G N. Morscher Composites Science and Technology 64 (2004)1311-1319 minicomposites based on processing data for each 450 composite pane 68:8.7epcm;f=02 (σ+) where oc is the composite stress, oth is the residual compressive stress in the matrix [21] which was found to be higher, in general, for higher volume fraction com- 嘉∞0 posites with inside debonding [14], and Ec is the mea sured composite elastic modulus from the a/E curve 100 012:71epcm;f=0.14 Fig. 7 shows the estimated stress-dependent matrix crack distribution versus ominimatrix. There is consider- able convergence of the matrix crack data with this 00.050.10.150.20.250.3035 normalization step even though there is a wide scatter in Strain, e and the differences in debonding and sliding character, Fig 8. Stress-strain predictions based on best-fit matrix crac i.e., interfacial shear stress. However, for specimens with for two different volume fraction composites with same t The solid lines are the measure 二N the fewer number of plies, the matrix crack distribution appears to be broader in o and ominimatrix, but still within right of the squares are the model predictions assuming 33%fewer and he range of matrix cracking exhibited by the standard 33% greater number of matrix cracks, respectively eight ply panels. Also, there appears to be a small sep- aration in gminimatrix, N10 MPa, between the lowest (4.9 epcm composites and those woven with higher (7.1-8.7) term in Eq (1). Finally, the data were compared using epcm. The matrix crack distribution for the lower epi only fo and no residual stress term. None of these at composites occurring at lower ominimatris range but with tempts resulted in the convergence of the data as well as about the same relative slopes as higher volume fraction the"minimatrix""approach composites. This perhaps does indicate an effect of ar chitecture on the nature of matrix cracking in these 3.3. Matrix cracking in double-tow woven composites composites; however, for the use of these materials in actual components, composite architecture will most The estimated crack density versus composite stress likely use the higher epcm ranges and higher fiber fr and ominimatrix for the composite specimen woven with a tions where the behavior was fairly consistent double-tow(specimen 041 in Table 1)are also shown in Other attempts were made to relate the crack-distri Figs. 5 and 7, respectively. Matrix cracking occurs over butions as well. The data were compared only using the a significantly narrower stress-range for the double-tow volume fraction of fibers in the loading direction, fo, and woven composites compared to the standard single-tow Er in Eq()instead of mini and Emini, respectively. The woven composites and at lower stresses when comparing data were compared without the use of a residual stress similar volume fraction composites(Fig. 5). This also is evident in the ominimatrix range of matrix cracking(Fig 8) where the matrix cracking in the double-tow composites occurs at significantly lower stresses. It should be noted 017:49 cpam, f=0.17 hat onset for 041 was significantly less than 01l which DaB: 8, epcm: f=D 01649pm12 has the same fo for a standard single-tow woven com posite but it had a similar Eonset(Fig. 6) 044:87epcm向=0.2 009:790pm018 4. Discussio 018;79epcm0.14 To model the stress-strain response of ceramic matrix composites, knowledge of the stress-dependent number of matrix cracks is essential [20-23]. Usually this can only be determined experimentally for the composite Mini Matrix Stress. MPa system studied. For example, Lamon and coworkers [9, 10] determined the distribution of matrix cracks in Fig. 7. Stress-dependent matrix cracking versus ominimatrix for standard tow woven composites and a double-tow woven com different parts of the 2D architecture, i.e, those ema 041). A simple best-fit of matrix crack density, up to mimimatrix= 150 nating from 90 tows or those emanating in minicom- MPa, for single-tow woven composites with epcm >7.1 is plotted as posite ligaments not adjacent to 90 bundles, as a open square function of strain for a CvI SiC matrix system. For theminicomposites based on processing data for each composite panel: rminimatrix ¼ ð Þ rc þ rth Ec Ec fminiEmini 1 fmini
; ð1Þ where rc is the composite stress, rth is the residual compressive stress in the matrix [21] which was found to be higher, in general, for higher volume fraction com￾posites with inside debonding [14], and Ec is the mea￾sured composite elastic modulus from the r=e curve. Fig. 7 shows the estimated stress-dependent matrix crack distribution versus rminimatrix. There is consider￾able convergence of the matrix crack data with this normalization step even though there is a wide scatter in E and the differences in debonding and sliding character, i.e., interfacial shear stress. However, for specimens with the fewer number of plies, the matrix crack distribution appears to be broader in r and rminimatrix, but still within the range of matrix cracking exhibited by the standard eight ply panels. Also, there appears to be a small sep￾aration in rminimatrix,
10 MPa, between the lowest (4.9) epcm composites and those woven with higher (7.1–8.7) epcm. The matrix crack distribution for the lower epi composites occurring at lower rminimatrix range but with about the same relative slopes as higher volume fraction composites. This perhaps does indicate an effect of ar￾chitecture on the nature of matrix cracking in these composites; however, for the use of these materials in actual components, composite architecture will most likely use the higher epcm ranges and higher fiber frac￾tions where the behavior was fairly consistent. Other attempts were made to relate the crack-distri￾butions as well. The data were compared only using the volume fraction of fibers in the loading direction, f0, and Ef in Eq. (1) instead of fmini and Emini, respectively. The data were compared without the use of a residual stress term in Eq. (1). Finally, the data were compared using only f0 and no residual stress term. None of these at￾tempts resulted in the convergence of the data as well as the ‘‘minimatrix’’ approach. 3.3. Matrix cracking in double-tow woven composites The estimated crack density versus composite stress and rminimatrix for the composite specimen woven with a double-tow (specimen 041 in Table 1) are also shown in Figs. 5 and 7, respectively. Matrix cracking occurs over a significantly narrower stress-range for the double-tow woven composites compared to the standard single-tow woven composites and at lower stresses when comparing similar volume fraction composites (Fig. 5). This also is evident in the rminimatrix range of matrix cracking (Fig. 8) where the matrix cracking in the double-tow composites occurs at significantly lower stresses. It should be noted that ronset for 041 was significantly less than 011 which has the same f0 for a standard single-tow woven com￾posite but it had a similar eonset (Fig. 6). 4. Discussion To model the stress–strain response of ceramic matrix composites, knowledge of the stress-dependent number of matrix cracks is essential [20–23]. Usually this can only be determined experimentally for the composite system studied. For example, Lamon and coworkers [9,10] determined the distribution of matrix cracks in different parts of the 2D architecture, i.e., those ema￾nating from 90
tows or those emanating in minicom￾posite ligaments not adjacent to 90
bundles, as a function of strain for a CVI SiC matrix system. For the Fig. 8. Stress–strain predictions based on best-fit matrix crack density for two different volume fraction composites with same s ¼ 70 MPa. The solid lines are the measured stress–strain curves. The squares are the predicted stress–strain curves and the dashed lines to the left and right of the squares are the model predictions assuming 33% fewer and 33% greater number of matrix cracks, respectively. Fig. 7. Stress-dependent matrix cracking versus rminimatrix for standard single-tow woven composites and a double-tow woven composite (041). A simple best-fit of matrix crack density, up to rminimatrix ¼ 150 MPa, for single-tow woven composites with epcm P7.1 is plotted as open squares. 1316 G.N. Morscher / Composites Science and Technology 64 (2004) 1311–1319