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
212 v. Kostopoulos et al 3-D SiC/SiC composites, while for the second one in this case(something which will be confirmed it was 0.75 of UTS. Each group was consisted by later based on the results of acoustic emission four samples. The results presented in the next are monitoring) referred to the monitored mean value of the pre- After the first 30 kcycles the effective dynamic sented parameter for four specimens in the case of modulus of elasticity remains almost constant, in the test specimens loaded up to a maximum case where the maximum applied load was 0.7 of applied load of 0-7 of UTS, while in the case of UTS, while it keeps decreasing with a lower rate maximum applied load of 0-75 of UTs the pre- until the final fracture in case where the maximum sented results are referred to the mean value of applied load was 0.75 of UTS. It is very interesting four specimens up to 100 kcycles, three specimens to notice that the higher the frequency where the up to 140 kcycles and two specimens up to 170 stiffness is calculated, the higher the effect of fati- kcycles. As it was expected all the tested samples, gue, and this is true for both cases of maximum which are exposed to a maximum applied stress of loading 0.7 of UTS, were run out of the fatigue experiment However, in the case of 0.7 of UTS maximum (106 cycles), while in the case of maximum applied applied load the highest monitored variation of the stress of 0.75 of UTS no specimen survived longer stiffness was 9% at the end of fatigue experiment, than 280 kcycles(mean fatigue life 174 cycles and while when the maximum applied load was 0.75 of fatigue life for each testing sample 274, 101, 148 UTS then at the end of its life, the specimen and 173 kcycles respectively). Figure 3 presents the appears a maximum stiffness decrease of 24% variation of the normalised effective dynamic Figure 4 presents the variation of the normalised modulus of elasticity in the loading direction versus damping coefficient (loss factor), which corre fatigue cycles in both applied maximum stress sponds to the monitored effective dynamic mod levels. Solid symbols stand for maximum applied ulus of elasticity, versus the fatigue cycles for both fatigue stress of 0.7 of UTS, while open symbols applied maximum stress levels. Again the solid and stand for maximum applied fatigue stress of 0-75 of the open symbols correspond to the different max UTS. According to these plots, there is a very steep imum applied stress level of 0-7 and 0.75 of UTS but limited reduction of the effective dynamic respectively modulus of elasticity, for both cases of loading, As shown in Fig. 4 for both maximum applied within the first 25 cycles. This region and this stress levels and for all the three first eigenmodes 么常民r。 ends to the formation of in each case the modal damping and the corre- behaviour mainly corres matrix crack netw nd its extension up to the sponding damping coefficient increases very fast saturation point, the development of fibre-matrix within the first 25 cycles. The rate of increase is debonding and the failure of some of the reinfor- almost the same for all the cases, although the cing fibres in the loading direction. These failure monitored damping in the case of maximum mechanisms are the reason for the monitored stiff- applied load of 0.75 of UTS was higher for all the ness reduction cases. After the 30 kcycles in the case of maximum e Comparing the stiffness reduction caused in the applied load of 0-7 of UTS the damping coefficient vo different maximum applied stress levels, it is keeps increasing, but at a lower rate. This rate clear that loading up to 0.75 of UTS produces remains almost constant until the end of the higher decrease of effective dynamic modulus of fatigue experiment. When the applied maximum lasticity, and this indicates additional fibre failures fatigue load is 0.75 of UTS (exceeds the endurance 一▲3 (42i Ho ia oi ar uis Ifor 075 d UTsI 0,78 Number of Fatigue cycles Number of Fatigue cycles Fig 3. Normalised effective dynamic modulus in the loading direction versus fatigue cycles of 3-D SiC/SiC for maximum Fig. 4. Normalised damping coefficient (loss factor) versus applied stress of 0-7(solid symbols) and 0-75(open symbols) fatigue cycles of 3-D SiC/SiC for maximum applied stress 0.7 of UTS respectively (solid symbols) and 0.75(open symbols)of UTS respectively
