Journal of the European Ceramic Society 19(1999)207-215 C 1998 Elsevier Science Limited Printed in Great Britain. All rights reserved PII:S0955-2219(98)00185-X 0955-2219/98/S--see front matter Fatigue Damage Accumulation in 3-Dimensional Sic/Sic Composites V Kostopoulos, Y.Z. Pappas and Y. P Markopoulos Applied Mechanics Laboratory, University of Patras, Patras University Campus, 265 00 Patras, Greece (Received 18 February 1998; revised version received 9 July 1998; accepted 31 July 1998) abstract development of damage modes, which affects the performance and the life of the structure. The The effect of fatigue loading on the mechanical per- damage propagation, the interaction between the formance of 3-D SiC/SiC composites was investigated. different damage modes and the resulting damage A non-destructive macromechanical approach was accumulation promotes critical damage modes applied which permits for the evaluation of the within the composite structure, alters the material material damage state by monitoring its dynamic stiffness and damping characteristics and reduces response as function of fatigue cycles. The correlation the strength together with the fatigue life of the of the results provided by this method to that of composite laminates other non-destructive techniques such as Acoustic More precisely, subcritical fatigue loading of Emission(AE), leads to a detail micromechanical- ceramic matrix composites(CMCs) appears when macromechanical monitoring of the material fatigue ever the maximum applied cyclic stress exceeds the behaviour. The damage modes identification and matrix strength for cracking. Then, the cyclic their successive appearance, together with the evalua- opening and closing of matrix cracks is the basic tion of the material performance at the different stages responsible mechanism of fatigue for CMCs offatigue loading, is among the inspection capabilities During fatigue, the fibre-matrix interfaces that provides the above mentioned combination of debond and slide between fibre and matrix is non-destructive techniques. The proposed methodology established as matrix cracking extends. Macro- applied in the case of a 3-D SiC/SiC ceramic matrix scopically, the damage development during fatigue composite material and the effect of fatigue loading in CMCs manifests itself by the appearance of on the material integrity was evaluated by measuring stress-strain hysterisis loops, which are more wide the degradation of the dynamic modulus of elasticity increasing the fatigue cycles(whenever the matrix nd the increase of the material damping Conclusions, cracking is not saturated ), the presence of oncerning design aspects using these materials, as inelastic-permanent strain, the decrease of the well as fatigue life prediction were provided. Finally, modulus of elasticity and the decrease of the tensile the sensitivity of the proposed methodology for the strength of the material. Each time, the intensity of definition, the characterisation of the development the above described effects is strongly related to ed the separation of the different damage modes the material system under consideration, the type uring fatigue loading has been discussed. C 1998 of the reinforcement structure and finally the resi- Elsevier Science Limited. All rights reserved dual stress field that experiences the given CMC Keywords: composites, fatigue, SiC, failure analy During the last years, some work has been Sis: acoustic emission done to the direction of understanding and quantifying the fatigue effect on ceramic matrix composites. -9 Among them, the pioneer work of 1 Introduction Kotil et al. 4 who first tried to model the hysterisis loops appeared during the fatigue of UD CMCs It is well known that subcritical fatigue loading and the very informative overview of Evans et al of composite structures is responsible for the where the role of the fibre and the matrix material has been discussed analytically for both 1-D and *To whom correspondence should be addressed. E-mail: 2-D reinforcement architecture, the cyclic crack kostopoulos(@ tech. mech. patras.gr growth has been quantified and a methodology for
