknown industrial method was also studied for comparison (CFO sample). According to the literature, it can be assumed that CFO was prepared following the conventional method of electrochemical oxidation. The diameter of the fibres was measured using a laser diffraction technique. At least three measurements were performed in each single filament. The diameter of the filament was then estimated from the average of the three measurements. Single filament tensile tests were performed according to a method described in the literature, adapted from the ASTM standard [6]. Tensile tests were carried out using an Instron 1122 universal testing machine equipped with a load beam of 5 N at a typical crosshead speed of 0.5 mm min1. Three gauge lengths, namely 20, 30 and 40 mm, were tested for each type of fibre; a minimum of 30 single filaments were tested at each gauge length. 3. Results and discussion Table 1 contains some of the results obtained from the single filament tensile tests. As mentioned in the experimental section, data of Table 1 are averaged (assuming a normal distribution) from, at least, results obtained from 30 specimens. Thus, in the case of the diameter values, at least 90 measurements were performed for each carbon fibre variety. From these results, it can be concluded that the surface treatments do not affect the fibre diameter, except in the case of the long time plasma treatment (CFP2 sample), where a statistically significant reduction of the fibre diameter is noticed (t-test, P ¼ 0:05).This reduction is, nonetheless, very small. On the other hand, the normal average of the tensile strength of all fibres tested decreases as the gauge length increases. The tensile strength of a material is a property that is statistically controlled at a microscopic level. For a given geometry, it depends mainly on the amount and nature of flaws (or defects) present in the solid. Thus, for carbon fibres in particular, it is expected that they will become weaker as the length tested increases, since it will be statistically more likely to contain a strength-reducing flaw. This length-dependency of the carbon fibres tensile strength is critical when predicting values of ultimate tensile strength at small lengths [7,8], which is fundamental to estimate the final performance of a composite material. The simple Weibull distribution and the end-effect model were both used to fit all the tensile strength data. The first is a two-parameter distribution (r01, m1), whereas the latter model includes two additional parameters (i.e., it is a four parameter distribution, r01, m1, r02, m2), to account for the hypothetical flaw population that the end-effects would originate. To estimate the parameters of each model the ‘‘maximum likelihood’’ theory was adopted to find the best fit of the experimental data. A maximum likelihood function (MLF) is thus defined and maximised using an iterative routine that was performed computationally. The parameters for the simple Weibull distribution were determined for all gauge lengths simultaneously. The results of the parameters estimation and the average tensile strength for a gauge length of 20 mm are presented in Table 2. In this table, r1 and r2 represent the mean strength resulting from true strength and end-effect related failures, respectively. The determination of the best model for a given set of experimental data is performed by direct observation of the model fitted to the strength data. The best fit is considered to be the best model. The ‘‘log-likelihood ratio statistic’’, T derived from the maximum likelihood function (MLF) of the two compared distributions [3], is only used if the model selection cannot be decided visually. Figs. 1 and 2 illustrate the difference between the simple Weibull distribution and the end-effect model for the untreated CF fibres, at 20 mm gauge length: the Table 1 Tensile and dimensional data determined for the carbon fibres under study (standard deviations in parentheses) Fibre Diameter (lm) Gauge lengths (mm) Tensile strength (GPa) CF 7.7 20.1 2.93 (0.46) (0.16) (0.560) 29.9 2.83 (0.12) (0.483) 40.7 2.79 (0.15) (0.468) CFP1 7.9 20.2 2.84 (0.61) (0.12) (0.335) 30.0 2.70 (0.11) (0.364) 40.8 2.55 (0.14) (0.517) CFP2 7.5 20.5 3.32 (0.48) (0.10) (0.543) 30.4 3.13 (0.15) (0.652) 40.6 3.05 (0.13) (0.487) CFP3 7.7 20.5 3.49 (0.38) (0.07) (0.615) 30.1 3.07 (0.20) (0.666) 40.1 2.77 (0.17) (0.683) CFO 7.7 20.3 3.33 (0.45) (0.14) (0.442) 30.4 3.01 (0.14) 0.573 40.5 2.56 (0.19) (0.374) 1276 M.A. Montes-Moran et al. / Carbon 42 (2004) 1275–1278
