G.N. Morscher et al Composites Science and Technology 67(2007)1009-1017 was used to model stress-strain. There is excellent agreement found to be very similar to that of single tow minicomposites between this modeling approach for matrix crack density For higher density composites, a lower stress on the load and stress-strain behavior. There was a slight overestimate bearing CVI SiC was required to form and propagate matrix for some of the Hi-Nicalon composites due to the overesti- cracks since the 90 minicomposites act as the source of mate of Ec in Ref [1]. Table 2 lists the model parameters that matrix flaws. For Sylramic-iBN CVI SiC composites, which were used in Fig. 7 were all of higher density, matrix cracking was dependent on Finally, it is instructive to compare the relationships fiber volume fraction in the loading direction and the size of governing the stress-distributions for matrix cracking for the unbridged region of a matrix crack For composites with the different fiber/matrix systems [68]. Matrix cracking a high volume fraction of fibers in the loading direction a for balanced weave CVI SiC composites with Hi-Nicalon higher stress-range distribution of load-bearing CVI SiC [8] and Sylramic fiber types both can be modeled on the stress was observed. For the un balanced composites when basis of stress in the load-bearing SiC. However, the stressed in the low fiber volume direction a lower stress- ress-range for matrix cracking for Hi-Nicalon composites range, steeper distribution of load-bearing CVI SiC stress is approximately 80 MPa lower in load-bearing SiC stress was observed which may have also been influenced by the than that for Sylramic CVI SiC. If the difference in matrix increased number of 90 minicomposites resulting in larger cracking stresses for different fiber composites was just due unbridged regions of a matrix crack. to the difference in fiber stiffness, they should have the same These distributions were used to determine two impor- stress and strain in the Cvi SiC for matrix cracking. But tant design parameters: the onset stress for matrix cracking this was not the case as described above. There is essen- and an estimated stress-dependent matrix crack density tially no measurable residual stress in Hi-Nicalon Cvi which is required to effectively model stress-strain behavior Sic composites [8 whereas there is residual compressive for these composites. Combining these relationships with stress in the matrix of Sylramic CVI SiC composites. This the model for elastic modulus of these 2D composites [1] would account for some of the disparity between the two gives designers useful tools to determine the entire stress- systems. The net fiber area in a Hi-Nicalon tow cross-sec- strain response in local areas of a composite component tion is approximately 22%/ greater than Sylramic based This is especially useful if local constituent content is on average fiber diameter(14 and 10 um, respectively) known to vary due to architectural and/or process varia- and number of fibers(500 and 800, respectively) which tions which cannot easily be replicated by simple panel- should result in similar differences in tow height of the based property generation. Also, these models could be 90 bundles, i. e, larger flaw sizes in Hi-Nicalon compos- used to optimize 2D architecture and constituent content ites. In addition, the flaw sources for matrix cracks in to optimize Ec and/or matrix cracking properties for a CVI SiC composites are not only the 90o bundles. The given application sharp notches of the macro-pore structure in the CVI SiC that exist where 90 and 0o bundles are adjacent to one another [13, 14] are the lowest stress flaw sources (highest References stress-concentrators on Cv SiC) and most likely greater [1 Morscher GN. The elastic modulus of 2D woven CVI SiC compos- n size for the larger tow size Hi-Nicalon composites. ites, Comp Sci Tech (i 2] Curtin WA, Ahn BK, Takeda N. Acta Mater 1998: 46(10): 3409-20. 