H Mei/Composites Science and Technology 68(2008)3285-3292 corresponds extremely well with both experimental result of loops in order to compare difference of TRS state in different CMCs. et al. [14]. In the present C/SiC, the Sic matrix is in residual tensile stress-free"origin o basically approaches the zero point o of p 30.84 MPa as measured above and of 140 MPa reported by Camus Using the method described in Section 3.3, thethermal-resio down from the processing temperature to room temperature. If tic strain still observed in Fig. 12. The models expressed by eqs the composite is applied to a compressive stress that is just equal(10)and(12)also give the zero value for the trs of the tested to TRS of 136.71 MPa, these processing-induced matrix microcracks 2D SiC/SiC composite because the Sic fibers have the nearly same should close completely and the residual tensile stress in matrix CTE as the Sic matrix( thermal misfit stress is equal to zero) would disappear immediately (reduce to zero ). At this time, the zero The applied stresses at which the loop width is zero provide point 0 of the external applied stress would be translated to now initial estimates of the onset stress for matrix cracking. As shown thermal-residual-stress-free"origin O. Thus, the whole properties in Fig. 12, the first matrix cracking stress omc of the tested sic/Sic of t dramatically. Consequently, composite approximates to 150 MPa. As expected, this parameter the trs is a key factor for improvement of the composite property. property was approximatively promoted 100 MPa in contrast to the C/Sic (only 50 MPa as measured in Fig. 5 by AE monitoring ). 3.5. Theoretical prediction of TRS with ideal interfacial bond and non- Obviously, the processing-induced TRS has a significant influence cracked matnⅸ on the first matrix cracking stress. The greater the tRs in the composites, the less the first matrix cracking stress and the Consider a composite with ideal interf nd and without any poorer the whole properties of the composites. Normally the first matrix cracks associated with relief of RS from processing matrix cracking stress can be predicted by the classical ACK mod- temperature to room temperature, the axial residual stress in a el based on steady-state matrix crack and constant sliding stress t non-cracked matrix then can be classically estimated by [21]J ErVe (12) ∫6EvE2r (13 where am and af refer to the linear cte of the matrix and fiber pectively t, and to are the processing temperature and opera- where I m is the matrix fracture energy, r the fiber radius. Using the tion temperature Using the data listed in Table 2, the axial residual data listed in Table 2 and Eq(13), the first matrix cracking stress of tress in non-cracked matrix gives 282.06 MPa, which should be the the c/Sic and Sic Sic composites are 41. 25 MPa and 155.58 MPa theoretical maximum TRS in matrix prior to relief and much higher Suming the misfit stress a'=100 MPa for C/Sic and O MPa for matrix cracks and interface sliding. However, the stiffness Em of the agreement with above expermendlos al predictions exhibit good cracking and interface sliding oo results, validating the preceding analysis and then applicability of ur, which in turn causes decrease and partial relief of the trs. those methods to the present composite systems. omparatively, the"regression line intersection"method is rel ative simple and rapid to obtain TRS and easy to identify the com- 4. Conclusions pressive or tensile state of TRs in the composites for engineering applications, whereas the analytical formula and theoretical model are either cumbersome with too many unknown parameters or ite systems stresses in two Sic-ceramic matrix compos d with carbon fiber(C/Sic)and silicon car impractical with too ideal assumption. Fortunately, the model of bide fiber ere completely investigated. Thermal Eq(12)can be further improved by modifying the matrix stiffness residual stress of.84+34.53 MPa in the 2D C/Sic was deter to reflect matrix cracking and interface debonding. mined by solving the geometric intersection points of the regres- 3.6. Comparison of Trs with a SiC/SiC system sion lines of consecutive unloading/reloading hysteresis loops. This experimentally measured result corresponded extremely curves of 2D Hi-Nicalon/SiC composites within several hysteresis and was severely less than the theoretical maximum TRS of 282.06 MPa in the composites with ideal interface bond and non-cracked matrix. In contrast to the C/Sic, the sic/Sic appar ently yielded a negligible trs(close to zero value)because the Sic fibers have the nearly same Cte as the SiC matrix that cause thermal misfit stress was equal to zero. Compared with the al lytical formula and theoretical models, the"regression line inter section"method is relatively simple and rapid to obtain tRS and easy to identify the compressive or tensile state of trs in the composites for engineering applications. The thermal residual D Hi-Nicalon/Sic stress has a significant influence on improvement in the proper ties of the composites. The less the thermal residual stress in the 0 composites, the greater the first matrix cracking stress and more the whole properties of the composite can be promoted -0.160.000.160.320.480.64 Acknowledgements Strain(% Financial support for this work was provided by the Natural Fig. 12. Example of unloading-reloading curves of 2D Hi-Nicalon/SiC composi Science Foundation of China(Contract No. 90405015)and the National Young Elitists Foundation(Contract No. 50425208 ). Thecorresponds extremely well with both experimental result of 130.84 MPa as measured above and of 140 MPa reported by Camus et al. [14]. In the present C/SiC, the SiC matrix is in residual tensile stress leading to opening microcracks in the materials once cooled down from the processing temperature to room temperature. If the composite is applied to a compressive stress that is just equal to TRS of 136.71 MPa, these processing-induced matrix microcracks should close completely and the residual tensile stress in matrix would disappear immediately (reduce to zero). At this time, the zero point O of the external applied stress would be translated to now ‘‘thermal-residual-stress-free” origin O’. Thus, the whole properties of the composite would be promoted dramatically. Consequently, the TRS is a key factor for improvement of the composite property. 