CARBON 47(2009)I034-I04 1041 ger constraints between fibers enabled the TRS relief more theoretically, and then validated by the experimental results difficult. One extreme example is 1D composite or micro/ reported previously and microstructural observations. The minicomposite that all the fibers were arranged in the same calculated results demonstrated that the models gave correct direction, which resulted in large numbers of matrix cracks trend and reliable prediction for the composite strength, and perpendicular to the unidirectional fibers in the as-fabricated well explained why differences in the composite i resulted in composites without any transverse fiber constraints [23] the substantial variations in TRS. Namely, the more the fibers arranged in the same direction, the les 3.4. UTS predic tween the highly-ordered fibers and the easier the RS relief of the composites in the form of transverse cracks durin UTSs of the composites strongly depend on the effective rein- cooling forcing fiber numbers parallel to the axial tensile loading rection. we are concerned with the relationship betweenAcknowledgements the constituent properties of the composites and mechanical properties (i.e, strength), and neglect the interface effect. This work has been supported by NPU Fundamental Research, Thus, the composite strength can be simply estimated, re- Foundation for Flying star and Natural science foundation of ted to efl .as China(Contract No. 50820145202) The authors also gratefully GuTs=[o'V/+omu(Vm-p) EmVm+ Euv (10) acknowledge Drs. Zhang J, Ma jQ, Nie J and Wang YQ for their experimental data and helpful discussion where o and mu denote the fracture strengths of fiber and matrix in the composites. Consider that CVI-Sic in the com- posite is not full dense Sic ceramic and commonly contains REFERENCES porosity and as-fabricated thermal cracks, thus strength of VI-Sic matrix can be calculated [24] [1] Halbig MC, Brewer DN, Eckel A]. Degradation of continuous Omu(Emv+Evo (11) fber CMCs under constant load conditions. NASA/TM- 209681, January2000,p.1-5. where ome denotes the first matrix cracking stress or the so- [2] Sullivan RM. A model for the oxidation of carbon silicon called proportional limit stress of the arbide composite structures. Carbon 2005: 43: 275-85 is usually identified by acoustic emission and by the limit of 3] Evans AG, Domergue JM,Vagaggini EMethodology for the linear domain on the tensile stress-strain curves. for a ting the tensile constitutive behavior of CMcs to C/SiC composite, it is widely reported to be about 50 MPa [4] Domergue JM, Vagaggini E, Evans AG. Relationships between hysteresis measurements and the consitutent properties of 58 MPa. Because the carbon fibers were also subjected CMCs. Part II: Experimental studies on unidirectional to mechanical degradation during cvi pre materials. J Am Ceram Soc 1995; 78 (10): 2721-31. d'=1.57 GPa. Using the data in Table 1 and the constituent [5] Vagaggini E, Domergue JM, Evans AG. Relationships between properties in Table 2, the UTS of the four composites were hysteresis measurements and the consitutent properties of CMCs. Part I: Theory. J Am Ceram Soc 1995: 78(10 2709-20 theoretically calculated and then the results were listed in Ta- 16 Wang M, Laird C Characterization of microstructure and ble 1. Namely, 152 MPa for the needled C/Sic, 230 MPa for the ensile behavior of a cross-woven C/Sic composite. Acta C/SiC, 347 MPa for the 2. 5D C/SiC, and 440 MPa for 3D C/Sic Mater1996;4(4):1371-87 composites.In contrast to the previously reported experimen Camus G, Guillaumat L, Baste S Development of damage in a tal UTS values in [10-13(see Table 1), the model of Eq. (10) 2D woven C/SiC composite under mechanical loading. Part 1: gave correct trend and reliable predictions for the composite Mechanical characterization Compos Sci Technol strengths. 