5. Conclusions [] Lamon J Comp Sci Tech 2001: 61: 2259-72. [4] Morscher GN, Cawley JD. J Eur Ceram Soc 2002; 22(14-15): 2777-88. M, The stress-dependence for matrix cracking in woven Hi- [5]Yun HM, Gyekenyesi JZ, Chen YL, Wheeler DR,DiCarlo JA Ceram Eng Sci Proc 2001; 22(3): 521-31 licalon and Sylramic-ibN fiber reinforced, CVI SiC matrix [6]Morscher GN Comp Sci Tech 2004: 64: 1311-9 composites was determined for balanced and unbalanced 2D [7]Morscher GN. Published in the 35th international SAMPE technical architectures. It was shown that higher volume fraction com conference proceedings(CD), Dayton, OH; 2003 posites usually exhibited higher matrix cracking stresses. [8 Steen M, Valles JL. ASTM STP 1309. In: Jenkins MG et al,editors Therefore. unbalanced architectures with increased fiber rials:1997.p.49-65 loading in the direction where an application requires a high [9]Pryce Aw, Smith PA. Br Ceram Trans 1993: 92(2): 49-54 matrix cracking stress are viable options to achieve higher [10] Martinez-Fernandez J, Morscher GN. Room and elevated matrix cracking stresses if needed ure tensile properties of single tow Hi-Nicalon, carbon interphase, Stress-dependent relationships for matrix cracking in this CVI SiC matrix minicomposites J Eur Ceram Soc 2000: 20: 2627-36 measurements. The stress-dependent matrix cracking Sion [1] Morscher GN, Martinez-Fernandez J Fiber effects on minicomposite composite system were determined from acoustic emission apor-infiltrated silicon carbide matrix systems. J Am Ceram Soc found to be dependent on the stress in the load-bearing SiC as dictated by the architecture and constituent content. For [2] Cox BN, Marshall DB. Crack initiation in fiber-reinforced brittle Hi-Nicalon CVI SiC composites, matrix cracking was aminates.J Am Ceram Soc 1996: 79(5): 1181-8 dependent on the degree of load-sharing in the 90 minicom- [13] Guillaumat L, Lamon J. In: Revue des composites et des materiaux avances, vol 3, 1993, p. 159-71 posites. For lower density composites which had little if any [14] Pluvinage P, Parvizi-Majidi A, Chou TW. J Mater Sci load-sharing in the 90 minicomposites, matrix cracking was 1996:31:232-41was used to model stress–strain. There is excellent agreement between this modeling approach for matrix crack density and stress–strain behavior. There was a slight overestimate for some of the Hi-Nicalon composites due to the overesti￾mate of Ec in Ref. [1]. Table 2 lists the model parameters that were used in Fig. 7. Finally, it is instructive to compare the relationships governing the stress-distributions for matrix cracking for the different fiber/matrix systems [6–8]. Matrix cracking for balanced weave CVI SiC composites with Hi-Nicalon [8] and Sylramic fiber types both can be modeled on the basis of stress in the load-bearing SiC. However, the stress-range for matrix cracking for Hi-Nicalon composites is approximately 80 MPa lower in load-bearing SiC stress than that for Sylramic CVI SiC. If the difference in matrix cracking stresses for different fiber composites was just due to the difference in fiber stiffness, they should have the same stress and strain in the CVI SiC for matrix cracking. But this was not the case as described above. There is essen￾tially no measurable residual stress in Hi-Nicalon CVI SiC composites [8] whereas there is residual compressive stress in the matrix of Sylramic CVI SiC composites. This would account for some of the disparity between the two systems. The net fiber area in a Hi-Nicalon tow cross-sec￾tion is approximately 22% greater than Sylramic based on average fiber diameter (14 and 10 lm, respectively) and number of fibers (500 and 800, respectively) which should result in similar differences in tow height of the 90 bundles, i.e., larger flaw sizes in Hi-Nicalon compos￾ites. In addition, the flaw sources for matrix cracks in CVI SiC composites are not only the 90 bundles. The sharp notches of the macro-pore structure in the CVI SiC that exist where 90 and 0 bundles are adjacent to one another [13,14] are the lowest stress flaw sources (highest stress-concentrators on CVI SiC) and most likely greater in size for the larger tow size Hi-Nicalon composites. 