《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_perform effect

CARBON47(2009)Io34-1042 availableatwww.sciencedirect.com .. Science Direct ELSEVIER ournalhomepagewww.elsevier.com/locate/carbon Comparison of the mechanical hysteresis of carbon/ceramic- matrix composites with different fiber preforms Hui Mei, Aifei Cheng National Key Laboratory of Thermostructure Composite Materials, School of Materials Science, Northwestem Polytechnical University, Xi'an Shaanxi 710072. PR China ARTICLEINF O ABSTRACT Article history The mechanical hysteresis of four ceramic matrix composites with different carbon fiber preforms, i.e. needled C/SiC, 2D C/SiC, 2.5D C/SiC, and 3D C/SiC, was investigated and com Accepted 8 December 2008 pared during cyclic reloading-unloading tests. An effective coefficient of the fiber volume le online 16 December 2008 fraction in the direction of loading(ECFl) was defined to characterize fiber architectures of the preforms. It is shown that an increase in permanent strain and a decrease in stiff ness with the applied stress were strongly affected by the ECFl The thermal residual stress (TRS) and ultimate tensile strength of the composites are predicted theoretically related to the ECFL, and then validated by experimental results and microstructural observations. he predicted results not only demonstrate good agreement with experimental measure- ments, but also explain why differences in the composite ECFL result in substantial varia- tions in TRS @2008 Elsevier Ltd. All rights reserved. ntroduction lowever, the mechanical hysteresis behaviors and perma nent strain of the above four representative composites were Carbon fiber reinforced silicon carbide matrix composite not yet obtained systematically and compared comprehen (C/Sic) is a type of ceramic matrix composite(CMC)that is sively related to the different fiber architectures. This is very rrently undergoing considerable investigation for applica- important issue to justify proper selections of the fiber pre tion in a wide range of aerospace applications (1, 2 The form architectures for a specified component and to optimize potential components of C/Sic mainly include thermal pro- thermo-mechanical structures for a specified engineering tection system(TPS)and hot structures such as shuttle nose, application case. For example, what fiber architecture in the wing leading edges, rocket thrusters, nozzle extensions, and composite is the best choice to fabricate a shuttle's nose aeroengine convergent/divergent flaps. All the parts are made and what fiber architecture can best withstand air dynamic of several typical fiber preform architectures: needled C/Sic, and thermal flux impact produced in this local place of the 2D C/SiC. 2. 5D C/SiC, and 3D C/Sic. overall surfaces During the last decade, theoretical methodology and In this study, the mechanical hysteresis and the experimental validity for assessing the stress-strain hyster- nent strain of several representative composites with diff sis and the permanent strain of the CMCs during unload/re- ent fiber architectures, i.e. the needled C/sic, 2D C/Sic, 2.5D load tests have been basically and widely reported [3-5], as C/SiC, and 3D C/Sic, during unload/reload cycles were com well as their significant monotonic tensile behaviors 16,7 pletely investigated and then compared systematically. and thermal residual stress(TRS)analysis due to extensive Changes in the hysteresis properties and permanent strain mismatch in coefficients of thermal expansion(CTE)[8, 9]. with increase of the applied stress were discussed with regard Corresponding author: Fax: +86 29 88494620. mailaddress:phdhuimei@yahoo.com(H.Mei) 0008-6223/$- see front matter o 2008 Elsevier Ltd. All rights reserved. do:10.1016/ j carbon200812025

Comparison of the mechanical hysteresis of carbon/ceramic￾matrix composites with different fiber preforms Hui Mei* , Laifei Cheng National Key Laboratory of Thermostructure Composite Materials, School of Materials Science, Northwestern Polytechnical University, Xi’an Shaanxi 710072, PR China ARTICLE INFO Article history: Received 18 April 2008 Accepted 8 December 2008 Available online 16 December 2008 ABSTRACT The mechanical hysteresis of four ceramic matrix composites with different carbon fiber preforms, i.e. needled C/SiC, 2D C/SiC, 2.5D C/SiC, and 3D C/SiC, was investigated and com￾pared during cyclic reloading–unloading tests. An effective coefficient of the fiber volume fraction in the direction of loading (ECFL) was defined to characterize fiber architectures of the preforms. It is shown that an increase in permanent strain and a decrease in stiff￾ness with the applied stress were strongly affected by the ECFL. The thermal residual stress (TRS) and ultimate tensile strength of the composites are predicted theoretically related to the ECFL, and then validated by experimental results and microstructural observations. The predicted results not only demonstrate good agreement with experimental measure￾ments, but also explain why differences in the composite ECFL result in substantial varia￾tions in TRS. 2008 Elsevier Ltd. All rights reserved. 1. Introduction Carbon fiber reinforced silicon carbide matrix composite (C/SiC) is a type of ceramic matrix composite (CMC) that is currently undergoing considerable investigation for applica￾tion in a wide range of aerospace applications [1,2]. The potential components of C/SiC mainly include thermal pro￾tection system (TPS) and hot structures such as shuttle nose, wing leading edges, rocket thrusters, nozzle extensions, and aeroengine convergent/divergent flaps. All the parts are made of several typical fiber preform architectures: needled C/SiC, 2D C/SiC, 2.5D C/SiC, and 3D C/SiC. During the last decade, theoretical methodology and experimental validity for assessing the stress–strain hystere￾sis and the permanent strain of the CMCs during unload/re￾load tests have been basically and widely reported [3–5], as well as their significant monotonic tensile behaviors [6,7] and thermal residual stress (TRS) analysis due to extensive mismatch in coefficients of thermal expansion (CTE) [8,9]. However, the mechanical hysteresis behaviors and perma￾nent strain of the above four representative composites were not yet obtained systematically and compared comprehen￾sively related to the different fiber architectures. This is very important issue to justify proper selections of the fiber pre￾form architectures for a specified component and to optimize thermo-mechanical structures for a specified engineering application case. For example, what fiber architecture in the composite is the best choice to fabricate a shuttle’s nose and what fiber architecture can best withstand air dynamic and thermal flux impact produced in this local place of the overall surfaces. In this study, the mechanical hysteresis and the perma￾nent strain of several representative composites with differ￾ent fiber architectures, i.e. the needled C/SiC, 2D C/SiC, 2.5D C/SiC, and 3D C/SiC, during unload/reload cycles were com￾pletely investigated and then compared systematically. Changes in the hysteresis properties and permanent strain with increase of the applied stress were discussed with regard 0008-6223/$ - see front matter 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2008.12.025 * Corresponding author: Fax: +86 29 88494620. E-mail address: phdhuimei@yahoo.com (H. Mei). CARBON 47 (2009) 1034 – 1042 available at www.sc iencedirect.com journal homepage: www.elsevier.com/locate/carbon