3-D SiC/SiC composites, while for the second one it was 0.75 of UTS. Each group was consisted by four samples. The results presented in the next are referred to the monitored mean value of the presented parameter for four specimens in the case of the test specimens loaded up to a maximum applied load of 0.7 of UTS, while in the case of maximum applied load of 0.75 of UTS the presented results are referred to the mean value of four specimens up to 100 kcycles, three specimens up to 140 kcycles and two specimens up to 170 kcycles. As it was expected all the tested samples, which are exposed to a maximum applied stress of 0.7 of UTS, were run out of the fatigue experiment (106 cycles), while in the case of maximum applied stress of 0.75 of UTS no specimen survived longer than 280 kcycles (mean fatigue life 174 kcycles and fatigue life for each testing sample 274, 101, 148 and 173 kcycles respectively). Figure 3 presents the variation of the normalised eective dynamic modulus of elasticity in the loading direction versus the fatigue cycles in both applied maximum stress levels. Solid symbols stand for maximum applied fatigue stress of 0.7 of UTS, while open symbols stand for maximum applied fatigue stress of 0.75 of UTS. According to these plots, there is a very steep but limited reduction of the eective dynamic modulus of elasticity, for both cases of loading, within the ®rst 25 kcycles. This region and this behaviour mainly corresponds to the formation of matrix crack network and its extension up to the saturation point, the development of ®bre±matrix debonding and the failure of some of the reinforcing ®bres in the loading direction. These failure mechanisms are the reason for the monitored sti- ness reduction. Comparing the stiness reduction caused in the two dierent maximum applied stress levels, it is clear that loading up to 0.75 of UTS produces higher decrease of eective dynamic modulus of elasticity, and this indicates additional ®bre failures in this case (something which will be con®rmed later based on the results of acoustic emission monitoring). After the ®rst 30 kcycles the eective dynamic modulus of elasticity remains almost constant, in case where the maximum applied load was 0.7 of UTS, while it keeps decreasing with a lower rate until the ®nal fracture in case where the maximum applied load was 0.75 of UTS. It is very interesting to notice that the higher the frequency where the stiness is calculated, the higher the eect of fatigue, and this is true for both cases of maximum loading. However, in the case of 0.7 of UTS maximum applied load the highest monitored variation of the stiness was 9% at the end of fatigue experiment, while when the maximum applied load was 0.75 of UTS then at the end of its life, the specimen appears a maximum stiness decrease of 24%. Figure 4 presents the variation of the normalised damping coecient (loss factor), which corresponds to the monitored eective dynamic modulus of elasticity, versus the fatigue cycles for both applied maximum stress levels. Again the solid and the open symbols correspond to the dierent maximum applied stress level of 0.7 and 0.75 of UTS respectively. As shown in Fig. 4 for both maximum applied stress levels and for all the three ®rst eigenmodes, in each case the modal damping and the corresponding damping coecient increases very fast within the ®rst 25 kcycles. The rate of increase is almost the same for all the cases, although the monitored damping in the case of maximum applied load of 0.75 of UTS was higher for all the cases. After the 30 kcycles in the case of maximum applied load of 0.7 of UTS the damping coecient keeps increasing, but at a lower rate. This rate remains almost constant until the end of the fatigue experiment. When the applied maximum fatigue load is 0.75 of UTS (exceeds the endurance Fig. 3. Normalised eective dynamic modulus in the loading direction versus fatigue cycles of 3-D SiC/SiC for maximum applied stress of 0.7 (solid symbols) and 0.75 (open symbols) of UTS respectively. Fig. 4. Normalised damping coecient (loss factor) versus fatigue cycles of 3-D SiC/SiC for maximum applied stress 0.7 (solid symbols) and 0.75 (open symbols) of UTS respectively. 212 V. Kostopoulos et al
