Availableonlineatwww.sciencedirect.com CARBON ELSEVIER Carbon42(2004)715-725 ww. elsevier. com/locate/carbon The tensile behavior of carbon fibers at high temperatures upto2400°C Cedric Sauder, Jacques Lamon, Rene Pailler Laboratoire des Composites Thermostructuraux, UMR 5801: CNRS-Snecma-CEA-UBl, Domaine Universitaire 3. Allee de la boetie. 33600 Pessac. Fr Received 17 June 2003: accepted 20 November 2003 abstract The tensile behavior of four different brands of carbon fibers(a rayon-based, a PAN-based, and 2 pitch-based fibers) has been investigated at various ratures up to 2400C. The tests were carried out using an original fiber testing apparatus. Various mechanical properties including strength and Youngs modulus, as well as Weibull statistical parameters were extracted from test data. Typical tensile behaviors were evidenced such as an essentially linear elastic behavior at room temperature and intermediate temperatures up to 1400-1800C, then a nonlinear elastic delayed response at higher temperatures and ultimately an inelastic esponse with permanent deformations at very high temperatures. Such unusual nonlinear responses for homogeneous materials were related to structure and texture features at the nanometer scale that were described through an X-ray diffraction technique C 2004 Elsevier Ltd. All rights reserved Keywords: A Carbon fibers, Carbon/carbon composites; D. Mechanical properties, Texture 1. Introduction fter a few minutes under zero load. This strain recovery was attributed to the reverse rotation of graphitic layers One of the main difficulties with C/C composites, is Mostovoi et al. [2] measured the mechanical proper- the lack of data on their constituent properties at high ties of a PAN-based carbon fiber(VMN-RK high tem- temperatures near the service conditions (up to 3000 perature carbon fiber) in the temperature range 20-2000 C). Such information is required for C/C composite C. Strength increased first by about 40% from room performance predictions as well as for design with re- temperature to 1500oC and then it dropped at 2000C. pect to end use. Today, only a limited amount of work Youngs modulus temperature dependence was similar on the mechanical properties of carbon fibers at high to that one reported by Bacon and Smith [1]. Plastic temperatures is reported in the literature. deformations were noticed at 2000 oC but this feature Bacon and Smith [1] determined mechanical proper- was not discussed ties in the temperature range 20-1900C for a rayon Tanabe et al. [3] examined a pitch-based carbon fiber based carbon fiber (VYB105 and VYB70 from Union (HM 70 from Petoca Co. )in the temperature range 20- Carbide Corp ) heat treated at 1900C for 5 min. 1300C. Neither strength nor Youngs modulus signif- Strength data displayed a pronounced maximum at icant temperature dependence was observed in this temperatures around 1700-1800C and then a steep narrow temperature range. rop at higher temperatures. Youngs mo In all the above mentioned tests, temperature was creased slightly as temperature increased to 1500C and uniform over the entire gauge length(hot grip tech then it dropped substantially. A marked nonlinear nique). The tests were performed using original appa stress-strain response was observed at these latter tem- ratuses. However, a major shortcoming is that since only peratures. A large part of deformations was recovered one fiber was generally tested at each temperature, the may Corresponding author. Tel. +33-5-5684-4700: fax: +33-5-5684- more, the nonlinear behavior at high temperatures was 1225 not investigated nor discussed with respect to structural E-inail address: lamon(alcts. ul-bordeaux fr( J. Lamon) features 0008-6223/S- see front matter 2004 Elsevier Ltd. All rights reserved doi:10.10l6 carbon2003.11020