CARBON 47(2009)I034-I04 1035 to different fiber architectures. The axial TRS in the direction composites were laminated with [0/90 carbon fiber-cloth of loading and ultimate tensile strength(UTS)of these com- layers [11]. Fig. 1c illustrates that in the 2. 5D C/Sic the warp posites with different fiber architectures were predicted theo- yams take on an approximately sinusoidal path, and the weft retically and then validated by the experimentally measured yams present cross-sectional shapes of lentils and parallelo results and microstructural observations grams alternately. Obviously, the warp yams undertake dual roles: main contribution to in-plane strength and particular Experimental procedures contnbuti on to improve delamination resistance[12 Fig. 1d shows that in the 3d C/Sic all the carbon fibers are braided 2.1 Materials along the load direction with a small angle of 0 z 22[131 The fiber volume fraction of each preform approximated to There were four types of C/Sic composites involved in this 40 vol. for the woven composites and 32% for the needled dy, i.e., needled C/SiC, 2D C/SiC, 2.5D C/SiC, and 3D C/Sic. composites. The density and porosity of the infiltrated com- These composites were processed by using the same isother- posites are listed in Table 1 mal chemical vapor infiltration(cvD)of Sic into the different carbon fiber preforms at x1000C. The detailed processing 2. 2. Mechanical tests procedures of the four C/Sic composites have been described ts 3D views of Periodic loading-unloading-reloading tests were con rchitecture of the as-fabricated Sic-matrix composites with ducted at room temperature on a servo-hydraulic load-frame different carbon fiber preforms. The needled C/SiC materials, with a loading rate of 0.06 mm/min(Instron 8801, Instron Ltd as shown in Fig. 1a, composed of the layers of o non-woven High Wycombe, England). Strain was assessed directly by a Dee cloth, short fiber web, 90 non-woven fiber cloth, and contact Instron extensometer with a gauge length of 25 mm. needled fibers. The layers of o non-woven fiber cloth, short The data generated from each hysteresis cycle is stored on fiber web, and 90 non-woven fiber cloth were repeatedly hard-disc of a personal computer and then analyzed in accor- erlapped [10]. In this kind of structure, non-woven cloth dance with the loading-unloading procedures. The cyclic parallel to the loading direction to improve the load-bearing unloading-reloading tests were performed up to final rupture capacity of the materials. Fig. 1b shows that the 2D C/Sic of the composite specimens with emphasis on the achieve 15a25m×0MA Fig. 1-Three-dimensional presentations of fiber architectures in(a)needled C/Sic, (b)2D C/Sic, (c)2.5D C/sic, and (d)3D C/sic

to different fiber architectures. The axial TRS in the direction of loading and ultimate tensile strength (UTS) of these com￾posites with different fiber architectures were predicted theo￾retically and then validated by the experimentally measured results and microstructural observations. 2. Experimental procedures 2.1. Materials There were four types of C/SiC composites involved in this study, i.e., needled C/SiC, 2D C/SiC, 2.5D C/SiC, and 3D C/SiC. These composites were processed by using the same isother￾mal chemical vapor infiltration (CVI) of SiC into the different carbon fiber preforms at 1000 C. The detailed processing procedures of the four C/SiC composites have been described elsewhere [10–13]. Fig. 1 presents 3D views of typical fiber architectures of the as-fabricated SiC-matrix composites with different carbon fiber preforms. The needled C/SiC materials, as shown in Fig. 1a, composed of the layers of 0 non-woven fiber cloth, short fiber web, 90 non-woven fiber cloth, and needled fibers. The layers of 0 non-woven fiber cloth, short fiber web, and 90 non-woven fiber cloth were repeatedly overlapped [10]. In this kind of structure, non-woven cloth parallel to the loading direction to improve the load-bearing capacity of the materials. Fig. 1b shows that the 2D C/SiC composites were laminated with [0/90] carbon fiber-cloth layers [11]. Fig. 1c illustrates that in the 2.5D C/SiC the warp yarns take on an approximately sinusoidal path, and the weft yarns present cross-sectional shapes of lentils and parallelo￾grams alternately. Obviously, the warp yarns undertake dual roles: main contribution to in-plane strength and particular contribution to improve delamination resistance [12]. Fig. 1d shows that in the 3D C/SiC all the carbon fibers are braided along the load direction with a small angle of h 22 [13]. The fiber volume fraction of each preform approximated to 40 vol.% for the woven composites and 32% for the needled composites. The density and porosity of the infiltrated com￾posites are listed in Table 1. 2.2. Mechanical tests Periodic loading–unloading–reloading tests were con￾ducted at room temperature on a servo-hydraulic load-frame with a loading rate of 0.06 mm/min (Instron 8801, Instron Ltd., High Wycombe, England). Strain was assessed directly by a contact Instron extensometer with a gauge length of 25 mm. The data generated from each hysteresis cycle is stored on hard-disc of a personal computer and then analyzed in accor￾dance with the loading–unloading procedures. The cyclic unloading–reloading tests were performed up to final rupture of the composite specimens with emphasis on the achieve￾Fig. 1 – Three-dimensional presentations of fiber architectures in (a) needled C/SiC, (b) 2D C/SiC, (c) 2.5D C/SiC, and (d) 3D C/SiC composite specimens. CARBON 47 (2009) 1034 – 1042 1035