1996;56:1363-72 [8 Steen M. Tensile mastercurve of CMCs: significance and implications for modeling. Mater Sci Eng 1998; A250: 241-8 Conclusions [9] Bobet JL, Naslain R, Guette A, JiN, Lebrun JL. Thermal residual stresses in CMCs. Part I]: Experimental results for model The mechanical hysteresis of four representative ceramic ma materials. Acta Metall Mater 1995: 43(6): 2255-68 trix composites with different carbon fiber performs, based [10 Nie JJ, Xu YD, Zhang LT, Cheng LF, Ma JQ Microstructure a on a new-defined structural parameter ECFL i normalized tensile behavior of multiply needled C/SiC composite fabricated by chemical vapor infiltration. J Mater Process load direction, was investigated and compared during cyclic Technol2009;209(1):576-92 reloading-unloading tests. The estimated values of 2 were [11] MeiH, Cheng LE, Zhang LT, Luan XG, Zhang/. Behavior of two- 0.375 for the needled C/Sic, 0.5 for the 2D C/Sic, 0.75 for the dimensional C/Sic composites subjected to thermal cycling 2.5D C/SiC, and 0.93 for the 3D C/SiC. Results show that in- in controlled environments. Carbon 2006: 44: 121-7. crease in permanent strain and decrease in stiffness of the [12] Ma JQ, Xu YD, Zhang LT, Cheng LF, Nie J, Dong N Microstructure characterization and tensile behavior of 2.5D C/Sic composites fabricated by chemical vapor infiltration. e parameter i. The greater the parameter 1, the more the Scr Mater2006;54:1967-71 load-bearing fibers, the slower the inelastic residual strain in-(13) Mei H, Cheng LF, Zhang LT, Xu YD Effect of fiber architectures ease during the reloading-unloading cycles. The axial TRS on thermal cycling damage of C/Sic composites in oxidizing and UTS of these four composites, related to i, were modeled atmosphere. Mater Sci Eng 2007: A460-461: 306-13ger constraints between fibers enabled the TRS relief more difficult. One extreme example is 1D composite or micro/ minicomposite that all the fibers were arranged in the same direction, which resulted in large numbers of matrix cracks perpendicular to the unidirectional fibers in the as-fabricated composites without any transverse fiber constraints [23]. 3.4. UTS prediction UTSs of the composites strongly depend on the effective rein￾forcing fiber numbers parallel to the axial tensile loading direction. We are concerned with the relationship between the constituent properties of the composites and mechanical properties (i.e., strength), and neglect the interface effect. Thus, the composite strength can be simply estimated, re￾lated to ECFL k, as rUTS ¼ ½r f kVf þ rmuðVm  pÞ  EmVm þ Ef kVf Em rm r ; ð10Þ where r f and rmu denote the fracture strengths of fiber and matrix in the composites. Consider that CVI-SiC in the com￾posite is not full dense SiC ceramic and commonly contains porosity and as-fabricated thermal cracks, thus strength of CVI-SiC matrix can be calculated [24] rmu ¼ Em ðEmVm þ EfVfÞ rmc; ð11Þ where rmc denotes the first matrix cracking stress or the so￾called proportional limit stress of the composite. This value is usually identified by acoustic emission and by the limit of the linear domain on the tensile stress–strain curves. For a C/SiC composite, it is widely reported to be about 50 MPa [6,20,25], and thus the fracture strength of SiC matrix rmu = 58 MPa. Because the carbon fibers were also subjected to mechanical degradation during CVI processing, here r f = 1.57 GPa. Using the data in Table 1 and the constituent properties in Table 2, the UTS of the four composites were theoretically calculated and then the results were listed in Ta￾ble 1. Namely, 152 MPa for the needled C/SiC, 230 MPa for the 2D C/SiC, 347 MPa for the 2.5D C/SiC, and 440 MPa for 3D C/SiC composites. In contrast to the previously reported experimen￾tal UTS values in [10–13] (see Table 1), the model of Eq. (10) gave correct trend and reliable predictions for the composite strengths. 