The tensile behavior of carbon fibers at high temperatures up to 2400 C Cedric Sauder, Jacques Lamon *, Rene Pailler Laboratoire des Composites Thermostructuraux, UMR 5801: CNRS––Snecma––CEA––UB1, Domaine Universitaire, 3, Allee de la Boetie, 33600 Pessac, France Received 17 June 2003; accepted 20 November 2003 Abstract The tensile behavior of four different brands of carbon fibers (a rayon-based, a PAN-based, and 2 pitch-based fibers) has been investigated at various temperatures up to 2400 C. The tests were carried out using an original fiber testing apparatus. Various mechanical properties including strength and Young’s modulus, as well as Weibull statistical parameters were extracted from test data. Typical tensile behaviors were evidenced such as an essentially linear elastic behavior at room temperature and intermediate temperatures up to 1400–1800 C, then a nonlinear elastic delayed response at higher temperatures and ultimately an inelastic response with permanent deformations at very high temperatures. Such unusual nonlinear responses for homogeneous materials were related to structure and texture features at the nanometer scale, that were described through an X-ray diffraction technique. 2004 Elsevier Ltd. All rights reserved. Keywords: A. Carbon fibers, Carbon/carbon composites; D. Mechanical properties, Texture 1. Introduction One of the main difficulties with C/C composites, is the lack of data on their constituent properties at high temperatures near the service conditions (up to 3000 C). Such information is required for C/C composite performance predictions as well as for design with respect to end use. Today, only a limited amount of work on the mechanical properties of carbon fibers at high temperatures is reported in the literature. Bacon and Smith [1] determined mechanical properties in the temperature range 20–1900 C for a rayonbased carbon fiber (VYB105 and VYB70 from Union Carbide Corp.), heat treated at 1900 C for 5 min. Strength data displayed a pronounced maximum at temperatures around 1700–1800 C and then a steep drop at higher temperatures. Young’s modulus decreased slightly as temperature increased to 1500 C and then it dropped substantially. A marked nonlinear stress–strain response was observed at these latter temperatures. A large part of deformations was recovered after a few minutes under zero load. This strain recovery was attributed to the reverse rotation of graphitic layers. Mostovoi et al. [2] measured the mechanical properties of a PAN-based carbon fiber (VMN-RK high temperature carbon fiber) in the temperature range 20–2000 C. Strength increased first by about 40% from room temperature to 1500 C and then it dropped at 2000 C. Young’s modulus temperature dependence was similar to that one reported by Bacon and Smith [1]. Plastic deformations were noticed at 2000 C but this feature was not discussed. Tanabe et al. [3] examined a pitch-based carbon fiber (HM 70 from Petoca Co.) in the temperature range 20– 1300 C. Neither strength nor Young’s modulus significant temperature dependence was observed in this narrow temperature range. In all the above mentioned tests, temperature was uniform over the entire gauge length (hot grip technique). The tests were performed using original apparatuses. However, a major shortcoming is that since only one fiber was generally tested at each temperature, the sample size may not be statistically sufficient. Furthermore, the nonlinear behavior at high temperatures was not investigated nor discussed with respect to structural features. * Corresponding author. Tel.: +33-5-5684-4700; fax: +33-5-5684- 1225. E-mail address: lamon@lcts.u-bordeaux.fr (J. Lamon). 0008-6223/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2003.11.020 Carbon 42 (2004) 715–725 www.elsevier.com/locate/carbon
C. Sauder et al. / Carbon 42(2004)715-725 Carbon fibers can be produced essentially from three the P100 fiber which was received as-treated(the fiber is recursor materials: rayon, polyacrylonitrile(PAN) and heat-treated at a temperature above 2400c by the pitch(isotropic or anisotropic). Their properties depend supplier) all the fibers were heat treated for 2 h at a mainly on the precursor material, but they can be im- temperature above 2000C so that they remain stable proved through high temperature treatments, possibly during the tensile tests. under load. In the past, the structure of different carbon The characteristics that are summarized in Table I fibers has been studied extensively and different struc- indicate that a wide spectrum of fibers was covered tural models were proposed [4-12]. It was observed that Except for the P100 fiber, these characteristics were