1036 CARBON47(2009)Io34-1042 Table 1-Comparisons of the thermo-mechanical properties of the composites with different fiber architectures Parameters Needled C/Sic 2D C/SIC 2.5D C/SIC 3D C/Sic Density p(g/cm2) Matrix volume fraction Vm (%) ECFL A 0.375 Porosity p(% 13 UTS Gu(MPa) Predicted Measured TRS Gr(MPa) Predicted Measured 91 Relief ratio (% 15 a See 10 b See(11 c See[12 d See[13] ments of several typical hysteresis loop evolutions. During For the 2. 5D C/Sic, ratio of the warp yarn density(load the tests, the loading directions were along with 0 non-wo- direction) to weft yarn density is 3: 1, and means ven cloth for the needled C/Sic, 0 fber ply for the 2D C/SiC, 5D=3=075 rarp yam for the 2. SD C/SiC, and axial fibers at a small angle. For 3D C/SiC, the longitudinal fibers are laid along the ten 0 for the 3D C/Sic (see Fig. 1). In order to characterize the fber sile axis at a small angle of 22, and thus i3D=cos architectures an effective coefficient of the fiber volume frac- 220=0.93. tion in the direction of loading(ECFL) could be defined as: Finally, morphologies of the specimens were observed (1) with a scanning electron microscope(SEM, Hitachi S-2700, Tokyo, Japan) where Ve and varial refer to the total fber volume fraction in the composites and the effective fiber volume fraction in 3. Results and discussion the direction of axial tensile loading. According to the fiber architectures as shown in Fig. 1 and woven parameters pro- 3. 1. Thermal cracks characterization ided by the preform suppliers, the values of ECFL for the nee- dled C/Sic, the 2D C/SiC, the 2.SD C/Sic, and the 3D C/Sic are Processing-induced microcracks are widely considered as the results of the significant TRS relief. And the more the thermal cracks formed. the more the trs relief normal to the cracks. For the needled C/SiC, the short-cut web accounts for 1/4 As typically shown in Fig. 2, C/Sic materials have a pre f perform, and thus nEedled=2(1-1/4)=0.375 cracked as-received condition due to the extensive thermal iC, only a half of the total fibers is parallel to expansion mismatch between fibers and matrix, resulting in the loading direction, and thus i2D=2=0.5 both matrix microcracks(Fig 2a)and partial debonding along the PyC interphase(Fig 2b). Two distinct categories of matrix Type I cracks Carbon fib Type I crack Carbon fiber Fig. 2-SEM micrographs showing the typical thermal misft microcracks existing in each individual fber and its surrounding Sic matrix unit of the as-received C/Sic composite

ments of several typical hysteresis loop evolutions. During the tests, the loading directions were along with 0 non-wo￾ven cloth for the needled C/SiC, 0 fiber ply for the 2D C/SiC, warp yarn for the 2.5D C/SiC, and axial fibers at a small angle h for the 3D C/SiC (see Fig. 1). In order to characterize the fiber architectures, an effective coefficient of the fiber volume frac￾tion in the direction of loading (ECFL) could be defined as: k ¼ Vaxial f Vf ; ð1Þ where Vf and V axial f refer to the total fiber volume fraction in the composites and the effective fiber volume fraction in the direction of axial tensile loading. According to the fiber architectures as shown in Fig. 1 and woven parameters pro￾vided by the preform suppliers, the values of ECFL for the nee￾dled C/SiC, the 2D C/SiC, the 2.5D C/SiC, and the 3D C/SiC are calculated as below: • For the needled C/SiC, the short-cut web accounts for 1/4 of perform, and thus kNeedled ¼ 1 2 ð1  1=4Þ ¼ 0:375. • For the 2D C/SiC, only a half of the total fibers is parallel to the loading direction, and thus k2D ¼ 1 2 ¼ 0:5. • For the 2.5D C/SiC, ratio of the warp yarn density (load direction) to weft yarn density is 3:1, and means k2:5D ¼ 3 1þ3 ¼ 0:75. • For 3D C/SiC, the longitudinal fibers are laid along the ten￾sile axis at a small angle of 22, and thus k3D = cos 22 = 0.93. Finally, morphologies of the specimens were observed with a scanning electron microscope (SEM, Hitachi S-2700, Tokyo, Japan). 3. Results and discussion 3.1. Thermal cracks characterization Processing-induced microcracks are widely considered as the results of the significant TRS relief. And the more the thermal cracks formed, the more the TRS relief normal to the cracks. As typically shown in Fig. 2, C/SiC materials have a pre￾cracked as-received condition due to the extensive thermal expansion mismatch between fibers and matrix, resulting in both matrix microcracks (Fig. 2a) and partial debonding along the PyC interphase (Fig. 2b). Two distinct categories of matrix Table 1 – Comparisons of the thermo-mechanical properties of the composites with different fiber architectures. Parameters Needled C/SiC 2D C/SiC 2.5D C/SiC 3D C/SiC Density q (g/cm3 ) 2.15 1.99 1.97 2.26 Fiber volume fraction Vf (%) 32 40 40 40 Matrix volume fraction Vm (%) 68 60 60 60 ECFL k 0.375 0.5 0.75 0.93 Porosity p (%) 14 13 13 13 UTS ru (MPa) Predicted 152 230 347 440 Measured 159a 248b 326c 413d TRS rr (MPa) Predicted 100 153 190 203 Measured 91 130 127 109 Relief ratio (%) 8 15 33 46 a See [10]. b See [11]. c See [12]. d See [13]. Fig. 2 – SEM micrographs showing the typical thermal misfit microcracks existing in each individual fiber and its surrounding SiC matrix unit of the as-received C/SiC composite. 1036 CARBON 47 (2009) 1034 – 1042

