Y.-C. Chiang/ Engineering Fracture Mechanics 65(2000)15-28 shown in Figs. 6 and 7. To develop a successful ceramic matrix composite, the interface should be optimally designed to have an appropriate interfacial bonding and/or frictional sliding to achieve the desired matrix cracking stress and, simultaneously, to provide a sufficient work of fracture Finally, the theoretical results are compared with the experimental data of three different composite systems. Compared with the experimental results, the initial thermal residual stress due to the thermal expansion mismatch between the fiber and the matrix needs to be considered. The critical stress for matrix cracking can be modified as where o' is the calculated matrix cracking stress and the initial axial stress due to thermal residual stress ted by Ee(xr-am)△ (31) where AT is the temperature change from the stress-free condition, and af and m, are the thermal expansion coefficients of the fiber and the matrix, respectively The matrix cracking stresses of SiC/borosilicate, SiC/LAS and C/borosilicate composite systems as a function of fiber volume fraction for different sa/sm are compared with the experimental data [15] and plotted in Figs. 8-10. The theoretical results of the ACK model for the frictional slipping interface are consistent with the case of d/5m=0 of the present analysis. The theoretical prediction of the BHE model for the perfectly bonded interface is also shown as a dotted line in Fig. 8. The BHE result for the perfectly bonded interface and the ACK or the frictiona interface are usually cited to provide the upper and ds of the cracking stress predictions. In the present analysis, the upper and of the τ=2MP 0.0 0.3 Fig. 7. Debonding length vs sa/sm at different frictional shear stress for SiC/borosilicate compositeshown in Figs. 6 and 7. To develop a successful ceramic matrix composite, the interface should be optimally designed to have an appropriate interfacial bonding and/or frictional sliding to achieve the desired matrix cracking stress and, simultaneously, to provide a sucient work of fracture. Finally, the theoretical results are compared with the experimental data of three di€erent composite systems. Compared with the experimental results, the initial thermal residual stress due to the thermal expansion mismatch between the ®ber and the matrix needs to be considered. The critical stress for matrix cracking can be modi®ed as scr ‡ st ˆ s …30† where s is the calculated matrix cracking stress and the initial axial stress due to thermal residual stress st can be approximated by st ˆ Ec…af ÿ am†DT 1 ‡ …VmEm ‡ VfEf† …31† where DT is the temperature change from the stress-free condition, and af and am, are the thermal expansion coecients of the ®ber and the matrix, respectively. The matrix cracking stresses of SiC/borosilicate, SiC/LAS and C/borosilicate composite systems as a function of ®ber volume fraction for di€erent zd=zm are compared with the experimental data [15] and plotted in Figs. 8±10. The theoretical results of the ACK model for the frictional slipping interface are consistent with the case of zd=zm ˆ 0 of the present analysis. The theoretical prediction of the BHE model for the perfectly bonded interface is also shown as a dotted line in Fig. 8. The BHE result for the perfectly bonded interface and the ACK result for the frictional interface are usually cited to provide the upper and lower bounds of the matrix cracking stress predictions. In the present analysis, the upper and lower bounds of the matrix cracking stress Fig. 7. Debonding length vs. zd=zm at di€erent frictional shear stress for SiC/borosilicate composite. Y.-C. Chiang / Engineering Fracture Mechanics 65 (2000) 15±28 25