《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