CARBON 47(2009)I034-I04 1037 Table 2-Constituent parameters and values of C/sic and is about 4. x 10-6/K for the isotropic Sic matrix. Wher composites thermal misfit generated in the C/Sic, both axial and radial residual tensile stress in brittle Sic matrix on the fibers easily Parameter led to these two families of matrix cracks. Below the processing matrix Em GPa temperature of 1000C, the type I cracks mainly occurred be- cTe of Sic matrix 10-6/K cause the sic matrix encountered the axial tensile residual Fracture strength of Sic matrix mu 58 stress resulted from its much greater shrinkage than the axial Youngs modulus of C fiber fiber (in this case, partial interficial debonding also initiated C Aber radius R 3.5 Room along fiber/matrix interfaces due to the greater shrinkage of mperature 1273 the radial fibers than the matrix upon cooling from the process CTE of C fber axial ing temperature). Above the processing temperature of 10(radial) 1000C, the type Il cracks tend to form because the Sic matrix a Coefficient of thermal encountered the loop tensile residual stress because it has much less expansion than the radial fiber. The type I cracks are now those cracks oriented perpendicular to the loading cracks: type I cracks perpendicular to fiber axis and type I direction(0 fibers). As a consequence some type II cracks be- cracks parallel to flber axis, are clearly indicated in Fig. 2a. come type I cracks when a load is applied parallel to fiber direc- As we know, the carbon fibers display a significant anisotropy tion. Many previous researchers also mainly observed the type in the axial and radial directions whereas the CVI-Sic matrix I cracks in the as-fabricated C/SiCs [14-17. Upon the extra is generally considered as isotropy. For the long and continu- mechanical loading, these type I thermal cracks transversely ous carbon fiber, as listed in Table 2, the radial cte is much grow and propagate leading to progressive increase inresidual larger than its surrounding matrix one whereas the axial strain of the composite [18] and continuous TRS relief in addi- CtE is much smaller than the matrix one. That is tion to the processing-induced thermal load damage 》 In the current study, therefore, we are type I cracks perpendicular to loading direction(parallel to fi- radal and f al were the CTE of the fibers in the radial and ax- ber axis) and their effect on the axial TRS evolution whereas ial direction, which were well known to be about 10- and the radial TRS relief (i.e, partial interficial debonding) will 0x10-/K, respectively. zm denotes the CTE of the CVI-matrix be neglected b240 200 80 20 0.00.10.20.3040.5060.7 Strain(%) Strain(%) 240 3D C/SiC 200 2. 5D C/SiC Strain(%) Strain(%) Fig 3- Typical reloading/unloading hysteresis loop evolutions of (a)needled C/Sic, (b)2D C/sic, (c)2.5D C/Sic, and (d 3D C/sic

cracks: type I cracks perpendicular to fiber axis and type II cracks parallel to fiber axis, are clearly indicated in Fig. 2a. As we know, the carbon fibers display a significant anisotropy in the axial and radial directions whereas the CVI-SiC matrix is generally considered as isotropy. For the long and continu￾ous carbon fiber, as listed in Table 2, the radial CTE is much larger than its surrounding matrix one whereas the axial CTE is much smaller than the matrix one. That is aradial f  am  aaxial f : ð2Þ aradial f and aaxial f were the CTE of the fibers in the radial and ax￾ial direction, which were well known to be about 10 · 106 and 0 · 106 /K, respectively. am denotes the CTE of the CVI-matrix and is about 4.6 · 106 /K for the isotropic SiC matrix. When thermal misfit generated in the C/SiC, both axial and radial residual tensile stress in brittle SiC matrix on the fibers easily led to these two families of matrix cracks. Below the processing temperature of 1000 C, the type I cracks mainly occurred be￾cause the SiC matrix encountered the axial tensile residual stress resulted from its much greater shrinkage than the axial fiber (in this case, partial interficial debonding also initiated along fiber/matrix interfaces due to the greater shrinkage of the radial fibers than thematrix upon cooling from the process￾ing temperature). Above the processing temperature of 1000 C, the type II cracks tend to form because the SiC matrix encountered the loop tensile residual stress because it has much less expansion than the radial fiber. The type I cracks are now those cracks oriented perpendicular to the loading direction (0 fibers). As a consequence some type II cracks be￾come type I cracks when a load is applied parallel to fiber direc￾tion. Many previous researchers also mainly observed the type I cracks in the as-fabricated C/SiCs [14–17]. Upon the extra mechanical loading, these type I thermal cracks transversely grow and propagate leading to progressive increase in residual strain of the composite [18] and continuous TRS relief in addi￾tion to the processing-induced thermal load damage. In the current study, therefore, we are concerned with the type I cracks perpendicular to loading direction (parallel to fi- ber axis) and their effect on the axial TRS evolution whereas the radial TRS relief (i.e., partial interficial debonding) will be neglected. Table 2 – Constituent parameters and values of C/SiC composites. Parameter Symbol Value Units Young’s modulus of SiC matrix Em 350 GPa CTEa of SiC matrix am 4.6 106 /K Fracture strength of SiC matrix rmu 58 MPa Young’s modulus of C fiber Ef 230 GPa C fiber radius R 3.5 lm Room temperature T0 298 K Processing temperature Tp 1273 K CTE of C fiber af 0 (axial) 10 (radial) 106 /K a Coefficient of thermal expansion. Fig. 3 – Typical reloading/unloading hysteresis loop evolutions of (a) needled C/SiC, (b) 2D C/SiC, (c) 2.5D C/SiC, and (d) 3D C/SiC composite specimens. CARBON 47 (2009) 1034 – 1042 1037