Fatigue Damage Accumulation in 3-Dimensional SiC/SiC Composites V. Kostopoulos,* Y. Z. Pappas and Y. P. Markopoulos Applied Mechanics Laboratory, University of Patras, Patras University Campus, 265 00 Patras, Greece (Received 18 February 1998; revised version received 9 July 1998; accepted 31 July 1998) Abstract The eect of fatigue loading on the mechanical performance of 3-D SiC/SiC composites was investigated. A non-destructive macromechanical approach was applied which permits for the evaluation of the material damage state by monitoring its dynamic response as function of fatigue cycles. The correlation of the results provided by this method to that of other non-destructive techniques such as Acoustic Emission (AE), leads to a detail micromechanicalmacromechanical monitoring of the material fatigue behaviour. The damage modes identi®cation and their successive appearance, together with the evaluation of the material performance at the dierent stages of fatigue loading, is among the inspection capabilities that provides the above mentioned combination of non-destructive techniques. The proposed methodology applied in the case of a 3-D SiC/SiC ceramic matrix composite material and the eect of fatigue loading on the material integrity was evaluated by measuring the degradation of the dynamic modulus of elasticity and the increase of the material damping. Conclusions, concerning design aspects using these materials, as well as fatigue life prediction were provided. Finally, the sensitivity of the proposed methodology for the de®nition, the characterisation of the development and the separation of the dierent damage modes during fatigue loading has been discussed. # 1998 Elsevier Science Limited. All rights reserved Keywords: composites, fatigue, SiC, failure analysis: acoustic emission. 1 Introduction It is well known that subcritical fatigue loading of composite structures is responsible for the development of damage modes, which aects the performance and the life of the structure. The damage propagation, the interaction between the dierent damage modes and the resulting damage accumulation promotes critical damage modes within the composite structure, alters the material stiness and damping characteristics and reduces the strength together with the fatigue life of the composite laminates. More precisely, subcritical fatigue loading of ceramic matrix composites (CMCs) appears whenever the maximum applied cyclic stress exceeds the matrix strength for cracking. Then, the cyclic opening and closing of matrix cracks is the basic responsible mechanism of fatigue for CMCs.1 During fatigue, the ®bre±matrix interfaces debond and slide between ®bre and matrix is established as matrix cracking extends. Macroscopically, the damage development during fatigue in CMCs manifests itself by the appearance of stress-strain hysterisis loops, which are more wide increasing the fatigue cycles (whenever the matrix cracking is not saturated2 ), the presence of inelastic-permanent strain, the decrease of the modulus of elasticity and the decrease of the tensile strength of the material. Each time, the intensity of the above described eects is strongly related to the material system under consideration, the type of the reinforcement structure and ®nally the residual stress ®eld that experiences the given CMC system. During the last years, some work has been done to the direction of understanding and quantifying the fatigue eect on ceramic matrix composites.3±9 Among them, the pioneer work of Kotil et al. 4 who ®rst tried to model the hysterisis loops appeared during the fatigue of UD CMCs and the very informative overview of Evans et al. 1 where the role of the ®bre and the matrix material has been discussed analytically for both 1-D and 2-D reinforcement architecture, the cyclic crack growth has been quanti®ed and a methodology for Journal of the European Ceramic Society 19 (1999) 207±215 # 1998 Elsevier Science Limited Printed in Great Britain. All rights reserved PII: S0955-2219(98)00185-X 0955-2219/98/$Ðsee front matter 207 *To whom correspondence should be addressed. E-mail: kostopoulos@tech.mech.upatras.gr
v. Kostopoulos et al the fatigue life prediction has been proposed In all been correlated to the changes in the dynamic the cases it is always emphasised response of 3-D SiC/SiC composite. Finally, the use of modal damping as a descriptor for the fati The critical role of fibre-matrix interface, its gue life prediction in the case of CMCs has been degradation during fatigue and the develop- discussed analytically ment of a sliding stress which diminishes upon The presence of the hysterisis loops which 2 Experimental Procedure show that inelastic strain increases. elastic modulus decreases together with a loop 2.1 Description of the material widening as fatigue proceeds and the matrix The 3-dimensional(3-D) SiC/SiC material was cracking has not reached the saturation point. produced by Aerospatiale bordeaux as a part of a Brite titled Develol present work the problem of fatigue Characterization of CMC and C/C Composites of CMCs has been treated through a ( Contract No BREU 0334-C). The 3-D SiC/Sic macroscopical approach, where both the stiffness material was made out of Nicalon fibres