5. Conclusions The stress-dependence for matrix cracking in woven Hi￾Nicalon and Sylramic-iBN fiber reinforced, CVI SiC matrix composites was determined for balanced and unbalanced 2D architectures. It was shown that higher volume fraction com￾posites usually exhibited higher matrix cracking stresses. Therefore, unbalanced architectures with increased fiber loading in the direction where an application requires a high matrix cracking stress are viable options to achieve higher matrix cracking stresses if needed. Stress-dependent relationships for matrix cracking in this composite system were determined from acoustic emission measurements. The stress-dependent matrix cracking was found to be dependent on the stress in the load-bearing SiC as dictated by the architecture and constituent content. For Hi-Nicalon CVI SiC composites, matrix cracking was dependent on the degree of load-sharing in the 90 minicom￾posites. For lower density composites which had little if any load-sharing in the 90 minicomposites, matrix cracking was found to be very similar to that of single tow minicomposites. For higher density composites, a lower stress on the load￾bearing CVI SiC was required to form and propagate matrix cracks since the 90 minicomposites act as the source of matrix flaws. For Sylramic-iBN CVI SiC composites, which were all of higher density, matrix cracking was dependent on fiber volume fraction in the loading direction and the size of the unbridged region of a matrix crack. For composites with a high volume fraction of fibers in the loading direction a higher stress-range distribution of load-bearing CVI SiC stress was observed. For the unbalanced composites when stressed in the low fiber volume direction a lower stress￾range, steeper distribution of load-bearing CVI SiC stress was observed which may have also been influenced by the increased number of 90 minicomposites resulting in larger unbridged regions of a matrix crack. These distributions were used to determine two impor￾tant design parameters: the onset stress for matrix cracking and an estimated stress-dependent matrix crack density which is required to effectively model stress–strain behavior for these composites. Combining these relationships with the model for elastic modulus of these 2D composites [1] gives designers useful tools to determine the entire stress– strain response in local areas of a composite component. This is especially useful if local constituent content is known to vary due to architectural and/or process varia￾tions which cannot easily be replicated by simple panel￾based property generation. Also, these models could be used to optimize 2D architecture and constituent content to optimize Ec and/or matrix cracking properties for a given application. References [1] Morscher GN. The elastic modulus of 2D woven CVI SiC compos￾ites, Comp Sci Tech (in press). [2] Curtin WA, Ahn BK, Takeda N. Acta Mater 1998;46(10):3409–20. [3] Lamon J. Comp Sci Tech 2001;61:2259–72. [4] Morscher GN, Cawley JD. J Eur Ceram Soc 2002;22(14–15):2777–88. [5] Yun HM, Gyekenyesi JZ, Chen YL, Wheeler DR, DiCarlo JA. Ceram Eng Sci Proc 2001;22(3):521–31. [6] Morscher GN. Comp Sci Tech 2004;64:1311–9. [7] Morscher GN. Published in the 35th international SAMPE technical conference proceedings (CD), Dayton, OH; 2003. [8] Steen M, Valles JL. ASTM STP 1309. In: Jenkins MG et al., editors. West Conshohocken, PA: American Society for Testing and Mate￾rials; 1997. p. 49–65. [9] Pryce AW, Smith PA. Br Ceram Trans 1993;92(2):49–54. [10] Martı´nez-Ferna´ndez J, Morscher GN. Room and elevated tempera￾ture tensile properties of single tow Hi-Nicalon, carbon interphase, CVI SiC matrix minicomposites. J Eur Ceram Soc 2000;20:2627–36. [11] Morscher GN, Martinez-Fernandez J. Fiber effects on minicomposite mechanical properties for several silicon carbide fiber – chemically vapor-infiltrated silicon carbide matrix systems. J Am Ceram Soc 1999;82(1):145–55. [12] Cox BN, Marshall DB. Crack initiation in fiber-reinforced brittle laminates. J Am Ceram Soc 1996;79(5):1181–8. [13] Guillaumat L, Lamon J. In: Revue des composites et des materiaux avances, vol. 3, 1993, p. 159–71. [14] Pluvinage P, Parvizi-Majidi A, Chou TW. J Mater Sci 1996;31:232–41. G.N. Morscher et al. / Composites Science and Technology 67 (2007) 1009–1017 1017