1038 CARBON47(2009)Io34-1042 3. 2. Mechanical hysteresis behavior analysi of 2D C/Sic by Mei[20]. Normally, if the matrix of the compos- ite is in residual compression, thermal-residual-stress-free Fig 3a-d summarized typical hysteresis loop evolutions of the origin lies in the positive stress-strain quadrant I(.g,Mor- iC, and 3D C/Sic composites scher[21 and if the matrix of the composite is in residual during the loading-unloading-reloading cycle tests. Gener- tension, "thermal-residual-stress-free"origin lies in the neg ally, in these figures the loading curve in each loop was ative stress-strain quadrant Ill(e. g, Camus et al. [7). In the mostly linear to the stress level of the preceding step and then present C/SiC composites, below the processing temperature became nonlinear, following the envelope which is basically of 1000C the Sic matrix is in residual tensile stress whereas alike with the monotonic tensile stress-strain curve of them- the longitudinal carbon fibers are in residual compressive stress since the Sic matrix usually has a greater CTE than Specifically, as illustrated in Fig 4, in each single hysteresis the longitudinal carbon fibers(see Table 2, i.e., apal Ox loop the loading curve is also alike with the monotonic tensile 10-and m 4. x 10-/K). Consequently, all the intersections urve of the composite containing cracks: a small elastic for indication of the axial residual stress states in the needled deformation occurs upon initial loading, followed by a transi- C/SiC, 2D C/SiC, 2. 5D C/SiC, and 3D C/SiC composites should tory nonlinear behavior with partial irreversible sliding and fi- localize in the negative stress-strain quadrant Il. The above ally the slip zone stops at the debond tip accompanied by theoretical analysis applies to these experimental curves in establishment of a large linear stress-strain relationship of Fig 3a-d, it can be found that the Sic matrices in four C/SiCs approaches. More importantly, below the stress level of the lie in the negative stress-strain quadrant l, Origins indeed the whole composite system until the preceding stress level are actual in residual tension and the axial TRS origins indeed preceding loop, almost no new crack initiation and previous In Fig. 4, the inelastic strain, ai, and elastic strain, fe, repre- crack propagation were expected in the cracked composites sent the irreversible and reversible strain after unloading except for re-opening of the existed cracks. As described else- The total strain e" at each peak applied stress p gives where [191, this process led to apparent linear stress-strain c=e+l relationship of the C/Sic composites and few acoustic emis sion(AE) activity. However, once the previous history stress where the inelastic strain a(also called permanent strain in level was reached, new damage with high-rate AE activities many other literatures [4, )upon each reloading includes a was unavoidable in the form of more crack multiplication, small sliding strain, 's, and a large thermal misfit relief strain, longer interface debonding and larger fiber fracture er. The thermal misfit relief strain er depends upon the SSM, As also shown in Fig. 4, the top portion of each loading Ep, of each hysteresis loop and can be written as curve exhibits apparent linearity and thus a final steady se- c=C cant modulus(SSM, Ep) can be obtained from the linear fitting of this linear portion. In this case, thermal misfit relief strain Additionally, the influence of the applied load on damage be determined directly from the abscissa coordinates of to the composites can be depicted through a damage factor, the intersection point of the compliance slopes(Ep) with X- Dr, as the classical formulas axis. Furthermore, the axial TRS (parallel to load direction is derived from the Y-coordinate of that common intersection Dr=1 point o'(en a)by extrapolations of those regression lines of several reloading-unloading loops. This intersection point o' where Eo is the initial elastic modulus before initial loading has been termed"thermal-residual-stress-free"origin by Ca- Fig 5 selectively presents changes in and comparisons of mus et al. [7 l, and measured successfully for a specified case the permanent strain, total strain and damage factor of the four C/Sic composites as a function of the peak applied stress. Obviously, as the peak applied stress increased the stiffness of the composites diminished whereas the perma nent strain increased as well as the total strain periodic load ing/unloading cycles could introduce damage into the CMCs in the major form of the transverse crack propagations, which exhibited a progressive decrease of the material's modulus and increase of the damage factor, De along with an extension of inelastic permanent strain. Comparatively, Fig. Sa and b give orders of the permanent strain rate and total strain rate from high to low as: the needled C/SiC, 2D C/SiC, 2.5D C/SiC, and 3D C/Sic composites. These orders are just contrary the above fiber perform parameter ECFL i, which are about 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. It is implied that in crease in the permanent strain and decrease in the stiffness Strain of the composites were strongly affected by the effective flber Fig. 4- Schematic of hysteresis loop with elastic strain and volume fraction parallel to tensile axis. The greater the ECFL inelastic strain in a C/SiC material system during the was. the slower the inelastic residual strain increase reloading-unloading cycles (Fig 5a) and the less the damage resulted from the loading/