4. Conclusions The mechanical hysteresis of four representative ceramic ma￾trix composites with different carbon fiber performs, based on a new-defined structural parameter ECFL k normalized to load direction, was investigated and compared during cyclic reloading–unloading tests. The estimated values of k were 0.375 for the needled C/SiC, 0.5 for the 2D C/SiC, 0.75 for the 2.5D C/SiC, and 0.93 for the 3D C/SiC. Results show that in￾crease in permanent strain and decrease in stiffness of the composites with the applied stress were strongly affected by the parameter k. The greater the parameter k, the more the load-bearing fibers, the slower the inelastic residual strain in￾crease during the reloading–unloading cycles. The axial TRS and UTS of these four composites, related to k, were modeled theoretically, and then validated by the experimental results reported previously and microstructural observations. The calculated results demonstrated that the models gave correct trend and reliable prediction for the composite strength, and well explained why differences in the composite k resulted in the substantial variations in TRS. Namely, the more the fibers arranged in the same direction, the less the constraint be￾tween the highly-ordered fibers and the easier the TRS relief of the composites in the form of transverse cracks during cooling. Acknowledgements This work has been supported by NPU Fundamental Research, Foundation for Flying Star, and Natural Science Foundation of China (Contract No. 50820145202). The authors also gratefully acknowledge Drs. Zhang J, Ma JQ, Nie JJ and Wang YQ for their experimental data and helpful discussion. REFERENCES [1] Halbig MC, Brewer DN, Eckel AJ. Degradation of continuous fiber CMCs under constant load conditions. NASA/TM- 209681, January 2000, p. 1–5. [2] Sullivan RM. A model for the oxidation of carbon silicon carbide composite structures. Carbon 2005;43:275–85. [3] Evans AG, Domergue JM, Vagaggini E. Methodology for relating the tensile constitutive behavior of CMCs to constituent properties. J Am Ceram Soc 1994;77:1425–35. [4] Domergue JM, Vagaggini E, Evans AG. Relationships between hysteresis measurements and the consitutent properties of CMCs. Part II: Experimental studies on unidirectional materials. J Am Ceram Soc 1995;78(10):2721–31. [5] Vagaggini E, Domergue JM, Evans AG. Relationships between hysteresis measurements and the consitutent properties of CMCs. Part I: Theory. J Am Ceram Soc 1995;78(10):2709–20. [6] Wang M, Laird C. Characterization of microstructure and tensile behavior of a cross-woven C/SiC composite. Acta Mater 1996;44(4):1371–87. [7] Camus G, Guillaumat L, Baste S. Development of damage in a 2D woven C/SiC composite under mechanical loading. Part I: Mechanical characterization. Compos Sci Technol 1996;56:1363–72. [8] Steen M. Tensile mastercurve of CMCs: significance and implications for modeling. Mater Sci Eng 1998;A250:241–8. [9] Bobet JL, Naslain R, Guette A, Ji N, Lebrun JL. Thermal residual stresses in CMCs. Part II: Experimental results for model materials. Acta Metall Mater 1995;43(6):2255–68. [10] Nie JJ, Xu YD, Zhang LT, Cheng LF, Ma JQ. Microstructure and tensile behavior of multiply needled C/SiC composite fabricated by chemical vapor infiltration. J Mater Process Technol 2009;209(1):576–92. [11] Mei H, Cheng LF, Zhang LT, Luan XG, Zhang J. Behavior of two￾dimensional C/SiC composites subjected to thermal cycling in controlled environments. Carbon 2006;44:121–7. [12] Ma JQ, Xu YD, Zhang LT, Cheng LF, Nie JJ, Dong N. Microstructure characterization and tensile behavior of 2.5D C/SiC composites fabricated by chemical vapor infiltration. Scr Mater 2006;54:1967–71. [13] Mei H, Cheng LF, Zhang LT, Xu YD. Effect of fiber architectures on thermal cycling damage of C/SiC composites in oxidizing atmosphere. Mater Sci Eng 2007;A460–461:306–13. CARBON 47 (2009) 1034 – 1042 1041