J.A. DiCarlo et al. Appl Math. Comput. 152(2004)473-481 assume isostrain conditions within the composite, so that the measured creep ate of the composite is equal to that of the fiber and matrix. Assuming near steady-state conditions are reached during composite life it is proposed that the composite creep rate and the MG lines of Fig. 2 could then be used to predict which constituent will rupture first for a given SiC/SiC creep rate. To determine whether this model has any validity, it is interesting to note that most Sic/Sic composites fabricated today contain SiC matrices produced by hemical vapor infiltration(CVI). Assuming these matrices creep and rupture in a manner equivalent to that of the Ultra-SCS fiber, Fig. 2 suggests that at any composite creep rate at temperatures of 1200C or higher, the Cvi SiC matrix should crack before the Nicalon or Hi-Nicalon fibers rupture. This should be the case no matter what the fiber stress or volume fraction within the composite On the other hand, the Sylramic fibers should rupture before the CVI SiC matrix cracks Although there currently exists very little SiC/Sic data to validate the condition(A)model, one can examine two recent papers by Zhu et al. who measured the creep-rupture behavior of two types of SiC/SiC composites containing CVI SiC matrices manufactured by the same vendor For the first composite type with Nicalon fibers, data taken at 30, 45, and 60 MPa and at 1300C in air show low composite creep curves and relatively long lives until an abrupt and rapid increase in creep strain occurs, followed by composite rupture within a time period less than 5% of the original creep stage [12]. This behavior supports the prediction described above in which the first abrupt change should be caused by matrix cracking of the CVI SiC matrix, and the final failure by rupture of the fully loaded Nicalon fibers. Assuming this to be the case, one can use the composite creep rates and times at matrix cracking to plot the three [+ data points shown in Fig 2. For the second composite type with Hi-Nicalon fibers, the authors were actually able to measure CVI SiC matrix cracking from periodic hysteresis tests [13]. The two [o] data points in the Fig. 2 display these time results versus the composite creep rates at cracking. The observations that all points fall very well on the same straight line and that this line has an m value of 1. 2 strongly support the assumptions of the condition(A) model. In addition the matrix cracking line falls below that Ultra-SCS fiber at 1200C, suggesting that the CVi SiC matrix is not pure and stoichiometric like the Ultra-sCS fiber. Indeed recent raman studies CVI SiC matrices made by the same vendor have detected free silicon in the matrix bulk [24]. Thus the dashed line can be considered the empirically de termined MG line for CVI SiC matrices fabricated by this particular vendor Recently, Sic/Sic matrices have been fabricated with Sylramic fibers and with the same CVI SiC matrix from the same vendor as the major structural component of the matrix. Stress-rupture data taken in air at 1315C and composite stresses from 70 to 105 MPa show composite creep curves with a transient and steady state stage, but with a small tertiary stage before finalassume isostrain conditions within the composite, so that the measured creep rate of the composite is equal to that of the fiber and matrix. Assuming near steady-state conditions are reached during composite life, it is proposed that the composite creep rate and the MG lines of Fig. 2 could then be used to predict which constituent will rupture first for a given SiC/SiC creep rate. To determine whether this model has any validity, it is interesting to note that most SiC/SiC composites fabricated today contain SiC matrices produced by chemical vapor infiltration (CVI). Assuming these matrices creep and rupture in a manner equivalent to that of the Ultra-SCS fiber, Fig. 2 suggests that at any composite creep rate at temperatures of 1200
C or higher, the CVI SiC matrix should crack before the Nicalon or Hi-Nicalon fibers rupture. This should be the case no matter what the fiber stress or volume fraction within the composite. On the other hand, the Sylramic fibers should rupture before the CVI SiC matrix cracks. Although there currently exists very little SiC/SiC data to validate the condition (A) model, one can examine two recent papers by Zhu et al. who measured the creep-rupture behavior of two types of SiC/SiC composites containing CVI SiC matrices manufactured by the same vendor. For the first composite type with Nicalon fibers, data taken at 30, 45, and 60 MPa and at 1300
C in air show low composite creep curves and relatively long lives until an abrupt and rapid increase in creep strain occurs, followed by composite rupture within a time period less than 5% of the original creep stage [12]. This behavior supports the prediction described above in which the first abrupt change should be caused by matrix cracking of the CVI SiC matrix, and the final failure by rupture of the fully loaded Nicalon fibers. Assuming this to be the case, one can use the composite creep rates and times at matrix cracking to plot the three [+] data points shown in Fig 2. For the second composite type with Hi-Nicalon fibers, the authors were actually able to measure the times for CVI SiC matrix cracking from periodic hysteresis tests [13]. The two [O] data points in the Fig. 2 display these time results versus the composite creep rates at cracking. The observations that all points fall very well on the same straight line and that this line has an m value of
1.2 strongly support the assumptions of the condition (A) model. In addition, the matrix cracking line falls below that Ultra-SCS fiber at 1200
C, suggesting that the CVI SiC matrix is not pure and stoichiometric like the Ultra-SCS fiber. Indeed, recent Raman studies on CVI SiC matrices made by the same vendor have detected free silicon in the matrix bulk [24]. Thus the dashed line can be considered the empirically de￾termined MG line for CVI SiC matrices fabricated by this particular vendor. Recently, SiC/SiC matrices have been fabricated with Sylramic fibers and with the same CVI SiC matrix from the same vendor as the major structural component of the matrix. Stress-rupture data taken in air at 1315
C and composite stresses from 70 to 105 MPa show composite creep curves with a transient and steady state stage, but with a small tertiary stage before final J.A. DiCarlo et al. / Appl. Math. Comput. 152 (2004) 473–481 479