3.2. Mechanical hysteresis behavior analysis Fig. 3a–d summarized typical hysteresis loop evolutions of the needled C/SiC, 2D C/SiC, 2.5D C/SiC, and 3D C/SiC composites during the loading–unloading–reloading cycle tests. Gener￾ally, in these figures the loading curve in each loop was mostly linear to the stress level of the preceding step and then became nonlinear, following the envelope which is basically alike with the monotonic tensile stress–strain curve of them￾selves reported earlier in [10–13]. Specifically, as illustrated in Fig. 4, in each single hysteresis loop the loading curve is also alike with the monotonic tensile curve of the composite containing cracks: a small elastic deformation occurs upon initial loading, followed by a transi￾tory nonlinear behavior with partial irreversible sliding and fi- nally the slip zone stops at the debond tip accompanied by establishment of a large linear stress–strain relationship of the whole composite system until the preceding stress level approaches. More importantly, below the stress level of the preceding loop, almost no new crack initiation and previous crack propagation were expected in the cracked composites except for re-opening of the existed cracks. As described else￾where [19], this process led to apparent linear stress–strain relationship of the C/SiC composites and few acoustic emis￾sion (AE) activity. However, once the previous history stress level was reached, new damage with high-rate AE activities was unavoidable in the form of more crack multiplication, longer interface debonding and larger fiber fracture. As also shown in Fig. 4, the top portion of each loading curve exhibits apparent linearity and thus a final steady se￾cant modulus (SSM, Ep) can be obtained from the linear fitting of this linear portion. In this case, thermal misfit relief strain eT can be determined directly from the abscissa coordinates of the intersection point of the compliance slopes (Ep) with X￾axis. Furthermore, the axial TRS (parallel to load direction) is derived from the Y-coordinate of that common intersection point O0 (er, rr) by extrapolations of those regression lines of several reloading–unloading loops. This intersection point O0 has been termed ‘‘thermal-residual-stress-free’’ origin by Ca￾mus et al. [7], and measured successfully for a specified case of 2D C/SiC by Mei [20]. Normally, if the matrix of the compos￾ite is in residual compression, ‘‘thermal-residual-stress-free’’ origin lies in the positive stress–strain quadrant I (e.g., Mor￾scher [21]); and if the matrix of the composite is in residual tension, ‘‘thermal-residual-stress-free’’ origin lies in the neg￾ative stress–strain quadrant III (e.g., Camus et al. [7]). In the present C/SiC composites, below the processing temperature of 1000 C the SiC matrix is in residual tensile stress whereas the longitudinal carbon fibers are in residual compressive stress since the SiC matrix usually has a greater CTE than the longitudinal carbon fibers (see Table 2, i.e., aaxial f 0 106 and am 4:6  106 /K). Consequently, all the intersections for indication of the axial residual stress states in the needled C/SiC, 2D C/SiC, 2.5D C/SiC, and 3D C/SiC composites should localize in the negative stress–strain quadrant III. The above theoretical analysis applies to these experimental curves in Fig. 3a–d, it can be found that the SiC matrices in four C/SiCs are actual in residual tension and the axial TRS origins indeed lie in the negative stress–strain quadrant III. In Fig. 4, the inelastic strain, ei, and elastic strain, ee, repre￾sent the irreversible and reversible strain after unloading. The total strain e* at each peak applied stress rp gives e  ¼ ei þ ee; ð3Þ where the inelastic strain ei (also called permanent strain in many other literatures [4,5]) upon each reloading includes a small sliding strain, es, and a large thermal misfit relief strain, eT. The thermal misfit relief strain eT depends upon the SSM, Ep, of each hysteresis loop and can be written as eT ¼ e   rp Ep : ð4Þ Additionally, the influence of the applied load on damage to the composites can be depicted through a damage factor, DE, as the classical formulas DE ¼ 1  Ep E0 ; ð5Þ where E0 is the initial elastic modulus before initial loading. Fig. 5 selectively presents changes in and comparisons of the permanent strain, total strain and damage factor of the four C/SiC composites as a function of the peak applied stress. Obviously, as the peak applied stress increased the stiffness of the composites diminished whereas the perma￾nent strain increased as well as the total strain. Periodic load￾ing/unloading cycles could introduce damage into the CMCs in the major form of the transverse crack propagations, which exhibited a progressive decrease of the material’s modulus and increase of the damage factor, DE along with an extension of inelastic permanent strain. Comparatively, Fig. 5a and b give orders of the permanent strain rate and total strain rate from high to low as: the needled C/SiC, 2D C/SiC, 2.5D C/SiC, and 3D C/SiC composites. These orders are just contrary to the above fiber perform parameter ECFL k, which are about 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. It is implied that in￾crease in the permanent strain and decrease in the stiffness of the composites were strongly affected by the effective fiber volume fraction parallel to tensile axis. The greater the ECFL was, the slower the inelastic residual strain increased (Fig. 5a) and the less the damage resulted from the loading/ Fig. 4 – Schematic of hysteresis loop with elastic strain and inelastic strain in a C/SiC material system during the reloading–unloading cycles. 1038 CARBON 47 (2009) 1034 – 1042

CARBON 47(2009)I034-I04 1039 between microcrack lips slightly removed from their initial 0 dled C/SIc 0.25 In contrast to the 2D, 2.SD and 3D C/Sic composite, the needled C/Sic exhibits the most extensive hysteresis loop 0.20 主 width in the last cycle and the largest inelastic residual strain accounting for considerable interficial sliding and crack clo sure impediment. On the one hand, only about 37.5% fibers in the needled C/Sic were arranged in the tensile load direc- tion. The few load-bearing fibers easily led to multiple matrix cracking transversely and extensive interfacial debonding upon loading. Also, due to too few reinforcing fibers in the load direction the applied stress induced damage strain (i.e 0 40 80 120 160 200 240 280 320 matrix cracking and interfacial debonding) became very diffi Peak applied stress(MPa) cult to recover upon unloading, resulting in rapid increase in residual strain and accumulation in damage. On the other hand, disorder of the large fibers in the other directions Needled C/Sic (non-load direction) enhanced the crack closure impediment 0.6 3D C/SiC manent strain and the damage accumulation of the needled C/Sic eventually resulted in the earlier fracture and lower 04 strength(Fig. Sa). Comparatively, equivalent 93% load-bearing fibers in the 3D C/Sic were regularly arranged along the load direction, which was very advantageous in recovery of the amage strain leading to much more elastic strain and less inelastic residual strain present in the composites after unloading. Consequently, it can be concluded from Fig. 5 that, 00 the more the effective load-bearing fibers parallel to tensile 04080120160200240280320 axis, the greater the ECFL, the slower the increase of inelastic Peak applied stress(MPa) residual strain and the smaller the damage factor associated with stiffness of the composites eedled C/SiC 3. 3. Axial TRS ●2Dc/siC A-2.5D C/SIC ←30csC According to the calculation methods reported in [20 0.5 through solving the Y-coordinates of the common interse on point of the regr lines of the reloading-l loops, the axial TRS could be measured out and then listed in Table 1. the measured TRs are: 91 MPa for the needled c Sic, 130 MPa for the 2D C/Sic, 127 MPa for the 2.5D C/Sic and 109 MPa for 3D C/SiC composites. The detailed calcula 00 tion procedure has been described in [20] for a specified case of 2D C/Sic material. It must be noted that the measured val 4080120160200240280320 ues herein were actual TRS present in these four composi plied stress(MPa) after partial relief of the maximum thermal misfit stress dur- Fig. 5-Comparison in key mechanical parameters of the ing the cooling from the processing temperature down to ture. Consider a composite with perfe ect inter. composites as a function of the peak applied stress: (a) face bond and non- cracked matrix, theoretical maximum val permanent strain,(b)total strain and (c)damage factor. ues of the axial TRS in matrix can be classically estimated as: zEvI+Em Vn (x-xm)(T。-Tp) unloading cycles(Fig. Sc) because the same level of load were where m and zf refer to the linear CTE of the matrix and fiber uniformly shared by the more reinforcing filbers. It is widely respectively. Tp and To are the processing temperature and accepted [7 that the increase of inelastic residual strain in operation temperature. vm and vi are the volume fraction of C/SiCs may be attributed to the interaction of several phe- the matrix and fiber. Em and Er are the Young moduli nomena: @)the release of axial residual stresses during the the matrix and fibers. It must be mentioned that Eq(6)is va- loading/unloading cycles; (n) partial irreversible sliding aris- lid along fiber direction only and thus the volume fraction of ing from the various energy dissipative frictional mecha- the fibers in this formulas was normalized by ECFl i.Note closure possibly related to fiber roughness and/or the contact assumed as the fully dense matrix modulus because of the

