H Mei/Composites Science and Technology 68(2008)3285-3292 250 Table 1 The experimental and calculational results of the parameters in the loading unloading-reloading cycle tests 200 p(MPa) fe(% Ep(GPa) b(MPa 0.30.02038000822 0286 241.1 00160922166 044340011590055930011509269 150 068230.0220900903200208488.54 8240.101470030460.1319300333683.6 0.13022 0.170130.042347881 0217130.048517208 3497 2D C/SiC 14180.20150062870.2643700528367.0 0.331700 298840.099890.398730.085855845 50 10203.50345750.117110462860.0960055.48-53.26 11223.70398690.1364305351201100952 0.00.1020.30.40.50.6 Strain(%) hysteresis loops of the 2D C/SiC composites with ding cycles ②≌oEo0 050500 200250 Peak applied stress(MPa) relief strain fr of the 2D C/SiC composites obtained upon unloading, along with the secant modulus of the hysteresis loop, as a function of the applied stress. material s modulus along with an extension of inelastic residual strains Ei. Camus et al. [14 pointed out that the inelastic residual Fig.7. Schematic of hysteresis loop with elastic strain and inelastic strain in a c/sic strains in CMCs may be attributed to the interaction of several phe- naterial system during the reloading-unloading cycles. nomena: (i)the release of axial residual stresses (i.e. parallel to the ε*=+ε=斷r+B5+le loading direction) present in the composite from processing: (11) partial irreversible sliding arising from the various energy dissipa The thermal misfit relief strain er depends upon the elastic stiffness, tive frictional mechanisms: and (iii)a mechanical impediment of Ep, of the damaged material and can be written as complete crack closure possibly related to fiber roughness and or the contact between microcrack lips slightly removed from their 2) initial positions, resulting in increased stiffnesses at the lower end of the loops once unloading In the present case of the 2D C SiC composite, narrow hysteresis loops in Fig. 6 account for negli- 3) gible frictional sliding whereas crack closure impediment effects are nearly absent. Thus, the inelastic strain ai is in large part as- cribed to the contribution from the release of axial residual stres- Below the stress level of the preceding step, the top portion of ses. It can be actually seen from Fig. 8 that at lower stresses each loading curve exhibits apparent linearity and Ep is obtained below 150 MPa the thermal misfit relief strain er of the 2D C/Sic from the linear fitting of the top linear portion, which can be called composites is closely superposed with the inelastic strain =p. At steady secant modulus(SSM)of each hysteresis loop. In this condi- higher stresses above 150 MPa, however, the sliding strain as is ion, thermal misfit relief strain Er can be determined directly from unavoidable to occur with gradually increasing applied stress. the abscissa coordinates of the intersection point by extrapolation resulting in slight deviation of the thermal misfit relief strain Er of the compliance slopes(Ep) from the inelastic strain a Table 1 and Fig. 8 show changes in the elastic strain ce, inelas The loading curve of each hysteresis loop is alike with the tic strain Ei and thermal misfit relief strain ar of the 2D C/Sic monotonic tensile curve of the composite containing cracks: a composites obtained upon unloading, along with the SSM Ep of small elastic deformation occurs upon initial reloading, followed each hysteresis loop, as a function of the applied stress. Obviously, by a nonlinear behavior with partial irreversible sliding and finally the peak applied stress increases the SSM Ep diminishes whereas the slip zone stops at the debond tip accompanied by establish the elastic strain ee, inelastic strain a and thermal misfit relief ment of a large linear response of the whole composite system un strain Er increase Periodic loading/unloading cycles can introduce til the preceding stress level approaches. Fig. 9 illustrates typical damage into the CMC, which exhibits a progressive decrease of the tangent modulus changes calculated directly from the slopes ofe ¼ ei þ ee ¼ eT þ es þ ee ð1Þ The thermal misfit relief strain eT depends upon the elastic stiffness, Ep, of the damaged