and a degradation and the hysterisis loop widening dur- metal-organic based Silicon Carbide matrix. The ing fatigue were monitored indirectly using the woven fibre perform has a 3-dimensional orthogo- change in the dynamic response of the fatigued nal architecture shown in Fig. 1. The development components, i.e. by measuring the eigenfrequency of the material includes optimisation of all the spectrum and the corresponding modal damping seven basic manufacturing steps . The final pro characteristics. Then, assuming an apparent linear duct has a density of 2. lgr cm-3and an open por viscoelastic behaviour for the material under con- osity of about 20%. The fibre volume fraction sideration, the eigenfrequency and the modal 36%, equally distributed in the three rectangular damping measurements were transformed to mate- directions. Plates of 6mm thickness were manu rial properties(stiffness and loss factor) factured. The mean diameter of the fibre bundles is The evaluation of the fatigue effect through the of the order of l mm. The material can be used up variation of the apparent viscoelastic properties of to 1200 C, however, an oxidation protection the material system under testing has been applied layer is necessary for oxidative application above first in the case of organic matrix composites 0, 500C and the loss factor has been identified as a very useful parameter for fatigue life prediction since it 2.2 Testing procedure is much more sensitive to fatigue compared to the A group of 3-D SiC/SiC straight strip specimens with gauge length 200 mm, width 10mm and Within the frame of this study, the effect of the thickness 6mm(the original plate thickness)were fatigue loading of 3-D Sic/Sic composite on both tested, according to ENV 1893 standards for ten- the dynamic modulus of elasticity and the damping sile and fatigue tests for advanced ceramics coefficient (loss factor) were investigated. Accord- Tapered aluminium end-tabs were bonded at the ing to the obtained results, modal damping mea- gripping area of the specimens using epoxy resin surements or equivalently loss factor calculations ( Ciba LY-564/ hardener HY 2954) could be a reliable measure of the fatigue damage state in the case of CMCs. This was expected, sine modal damping is a measure of the energy loss per cycle of vibration and it is in a direct relation to the area of the hysterisis loop at a given fatigue cycle What makes the modal damping more attractive as a descriptor for the evaluation of the fatigue damage state in CMCs is the easy way of measur ing it under real working conditions. Furthermore. in order to correlate the macro- microscopical failure mechanisms, which are responsible for the material deterioration, con tinuous acoustic emission monitoring has been performed during fatigue. Acoustic emission data have been corresponded to the main failure mechan- Fig. 1 Schematic representation of the 3-D SiC/Sic orthogo- isms and the activation of these mechanisms have nal preform
the fatigue life prediction has been proposed. In all the cases it is always emphasised: . The critical role of ®bre±matrix interface, its degradation during fatigue and the development of a sliding stress which diminishes upon cycling. . The presence of the hysterisis loops which show that inelastic strain increases, elastic modulus decreases together with a loop widening as fatigue proceeds and the matrix cracking has not reached the saturation point. In the present work the problem of fatigue behaviour of CMCs has been treated through a macroscopical approach, where both the stiness degradation and the hysterisis loop widening during fatigue were monitored indirectly using the change in the dynamic response of the fatigued components, i.e. by measuring the eigenfrequency spectrum and the corresponding modal damping characteristics. Then, assuming an apparent linear viscoelastic behaviour for the material under consideration, the eigenfrequency and the modal damping measurements were transformed to material properties (stiness and loss factor). The evaluation of the fatigue eect through the variation of the apparent viscoelastic properties of the material system under testing has been applied ®rst in the case of organic matrix composites10,11 and the loss factor has been identi®ed as a very useful parameter for fatigue life prediction since it is much more sensitive to fatigue compared to the stiness. Within the frame of this study, the eect of the fatigue loading of 3-D SiC/SiC composite on both the dynamic modulus of elasticity and the damping coecient (loss factor) were investigated. According to the obtained results, modal damping measurements or equivalently loss factor calculations