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