J.A. DiCarlo et al. /Appl. Math. Comput. 152(2004)473-481 rupture strain with longer rupture time. This reduction in strain with time may be related to detrimental effects associated with long-term microstructural hanges or oxidation. Thus the constant C in Eq. (1)should be dependent be on SiC fiber microstructure and test temperature, but is fairly independent fiber stress or fiber cross-sectional area since the creep rate variation was ob- tained by changing the applied load on the fibers. It follows then from Fig. 2 that for a particular SiC/SiC application temperature, one cannot select fibe rupture time independently of fiber creep rate. For example, up to 1200C, the only approach for obtaining a 1000-h fiber lifetime is to assure that the posite application conditions do not create fiber creep rates more than 10 s for the creep-prone Nicalon and Hi-Nicalon fibers, and more than 10 s- for the more creep-resistant Sylramic fiber 3. SiC/SiC composite creep-rupture The single fiber results presented above indicate that many intrinsic extrinsic mechanistic factors control the high-temperature rupture of Sic types of current interest. As an initial step toward understanding how factors can in turn affect SiC/SiC composite behavior, the following discussion uses elementary composite theory and the single fiber data to develop simple mechanistic models for composite fracture at high temperatures under typical stress-rupture testing conditions. Common practice for these tests is to first raise the composites to the test temperature in ambient air, and then to increase load to a given level where creep strain is measured versus time until composite fracture. Typically the load is applied in a direction parallel to a set of fiber bundles that have an effective volume fraction of from 15% to 25% in the load direction. In this situation, there are two conditions of practical interest:(A) the maximum applied load is low enough to initially inhibit through-thickness cracking of the matrix, and(b)the maximum applied load is high enough to initially cause through-thickness cracking of the matrix, thereby leaving the fiber bundles bridging the matrix cracks and exposed to the test environment For this latter situation, the stress on the bridging fibers can be directly cal- culated from the composite stress; so that composite rupture can be predicted based on the stress dependence for creep-rupture of the reinforcing fibers. The details of one simple rupture model for condition(B)and its verification data are presented elsewhere [22, 23 For condition(A), a more desirable situation for long-term composite use the average stresses on the fibers and matrix are not constant; but change with time in a complicated manner due to differences in creep behavior between the two constituents. The initial creep rate of the uncracked composite will gen- erally be controlled by the more creep-prone constituent and the final creep rate by the more creep-resistant constituent. For modeling purposes, one canrupture strain with longer rupture time. This reduction in strain with time may be related to detrimental effects associated with long-term microstructural changes or oxidation. Thus the constant C in Eq. (1) should be dependent both on SiC fiber microstructure and test temperature, but is fairly independent of fiber stress or fiber cross-sectional area since the creep rate variation was ob￾tained by changing the applied load on the fibers. It follows then from Fig. 2 that for a particular SiC/SiC application temperature, one cannot select fiber rupture time independently of fiber creep rate. For example, up to 1200
C, the only approach for obtaining a 1000-h fiber lifetime is to assure that the com￾posite application conditions do not create fiber creep rates more than
108 s1 for the creep-prone Nicalon and Hi-Nicalon fibers, and more than
109 s1 for the more creep-resistant Sylramic fiber. 3. SiC/SiC composite creep-rupture The single fiber results presented above indicate that many intrinsic and extrinsic mechanistic factors control the high-temperature rupture of SiC fiber types of current interest. As an initial step toward understanding how these factors can in turn affect SiC/SiC composite behavior, the following discussion uses elementary composite theory and the single fiber data to develop simple mechanistic models for composite fracture at high temperatures under typical stress-rupture testing conditions. Common practice for these tests is to first raise the composites to the test temperature in ambient air, and then to increase load to a given level where creep strain is measured versus time until composite fracture. Typically the load is applied in a direction parallel to a set of fiber bundles that have an effective volume fraction of from 15% to 25% in the load direction. In this situation, there are two conditions of practical interest: (A) the maximum applied load is low enough to initially inhibit through-thickness cracking of the matrix, and (B) the maximum applied load is high enough to initially cause through-thickness cracking of the matrix, thereby leaving the fiber bundles bridging the matrix cracks and exposed to the test environment. For this latter situation, the stress on the bridging fibers can be directly cal￾culated from the composite stress; so that composite rupture can be predicted based on the stress dependence for creep-rupture of the reinforcing fibers. The details of one simple rupture model for condition (B) and its verification data are presented elsewhere [22,23]. For condition (A), a more desirable situation for long-term composite use, the average stresses on the fibers and matrix are not constant; but change with time in a complicated manner due to differences in creep behavior between the two constituents. The initial creep rate of the uncracked composite will gen￾erally be controlled by the more creep-prone constituent and the final creep rate by the more creep-resistant constituent. For modeling purposes, one can 478 J.A. DiCarlo et al. / Appl. Math. Comput. 152 (2004) 473–481