D. Loid/ et al. /Carbon 4(2003)563-570 significantly larger than that of crystalline graphite, al 2. Experimental though in some very high-modulus fibers, a three-dimen- sional graphite structure could be observed Five types of pitch-based fibers and a single type of Different models have been proposed to describe the PAN-based fiber were investigated. The pitch-based fibers relation between the orientation distribution of the basal were chosen so that they exhibited a considerable differ- planes and the elastic properties of carbon fibers: the ence in Youngs modulus. The PAN-based fibers were uniform strain model [21, 22], the uniform stress model exposed to a heat treatment temperature(hTT)to obtain [21, 22] and the unwrinkling model [13, 14, 22]. Experi- the same effect. Four PAN-based fibers were investigated ments have been presented for carbon fibers which strong. as-received, and with a HTT of 1800, 2100 and 2400C ly favored the uniform stress model [21]. In a recent work Some properties of the fibers are shown in Table I [22], different models were compared and a mosaic model The diameter of single fibers was measured by a laser was developed, which could explain the non-linearity in diffraction technique [ 31]. The fibers were then glued into the stress-strain curve of carbon fibers, i.e. the increase in a stretching cell, which was especially designed for in-situ the young's modulus during loading tensile tests of single fibers [24]. The Youngs modulus In the present work, we used a high brilliance synchrot was obtained from the slope of the stress-strain curve ron radiation X-ray microbeam to determine the structural during in-situ experiments. As a precise determination of changes of single carbon fibers during in-situ loading. a the Youngs modulus of single fibers is generally difficult small beam diameter has already been successfully applied due to uncertainties in the fiber diameter and in the fiber to obtain local structural information for different polymer strain, as well as due to the non-linearity of the stress- [23-25], natural [26, 27] and carbon fibers [28-30]. Where- strain curve, additional ex-situ experiments on single fibers as, in laboratory experiments, inevitable tilts in a fiber from the same bundle were performed using the method of bundle cannot be separated from the tilts of the layers laser speckle correlation for direct strain measurements within the fibers, this method allows the determination of [32, 33]. The results for the Youngs moduli of the in-situ the change of the orientation of the basal planes from the and ex-situ experiments were comparable, but the values intensity distribution of the 002 reflection with utmost from the latter were used for further evaluation due to the precision [30]. The measurement of single fibers instead of greater precision of this method. The Youngs modulus of bundles equally increases the reliability of the results, as the fibers increases significantly with increasing load [22] the same fiber is always located in the beam For some MPP-based fibers. the maximum value can be The shift of the 10 band in the meridional direction greater than the initial value by 30%. Thus, in Table I during in-situ loading was evaluated to directly obtain the only the initial value in the limit to small strains is given, Youngs modulus of the crystallites. Their shear modulus and used in the equations. was determined by an indirect method from the reduction Tension tests with in-situ X-ray diffraction were carried of the azimuthal width of the 002 reflection using theoret- out at microfocus beamline ID13 at the European cal models from the literature [21,22 Synchrotron Radiation Facility (ESRF) in grenoble name and ype E(o=o) MPP 3.4 HTA7-AR(Tenax) 332 by SEM and laser diffraction on the same fibers used fo ex-situ tension tests(see text). Due to the non-linearity can be greater than the initial modulus by more than 30% and is usually the one found in data sheets. The initial orientation parameter Ihwtm was deduced from the X-ray diffraction patterns and the density data were supplied by data sheets from the companies564 D. Loidl et al. / Carbon 41 (2003) 563–570 significantly larger than that of crystalline graphite, al- 2. Experimental though in some very high-modulus fibers, a three-dimen￾sional graphite structure could be observed. Five types of pitch-based fibers and a single type of Different models have been proposed to describe the PAN-based fiber were investigated. The