could be a reliable measure of the fatigue damage state in the case of CMCs. This was expected, since modal damping is a measure of the energy loss per cycle of vibration and it is in a direct relation to the area of the hysterisis loop at a given fatigue cycle. What makes the modal damping more attractive as a descriptor for the evaluation of the fatigue damage state in CMCs is the easy way of measuring it under real working conditions. Furthermore, in order to correlate the macroscopical monitored fatigue damage state to the microscopical failure mechanisms, which are responsible for the material deterioration, continuous acoustic emission monitoring has been performed during fatigue. Acoustic emission data have been corresponded to the main failure mechanisms and the activation of these mechanisms have been correlated to the changes in the dynamic response of 3-D SiC/SiC composite. Finally, the use of modal damping as a descriptor for the fatigue life prediction in the case of CMCs has been discussed analytically. 2 Experimental Procedure 2.1 Description of the material The 3-dimensional (3-D) SiC/SiC material was produced by Aerospatiale Bordeaux as a part of a Brite/Euram Project entitled `Development and Characterization of CMC and C/C Composites' (Contract No. BREU 0334-C). The 3-D SiC/SiC material was made out of Nicalon ®bres and a metal-organic based Silicon Carbide matrix. The woven ®bre perform has a 3-dimensional orthogonal architecture shown in Fig. 1. The development of the material includes optimisation of all the seven basic manufacturing steps.7,8 The ®nal product has a density of 2.1gr cmÿ3 and an open porosity of about 20%. The ®bre volume fraction is 36%, equally distributed in the three rectangular directions. Plates of 6 mm thickness were manufactured. The mean diameter of the ®bre bundles is of the order of 1 mm. The material can be used up to 1200C, however, an oxidation protection layer is necessary for oxidative application above 500C. 2.2 Testing procedure A group of 3-D SiC/SiC straight strip specimens with gauge length 200 mm, width 10 mm and thickness 6 mm (the original plate thickness) were tested, according to ENV 1893 standards for tensile and fatigue tests for advanced ceramics. Tapered aluminium end-tabs were bonded at the gripping area of the specimens using epoxy resin (Ciba LY-564 / hardener HY 2954). Fig. 1. Schematic representation of the 3-D SiC/SiC orthogonal preform. 208 V. Kostopoulos et al
Fatigue damage accumulation in 3-D SiC/SiC composites Tension-tension fatigue tests were performed for each specimen. The results are presented in the under load control condition. The cyclic frequency form of normalised data using reference values the was 10 Hz having a sinusoidal wave form and the relative results of the same initially tested virgin stress ratio was R=0-1(R=Omin/omax). Tensile specimen. A schematic representation of the tests were also accomplished using a cross head experimental set up for the monitoring of the velocity of 0. 1 mm/min, in order to have a com- dynamic response of the tested samples is given in plete material characterization Fig 2(a) All the test were carried out on a closed loop Figure 2(b)shows the experimental set up, which servo-hydraulic testing machine equipped with a was used for AE measurements. The following AE hydraulic gripping system, at room temperature, in parameters were monitored continuously during air. During both tensile and fatigue tests, acoustic the fatigue experiment: Amplitude(A), Rise Time emission (AE)activity was monitored using a (RT), Energy(E), Duration(D)and Counts(C) 150 kHz resonant transducer and Ae events were Their physical meaning is has been extensively dis- tracked using a Physical Acoustic Corporation cussed. 2 Applying pattern recognition techniques, (SPARTAN AT 8000) system. The acoustic emis- which are presented in detail elsewhere, the AE sion parameters used were total amplification level events which correspond to fibre breakage have 20 dB, threshold 60 dB, peak definition time 30 us been separated and a high-pass filter of cut-off frequency of 100 kHZ 2.4 Theoretical analysis In the present Section, the inversion algorithm, in 2.3 Measurements of the dynamic response order to calculate the dynamic material properties The effect of fatigue on both effective dynamic based on the eigenfrequency and modal damping modulus of elasticity and the relative loss factor measurements, will be given. The material of the (damping coefficient) was investigated using the vibrating beam assumed to be macroscopically free flexural vibration of test coupons exposed to homogeneous and transversely isotropic exhibits fatigue. The following