Fatigue damage accumulation in 3-D SiC/SiC composites 213 fatigue limit)then the rate of increase of the mate- response monitoring of the material the more pro- rial damping for all the first three eigenfrequencies nounced the measured variation is remains high but slightly lower compared to one appearing during the first stage, with the 3.2 Correlation with acoustic emission results exception of the damping monitored for the first As has already been mentioned, during fatigue eigenfrequency experiments at h maximum applied load After the threshold of 150 kcycles, all the sur- levels, continuous AE monitoring was applied. riving specimens appeared with a higher rate of Then, pattern recognition techniques were applied increase for the material damping as they approach and the events which are related to fibre failure the end of their life. This was valid for all the have been separated in order to be correlated to the eigenfrequencies. What it is very interesting to stiffness degradation presented in the former Sec- notice here is that the increase of damping during tion. More precisely, the applied pattern recogni he first 25 kcycles is of the order of 170%, while tion technique provides a new analysis algorithm the maximum damping increase for loading up to of ae data and has been proposed elsewhere. 3It 0-7 of UTS was 320% and for loading up to 0.75 of contains descriptor selection procedures, validation UTS was 500%. Comparison of these values to the steps, filtering and statistical analysis of AE data, relative variation of effective dynamic modulus of taking into account the stochastic character of AE elasticity, indicates that a loss factor or equiva- events and the failure mechanisms appearing in the lently the damping of the relative eigenmodes is a specific material under consideration. a key point much more sensitive parameter to fatigue damage of the used algorithm is the cluster activation in compared to the effective modulus of elasticity. time informing which increases the reliability of Furthermore, the fact that during the last stage correlation between clusters and failure mechan of fatigue life(for maximum applied stress 0-75 isms. The corresponding results are given in Figs 5 of UTS), modal damping and the corresponding and 6 loss factor has a higher rate of increase That Both Figs 5 and 6 represent the AE events, could be easily explained by the development of which correspond to fibre breakage, as a function fibre failures which will finally lead the fatigue of the fatigue cycles for maximum applied stress sample to failure and could be used as an indicator of 0.7 and 0.75 respectively. The broken lines to the stage of damage, forming a predictor for the both figures indicate the degradation of the nor on-coming material failure due to fatigue. The malise effective dynamic modulus versus fatigue failure fibres create a new friction surface and cycles establish new energy dissipation mechanisms, In general, these types of diagrams, have a bath which are activated during the transverse vibration type shape that could be derived in three different of the specimen and are monitored as damping regions:(i)a Burn-in phase, (ii)a Steady-state region and (iii)a Burn-out stage. Regarding the Table 2 summarises the maximum normalised Burn-in phase (in both Figures up to 25 kcycles),it variations measured by using the dynamic response accounts for fibre fracture events during the appli monl itoring during the fatigue of 3-D SiC/Sic cation of fatigue mean load and the first cycles of composites under two different maximum applied the fatigue test. The steady-state phase represents stress levels an increase of damage. which weakens the material According to these results, in general, damping structure, causing degradation of its performance coefficient is a much more sensitive damage ind cator compared to the effective dynamic modulus of elasticity and additionally the higher the eigen- Fatigue test for omux/ut 07 frequency and the eigenmode used for the dynami Table 2. Dynamic response monitoring of 3-D SiC/SiC of amax/oudt Maximum applied (Exx o)(nxx/nxxo) ue cycles nIck Steady-state f2:0.9 3-012 f3:0.89 Number of Fatigue keycles 0-75 2716 f:0-85 Fig. 5. Correlation between AE activity related to fibre frac- f3:0-77 6-084 ture and normalised effective dynamic modulus for fatigue loading of 3-D SiC/Sic up to 0.7 of UTS