pitch-based fibers relation between the orientation distribution of the basal were chosen so that they exhibited a considerable differ￾planes and the elastic properties of carbon fibers: the ence in Young’s modulus. The PAN-based fibers were uniform strain model [21,22], the uniform stress model exposed to a heat treatment temperature (HTT) to obtain [21,22], and the unwrinkling model [13,14,22]. Experi- the same effect. Four PAN-based fibers were investigated: ments have been presented for carbon fibers which strong- as-received, and with a HTT of 1800, 2100 and 2400 8C. ly favored the uniform stress model [21]. In a recent work Some properties of the fibers are shown in Table 1. [22], different models were compared and a mosaic model The diameter of single fibers was measured by a laser was developed, which could explain the non-linearity in diffraction technique [31]. The fibers were then glued into the stress–strain curve of carbon fibers, i.e. the increase in a stretching cell, which was especially designed for in-situ the Young’s modulus during loading. tensile tests of single fibers [24]. The Young’s modulus In the present work, we used a high brilliance synchrot- was obtained from the slope of the stress–strain curves ron radiation X-ray microbeam to determine the structural during in-situ experiments. As a precise determination of changes of single carbon fibers during in-situ loading. A the Young’s modulus of single fibers is generally difficult small beam diameter has already been successfully applied due to uncertainties in the fiber diameter and in the fiber to obtain local structural information for different polymer strain, as well as due to the non-linearity of the stress– [23–25], natural [26,27] and carbon fibers [28–30]. Where- strain curve, additional ex-situ experiments on single fibers as, in laboratory experiments, inevitable tilts in a fiber from the same bundle were performed using the method of bundle cannot be separated from the tilts of the layers laser speckle correlation for direct strain measurements within the fibers, this method allows the determination of [32,33]. The results for the Young’s moduli of the in-situ the change of the orientation of the basal planes from the and ex-situ experiments were comparable, but the values intensity distribution of the 002 reflection with utmost from the latter were used for further evaluation due to the precision [30]. The measurement of single fibers instead of greater precision of this method. The Young’s modulus of bundles equally increases the reliability of the results, as the fibers increases significantly with increasing load [22]. the same fiber is always located in the beam. For some MPP-based fibers, the maximum value can be The shift of the 10 band in the meridional direction greater than the initial value by 30%. Thus, in Table 1, during in-situ loading was evaluated to directly obtain the only the initial value in the limit to small strains is given, Young’s modulus of the crystallites. Their shear modulus and used in the equations. was determined by an indirect method from the reduction Tension tests with in-situ X-ray diffraction were carried of the azimuthal width of the 002 reflection using theoret- out at microfocus beamline ID13 at the European ical models from the literature [21,22]. Synchrotron Radiation Facility (ESRF) in Grenoble Table 1 Some parameters of the fibers investigated in this work Fiber name and Type Diameter Density E (s 5 0) P (s 5 0) eff hwhm 3 manufacturer (mm) (g/cm ) (GPa) (deg) K321 (Mitsubishi) MPP 10.48 1.9 136 17.6 E35 (DuPont) MPP 9.7 2.10 197 12.0 E55 (DuPont) MPP 10.18 2.10 358 7.09 FT500 (Tonen) MPP 10.0 2.11 380 6.69 K137 (Mitsubishi) MPP 9.54 2.12 500 3.42 HTA7-AR (Tenax) PAN 6.84 1.77 198 19.0 HTA7-18 (Tenax) PAN 7.3 1.77 273 16.3 HTA7-21 (Tenax) PAN 6.44 1.78 332 11.8 HTA7-24 (Tenax) PAN 6.2 1.91 349 9.64 The four PAN-based fibers differed in their final HTT (as-received, 1800, 2100 and 2400 8C, as indicated). The diameter was determined by SEM and laser diffraction on the same fibers used for the X-ray diffraction experiments. The initial modulus Eeff was obtained from ex-situ tension tests (see text). Due to the non-linearity, the maximum modulus can be greater than the initial modulus by more than 30% and is usually the one found in data sheets. The initial orientation parameter P was deduced from the X-ray diffraction patterns and the hwhm density data were supplied by data sheets from the companies