October 1998 Stress Concentration Due to Fiber-Matrix Fusion in Ceramic-Matrix Composite. typically exists remote from the matrix crack plane. Figure A4 illustrates Fem used to evaluate the stress concentration in an Matr x interrupted interphase system. It is assumed that the radius of curvature at the seal is one-half the interphase thickness. This assumption represents a lower limit to stress concentration in act A contour plot of maximum principal stress(fiber nomi- nal 1)for a SiC-SiC system with an interrupted interphase thickness of r/25 (i.e, a 70 um fiber with a 3 um interphase) is shown in Fig. A5. A stress at the seal that is 5.3 times the feer ber nominal is observed A systematic parametric study has Fig. A3. Schematic of the interrupted interphase approach to inter- tions and that reducing the elastic modulus of the matrix/seal m Periodic fiber-matrix seals prevent runaway oxidation with respect to that of the fiber decreases the magnitude of the ase material upon exposure to the atmosphere following stress concentration leads to two probable outcomes. The first is crack propagation tration. The first occurs within the fiber adjacent to the SiO2 along the seal-fiber interface, separating the seal from the fi- seal. The increase in local stress in this region is-6 times ber. The second is crack extension across the interface and into higher than the nominal fiber stress The second occurs with the fiber. If the toughness of the seal or seal-fiber interface is the SiO2 seal near the end of the gap at the matrix crack plane ufficiently low. the an fail eav the fiber intact. That In this region, an increase in the stress is observed that is -3.5 is, crack propagation occurs parallel, rather than perpendicular modulus of the sic fiber is 6 times that of sio,. the stress in to the fiber axis. However the intended function of the seal is to localize interphase oxidation. Failure of the seal would de the SiO, seal at the crack plane is -20 times that expected for continued oxidation of the carbol the sio, in the absence of stress concentration effects. thus, a significant reduction in the effective fiber strength, or compos- interrupted interphase concept to provide oxidation resistance using a tough seal) can be achieved only at the expense of tion is larger than that expected for the microcomposite by a decreased composite strength associated with stress concentra factor >2. This is primarily due to the differences in the ge- tion at the interrupt ometry at the seal and indicates an even sharper decrease in load-bearing capacity than indicated by the data in Fig. 6 An interrupted interphase(Fig. A3) presents a slightly dif- ferent geometric situation than does the SiO, -sealed system. In this case, the matrix is bonded directly to the fiber rather than through a reaction product intermediary, and the bonded region Fice Matrix lar Interfacial Interfacial r了20 Fiber. Matrix o Fig. A4. Schematic axisymmetric FEM of an interrupted interphase system following matrix cracking and local interphase removal Linea elastic behavior is assumed (for SiC, E=400 GPa and v = 0.2, for urvature at the crack plane is assumed to be one-half the thickness of the original interphase (120), and the distance between the matrix crack plane and SiO, seal the increase in local stress relative to the increase in the fiber nominal vas chosen to be 4 times the fiber radius stress with tensile straintration. The first occurs within the fiber adjacent to the SiO2 seal. The increase in local stress in this region is ∼6 times higher than the nominal fiber stress. The second occurs within the SiO2 seal near the end of the gap at the matrix crack plane. In this region, an increase in the stress is observed that is ∼3.5 times the fiber nominal stress. Considering that the elastic modulus of the SiC fiber is ∼6 times that of SiO2, the stress in the SiO2 seal at the crack plane is ∼20 times that expected for the SiO2 in the absence of stress concentration effects. Thus, a significant reduction in the effective fiber strength, or compos￾ite load-carrying capacity, is predicted. The stress concentra￾tion is larger than that expected for the microcomposite by a factor >2. This is primarily due to the differences in the ge￾ometry at the seal and indicates an even sharper decrease in load-bearing capacity than indicated by the data in Fig. 6. An interrupted interphase (Fig. A3) presents a slightly dif￾ferent geometric situation than does the SiO2-sealed system. In this case, the matrix is bonded directly to the fiber rather than through a reaction product intermediary, and the bonded region typically exists remote from the matrix crack plane. Figure A4 illustrates FEM used to evaluate the stress concentration in an interrupted interphase system. It is assumed that the radius of curvature at the seal is one-half the interphase thickness. This assumption represents a lower limit to stress concentration in actual systems. A contour plot of maximum principal stress (fiber nomi￾nal 4 1) for a SiC–SiC system with an interrupted interphase thickness of r/25 (i.e., a 70 mm fiber with a 3 mm interphase) is shown in Fig. A5. A stress at the seal that is 5.3 times the fiber nominal is observed. A systematic parametric study has indicated, as expected, that thinner interphases (yielding lower radii of curvature at the seal) produce higher stress concentra￾tions and that reducing the elastic modulus of the matrix/seal with respect to that of the fiber decreases the magnitude of the stress concentration. Assuming failure of the interfacial seal precedes fiber failure leads to two probable outcomes. The first is crack propagation along the seal–fiber interface, separating the seal from the fi￾ber. The second is crack extension across the interface and into the fiber. If the toughness of the seal or seal–fiber interface is sufficiently low, the seal can fail, leaving the fiber intact. That is, crack propagation occurs parallel, rather than perpendicular, to the fiber axis. However, the intended function of the seal is to localize interphase oxidation. Failure of the seal would de￾feat this purpose by allowing continued oxidation of the carbon interphase. From this perspective, it is clear that the use of an interrupted interphase concept to provide oxidation resistance (using a tough seal) can be achieved only at the expense of decreased composite strength associated with stress concentra￾tion at the interrupt. Fig. A3. Schematic of the interrupted interphase approach to inter￾facial sealing. Periodic fiber–matrix seals prevent runaway oxidation of the interphase material upon exposure to the atmosphere following matrix cracking.5 Fig. A4. Schematic axisymmetric FEM of an interrupted interphase system following matrix cracking and local interphase removal. Linear elastic behavior is assumed (for SiC, E 4 400 GPa and n 4 0.2; for SiO2, E 4 70 GPa and n 4 0.2). Radius of curvature at the crack plane is assumed to be one-half the thickness of the original interphase (r/20), and the distance between the matrix crack plane and SiO2 seal was chosen to be 4 times the fiber radius. Fig. A5. Contour plot of maximum principal stress local to the fiber– matrix seal in an interrupted interphase system (Fig. A4). Scale reports the increase in local stress relative to the increase in the fiber nominal stress with tensile strain. October 1998 Stress Concentration Due to Fiber–Matrix Fusion in Ceramic-Matrix Composites 2603