.A. Montes- Moran et aL. Carbon 42(2004)1275-1278 Table 2 Simple Weibull and end-effect distribution parameters for the fibres under study, at 20 mm gauge length CFP CFP3 CFO 6.207 GI(GPa) 3.02l 3.317 85.0 End-effect 6.523 5.719 9.270 5.564 6.867 GI(GPa) G2(GPa) 3.967 MLF -72.9 Simple Weibull end-effect model fits the experimental results better thar the simple Weibull distribution. In Figs. I and 2, the experimental and calculated Weibull quantities Ow are plotted versus In(a). ow is defined as In F(o: ai, mi) (1) where F(o: ai, mi) is the corresponding cumulative dis tribution function according to the Weibull or end-effect models Comparison of the end-effect model and simple eibull distribution showed that the experimental data of CF fibres and CFPl seem to be dominated by end effects. This result is confirmed by the higher (less neg ative) MlF values obtained in the case of the end-effect model (see Table 2). For the rest of fibres, graphical Fig. I. Experimental and predicted Weibull quantity using a single Weibull distribution(CF fibres, 20 mm gauge length) comparison of the end-effect model and the simple Weibull distribution did not show any difference be tween the plots. This result is also confirmed in the light of the mlf values collected in Table 2. In this situation the decision of which distribution should account for the gauge dependency of the tensile strength should be ta ken attending to simplicity. That is, the best model is the one which includes less parameters for describing a set of data, in our case, the simple Weibull model. Never theless it should be mentioned here that the trends followed by the end-effect prediction are, for the CFP2 CFP3 and CFO samples, essentially the same than those given by a simple Weibull distribution. The possible reason that would explain the secondary role played by the end-effects in the mentioned fibres should be linked to the oxidation treatment. In the case of the plasma oxidation, it seems reasonable to expect the increase of surface pitting following the more severe surface treat ments for CFP2 (75 W/10 min) and CFP3(150 W/3 min). Regarding the fibres treated commercially(CFO) the selectivity of the electrochemical treatment(see be- low)would also originate a more severe flaw population Fig. 2. Experimental and predicted Weibull quantity using an end. that would reduces the importance of the end-effects effect model (CF fibres, 20 summary, the statistical analysis of the tensile strengtH
end-effect model fits the experimental results better than the simple Weibull distribution. In Figs. 1 and 2, the experimental and calculated Weibull quantities QW are plotted versus lnðrÞ. QW is defined as: QW ¼ ln 1 1 F ðr; ri; miÞ ð1Þ where F ðr; ri; miÞ is the corresponding cumulative distribution function according to the Weibull or end-effect models. Comparison of the end-effect model and simple Weibull distribution showed that the experimental data of CF fibres and CFP1 seem to be dominated by endeffects. This result is confirmed by the higher (less negative) MLF values obtained in the case of the end-effect model (see Table 2). For the rest of fibres, graphical comparison of the end-effect model and the simple Weibull distribution did not show any difference between the plots. This result is also confirmed in the light of the MLF values collected in Table 2. In this situation, the decision of which distribution should account for the gauge dependency of the tensile strength should be taken attending to simplicity. That is, the best model is the one which includes less parameters for describing a set of data, in our case, the simple Weibull model. Nevertheless, it should be mentioned here that the trends followed by the end-effect prediction are, for the CFP2, CFP3 and CFO samples, essentially the same than those given by a simple Weibull distribution. The possible reason that would explain the secondary role played by the end-effects in the mentioned fibres should be linked to the oxidation treatment. In the case of the plasma oxidation, it seems reasonable to expect the increase of surface pitting following the more severe surface treatments for CFP2 (75 W/10 min) and CFP3 (150 W/3 min). Regarding the fibres treated commercially (CFO) the selectivity of the electrochemical treatment (see below) would also originate a more severe flaw population that would reduces the importance of the end-effects. In summary, the statistical analysis of the tensile strength Table 2 Simple Weibull and end-effect distribution parameters for the fibres under study, at 20 mm gauge length Model CF CFP1 CFP2 CFP3 CFO SWa r01 5.441 4.896 5.501 6.207 5.719 M1 5.853 6.438 6.981 5.481 5.687 r1 (GPa) 3.021 2.863 3.350 3.317 3.124 MLF )82.1 )67.1 )66.6 )85.0 )72.9 End-effect r01 5.110 6.523 5.884 6.287 5.719 M1 9.270 5.564 6.345 5.392 5.687 r02 3.286 3.065 4.123 5.075 12.12 M2 4.650 6.867 13.37 12.06 11.96 r1 (GPa) 3.508 3.517 3.415 3.326 3.124 r2 (GPa) 3.004 2.864 3.967 4.864 11.62 MLF )79.8 )64.9 )66.1 )85.0 )72.9 a Simple Weibull. 0.6 0.8 1.0 1.2 1.4 -4 -3 -2 -1 0 1 2 Weibull Quantity ln σ Fig. 1. Experimental and predicted Weibull quantity using a single Weibull distribution (CF fibres, 20 mm gauge length). 0.6 0.8 1.0 1.2 1.4 -4 -3 -2 -1 0 1 2 Weibull Quantity ln σ Fig. 2. Experimental and predicted Weibull quantity using an endeffect model (CF fibres, 20 mm gauge length). M.A. Montes-Moran et al. / Carbon 42 (2004) 1275–1278 1277