unloading cycles (Fig. 5c) because the same level of load were uniformly shared by the more reinforcing fibers. It is widely accepted [7] that the increase of inelastic residual strain in C/SiCs may be attributed to the interaction of several phe￾nomena: (i) the release of axial residual stresses during the loading/unloading cycles; (ii) partial irreversible sliding aris￾ing from the various energy dissipative frictional mecha￾nisms; and (iii) a mechanical impediment of complete crack closure possibly related to fiber roughness and/or the contact between microcrack lips slightly removed from their initial positions. In contrast to the 2D, 2.5D and 3D C/SiC composite, the needled C/SiC exhibits the most extensive hysteresis loop width in the last cycle and the largest inelastic residual strain accounting for considerable interficial sliding and crack clo￾sure impediment. On the one hand, only about 37.5% fibers in the needled C/SiC were arranged in the tensile load direc￾tion. The few load-bearing fibers easily led to multiple matrix cracking transversely and extensive interfacial debonding upon loading. Also, due to too few reinforcing fibers in the load direction the applied stress induced damage strain (i.e., matrix cracking and interfacial debonding) became very diffi- cult to recover upon unloading, resulting in rapid increase in residual strain and accumulation in damage. On the other hand, disorder of the large fibers in the other directions (non-load direction) enhanced the crack closure impediment after unloading. As a consequence, rapid increase in the per￾manent strain and the damage accumulation of the needled C/SiC eventually resulted in the earlier fracture and lower strength (Fig. 5a). Comparatively, equivalent 93% load-bearing fibers in the 3D C/SiC were regularly arranged along the load direction, which was very advantageous in recovery of the damage strain leading to much more elastic strain and less inelastic residual strain present in the composites after unloading. Consequently, it can be concluded from Fig. 5 that, the more the effective load-bearing fibers parallel to tensile axis, the greater the ECFL, the slower the increase of inelastic residual strain and the smaller the damage factor associated with stiffness of the composites. 3.3. Axial TRS comparison According to the calculation methods reported in [20], through solving the Y-coordinates of the common intersec￾tion point of the regression lines of the reloading–unloading loops, the axial TRS could be measured out and then listed in Table 1. the measured TRS are: 91 MPa for the needled C/ SiC, 130 MPa for the 2D C/SiC, 127 MPa for the 2.5D C/SiC, and 109 MPa for 3D C/SiC composites. The detailed calcula￾tion procedure has been described in [20] for a specified case of 2D C/SiC material. It must be noted that the measured val￾ues herein were actual TRS present in these four composites after partial relief of the maximum thermal misfit stress dur￾ing the cooling from the processing temperature down to room temperature. Consider a composite with perfect inter￾face bond and non-cracked matrix, theoretical maximum val￾ues of the axial TRS in matrix can be classically estimated as: rm r ¼ E m kEfVf kEfVf þ EmVm ðaf  amÞðTo  TpÞ; ð6Þ where am and af refer to the linear CTE of the matrix and fiber, respectively. Tp and To are the processing temperature and operation temperature. Vm and Vf are the volume fraction of the matrix and fiber. Em and Ef are the Young moduli of the matrix and fibers. It must be mentioned that Eq. (6) is va￾lid along fiber direction only and thus the volume fraction of the fibers in this formulas was normalized by ECFL k. Note that the effective matrix modulus E m here can not be assumed as the fully dense matrix modulus because of the Fig. 5 – Comparison in key mechanical parameters of the needled C/SiC, 2D C/SiC, 2.5D C/SiC, and 3D C/SiC composites as a function of the peak applied stress: (a) permanent strain, (b) total strain and (c) damage factor. CARBON 47 (2009) 1034 – 1042 1039