procedure was applied linear viscoelastic behaviour. The latter assumption Initially, each sample before being subjected to consists of the theoretical tool for incorporating fatigue, was tested to free flexural vibration trig. frequency dependent damping behaviour in the gered by an initial velocity, under a cantilever present analysis. The specimen, which experiences beam configuration. The response of the specimen the flexural vibration is of rectangular cross was monitored by an accelerometer having a mass section and has been supported under cantilever of 0.5g, which was mounted on the free edge of the configuration specimen. The accelerometer had a dynamic range The differential equation which describes the free of 500g(g=9.81ms-2 and a sensitivity of 3.46 vibration of a linear viscoelastic beam and fulfils the Euler-Bernoulli assumptions is given by In the sequence, the specimen was loaded to tension-tension fatigue up to fracture or up to a aw(x, 1) aw(x,t) number of fatigue cycles defined as endurance fati- 0 gue limit (10 cycles). At regular time intervals corresponding to 10, 20, 50, 100, 200,..,1000 where we is the transverse displacement of the kcycles, the fatigue process was stopped, the upper beam and af a complex constant. The explicit form part of the gripping system was opened and the of af is given by the relation accelerometer was mounted again on the free edge of the specimen. Following this procedure both fatigue and boundary conditions for the free flex ph[Di] ural vibration experiment were secured unchanged Then, the specimen was exposed again to free flex- where p is the linear density of the vibrating beam, ural vibration and its response was monitored. An h is the thickness of the beam and [Dex-is the A/d board (National Instrument 2000) with element of the inverse of the bending stiffness 2.5mV sensitivity and maximum sampling fre- matrix [D]. De is account as the complex bending quency 1 MHz, connected to a PC was used to stiffness of the 3 D Sic/Sic along the loading collect and store the amplified analogue signal direction according to the analysis presented else- of the accelerometer. FFT analysis of the signal of where. 4 Assuming harmonic time dependence eqn accelerometer provides the eigenfrequency spec- (1)obtains the form trum of the vibrated specimen. Short FFT analysis of the same signal furnishes the decay rate of the a5(x)w(x)=0 amplitude at each mode shape(modal damping)
Tension±tension fatigue tests were performed under load control condition. The cyclic frequency was 10 Hz having a sinusoidal wave form and the stress ratio was R=0.1 (R=min/max). Tensile tests were also accomplished using a cross head velocity of 0.1 mm/min, in order to have a complete material characterization. All the test were carried out on a closed loop servo-hydraulic testing machine equipped with a hydraulic gripping system, at room temperature, in air. During both tensile and fatigue tests, acoustic emission (AE) activity was monitored using a 150 kHz resonant transducer and AE events were tracked using a Physical Acoustic Corporation (SPARTAN AT 8000) system. The acoustic emission parameters used were total ampli®cation level 20 dB, threshold 60 dB, peak de®nition time 30s and a high-pass ®lter of cut-o frequency of 100 kHz. 2.3 Measurements of the dynamic response The eect of fatigue on both eective dynamic modulus of elasticity and the relative loss factor (damping coecient) was investigated using the free ¯exural vibration of test coupons exposed to fatigue. The following procedure was applied. Initially, each sample before being subjected to fatigue, was tested to free ¯exural vibration triggered by an initial velocity, under a cantilever beam con®guration. The response of the specimen was monitored by an accelerometer having a mass of 0.5 g, which was mounted on the free edge of the specimen. The accelerometer had a dynamic range of 500 g (g = 9.81m sÿ2 and a sensitivity of 3.46 mV gÿ1 . In the sequence, the specimen was loaded to tension±tension fatigue up to fracture or up to a number of fatigue cycles de®ned as endurance fatigue limit (106 cycles). At regular time intervals corresponding to 10, 20, 50, 100, 200,...,1000 kcycles, the fatigue process was stopped, the upper part of the gripping system was opened and the accelerometer was mounted again on the free edge of the specimen. Following this procedure both fatigue and boundary conditions for the free ¯exural vibration experiment were secured unchanged. Then, the specimen was exposed again to free ¯exural vibration and its response was monitored. An A/D board (National Instrument 2000) with 2.5 mV sensitivity and maximum sampling frequency 1MHz, connected