fatigue limit) then the rate of increase of the material damping for all the ®rst three eigenfrequencies remains high but slightly lower compared to the one appearing during the ®rst stage, with the exception of the damping monitored for the ®rst eigenfrequency. After the threshold of 150 kcycles, all the surviving specimens appeared with a higher rate of increase for the material damping as they approach the end of their life. This was valid for all the eigenfrequencies. What it is very interesting to notice here is that the increase of damping during the ®rst 25 kcycles is of the order of 170%, while the maximum damping increase for loading up to 0.7 of UTS was 320% and for loading up to 0.75 of UTS was 500%. Comparison of these values to the relative variation of eective dynamic modulus of elasticity, indicates that a loss factor or equivalently the damping of the relative eigenmodes is a much more sensitive parameter to fatigue damage compared to the eective modulus of elasticity. Furthermore, the fact that during the last stage of fatigue life (for maximum applied stress 0.75 of UTS), modal damping and the corresponding loss factor has a higher rate of increase. That could be easily explained by the development of ®bre failures which will ®nally lead the fatigue sample to failure and could be used as an indicator to the stage of damage, forming a predictor for the on-coming material failure due to fatigue. The failure ®bres create a new friction surface and establish new energy dissipation mechanisms, which are activated during the transverse vibration of the specimen and are monitored as damping increase. Table 2 summarises the maximum normalised variations measured by using the dynamic response monitoring during the fatigue of 3-D SiC/SiC composites under two dierent maximum applied stress levels. According to these results, in general, damping coecient is a much more sensitive damage indicator compared to the eective dynamic modulus of elasticity and additionally the higher the eigenfrequency and the eigenmode used for the dynamic response monitoring of the material the more pronounced the measured variation is. 3.2 Correlation with acoustic emission results As has already been mentioned, during fatigue experiments at both maximum applied load levels, continuous AE monitoring was applied. Then, pattern recognition techniques were applied and the events which are related to ®bre failure have been separated in order to be correlated to the stiness degradation presented in the former Section. More precisely, the applied pattern recognition technique provides a new analysis algorithm of AE data and has been proposed elsewhere.13 It contains descriptor selection procedures, validation steps, ®ltering and statistical analysis of AE data, taking into account the stochastic character of AE events and the failure mechanisms appearing in the speci®c material under consideration. A key point of the used algorithm is the cluster activation in time informing which increases the reliability of correlation between clusters and failure mechanisms. The corresponding results are given in Figs 5 and 6. Both Figs 5 and 6 represent the AE events, which correspond to ®bre breakage, as a function of the fatigue cycles for maximum applied stress of 0.7 and 0.75 respectively. The broken lines in both ®gures indicate the degradation of the normalised eective dynamic modulus versus fatigue cycles. In general, these types of diagrams, have a bathtype shape that could be derived in three dierent regions7 : (i) a Burn-in phase, (ii) a Steady±state region and (iii) a Burn-out stage. Regarding the Burn-in phase (in both Figures up to 25 kcycles), it accounts for ®bre fracture events during the application of fatigue mean load and the ®rst cycles of the fatigue test. The steady-state phase represents an increase of damage, which weakens the material structure, causing degradation of its performance Table 2. Dynamic response monitoring of 3-D SiC/SiC of composites max/ult Maximum applied fatigue cycles (kcycles) (Exxc,e/Exxc,e0) min (nxxe /nxxe 0) max 0.7 1000 f1: 0.96 2.213 f2: 0.93 3.012 f3: 0.89 4.258 0.75 174 f1: 0.89 2.716 f2: 0.85 5.342 f3: 0.77 6.084 Fig. 5. Correlation between AE activity related to ®bre fracture and normalised eective dynamic modulus for fatigue loading of 3-D SiC/SiC up to 0.7 of UTS. Fatigue damage accumulation in 3-D SiC/SiC composites 213