most carbon fibers consist of two-dimensional graphite measured in the laboratory. The technique described in crystals oriented preferentially along the fiber axis. The the next section was used. Density was measured using relationship between the structure and the mechanical an helium pycnometer. Fiber diameters were estimated properties of both PAN-and pitch-based carbon fibers from scanning electron micrographs of fiber cross sec- has been studied in detail [10]. Models for the inter- tions and also using in situ laser diffractometry(the laser pretation of the relationship between Youngs modulus was mounted on the testing machine and the angular distribution of layer normals have been proposed [12, 13]. Equations combine the elastic con- stants of individual particles with definite integrals of 2.2. Tensile tests he angular distribution of layer normals. They can b used for the interpretation of fiber stiffening observed The fibers were taken from tows. Graphite grips were at room temperature. This effect is attributed to a ffixed to sample ends using a carbon based cement gradual straightening of the crystalline regions along (gauge length 50 mm). Tensile tests were performed the loading direction. This interpretation is consistent using an original device described in details elsewhere with the correlation between preferred orientation and [15]. An electric current is applied to the test specimen Youngs modulus for a variety of rayon-based carbo under secondary vacuum(residual pressure <10-3 Pa), so that temperatures as high as 3000C can be generated The dual intent of this paper is, therefore, to deter- uniformly along the gauge length. Computatio mine the mechanical properties and to investigate the tensile behavior of various carbon fibers with respect to conductivity showed that the temperature gradient temperature and to fiber structure and texture. less than 2.5oC between the surface and the heart of fibers, at 2000C. Temperatures at the surface of fibe were measured using a bichromatic pyrometer. Tem- perature profiles were uniform over a domain longer 2. Materials and structural characterizations than 95% of gauge length. It thus appeared that the grips remained at room temperature during the tests. 2.1. Description of materials Then, the loading frame compliance was not affected. The displacement of grips was measured by a sensor Four of carbon fibers were investigated: whose sensitivity was less than 0 I um. All the tests were XNO5. P P100 and FC2 fibers. The PANEX performed in the following temperature ranges: 1000- 33 fiber ZOLTEK Corp )is produced from a 2000C for the XNO5, PANEX 33 et FC2 fibers and PAN precursor, the XN05 fiber(from Nippon Graphite 1000-2400C for the P100 fiber. Most of the tests were Fiber Co. )from an isotropic pitch precursor, the P100 carried out at a slow displacement rate(0.5 mm/min) fiber(from AMOCO Performance Products Co Then. the influence of strain rate was examined merly Union Carbide Co. )from an anisotropic the following displacement rates: 0.05 and 5 mm/min precursor and the FC2 fiber(from SNECMA PRO- Strains were derived from grip displacement taking inte PULSION SOLIDE) from a rayon precursor. Except account deformations of the loading frame. The system Table I Main characteristics of as-received fibers at room temperature PANEX 33 Precursors Anisotropic pitch Isotropic pitch D s modulus(GPa) hs in MPa (Lo 50 mm) 2100 1.37 l81 2.15 iameter(um)
Carbon fibers can be produced essentially from three precursor materials: rayon, polyacrylonitrile (PAN) and pitch (isotropic or anisotropic). Their properties depend mainly on the precursor material, but they can be improved through high temperature treatments, possibly under load. In the past, the structure of different carbon fibers has been studied extensively and different structural models were proposed [4–12]. It was observed that most carbon fibers consist of two-dimensional graphite crystals oriented preferentially along the fiber axis. The relationship between the structure and the mechanical properties of both PAN- and pitch-based carbon fibers has been studied in detail [10]. Models for the interpretation of the relationship between Young’s modulus and the angular distribution