to a PC was used to collect and store the ampli®ed analogue signal of the accelerometer. FFT analysis of the signal of accelerometer provides the eigenfrequency spectrum of the vibrated specimen. Short FFT analysis of the same signal furnishes the decay rate of the amplitude at each mode shape (modal damping) for each specimen. The results are presented in the form of normalised data using reference values the relative results of the same initially tested virgin specimen. A schematic representation of the experimental set up for the monitoring of the dynamic response of the tested samples is given in Fig. 2(a). Figure 2(b) shows the experimental set up, which was used for AE measurements. The following AE parameters were monitored continuously during the fatigue experiment: Amplitude (A), Rise Time (RT), Energy (E), Duration (D) and Counts (C). Their physical meaning is has been extensively discussed.12 Applying pattern recognition techniques, which are presented in detail elsewhere,13 the AE events which correspond to ®bre breakage have been separated. 2.4 Theoretical analysis In the present Section, the inversion algorithm, in order to calculate the dynamic material properties based on the eigenfrequency and modal damping measurements, will be given. The material of the vibrating beam assumed to be macroscopically homogeneous and transversely isotropic exhibits linear viscoelastic behaviour. The latter assumption consists of the theoretical tool for incorporating frequency dependent damping behaviour in the present analysis. The specimen, which experiences the ¯exural vibration is of rectangular cross section and has been supported under cantilever con®guration. The dierential equation which describes the free vibration of a linear viscoelastic beam and ful®ls the Euler±Bernoulli assumptions is given by a2 c @4wc x; t @x4 @2wc x;t @t2 0 1 where wc is the transverse displacement of the beam and a2 c a complex constant. The explicit form of a2 c is given by the relation a2 c 1 h Dc xx ÿ1 2 where is the linear density of the vibrating beam, h is the thickness of the beam and Dc xx ÿ1 is the element of the inverse of the bending stiness matrix Dc : Dc xx is account as the complex bending stiness of the 3 D SiC/SiC along the loading direction according to the analysis presented elsewhere.14 Assuming harmonic time dependence eqn (1) obtains the form @4wc x @x4 ÿ !2 a2 c wc x 0 3 Fatigue damage accumulation in 3-D SiC/SiC composites 209
210 v. Kostopoulos et al Accelerometer 0.5 Spectrum Analysis Initial Velocity ditioning Amplifier A/D Gripping System Signal from stress measuring device sinusoid load Gate for selected measures Waveform Emission SPARTAN AT 8000 Acoustic Preamplif Emission 40dB System Analysing System Gripping system of the Universal testing machine Fig. 2.(a) Representation of the experimental set up for the dynamic response measurements;(b) Representation of the experi- mental set up for the acoustic emission The general solution of eqn(3)exhibits the form Wn(x, t)=Cmen+C2ne-kn+CS,en+ C4, e-inAI [D=正E=下成(1+r where the following relation has been used where Ex is the real part of Exe, Ere is the mea sure of El, e and ne is the effective loss factor which is defined as Assuming the wave number kep then the vibration frequency is a complex quantity of the form nex= Rx(Ee is the imaginary part of Exe)(8) Finally the application of the boundary conditions and for physical reasons Imposing for De"the for the case of a cantilever beam concludes to the form that contains the effective complex bending following expression for the eigenfrequencies of the modulus of elasticity then problem4
The general solution of eqn (3) exhibits the form Wn x;t Cc 1nenxCc 2neÿnxCc 3neinxCc 4neÿinx 4 where the following relation has been used k4 n !c2 n a2 c 5 Assuming the wave number k" then the vibration frequency is a complex quantity of the form !c n !n ÿ idn 6 and for physical reasons Imposing for Dc xx ÿ1 the form that contains the eective complex bending modulus of elasticity then Dc xx ÿ1 12 h3 : 1 Ec;e xx 12 h3 1 ER;e xx 1 ne xx ÿ 12 h3 : 1 jEc;e xx jei: arctan ne xx 7 where ER;e xx is the real part of Ec;e xx ; jEc;e xx j is the measure of Ec;e xx and ne xx is the eective loss factor which is de®ned as ne xx EI;e xx ER;e xx EI;e xx is the imaginary part of Ec;e xx 8 Finally the application of the boundary conditions for the case of a cantilever beam concludes to the following expression for the eigenfrequencies of the problem14 Fig. 2. (a) Representation of the experimental set up for the dynamic response measurements; (b) Representation of the experimental set up for the acoustic emission measurements. 210 V. Kostopoulos et al.