214 v. Kostopoulos et al Fatigue test for a /o.-075 coefficient in our case or through the hysterisis Steady-state loops elsewhere and could be a very reliable damage indicator for the material under investigation 4 Conclusions The present work deals with the characterisation of damage development in 3-D SiC/SiC composites under fatigue loading using as indicators of the Number of Fatigue keycles fatigue damage the effective dynamic modulus of elasticity and the corresponding damping coeffi Fig.6.Correlation between AE activity related to fibre frac- cient. The main conclusions of the present stud ure and normalised effective dynamic modulus for fatigue loading of 3-D Sic/SiC up to 0-75 of UTS. are the following: The fatigue the effective dynamic modulus damage produces a progressive and increase of internal damping. Due to the redistribution of the stress field around the fibre during the first 30 kcycles of fatigue life(for during this period, the crack saturation phase maximum applied stress of 0.7 of UTS) while approaches and an unstable damage propagation the damping coefficient increases drastically initiates. This period involves an increase rate of Damping coefficient is more sensitive to fati- fibre fracture and corresponds to the burn-out gue damage than the storage modulus phase. It leads to the materials final failure. The The damage stage associated to the interfacial burn out phase is absent from Fig. 5 since th rear and internal friction is very well corre material is loaded lower to its endurance fatigue lated to the monitored damping coefficient limit. In contrast to this, in the case of Fig. 6 a. The damping coefficient is in a direct relation more massive destruction of the material appears to the elsewhere used area of the hysterisis from the beginning of loading, since the applied loop which is also a fatigue damage indicator load exceeds the endurance fatigue limit, the num in the case of CMcs ber of fibre breakages is higher and close to the end of the life of the material the burn out phase The combination of dynamic response monitor appears. These results are in good correlation with ing with other damage evaluation methods such as that provided by the monitoring of the dynamic Ae could be a powerful tool in the study of the response of the material during fatigue fatigue damage of CMCs and could be used for The monitoring of the dynamic response of the establishing safe criteria for the stability of fatigu material could be accounted as a macroscopic damage and the remaining life of the material approach, while the AE monitored stands for a under investigation microscopic approach and based on this, the cri tical role of fibre fracture on the 3-D Sic/Sic stiff- ness degradation could be confirmed. The Acknowledgements degradation of the effective dynamic storage mod ulus is directly related to the number of fibre frac- The authors want gratefully to acknowledge the tures and this is confirmed comparing the results support of the Greek Ministry of Development, presented in Figs 5 and 6. On the other hand, General Secretariat of Research and Technology to additionaly to the matrix cracking that occurred the present work within the frame of pened pro- during fatigue loading, the failure of a fibre bundle ject( Contract no 615) leads to a stress redistribution in the vicinity of the broken fibre. This produces a stress concentration site, and as a result to fibre-matrix debonding. References Then the friction is the only load transfer mechan ism between matrix and fibres, but is the presence 1. Evans, A G Zok, F.w. and MeMeeking, R. M. Fati- of this friction that is recognised as internal damp- ing increase. Thus, the fibre fracture promotes Mater.,1995,43,859-875 2. Reynaud, P, Cyclic fatigue of ceramic-matrix composites fibre-matrix debonding and then friction plays a very critical role for the mechanical behaviour of Tech,1996,56,809814 CMCs during fatigue. The presence of the internal 3. Evans, A. G, Design and life prediction issues for high perature engineering ceramics and their composites. friction is monitored either through damping Acta metall. Mater.1997.45. 23-40