of layer normals have been proposed [12,13]. Equations combine the elastic constants of individual particles with definite integrals of the angular distribution of layer normals. They can be used for the interpretation of fiber stiffening observed at room temperature. This effect is attributed to a gradual straightening of the crystalline regions along the loading direction. This interpretation is consistent with the correlation between preferred orientation and Young’s modulus for a variety of rayon-based carbon fibers [14]. The dual intent of this paper is, therefore, to determine the mechanical properties and to investigate the tensile behavior of various carbon fibers with respect to temperature and to fiber structure and texture. 2. Materials and structural characterizations 2.1. Description of materials Four brands of carbon fibers were investigated: XNO5, PANEX 33, P100 and FC2 fibers. The PANEX 33 fiber (from ZOLTEK Corp.) is produced from a PAN precursor, the XN05 fiber (from Nippon Graphite Fiber Co.) from an isotropic pitch precursor, the P100 fiber (from AMOCO Performance Products Co., formerly Union Carbide Co.) from an anisotropic pitch precursor and the FC2 fiber (from SNECMA PROPULSION SOLIDE) from a rayon precursor. Except the P100 fiber which was received as-treated (the fiber is heat-treated at a temperature above 2400 C by the supplier) all the fibers were heat treated for 2 h at a temperature above 2000 C so that they remain stable during the tensile tests. The characteristics that are summarized in Table 1, indicate that a wide spectrum of fibers was covered. Except for the P100 fiber, these characteristics were measured in the laboratory. The technique described in the next section was used. Density was measured using an helium pycnometer. Fiber diameters were estimated from scanning electron micrographs of fiber cross sections and also using in situ laser diffractometry (the laser was mounted on the testing machine). 2.2. Tensile tests The fibers were taken from tows. Graphite grips were affixed to sample ends using a carbon based cement (gauge length 50 mm). Tensile tests were performed using an original device described in details elsewhere [15]. An electric current is applied to the test specimen under secondary vacuum (residual pressure < 103 Pa), so that temperatures as high as 3000 C can be generated uniformly along the gauge length. Computations of temperature distributions for various values of thermal conductivity showed that the temperature gradient is less than 2.5 C between the surface and the heart of fibers, at 2000 C. Temperatures at the surface of fibers were measured using a bichromatic pyrometer. Temperature profiles were uniform over a domain longer than 95% of gauge length. It thus appeared that the grips remained at room temperature during the tests. Then, the loading frame compliance was not affected. The displacement of grips was measured by a sensor whose sensitivity was less than 0.1 lm. All the tests were performed in the following temperature ranges: 1000– 2000 C for the XNO5, PANEX 33 et FC2 fibers and 1000–2400 C for the P100 fiber. Most of the tests were carried out at a slow displacement rate (0.5 mm/min). Then, the influence of strain rate was examined at the following displacement rates: 0.05 and 5 mm/min. Strains were derived from grip displacement taking into account deformations of the loading frame. The system Table 1 Main characteristics of as-received fibers at room temperature Fibers FC2 PANEX 33 P100 XN05 Precursors Rayon PAN Anisotropic pitch Isotropic pitch Young’s modulus (GPa) 33 300a 690a 53 Strengths in MPa (L0 ¼ 50 mm) 720 2110 2100a;b 980 Density 1.37 1.81 2.15a 1.63 Mean diameter (lm) 6.5 7 11a 10 aFrom supplier. b L0 ¼ 25 mm. 716 C. Sauder et al. / Carbon 42 (2004) 715–725