3.5. Theoretical prediction of TRS with ideal interfacial bond and non￾cracked matrix Consider a composite with ideal interface bond and without any matrix cracks associated with relief of the TRS from processing temperature to room temperature, the axial residual stress in a non-cracked matrix then can be classically estimated by rm r ¼ Em kEfVf kEfVf þ EmVm ðaf  amÞðTo  TpÞ ð12Þ where am and af refer to the linear CTE of the matrix and fiber, respectively. Tp and To are the processing temperature and opera￾tion temperature. Using the data listed in Table 2, the axial residual stress in non-cracked matrix gives 282.06 MPa, which should be the theoretical maximum TRS in matrix prior to relief and much higher than the above experimental and calculational results that consider matrix cracks and interface sliding. However, the stiffness Em of the matrix decreases once the matrix cracking and interface sliding oc￾cur, which in turn causes decrease and partial relief of the TRS. Comparatively, the ‘‘regression line intersection” method is rel￾ative simple and rapid to obtain TRS and easy to identify the com￾pressive or tensile state of TRS in the composites for engineering applications, whereas the analytical formula and theoretical model are either cumbersome with too many unknown parameters or impractical with too ideal assumption. Fortunately, the model of Eq. (12) can be further improved by modifying the matrix stiffness to reflect matrix cracking and interface debonding. 3.6. Comparison of TRS with a SiC/SiC system Fig. 12 presents a typical example of unloading–reloading curves of 2D Hi-Nicalon/SiC composites within several hysteresis loops in order to compare difference of TRS state in different CMCs. Using the method described in Section 3.3, the ‘‘thermal-residual￾stress-free” origin O0 basically approaches the zero point O of the external applied stress although there is a little irreversible inelas￾tic strain still observed in Fig. 12. The models expressed by Eqs. (10) and (12) also give the zero value for the TRS of the tested 2D SiC/SiC composite because the SiC fibers have the nearly same CTE as the SiC matrix (thermal misfit stress is equal to zero). The applied stresses at which the loop width is zero provide initial estimates of the onset stress for matrix cracking. As shown in Fig. 12, the first matrix cracking stress rmc of the tested SiC/SiC composite approximates to 150 MPa. As expected, this parameter property was approximatively promoted 100 MPa in contrast to the C/SiC (only 50 MPa as measured in Fig. 5 by AE monitoring). Obviously, the processing-induced TRS has a significant influence on the first matrix cracking stress. The greater the TRS in the composites, the less the first matrix cracking stress and the poorer the whole properties of the composites. Normally, the first matrix cracking stress can be predicted by the classical ACK mod￾el based on steady-state matrix crack and constant sliding stress s [21], rmc ¼ 6EfV2 f sE2 Cm ð1  VfÞRE2 m ( )1=3  rT ð13Þ where Cm is the matrix fracture energy, R the fiber radius. Using the data listed in Table 2 and Eq. (13), the first matrix cracking stress of the C/SiC and SiC/SiC composites are 41.25 MPa and 155.58 MPa (Assuming the misfit stress rT = 100 MPa for C/SiC and 0 MPa for SiC/SiC), respectively. These theoretical predictions exhibit good agreement with above experimental observations and calculational results, validating the preceding analysis and then applicability of those methods to the present composite systems. 4. Conclusions Thermal residual stresses in two SiC-ceramic matrix compos￾ite systems reinforced with carbon fiber (C/SiC) and silicon car￾bide fiber (SiC/SiC) were completely investigated. Thermal residual stress of 130.84 ± 34.53 MPa in the 2D C/SiC was deter￾mined by solving the geometric intersection points of the regres￾sion lines of consecutive unloading/reloading hysteresis loops. This experimentally measured result corresponded extremely well with the analytically calculated TRS of 136.71 MPa in the C/SiC material containing matrix cracking and interface sliding, and was severely less than the theoretical maximum TRS of 282.06 MPa in the composites with ideal interface bond and non-cracked matrix. In contrast to the C/SiC, the SiC/SiC appar￾ently yielded a negligible TRS (close to zero value) because the SiC fibers have the nearly same CTE as the SiC matrix that cause thermal misfit stress was equal to zero. Compared with the ana￾lytical formula and theoretical models, the ‘‘regression line inter￾section” method is relatively simple and rapid to obtain TRS and easy to identify the compressive or tensile state of TRS in the composites for engineering applications. The thermal residual stress has a significant influence on improvement in the proper￾ties of the composites. The less the thermal residual stress in the composites, the greater the first matrix cracking stress and the more the whole properties of the composite can be promoted. Acknowledgements Financial support for this work was provided by the Natural Science Foundation of China (Contract No. 90405015) and the National Young Elitists Foundation (Contract No. 50425208). The Fig. 12. Example of unloading–reloading curves of 2D Hi-Nicalon/SiC composites within several hysteresis loops. H. Mei / Composites Science and Technology 68 (2008) 3285–3292 3291