and increase of internal damping. Due to the redistribution of the stress ®eld around the ®bre during this period, the crack saturation phase approaches and an unstable damage propagation initiates. This period involves an increase rate of ®bre fracture and corresponds to the burn-out phase. It leads to the materials ®nal failure. The burn out phase is absent from Fig. 5 since the material is loaded lower to its endurance fatigue limit. In contrast to this, in the case of Fig. 6 a more massive destruction of the material appears from the beginning of loading, since the applied load exceeds the endurance fatigue limit, the number of ®bre breakages is higher and close to the end of the life of the material the burn out phase appears. These results are in good correlation with that provided by the monitoring of the dynamic response of the material during fatigue. The monitoring of the dynamic response of the material could be accounted as a macroscopic approach, while the AE monitored stands for a microscopic approach and based on this, the critical role of ®bre fracture on the 3-D SiC/SiC sti- ness degradation could be con®rmed. The degradation of the eective dynamic storage modulus is directly related to the number of ®bre fractures and this is con®rmed comparing the results presented in Figs 5 and 6. On the other hand, additionaly to the matrix cracking that occurred during fatigue loading, the failure of a ®bre bundle leads to a stress redistribution in the vicinity of the broken ®bre. This produces a stress concentration site, and as a result to ®bre±matrix debonding. Then the friction is the only load transfer mechanism between matrix and ®bres, but is the presence of this friction that is recognised as internal damping increase. Thus, the ®bre fracture promotes ®bre-matrix debonding and then friction plays a very critical role for the mechanical behaviour of CMCs during fatigue. The presence of the internal friction is monitored either through damping coecient in our case or through the hysterisis loops elsewhere and could be a very reliable damage indicator for the material under investigation. 4 Conclusions The present work deals with the characterisation of damage development in 3-D SiC/SiC composites under fatigue loading using as indicators of the fatigue damage the eective dynamic modulus of elasticity and the corresponding damping coe- cient. The main conclusions of the present study are the following: . The fatigue damage produces a progressive reduction of the eective dynamic modulus during the ®rst 30 kcycles of fatigue life (for maximum applied stress of 0.7 of UTS) while the damping coecient increases drastically. . Damping coecient is more sensitive to fatigue damage than the storage modulus. . The damage stage associated to the interfacial wear and internal friction is very well correlated to the monitored damping coecient . The damping coecient is in a direct relation to the elsewhere used area of the hysterisis loop1 which is also a fatigue damage indicator in the case of CMCs. The combination of dynamic response monitoring with other damage evaluation methods such as AE could be a powerful tool in the study of the fatigue damage of CMCs and could be used for establishing safe criteria for the stability of fatigue damage and the remaining life of the material under investigation. Acknowledgements The authors want gratefully to acknowledge the support of the Greek Ministry of Development, General Secretariat of Research and Technology to the present work within the frame of PENED project (Contract no. 615). References 1. Evans, A. G., Zok, F. W. and McMeeking, R. M., Fatigue of ceramic matrix compositesÐoverview. Acta metall. Mater., 1995, 43, 859±875. 2. Reynaud, P., Cyclic fatigue of ceramic-matrix composites at ambient and elevated temperatures. Comp. Sci. and Tech., 1996, 56, 809±814. 3. Evans, A. G., Design and life prediction issues for hightemperature engineering ceramics and their composites. Acta Metall. Mater., 1997, 45, 23±40. Fig. 6. Correlation between AE activity related to ®bre fracture and normalised eective dynamic modulus for fatigue loading of 3-D SiC/SiC up to 0.75 of UTS. 214 V. Kostopoulos et al