C. Sauder et al. Carbon 42(2004)715-725 (d) 8=9041 zHz=u>H 中( degrees) Fig. 1 Schematic diagram of crystallite orientation with diagram of some X-ray diffraction o scan profiles 1(o): (a)E=210 GPa, (b)E=350 GPa, (c)E=490GPa,(d)E=690GPa[19 compliance was estimated at room temperature using the mean distance between two successive layers. La, Le, the conventional calibration technique [15, 16 and dooz were determined using the Scherrer equation The stress-strain behavior at high temperatures was from the positions of the diffraction maxima and the determined on batches of five test specimens. Statistical width at half-maximum intensity of the(002)and distributions of strength data were determined on bat 10)peaks. The microvoid content in the fibers was ches of 25 test specimens, for the FC2, PANEX 33 and derived from the structural parameters using the fol- XN05 fibers at room temperature, and for the FC2 and lowing equatio PANEX 33 fibers at high temperatures. The well-known Weibull,s model was used for the P=l description of the statistical distributions of failure strengths. Failure probability under a uniform stress where Pr is the fiber density, Pg is the graphite density state is given by (2.26 g/cm)and dg=0.3354 nm for graphite crystal P=1-exp(v/Vo)(o/oo)" The orientation distribution of graphitic planes was where m is the shape parameter (often referred to as determined by X-ray analysis of the fibers, as described Weibull modulus), Go is the scale factor, v is the fiber by Ruland [19]. It was obtained from an azimuthal volume under stresses, Vo is a reference volume (o=1 spread of the 002 reflection arc, which provides mm ), o is the applied stress. indication of the preferred orientation of the basic Probabilities of failure were determined using ranking structural units relative to fiber axis as illustrated on Fig statistics[17]. Ordering the failure data from smallest to 1. The orientation parameter Z is the full width at half largest and assigning a ranking number i, the probabil- the maximum intensity obtained in the azimuthal scan ities of failure were then assigned by the following measured in degrees. Fiber texture was described using relationship the distribution of the intensity of scattering at angle 0.5)/N, p(1(o)), and using the orientation parameter Z where N is the total number of specim 3. Results The statistical parameters were then extracted from strength distributions using the conventional Weibull 3.1. Stress-strain behavior under a slow strain rate linear regression estimator [17] The tensile stress-strain curves exhibit temperature 23. Structural characterization of fibers dependent features(Fig. 2) The common parameters used in the description of The stress-strain relation is essentially linear carbon structures Le, La, and dooz were determined using room temt perature to temperatures as high as X-ray diffraction on ground-up samples of the fibers. La and Le are the dimensions of crystallites (La is the A more and more pronounced nonlinear deformation longitudinal whereas Le is the lateral extension). door is is then observed at higher temperatures
compliance was estimated at room temperature using the conventional calibration technique [15,16]. The stress–strain behavior at high temperatures was determined on batches of five test specimens. Statistical distributions of strength data were determined on batches of 25 test specimens, for the FC2, PANEX 33 and XN05 fibers at room temperature, and for the FC2 and PANEX 33 fibers at high temperatures. The well-known Weibull’s model was used for the description of the statistical distributions of failure strengths. Failure probability under a uniform stress state is given by P ¼ 1 exp½ðV =V0Þðr=r0Þ m; ð1Þ where m is the shape parameter (often referred to as Weibull modulus), r0 is the scale factor, V is the fiber volume under stresses, V0 is a reference volume (V0 ¼ 1 mm3), r is the applied stress. Probabilities of failure were determined using ranking statistics [17]. Ordering the failure data from smallest to largest and assigning a ranking number i, the probabilities of failure were then assigned by the following relationship: Pi ¼ ði 0:5Þ=N; ð2Þ where N is the total number of specimens. The statistical parameters were then extracted from strength distributions using the conventional Weibull linear regression estimator [17]. 