Carbon-fiber-reinforced Ymas glass-cerc 413 00501o020300400507008090010 015 A200300400506070800 0010001100 Temperature(°C Temperature°C Fig. 2. Relative variation Fig. 3. Relative variation of the apparent longitudinal Youngs modulus(ultrasonic lue)in a P25-fiber-rein- Young's modulus (ultrasonic technique)in a T400H-fiber forced YMAS-matrix composit he matrix is kept vitr reinforced YMAS-matrix composite when the matrix is kept eous(a)and when the matrix is crystallized(b) vitreous(a)and when the matrix is crystallized(b) has been approximately determined by the ultrason be made owing to the lack of studies on these fibers. It technique, the CTEs of the fibers should be equivalent, can only be noted that the orders of magnitude and the whatever the conditions of calculation are shape of the relative expansion curves are close to the The elastic data used for the calculations are sum- results obtained for other fibers sometimes obtained marized in Table 2. The value for the Poisson's ratio vf with other techniques.21-23 Nevertheless, if our calcula of the P25 fiber, since no result exists in the literature tions had been carried out without considering that was based on other results obtained for pitch-based af=af, the results would have been different but still fibers, even though their textures are different.18-21 In credible, except at low temperature 24.25 the same way, the value for the T400H fiber was also chosen to equal 0.2, on the hasis of manufacturer's data 3. 4 Calculation of the thermal residual stresses and results obtained for T300 fiber, which has a texture The thermal residual stresses have been calculated for a similar to that of the T400H I fiber volume fraction of 0.35 in three cases The results of the calculations [eqns(1)and and (3) Ising the assumption that af=ai are shown in Fig. 5 1. on cooling from 800 to 20C for a vitreous matrix ind Table 3. a great difference is seen between the [composites equivalent to the composites P3 and longitudinal and transverse CTEs of the carbon fibers TI; Figs 6(a)and Fig. 71(a)] since, above 800C, as could be foreseen from their textures. No compar the dilatometric curve has shown that the stresses ison between our results and those of other authors can n still be relaxed: 24 Table 2. Elastic data for the matrix, and the p25 and T400H carbon fibers YMAS matrix T400H fiber En=157 GPa Poissons ratio m=0.29 =02Carbon-jber-reinforced YMAS glass-ceramic-matrix composites-IV 413 ?(x1 400 500 600 700 800 Tempemlure (“C) Tempemture (“C) Temperature (“C) (b) Fig. 2. Relative variation of the apparent longitudinal Fig. 3. Relative variation of the apparent longitudinal Young’s modulus (ultrasonic technique) in a PZS-fiber-rein- Young’s modulus (ultrasonic technique) in a T400H-fiber￾forced YMAS-matrix composite when the matrix is kept vitr- reinforced YMAS-matrix composite when the matrix is kept eous (a) and when the matrix is crystallized (b). vitreous (a) and when the matrix is crystallized (b). has been approximately determined by the ultrasonic technique, the CTEs of the fibers should be equivalent, whatever the conditions of calculation are. The elastic data used for the calculations are sum￾marized in Table 2. The value for the Poisson’s ratio uf, of the P25 fiber, since no result exists in the literature, was based on other results obtained for pitch-based fibers, even though their textures are different.18-*’ In the same way, the value for the T400H fiber was also chosen to equal 0.2, on the basis of manufacturer’s data and results obtained for T300 fiber, which has a texture similar to that of the T400H.’ The results of the calculations [eqns (1) and and (3)] using the assumption that of = of are shown in Fig. 5 and Table 3. A great difference is seen between the longitudinal and transverse CTEs of the carbon fibers, as could be foreseen from their textures.’ No compar￾ison between our results and those of other authors can 0.3 0.25 0.2 Ip 0.15 s^ o-1 fk 0.05 0 -0.05 -0.1 Temperature (“C) (a) 03 - 0.25 -- (b) be made owing to the lack of studies on these fibers. It can only be noted that the orders of magnitude and the shape of the relative expansion curves are close to the results obtained for other fibers, sometimes obtained with other techniques. *i-*3 Nevertheless, if our calcula￾tions had been carried out without considering that of = c$, the results would have been different but still credible, except at low temperature.24*25 3.4 Calculation of the thermal residual stresses The thermal residual stresses have been calculated for a fiber volume fraction of 0.35 in three cases: 1. on cooling from 800 to 20°C for a vitreous matrix [composites equivalent to the composites P3 and Tl; Figs 6(a) and Fig. 71(a)] since, above 800°C the dilatometric curve has shown that the stresses can still be relaxed;24 Table 2. Elastic data for the matrix, and the P25 and T4OOH carbon fibers Young’s modulus Poisson’s ratio YMAS matrix E,= 157GPa u,=O.29 P25 fiber T400H fiber 2: ;$$$ $::;;2: &=0.2 vf, = 0.2n uf, = 0.4 4, = 0.4