M.A. Montes.Moran et al. Carbon 42(2004)1275-1278 quired. Furthermore, this work shows that the final dif- ferences in strength found between treated and untreated fibres depend strongly on the statistical model employed to interpret the experimental data On the one hand, the results obtained with a simple Weibull distribution do not show any dependence of the tensile strength with the surface treatments On the other hand, analyses of the results using an end-effect model show a significant lowering of the tensile strength with the plasma oxida- 3.00 tion. According also to this model, the standard indus- trial surface treatment causes the maximum loss in the tensile strength of the fibres, when compared to any of the plasma surface treatments used here. This constitutes an additional advantage of plasma treatments over Gauge Length, mm industrial, presumably electrochemical, ones Fig. 3. Tensile strength variation with gauge length for the fibres under study, using different distributions(see text) Acknowledgements data recommends the use of the end-effect model for Financial support from DGiCYT (project PB98- describing the results obtained for the CF and CFPl 0492)and MCYT/FEDER (project MAT2002-00341)is samples, and the simple Weibull for the rest of fibres gratefully acknowledged. Thanks are also due to Dr M under consideration C. Paiva and prof. c.A. bernardo from universidade strength for all the fibres studied according to the sta- machine and for helpful discusso n Ccess to the Instron Fig. 3 shows now the variation of the average tensi do minho(portugal) for providing tistical model selected, at the three different gauge lengths tested. It can be seen how the treatments tend to References decrease the tensile strength of the fibres, although to a different extent. The mildest treatment, 75 W/3 min, has [1 Peebles LH Carbon fibers: formation, structure and properties little effect on the mechanical properties of these fibres Boca raton fl: crc Press: 1995 Increasing the power or the time of treatment led to fi- [2 Montes-Moran MA, Young RJ. Raman spectroscopy study of bres(CFP3 and CFP2, respectively) of similar charac HM carbon fibres: effect of plasma treatment on the interfacial teristics, both exhibiting a significant strength loss with properties of single fibre/epoxy composites. Part II: Characteris- respect to that of CF and CFPl fibres. Finally, the tion of the fibre- matrix interface. Carbon 2002: 40: 857-75. 3 Paiva MC, Bernardo CA, Edie DD. A comparative analysis of industrial oxidation seems to deteriorate the tensile Iterative models to predict the tensile strength of untreated and strength of the fibres the most. This observation can be surface oxidised carbon fibers. Carbon 2001: 39: 1091-101 explained in terms of the different mechanisms govern [4 Stoner EG, Edie DD, Durham SD. An end-effect model for the the oxidation of carbon fibres under plasma and single filament tensile test. J Mater Sci 1994: 29: 6561- electrochemical conditions. In the case of plasma, the 5 Weibull w. A statistical distribution function of wide applicabil- ity. J Appl Mech 1951: 18: 293-7 environment is so reactive that the attack of the active [6 ASTM Standard, D3379-75( Reapproved 1989) is quite homogeneous [9, 10]. On the other hand, [7 Padgett wJ, Durham SD, Mason AM. Weibull analysis of the ectrochemical treatment is much less effective in strength of carbon fibres using linear and power law models for oxidising well-ordered regions of the fibre [ll]. It is thus the length effect. J Comp Mater 1995: 29: 1873-84 expected that previous flaws present in the untreated [8] Asloun EM, Donnet JB, Guilpain G, Nardin M, Schultz. On the estimation of the tensile strength of carbon fibres at short lengths. fibres would be somehow enlarged after the electro- J Mater sci1989:24:3504-10. chemical treatment. the likelihood of one of these flaws [9 Paredes JI, Martinez-Alonso A, Tascon JMD. Early stages of to become severe should increase after such a treatment plasma oxidation of graphite: nanoscale physicochemical changes thus bringing about more fragile fibres as detected by 2002:18:4314-23 [10 Paredes JI, Martinez-Alonso A, Tascon JMD. Comparative study of the air and oxygen plasma oxidation of highly oriented 4. conclusions pyrolytic graphite: a scanning tunnelling and atomic force oscopy investigation. Carbon 2000: 38: 1183-97 In order to evaluate the effect of different surface [Il] Peng JCM, Donnet JB, Wang TK, Rebouillat S.Surface treatment of carbon fibers. In: Donnet JB, Wang TK, Peng treatments performed on HT carbon fibres on their JCM. Rebouillat s. editors. Carbon fibers, 3rd ed. New york. tensile strength, an appropriate statistical analysis is re- Dekker: 1998. p. 161-229