2.3. Structural characterization of fibers The common parameters used in the description of carbon structures Lc, La, and d002 were determined using X-ray diffraction on ground-up samples of the fibers. La and Lc are the dimensions of crystallites (La is the longitudinal whereas Lc is the lateral extension). d002 is the mean distance between two successive layers. La, Lc, and d002 were determined using the Scherrer equation from the positions of the diffraction maxima and the width at half-maximum intensity of the (0 0 2) and (1 1 0) peaks. The microvoid content in the fibers was derived from the structural parameters using the following equation: Vp ¼ 1 qfd002 qgdg ; ð3Þ where qf is the fiber density, qg is the graphite density (¼ 2:26 g/cm3) and dg ¼ 0:3354 nm for graphite crystals [18]. The orientation distribution of graphitic planes was determined by X-ray analysis of the fibers, as described by Ruland [19]. It was obtained from an azimuthal spread of the 002 reflection arc, which provides an indication of the preferred orientation of the basic structural units relative to fiber axis as illustrated on Fig. 1. The orientation parameter Z is the full width at half the maximum intensity obtained in the azimuthal scan, measured in degrees. Fiber texture was described using the distribution of the intensity of scattering at angle /ðIð/ÞÞ, and using the orientation parameter Z. 3. Results 3.1. Stress–strain behavior under a slow strain rate The tensile stress–strain curves exhibit temperature dependent features (Fig. 2): • The stress–strain relation is essentially linear from room temperature to temperatures as high as 1200 C. • A more and more pronounced nonlinear deformation is then observed at higher temperatures. Fig. 1. Schematic diagram of crystallite orientation with diagram of some X-ray diffraction / scan profiles Ið/Þ: (a) E ¼ 210 GPa, (b) E ¼ 350 GPa, (c) E ¼ 490 GPa, (d) E ¼ 690 GPa [19]. C. Sauder et al. / Carbon 42 (2004) 715–725 717
71 C. Sauder et al. Carbon 42(2004)715-72 (a)FC2 (b)XN05 1000°c 1400°C 1800°c 三 0 (c) PANEX 33 (d)P100 2400 2000 2500 1600 1200 1500 1600°c 1800°C-20 04 Strain E(%) Strain E(s) Fig. 2. Evolution of stress-strain curves obtained at various temperatures for all the fibers of this study: (a)FC2,(b)xN05, (c) PANEX 33 and (d)P100. The associated strains are also larger and larger The transition from linear to nonlinear deformation occurs at temperatures depending on tested fiber 1200-1400 oC for the Fc2 fibers. 1000-1200 oC for the xnos fibers 1600-1800 oC for the panex 33 -e- FC2 fiber fibers and 2000-2200 oC for the p100 fibers xNo5 fiber r - PANEX 33 fiber It is also worth mentioning that a slight increase in the fiber Youngs modulus was observed on the PANEX 33 fibers at room temperature. The data were fitted satisfactorily by the empirical equation a= Eo(1+fa)E, 0.4 4008001200160020002400 where Eo is the initial tangent modulus Table 1),f is a measure of the degree of nonlinearity (f= 23) Fig 3. Dependence of relative initial Youngs modulus E(T)/Eo The influence of temperature on Youngs modulus is (Eo=E(4C)on temperature shown in Fig 3. Young's modulus decreases gently in a first step, and then rather steeply at temperatures above ≈1000° for the Fo2 fiber and≈1200° for the other The failure data determined at various temperatures fibers. This trend is similar to that one reported in the e summarized in Table 2. Fig. 4 shows that the literature [1-3] strength of FC2 fibers increases first slightly as temper
• The associated strains are also larger and larger. • The transition from linear to nonlinear deformation occurs at temperatures depending on tested fiber: 1200–1400 C for the FC2 fibers, 1000–1200 C for the XN05 fibers, 1600–1800 C for the PANEX 33 fibers and 2000–2200 C for the P100 fibers. It is also worth mentioning that a slight increase in the fiber Young’s modulus was observed on the PANEX 33 fibers at room temperature. The data were fitted satisfactorily by the empirical equation r ¼ E0ð1 þ f eÞe; ð4Þ where E0 is the initial tangent modulus (Table 1), f is a measure of the degree of nonlinearity (f ¼ 23). The influence of temperature on Young’s modulus is shown in Fig. 3. Young’s modulus decreases gently in a first step, and then rather steeply at temperatures above 1000 C for the FC2 fiber and 1200 C for the other fibers. This trend is similar to that one reported in the literature [1–3]. The failure data determined at various temperatures are summarized in Table 2. Fig. 4 shows that the strength of FC2 fibers increases first slightly