Fatigue damage accumulation in 3-D SiC/SiC composites 211 k4h2 arcta n(ney) The above given statements mainly concern the cos (9) development of the damage modes during the first fatigue cycle and their dependence upon the max imum applied fatigue stress. However, summaris- ing the fatigue modes appearing during fatigue 12p.EV. sin(arctan(nex) k4h2 tests performed on 3-D SiC/SiC composites the (10) following may be concluded. Matrix cracking is the first damage mode and in case of knowing/measuring n and dn then appearing during the first fatigue cycle, when the unknown quantities are Ere and ner. Solving ever the applied maximum fatigue stress qns(9)and (10)with respect to Er,]l and nerone exceeds the strength of the matrix material Matrix cracking typically stabilises very early the fat f 3-D SiC/SiC composit Ere The initially developed matrix crack network k412 is combined with the already existed, due to processing, matrix cracks and matrix porosity nex=tan( 2 arctan d, and under the applied cyclic loading leads to (12) the saturation point for the matrix cracking During this stage, the matrix cracking is Equations (11)and(12), are the expressions which accompanied by an extensive fibre matrix will be applied in the next in order to calculate the debonding. Once the matrix cracking satu effective complex modulus of elasticity rates. the matrix is cracked and the fibres are sufficiently debonded, the stress-strain curve regains an almost linear form. 6 3 Results and discussion Although matrix cracking is prerequisite for fatigue failure, does not control the fatigue The tensile and fatigue properties of 3-D SiC/SiC life. The extensive matrix cracking and the composites are reported in Table 1. During fati- interfacial debonding result in the interfacial gue, whenever the maximum applied stress exceeds sliding and wear. Additionally, in the vicinity the strength of the matrix material, an extensive of the intersection points in the case of 3-D matrix crack network is established within the 3-D SiC/SiC composites, the matrix cracking and SiC/Sic structure. This, together with the matrix the interfacial debonding reduce the stress cracks produced during the processing phase, and concentration and allow for a better align- he accompanied fibre matrix debonding consist ment of the fibre preform to the loading the first obvious group of damage mechanisms, direction. During both phenomena extensive which are developed during the first fatigue cycle frictional slip is presented Depending upon the magnitude of the maximum Finally, fibre fractures are localised during a applied stress, the matrix cracking may or may not short period at the end of the fatigue life. reach the saturation point, which is denoted by a although there are some fibre failures during characteristic spacing of the matrix cracks. Once the first fatigue cycle even when the applied the maximum applied load exceeds the stress rela maximum fatigue load does not exceed the endurance fatigue limit ted to the saturation point, then the load is trans- ferred by the fibres and macroscopically material appears as an almost linear stress-strain 3.1 Dynamic characterisation of 3-D SiC/siC curve which deviates from linearity once fibre fail- composites ures initiate In the present case of 3 D SiC/SiC composites,two different groups of fatigue tests were performed Table 1. Tensile and fatigue properties of 3-D SIC/SiC com and the stop and go' procedure described earlier posites was applied. Using this procedure the monitoring Mean value SDD of the variation of the effective dynamic modulus of elasticity along the loading direction of 3-D Sic Tensile strength (UTS) l61 0-7 MPa) Sic composites and the associated loss factor have Tensile tangent modulus 0-7 been provided as a function of the number of fati of elasticity (GPa) gue cycles Endurance fatigue limit 0-02 (R=01,f=10Hz)(%UTS) The maximum applied stress for the first group was 0.7 of the ultimate tensile strength(UTS) of
