M. Shioya, M. Nakatani/ Composites Science and Technology 60(2000)219-229 a 10 um (d) O um Fig. 4. SEM images of fracture surfaces of (a)X7epoxy.A and(b) H4/epoxy.A composite strands after axial compression test and magnified images of fibres near fracture surface of (c)T4/epoxy-B and(d) H4/epoxy.A composite strands Po the density of graphite(2.26 g cm-3), pr the density of the compressive strength of the fibre can be obtained by fibre, doo2 the interlayer spacing of carbon layer stacks, finding the pretensioning stress at which compressive S3 the average area of microvoid cross-section per fracture takes place during the recoil process ular to the fibre axis and a the ratio of the axial length In the actual test, the compressive fracture occurs against the transverse diameter of the microvoids. The stocastically, so that the probability of the compressive relation between the compressive strength determined with fracture, F, is obtained as a function of the pretensioning the micro-compression test and the average area of micro- stress, o. The fracture probability versus pretensioning void cross-section determined with small-angle X-ray stress curves obtained for two types of carbon fibres are scattering is shown in Fig. 7 together with the compressive shown in Fig 8. The fracture probability can be repre- strength predicted by Eq (1)for a= 3.2 sented by a logistic distribution function [4] 3.3. Compressive strength determined with the recoil test fla)- exp(o+ Bio) +exp(o+Bio) The development of compressive stress during the recoil process of a fibre has been described by Allen [3]. where Bo and BI are the constants. In Fig. 8, the best fit When the pretensioned fibre is cut between fixed ends, a of the above equation to the observed fracture prob- zero stress front moves toward the fixed end of the fibre ability is shown by solid lines. From the logistic dis- as the initial tensile strain energy is converted to kinetic tribution function, the compressive strength was energy. After the zero stress front reaches at the fixed determined as the pretensioning stress at the fracture end of the fibre, the kinetic energy is transformed back probability of 0.5 into strain energy and a compressive stress begins to compressive strength determined with the recoil propagate back toward the free end of the fibre. If test is almost in proportion to the value determined with energy dissipation due to damping in the fibre and at the the micro-compression test as shown in Fig 9. The ratio fixed end of the fibre is neglected, the compressive stress of the compressive strength determined with the recoil is equal in magnitude to the pretensioning stress. Thus, test against those of the micro-compression test is 0.74o the density of graphite (2.26 g cmÿ3 ), f the density of ®bre, d002 the interlayer spacing of carbon layer stacks, S3 the average area of microvoid cross-section perpendi￾cular to the ®bre axis and  the ratio of the axial length against the transverse diameter of the microvoids. The relation between the compressive strength determined with the micro-compression test and the average area of micro￾void cross-section determined with small-angle X-ray scattering is shown in Fig. 7 together with the compressive strength predicted by Eq. (1) for  ˆ 3:2. 3.3. Compressive strength determined with the recoil test The development of compressive stress during the recoil process of a ®bre has been described by Allen [3]. When the pretensioned ®bre is cut between ®xed ends, a zero stress front moves toward the ®xed end of the ®bre as the initial tensile strain energy is converted to kinetic energy. After the zero stress front reaches at the ®xed end of the ®bre, the kinetic energy is transformed back into strain energy and a compressive stress begins to propagate back toward the free end of the ®bre. If energy dissipation due to damping in the ®bre and at the ®xed end of the ®bre is neglected, the compressive stress is equal in magnitude to the pretensioning stress. Thus, the compressive strength of the ®bre can be obtained by ®nding the pretensioning stress at which compressive fracture takes place during the recoil process. In the actual test, the compressive fracture occurs stocastically, so that the probability of the compressive fracture, F, is obtained as a function of the pretensioning stress, . The fracture probability versus pretensioning stress curves obtained for two types of carbon ®bres are shown in Fig. 8. The fracture probability can be repre￾sented by a logistic distribution function [4], F… †ˆ  exp… † 0 ‡ 1 1 ‡ exp… † 0 ‡ 1 …2† where 0 and 1 are the constants. In Fig. 8, the best ®t of the above equation to the observed fracture prob￾ability is shown by solid lines. From the logistic dis￾tribution function, the compressive strength was determined as the pretensioning stress at the fracture probability of 0.5. The compressive strength determined with the recoil test is almost in proportion to the value determined with the micro-compression test as shown in Fig. 9. The ratio of the compressive strength determined with the recoil test against those of the micro-compression test is 0.74. Fig. 4. SEM images of fracture surfaces of (a) X7/epoxy-A and (b) H4/epoxy-A composite strands after axial compression test and magni®ed images of ®bres near fracture surface of (c) T4/epoxy-B and (d) H4/epoxy-A composite strands. 224 M. Shioya, M. Nakatani / Composites Science and Technology 60 (2000) 219±229