as temper- 0 200 400 600 800 1000 1200 0123456 Strain ε (%) Stress (MPa) 24°C 1000°C 1200°C 1400°C 1600°C 1800°C 2000°C 0 150 300 450 600 750 0 1.5 3 4.5 6 7.5 9 Strain ε (%) Stress (MPa) 24°C 1000°C 1200°C 1400°C 1600°C 1800°C 2000°C 0 500 1000 1500 2000 2500 3000 3500 01234 Strain ε (%) Stress (MPa) 24°C 1000°C 1200°C 1400°C 1600°C 1800°C 2000°C 0 400 800 1200 1600 2000 2400 0 0.2 0.4 0.6 0.8 Strain ε (%) Stress (MPa) 24°C 1600°C 1800°C 2000°C 2200°C 2400°C (a) FC2 (c) PANEX 33 (b) XN05 (d) P100 Fig. 2. Evolution of stress–strain curves obtained at various temperatures for all the fibers of this study: (a) FC2, (b) XN05, (c) PANEX 33 and (d) P100. 0.4 0.5 0.6 0.7 0.8 0.9 1 0 400 800 1200 1600 2000 2400 Temperature (°C) E/Eo FC2 fiber XN05 fiber PANEX 33 fiber P100 fiber Fig. 3. Dependence of relative initial Young’s modulus EðT Þ=E0 (E0 ¼ E (24 C)) on temperature. 718 C. Sauder et al. / Carbon 42 (2004) 715–725
C. Sauder et al. Carbon 42(2004)715-725 Table 2 Influence of tture on strength data for paneX 33 and Fc2 fibers Temperature(C) PANEX 33 fiber FC2 fiber Go(MPa) GR(MPa) MPa) 2107(405) 0.71(0.13) 719(157) 2.16(045) 2292(410)0.80(0.14) 789(103) 2.39(0.31) 0.86(0.18)5 756(118)232(0.38) 2386(507)0.85(0.18) 825(116)2.680.36) 2359(520) 0.91(0.23) 82l(114) 5.4l(1.75) 79b 857(6l1) .53(0.44) 605(72) 12(6.7 ND ND 2348(443)3.71(1.84)59° 850 127(6.1) ND: nondetermined, O standard error b Result to take with care because of the nonlinear elastic tensile curve to the above mentioned transition temperatures, iden PANEX 33 fiber tified at a slow strain rate Figs. 7 and 8 show the presence of residual defor- 62500 mations at zero load. It can be noticed from Fig. 7 that the residual strains were relieved after 30 min under zero 2000 load, at the temperatures of 1600C for the FC2 fiber, and 1800C for the PanEX 33 fiber. This complete recove indicative of a delayed elastic 1000 coelastic type behavior. At higher temperatures, only a partial recovery is observed(Fig. 8), indicating the presence of permanent deformations. This feature is typical of a viscoplastic behavior. 4008001200160020002400 For the XNO5 fiber, nonlinear elasticity appeared at 400C, and permanent deformations were detected at Fig. 4. Dependence of average failure stress for FC2 and PANEX 33 temperatures above 1800C. For the P100 fiber, non linear elasticity was observed above 1800C, and per manent residual deformations were not detected in the range of temperatures that was examined (<2400C) ature increases, and then drops at temperatures above It is worth mentioning that the elastic-inelastic transition temperatures mentioned above for the FC2 1600C. For the PANEX 33 fibers, the strength increase and the paneX 33 fibers coincide to the temperatures is more significant. A peak is reached at 1800C. It can at which a strength drop was observed( Fig 4) be noticed from Table 2 that the strain-to-failure in- creases substantially. The statistical parameters do not In summary, all the carbon fibers examined in the exhibit a significant dependence on temperature, indi present paper exhibited three different stress-strain cating that no significant change occurred in the popu behaviors depending upon temperature lations of fracture inducing flaws 4 The above trend in strength seems to be at variance a purely elastic behavior at low temperatures h that observed on most materials which a viscoelastic behavior(delayed elasticity) at interme- generally a fracture stress decrease as temperature in diate temperatures, creases, and steep strength drops at fragile-ductile a viscoplastic behavior (inelastic deformations)at high temperatures. transition The transition temperatures are reported in Table 3. 3. 2. Stress-strain behavior under increasing strain rates It can be noticed that they depend upon fiber. Figs. 5 and 6 show the influence of loading rate on the 3.3. Description of the structure and the texture of fibers tress-strain behavior at various temperatures. It can be noticed that nonlinearity is enhanced by decreasing strain rates above 1400 oC for the Fc2 fiber. and above e The parameters describing the structure and the tex- ire of fibers are summarized in Table 4. The fibers are 1600C for the PANEX 33 fiber. Below these temper- put according to increasing Young's modulus It can be atures, the behavior is essentially linear elastic and noticed that the respective parameters vary in a logical insensitive to strain rate. These temperatures correspond way with respect to fibers stiffness
