LIU et al.: LAMINATED COMPOSITE 4847 Table 1. Elastic stiffness constants of 0/90 cross-ply CAS/SiC composites determined by RUS [11] and laser-generated ultrasound(units: GPa) C(±%) C3(±2%) C(土%) C1(%0) C4(土%) C.(% 14745(0.11)145.19(0.28 5223(0.39) 499 461200.01) 46.35(0.02) Ultrasound method 150.0(3.3) 542(14.6) 42.5(10.1) 45.3(4.9 90° ply o0°pam have only half the number of 0 plies unidirectional laminates. the stiffness transverse direction for the o°/90°lar there- fore less than that observed in unidirectional 120- CAS/SIC [10, 18 Figure 8 indicates that partial crack closure appears to have occurred in the 90 ply upon unloading. This is consistent with the observation of a slight increase The deduced values of Cul and Cax durig to 10 MPa in ultrasonic velocity during unl 33 during loading and unloading are shown in Fig. 11. Error bars(similar to 0 30 60 90 120 150 180 those given in Fig. 10) are not included for clarity Since partial crack closure occurs mainly in the load direction. an Cu is seen during 0Soo0N unloading while C33 appears to have remained con- stant. It should be pointed out that the results in Fig Il are from two tests. and some of the scatter can be ributed to sample 5. RESIDUAL STRESS AND MATRIX CRACK INITIATION The initiation stress for matrix cracking is an Stress(MPa important issue for fiber-reinforced CMCs, because it denotes not only the onset of damage but also the los laser-ultrasonic wave velocity measurements. Young's modu. of protection provided by the matrix against environ- lus E, measured from unloading stress-strain curve is also mental corrosion and/or oxidation of the fibers [191 shown.(b) Normalized curves showing the relative trends of Prediction of the matrix crack initiation stress(omd) stiffness reduction requires knowledge of the(statistical flaw population controlled)strength of the ceramic matrix and an Normalized data are also included [Fig. 10(b) to understanding of the residual stress state. There are show the relative reductions. Similar to unidirectional ponents to the residual stress in la CAS/SiC, Cu in the loading direction exhibited the nates: that of the individual lamina, and that within largest stiffiness reduction as a result of many trans- verse matrix cracks. Its relative trend with stress [ Fig 10(b)] is about identical to the change of E, measured by mechanical testing. Cll and C22 have approxi- mately the same initial value, but lose their degener- a acy as damage develops. Normalized data indicate that C2? and C33 have a similar reduction trend [Fig. 120 o(b)]. The softening of C2 and C33 implies that 9 120 acks with opening displacement in the 2-and 3 direction exist and are most likely a consequence of 80 fiber/matrix interface debonding C,(unloading Although debonding occurs both in the 0 and 90 g plies, softening in the transverse plane C.(unloading be a consequence of interfacial debonding in the 0 plies. This is because the matrix cracks are nearly par- allel to the transverse plane, and micromechanical calculations show that the elastic constants in the Stress(MPa) directions parallel to the crack plane are insensitive Fig. 11. Comparison of elastic stiffiness constants Cu and C to the crack density [17]. Because 0/90 laminates during loading and unloading at different stress levelsLIU et al.: LAMINATED COMPOSITE 4847 Table 1. Elastic stiffness constants of 0°/90° cross-ply CAS/SiC composites determined by RUS [11] and laser-generated ultrasound (units: GPa) C11 (±%) C33 (±%) C13 (±%) C12 (±%) C44 (±%) C66 (±%) RUS 147.45 (0.11) 145.19 (0.28) 52.23 (0.39) 49.96 (0.88) 46.12 (0.01) 46.35 (0.02) Ultrasound method 150.0 (3.3) 144.2 (2.4) 54.2 (14.6) – 42.5 (10.1) 45.3 (4.9) Fig. 10. (a) Elastic constants C11, C22 and C33 determined from laser-ultrasonic wave velocity measurements. Young’s modu￾lus E1 measured from unloading stress–strain curve is also shown. (b) Normalized curves showing the relative trends of stiffness reduction. Normalized data are also included [Fig. 10(b)] to show the relative reductions. Similar to unidirectional CAS/SiC, C11 in the loading direction exhibited the largest stiffness reduction as a result of many trans￾verse matrix cracks. Its relative trend with stress [Fig. 10(b)] is about identical to the change of E1 measured by mechanical testing. C11 and C22 have approxi￾mately the same initial value, but lose their degener￾acy as damage develops. Normalized data indicate that C22 and C33 have a similar reduction trend [Fig. 10(b)]. The softening of C22 and C33 implies that cracks with opening displacement in the 2- and 3- direction exist and are most likely a consequence of fiber/matrix interface debonding. Although debonding occurs both in the 0° and 90° plies, softening in the transverse plane is presumed to be a consequence of interfacial debonding in the 0° plies. This is because the matrix cracks are nearly par￾allel to the transverse plane, and micromechanical calculations show that the elastic constants in the directions parallel to the crack plane are insensitive to the crack density [17]. Because 0°/90° laminates have only half the number of 0° plies compared with unidirectional laminates, the stiffness reduction in the transverse direction for the 0°/90° laminates is there￾fore less than that observed in unidirectional CAS/SiC [10, 18]. Figure 8 indicates that partial crack closure appears to have occurred in the 90° ply upon unloading. This is consistent with the observation of a slight increase in ultrasonic velocity during unloading to 10 MPa. The deduced values of C11 and C33 during loading and unloading are shown in Fig. 11. Error bars (similar to those given in Fig. 10) are not included for clarity. Since partial crack closure occurs mainly in the load￾ing direction, an increase in C11 is seen during unloading while C33 appears to have remained con￾stant. It should be pointed out that the results in Fig. 11 are from two tests, and some of the scatter can be attributed to sample variations. 5. RESIDUAL STRESS AND MATRIX CRACK INITIATION The initiation stress for matrix cracking is an important issue for fiber-reinforced CMCs, because it denotes not only the onset of damage but also the loss of protection provided by the matrix against environ￾mental corrosion and/or oxidation of the fibers [19]. Prediction of the matrix crack initiation stress (smc) requires knowledge of the (statistical flaw population controlled) strength of the ceramic matrix and an understanding of the residual stress state. There are two main components to the residual stress in lami￾nates: that of the individual lamina, and that within Fig. 11. Comparison of elastic stiffness constants C11 and C33 during loading and unloading at different stress levels