data recommends the use of the end-effect model for describing the results obtained for the CF and CFP1 samples, and the simple Weibull for the rest of fibres under consideration. Fig. 3 shows now the variation of the average tensile strength for all the fibres studied according to the statistical model selected, at the three different gauge lengths tested. It can be seen how the treatments tend to decrease the tensile strength of the fibres, although to a different extent. The mildest treatment, 75 W/3 min, has little effect on the mechanical properties of these fibres. Increasing the power or the time of treatment led to fi- bres (CFP3 and CFP2, respectively) of similar characteristics, both exhibiting a significant strength loss with respect to that of CF and CFP1 fibres. Finally, the industrial oxidation seems to deteriorate the tensile strength of the fibres the most. This observation can be explained in terms of the different mechanisms governing the oxidation of carbon fibres under plasma and electrochemical conditions. In the case of plasma, the environment is so reactive that the attack of the active species is quite homogeneous [9,10]. On the other hand, the electrochemical treatment is much less effective in oxidising well-ordered regions of the fibre [11]. It is thus expected that previous flaws present in the untreated fibres would be somehow enlarged after the electrochemical treatment. The likelihood of one of these flaws to become severe should increase after such a treatment, thus bringing about more fragile fibres. 4. Conclusions In order to evaluate the effect of different surface treatments performed on HT carbon fibres on their tensile strength, an appropriate statistical analysis is required. Furthermore, this work shows that the final differences in strength found between treated and untreated fibres depend strongly on the statistical model employed to interpret the experimental data. On the one hand, the results obtained with a simple Weibull distribution do not show any dependence of the tensile strength with the surface treatments. On the other hand, analyses of the results using an end-effect model show a significant lowering of the tensile strength with the plasma oxidation. According also to this model, the standard industrial surface treatment causes the maximum loss in the tensile strength of the fibres, when compared to any of the plasma surface treatments used here. This constitutes an additional advantage of plasma treatments over industrial, presumably electrochemical, ones. Acknowledgements Financial support from DGICYT (project PB98- 0492) and MCYT/FEDER (project MAT2002-00341) is gratefully acknowledged. Thanks are also due to Dr. M. C. Paiva and Prof. C. A. Bernardo from Universidade do Minho (Portugal) for providing access to the Instron machine and for helpful discussions. References [1] Peebles LH. Carbon fibers: formation, structure and properties. Boca Raton, FL: CRC Press; 1995. [2] Montes-Moran MA, Young RJ. Raman spectroscopy study of HM carbon fibres: effect of plasma treatment on the interfacial properties of single fibre/epoxy composites. Part II: Characterisation of the fibre-matrix interface. Carbon 2002;40:857–75. [3] Paiva MC, Bernardo CA, Edie DD. A comparative analysis of alternative models to predict the tensile strength of untreated and surface oxidised carbon fibers. Carbon 2001;39:1091–101. [4] Stoner EG, Edie DD, Durham SD. An end-effect model for the single filament tensile test. J Mater Sci 1994;29:6561–8. [5] Weibull W. A statistical distribution function of wide applicability. J Appl Mech 1951;18:293–7. [6] ASTM Standard, D3379-75 (Reapproved 1989). [7] Padgett WJ, Durham SD, Mason AM. Weibull analysis of the strength of carbon fibres using linear and power law models for the length effect. J Comp Mater 1995;29:1873–84. [8] Asloun EM, Donnet JB, Guilpain G, Nardin M, SchultzJ. On the estimation of the tensile strength of carbon fibres at short lengths. J Mater Sci 1989;24:3504–10. [9] Paredes JI, Martınez-Alonso A, Tascon JMD. Early stages of plasma oxidation of graphite: nanoscale physicochemical changes as detected by scanning probe microscopies. Langmuir 2002;18:4314–23. [10] Paredes JI, Martınez-Alonso A, Tascon JMD. Comparative study of the air and oxygen plasma oxidation of highly oriented pyrolytic graphite: a scanning tunnelling and atomic force microscopy investigation. Carbon 2000;38:1183–97. [11] Peng JCM, Donnet JB, Wang TK, Rebouillat S. Surface treatment of carbon fibers. In: Donnet JB, Wang TK, Peng JCM, Rebouillat S, editors. Carbon fibers. 3rd ed. New York: Dekker; 1998. p. 161–229. 20 25 30 35 40 2.50 2.75 3.00 3.25 3.50 3.75 4.00 Tensile Strength ( σ), GPa Gauge Length, mm CF CFP1 CFP2 CFP3 CFO Fig. 3. Tensile strength variation with gauge length for the fibres under study, using different distributions (see text). 1278 M.A. Montes-Moran et al. / Carbon 42 (2004) 1275–1278