ature increases, and then drops at temperatures above 1600 C. For the PANEX 33 fibers, the strength increase is more significant. A peak is reached at 1800 C. It can be noticed from Table 2 that the strain-to-failure increases substantially. The statistical parameters do not exhibit a significant dependence on temperature, indicating that no significant change occurred in the populations of fracture inducing flaws. The above trend in strength seems to be at variance with that observed on most materials, which show generally a fracture stress decrease as temperature increases, and steep strength drops at fragile–ductile transition. 3.2. Stress–strain behavior under increasing strain rates Figs. 5 and 6 show the influence of loading rate on the stress–strain behavior at various temperatures. It can be noticed that nonlinearity is enhanced by decreasing strain rates above 1400 C for the FC2 fiber, and above 1600 C for the PANEX 33 fiber. Below these temperatures, the behavior is essentially linear elastic and insensitive to strain rate. These temperatures correspond to the above mentioned transition temperatures, identified at a slow strain rate. Figs. 7 and 8 show the presence of residual deformations at zero load. It can be noticed from Fig. 7 that the residual strains were relieved after 30 min under zero load, at the temperatures of 1600 C for the FC2 fiber, and 1800 C for the PANEX 33 fiber. This complete recovery is indicative of a delayed elastic response: viscoelastic type behavior. At higher temperatures, only a partial recovery is observed (Fig. 8), indicating the presence of permanent deformations. This feature is typical of a viscoplastic behavior. For the XN05 fiber, nonlinear elasticity appeared at 1400 C, and permanent deformations were detected at temperatures above 1800 C. For the P100 fiber, nonlinear elasticity was observed above 1800 C, and permanent residual deformations were not detected in the range of temperatures that was examined ( 6 2400 C). It is worth mentioning that the elastic–inelastic transition temperatures mentioned above for the FC2 and the PANEX 33 fibers coincide to the temperatures at which a strength drop was observed (Fig. 4). In summary, all the carbon fibers examined in the present paper exhibited three different stress–strain behaviors depending upon temperature: • a purely elastic behavior at low temperatures, • a viscoelastic behavior (delayed elasticity) at intermediate temperatures, • a viscoplastic behavior (inelastic deformations) at high temperatures. The transition temperatures are reported in Table 3. It can be noticed that they depend upon fiber. 3.3. Description of the structure and the texture of fibers The parameters describing the structure and the texture of fibers are summarized in Table 4. The fibers are put according to increasing Young’s modulus. It can be noticed that the respective parameters vary in a logical way with respect to fibers stiffness: Table 2 Influence of test temperature on strength data for PANEX 33 and FC2 fibers Temperature (C) PANEX 33 fiber FC2 fiber rR (MPa) eR (%) m r0 a (MPa) rR (MPa) eR (%) m r0 a (MPa) 24 2107 (405) 0.71 (0.13) 5.1 660 719 (157) 2.16 (0.45) 5.1 230 1000 2292 (410) 0.80 (0.14) 6.5 950 789 (103) 2.39 (0.31) 8.3 390 1200 2401 (540) 0.86 (0.18) 5.2 890 756 (118) 2.32 (0.38) ND ND 1400 2386 (507) 0.85 (0.18) 5.4 810 825 (116) 2.68 (0.36) ND ND 1600 2359 (520) 0.91 (0.23) 5.4 800 821 (114) 5.41 (1.75) 7.9b 390 1800 2857 (611) 1.53 (0.44) 5.6b 1020 605 (72) 12 (6.7) ND ND 2000 2348 (443) 3.71 (1.84) 5.9b 850 371 (39) 12.7 (6.1) 10b 200 ND: nondetermined, () standard error. a V0 ¼ 1 mm3. b Result to take with care because of the nonlinear elastic tensile curve. 0 500 1000 1500 2000 2500 3000 3500 0 400 800 1200 1600 2000 2400 Temperature (°C) Average failure stress σ R (MPa) FC2 fiber PANEX 33 fiber Fig. 4. Dependence of average failure stress for FC2 and PANEX 33 on temperature. C. Sauder et al. / Carbon 42 (2004) 715–725 719