!n k4h2 12 :jEc;e xx j s : cos arctan ne xx 2 9 dn k4h2 12 :jEc;e xx j s :sin arctan ne xx 2 10 and in case of knowing/measuring !n and dn then the unknown quantities are jEc;e xx j and ne xx. Solving eqns (9) and (10) with respect to jEc;e xx j and ne xx one obtains14 jEc;e xx j !2 n d2 n ÿ : 12 k4h2 11 ne xx tan 2: arctan dn !n 12 Equations (11) and (12), are the expressions which will be applied in the next in order to calculate the eective complex modulus of elasticity. 3 Results and Discussion The tensile and fatigue properties of 3-D SiC/SiC composites are reported in Table 1.8 During fatigue, whenever the maximum applied stress exceeds the strength of the matrix material, an extensive matrix crack network is established within the 3-D SiC/SiC structure. This, together with the matrix cracks produced during the processing phase, and the accompanied ®bre matrix debonding consist the ®rst obvious group of damage mechanisms, which are developed during the ®rst fatigue cycle. Depending upon the magnitude of the maximum applied stress, the matrix cracking may or may not reach the saturation point, which is denoted by a characteristic spacing of the matrix cracks. Once the maximum applied load exceeds the stress related to the saturation point, then the load is transferred by the ®bres and macroscopically the material appears as an almost linear stress±strain curve which deviates from linearity once ®bre failures initiate. The above given statements mainly concern the development of the damage modes during the ®rst fatigue cycle and their dependence upon the maximum applied fatigue stress. However, summarising the fatigue modes appearing during fatigue tests performed on 3-D SiC/SiC composites the following may be concluded.7,8 . Matrix cracking is the ®rst damage mode appearing during the ®rst fatigue cycle, whenever the applied maximum fatigue stress exceeds the strength of the matrix material. Matrix cracking typically stabilises very early in the fatigue life of 3-D SiC/SiC composites. . The initially developed matrix crack network is combined with the already existed, due to processing, matrix cracks and matrix porosity and under the applied cyclic loading leads to the saturation point for the matrix cracking. During this stage, the matrix cracking is accompanied by an extensive ®bre matrix debonding. Once the matrix cracking saturates, the matrix is cracked and the ®bres are suciently debonded, the stress±strain curve regains an almost linear form.6 . Although matrix cracking is prerequisite for fatigue failure, does not control the fatigue life.6 The extensive matrix cracking and the interfacial debonding result in the interfacial sliding and wear. Additionally, in the vicinity of the intersection points in the case of 3-D SiC/SiC composites, the matrix cracking and the interfacial debonding reduce the stress concentration and allow for a better alignment of the ®bre preform to the loading direction. During both phenomena extensive frictional slip is presented. . Finally, ®bre fractures are localised during a short period at the end of the fatigue life, although there are some ®bre failures during the ®rst fatigue cycle even when the applied maximum fatigue load does not exceed the endurance fatigue limit. 3.1 Dynamic characterisation of 3-D SiC/SiC composites In the present case of 3 D SiC/SiC composites, two dierent groups of fatigue tests were performed and the `stop and go' procedure described earlier was applied. Using this procedure the monitoring of the variation of the eective dynamic modulus of elasticity along the loading direction of 3-D SiC/ SiC composites and the associated loss factor have been provided as a function of the number of fatigue cycles. The maximum applied stress for the ®rst group was 0.7 of the ultimate tensile strength (UTS) of Table 1. Tensile and fatigue properties of 3-D SIC/SiC composites Mean value SDD Tensile strength (UTS) (MPa) 161 0.7 Tensile tangent modulus of elasticity (GPa) 27 0.7 Endurance fatigue limit (R=0.1, f=10Hz) (% UTS) 70 0.02 Fatigue damage accumulation in 3-D SiC/SiC composites 211