material and can be written as eT ¼ e  rp Ep ð2Þ and es þ ee ¼ rp Ep ð3Þ Below the stress level of the preceding step, the top portion of each loading curve exhibits apparent linearity and Ep is obtained from the linear fitting of the top linear portion, which can be called steady secant modulus (SSM) of each hysteresis loop. In this condi￾tion, thermal misfit relief strain eT can be determined directly from the abscissa coordinates of the intersection point by extrapolation of the compliance slopes (Ep). Table 1 and Fig. 8 show changes in the elastic strain ee, inelas￾tic strain ei and thermal misfit relief strain eT of the 2D C/SiC composites obtained upon unloading, along with the SSM Ep of each hysteresis loop, as a function of the applied stress. Obviously, as the peak applied stress increases the SSM Ep diminishes whereas the elastic strain ee, inelastic strain ei and thermal misfit relief strain eT increase. Periodic loading/unloading cycles can introduce damage into the CMC, which exhibits a progressive decrease of the material’s modulus along with an extension of inelastic residual strains ei. Camus et al. [14] pointed out that the inelastic residual strains in CMCs may be attributed to the interaction of several phe￾nomena: (i) the release of axial residual stresses (i.e. parallel to the loading direction) present in the composite from processing; (ii) partial irreversible sliding arising from the various energy dissipa￾tive frictional mechanisms; 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, resulting in increased stiffnesses at the lower end of the loops once unloading. In the present case of the 2D C/ SiC composite, narrow hysteresis loops in Fig. 6 account for negli￾gible frictional sliding whereas crack closure impediment effects are nearly absent. Thus, the inelastic strain ei is in large part as￾cribed to the contribution from the release of axial residual stres￾ses. It can be actually seen from Fig. 8 that at lower stresses below 150 MPa the thermal misfit relief strain eT of the 2D C/SiC composites is closely superposed with the inelastic strain ei. At higher stresses above 150 MPa, however, the sliding strain es is unavoidable to occur with gradually increasing applied stress, resulting in slight deviation of the thermal misfit relief strain eT from the inelastic strain ei. The loading curve of each hysteresis loop is alike with the monotonic tensile curve of the composite containing cracks: a small elastic deformation occurs upon initial reloading, followed by a nonlinear behavior with partial irreversible sliding and finally the slip zone stops at the debond tip accompanied by establish￾ment of a large linear response of the whole composite system un￾til the preceding stress level approaches. Fig. 9 illustrates typical tangent modulus changes calculated directly from the slopes of Fig. 6. Tensile stress/strain hysteresis loops of the 2D C/SiC composites with interrupted unloading/reloading cycles. Fig. 7. Schematic of hysteresis loop with elastic strain and inelastic strain in a C/SiC material system during the reloading–unloading cycles. Table 1 The experimental and calculational results of the parameters in the loading– unloading–reloading cycle tests n rp (MPa) ee (%) ei (%) e * (%) eT (%) Ep (GPa) b (MPa) 1 20.3 0.02038 0.00822 0.0286 0.00686 93.57 6.42 2 41.1 0.04434 0.01159 0.05593 0.01150 92.69 10.66 3 61.5 0.06823 0.02209 0.09032 0.02084 88.54 18.45 4 82.4 0.10147 0.03046 0.13193 0.03336 83.62 27.90 5 100.7 0.13022 0.03991 0.17013 0.04234 78.81 33.37 6 121.5 0.16963 0.0475 0.21713 0.04851 72.08 34.97 7 141.8 0.2015 0.06287 0.26437 0.05283 67.03 35.41 8 162.6 0.25067 0.08103 0.3317 0.06885 61.89 42.62 9 182.8 0.29884 0.09989 0.39873 0.08585 58.45 50.18 10 203.5 0.34575 0.11711 0.46286 0.09600 55.48 53.26 11 223.7 0.39869 0.13643 0.53512 0.11009 52.65 57.97 Fig. 8. Development of the elastic strain ee, inelastic strain ei and thermal misfit relief strain eT of the 2D C/SiC composites obtained upon unloading, along with the secant modulus of the hysteresis loop, as a function of the applied stress. 3288 H. Mei / Composites Science and Technology 68 (2008) 3285–3292