1040 CARBON47(2009)Io34-1042 considerable porosity, which is distributed heterogeneously indicated that the more the fibers arranged in the same direc- throughout the matrix. Hence, the effective modulus of ma- tion, the less the constraint between the highly-ordered fibers trix can be depicted as [22] and the easier the tRS relief in the composites during cooling During cooling from the processing temperature, as de- E (7) scribed earlier in Section 3. 1, the C/SiCs mainly generated where Em is the fully dense matrix modulus, 0 is the relative matrix microcracks perpendicular to the axial fibers and the microcracks propagated transversely inside the brittle matrix across the entire width of flber spacing. It is obvious that (8) highly-ordered fiber arrangements oriented in the same direction are more advantageous in releasing thermal misf here p is the porosity. Using the data in Table 1 and the con- stress in the absence of transverse fiber constraint by produc stituent properties in Table 2, theoretically predicted results ing the more transverse cracks and thus allow the less TRS of the axial residual stress in the composite matrix were ob- left in the composites. Hence, the more the fibers arranged tained and then listed in Table 1. It can be seen from the ob- in the same direction, the less the constraint between the tained TRS that the experimentally measured values highly-ordered fibers, the more the relief of thermal misfit always lower than the theoretically predicted results because stress between fibers and matrix in the major form of matrix of the partial TRS relief in the major form of the thermal cracks cracking during cooling. This explained why high ECFL of the during cooling from processing temperature. The difference composites can receive high TRS relief ratio during cooling between experimental measurement and theoretical predic- Namely, tRS relief ratios are 46% for 3D C/Sic when 2=0.93, tion directly reflects the TRS relief extent in the C/Sic compos- 33% for the 2. 5D C/Sic when 1=0.75, 15% for the 2D C/Sic ites once cooled down to room temperature, which is believed when i=0.5, and 8% for the needled C/Sic when 2=0.375 to be strongly related to the ECFl of the composite preforms. Micrographs in Fig. 6 show that numbers of the matrix The TRS relief ratio during cooling may be defined as cracks in the as-fabricated composites from few to many give the following orders: the needled C/SiC, 2D C/SiC, 2.5D C/Sic. 100% (9) and 3D C/Sic composites. According to Fig. 1, almost 75% and 93% fibers in the 2.5D and 3D C/SiC composites were equiva As shown in Table 1, the TRS relief ratios of the four compos- lently arranged along the tensile axis, which allowed multiple ites during cooling are found to increase with increasing matrix cracking to release the tRS relatively easier(Fig. 6c and ECFL. Orders of the TRS relief ratios of four composites from d )due to the less transverse fiber constraints. Contrastively, low to high are: 8% for the needled C/SiC, 15% for the 2D C/Sic, the matrix cracks could be hardly found in the needled and 33% for the 2.SD C/SiC, and 46% for 3D C/SiC composites. It 2D C/Sic composites(Fig 6a and b), indicating that the stror 200um c 200um 200um Fig 6- Micrographs showing the as-fabricated CVI-Sic matrix crack conditions in(a) needled C/Sic, b 2D C/Sic,(c)2.5D C Sic, and d)3D C/SiC composites

considerable porosity, which is distributed heterogeneously throughout the matrix. Hence, the effective modulus of ma￾trix can be depicted as [22] E m ¼ Em 1  h 1 þ 2:5h ; ð7Þ where Em is the fully dense matrix modulus, h is the relative porosity and gives h ¼ p 1  kVf  p ; ð8Þ where p is the porosity. Using the data in Table 1 and the con￾stituent properties in Table 2, theoretically predicted results of the axial residual stress in the composite matrix were ob￾tained and then listed in Table 1. It can be seen from the ob￾tained TRS that the experimentally measured values are always lower than the theoretically predicted results because of the partial TRS relief in the major form of the thermal cracks during cooling from processing temperature. The difference between experimental measurement and theoretical predic￾tion directly reflects the TRS relief extent in the C/SiC compos￾ites once cooled down to room temperature, which is believed to be strongly related to the ECFL of the composite preforms. The TRS relief ratio during cooling may be defined as b ¼ rpredicted r  rmeasured r rpredicted r  100%: ð9Þ As shown in Table 1, the TRS relief ratios of the four compos￾ites during cooling are found to increase with increasing ECFL. Orders of the TRS relief ratios of four composites from low to high are: 8% for the needled C/SiC, 15% for the 2D C/SiC, 33% for the 2.5D C/SiC, and 46% for 3D C/SiC composites. It indicated that the more the fibers arranged in the same direc￾tion, the less the constraint between the highly-ordered fibers and the easier the TRS relief in the composites during cooling. During cooling from the processing temperature, as de￾scribed earlier in Section 3.1, the C/SiCs mainly generated matrix microcracks perpendicular to the axial fibers and the microcracks propagated transversely inside the brittle matrix across the entire width of fiber spacing. It is obvious that highly-ordered fiber arrangements oriented in the same direction are more advantageous in releasing thermal misfit stress in the absence of transverse fiber constraint by produc￾ing the more transverse cracks and thus allow the less TRS left in the composites. Hence, the more the fibers arranged in the same direction, the less the constraint between the highly-ordered fibers, the more the relief of thermal misfit stress between fibers and matrix in the major form of matrix cracking during cooling. This explained why high ECFL of the composites can receive high TRS relief ratio during cooling. Namely, TRS relief ratios are 46% for 3D C/SiC when k = 0.93, 33% for the 2.5D C/SiC when k = 0.75, 15% for the 2D C/SiC when k = 0.5, and 8% for the needled C/SiC when k = 0.375. Micrographs in Fig. 6 show that numbers of the matrix cracks in the as-fabricated composites from few to many give the following orders: the needled C/SiC, 2D C/SiC, 2.5D C/SiC, and 3D C/SiC composites. According to Fig. 1, almost 75% and 93% fibers in the 2.5D and 3D C/SiC composites were equiva￾lently arranged along the tensile axis, which allowed multiple matrix cracking to release the TRS relatively easier (Fig. 6c and d) due to the less transverse fiber constraints. Contrastively, the matrix cracks could be hardly found in the needled and 2D C/SiC composites (Fig. 6a and b), indicating that the stron￾Fig. 6 – Micrographs showing the as-fabricated CVI-SiC matrix crack conditions in (a) needled C/SiC, (b) 2D C/SiC, (c) 2.5D C/ SiC, and (d) 3D C/SiC composites. 1040 CARBON 47 (2009) 1034 – 1042

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: 306-13

ger 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. 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