Fatigue damage accumulation in 3-D SiC/SiC composites 215 4. Kotil, T, Holmes, W. J. and Comnimou, M., Origin of and characterization of CMC and C/C composites, Pub- hysterisis during fatigue of ceramic-matrix composites. J. fishable synthesis report of BRITE/EURAM Project, 5. Rouby, D. and Reynaud, P, Fatigue behaviour related to 10. Contract N. BREU 0334-C. 199 Vellios, L, Kostopoulos, V and Paipetis, S. A, Fatigue terface modification during load cycling in ceramic-matrix effect on dynamic characteristics of composite laminates. fibre composites. Comp. Sci and Tech, 1993, 48, 109-118 Adv. Comp. Letters, 1994, 5, 121-128. 6. Holmes, J. w. and Sorensen, B F, Fatigue behaviour of l1. Vellios, L, Kostopoulos, V. and Paipetis, S.A., Fatigue continuous fibre- reinforced ceramic matrix composites damage growth monitoring of ud-composites using vibl n High Temperature Mechanical Behaviour of ceramic ion and acoustic emission techniques. In Proceedings of Ya:mposites eds. Nair, S. V. and Yakus, K, Butterworth- CCM/9, Vol. V, Composite Behaviour, ed. Miravete, A mann, London, 1995, pp. 261-327 7. Vellios, L, Pappas, Y. Z, Kostopoulos, V and Paipetis, Zaragoza, Spain, 1993, pp. 811-818 S. A, Fatigue damage characterization of 3-D SiC/SIC 12. hysical Acoustic Corporation, 8000 SPARTAN AT composites using non destructive techniques. In High Users manuaL. PAC. N. uSA. 1988. Techn 13. Pappas, Y. Z, Markopoulos, Y. Z and Kostopoulos, V Paipetis, S. A. and Youtsos, A. G, AML/University of Failure mechanisms analysis of 2-D carbon /carbon using Patras, Patras, Greece, 1995, pp. 434443 coustic emission monitoring NDT&E Int, 1998, 31 8. Kostopoulos, V, Vellios, L. and Pappas, Y. Z, Fatigue behavior of 3-D SiC/SiC composites. J. Mar. Sc, 1997, 14. Korotzis, D. T, Vellios, L and Kostopoulos, V 32,215-220 viscoelastic response of composite laminates (Visco 9. Schoberth, A. W, Condlifel, I, Michorious, M.,Kosto- Lamination Theory). J. of Mech. of Time Dep poulos, V, Martin, E and Anifrani, J. C, Development
4. Kotil, T., Holmes, W. J. and Comnimou, M., Origin of hysterisis during fatigue of ceramic-matrix composites. J. Am. Ceram. Soc., 1990, 73, 1879±1983. 5. Rouby, D. and Reynaud, P., Fatigue behaviour related to interface modi®cation during load cycling in ceramic-matrix ®bre composites. Comp. Sci. and Tech., 1993, 48, 109±118. 6. Holmes, J. W. and Sorensen, B. F., Fatigue behaviour of continuous ®bre-reinforced ceramic mactrix composites. In High Temperature Mechanical Behaviour of Ceramic Composites eds. Nair, S. V. and Yakus, K., ButterworthHeinemann, London, 1995, pp. 261±327. 7. Vellios, L., Pappas, Y. Z., Kostopoulos, V. and Paipetis, S. A., Fatigue damage characterization of 3-D SiC/SiC composites using non destructive techniques. In High Technology Composites in Modern Applications, eds. Paipetis, S. A. and Youtsos, A. G., AML/University of Patras, Patras, Greece, 1995, pp. 434±443 8. Kostopoulos, V., Vellios, L. and Pappas, Y. Z., Fatigue behavior of 3-D SiC/SiC composites. J. Mat. Sc., 1997, 32, 215±220. 9. Schoberth, A. W., Condlifel, I., Michorious, M., Kostopoulos, V., Martin, E. and Anifrani, J. C., Development and characterization of CMC and C/C composites, Publishable synthesis report of BRITE/EURAM Project, Contract N. BREU 0334-C, 1994. 10. Vellios, L., Kostopoulos, V. and Paipetis, S. A., Fatigue eect on dynamic characteristics of composite laminates. Adv. Comp. Letters, 1994, 5, 121±128. 11. Vellios, L., Kostopoulos, V. and Paipetis, S. A., Fatigue damage growth monitoring of ud-composites using vibration and acoustic emission techniques. In Proceedings of ICCM/9, Vol. V, Composite Behaviour, ed. Miravete, A., University of Zaragoza, Woodhead Publishing Ltd., Zaragoza, Spain, 1993, pp. 811±818. 12. Physical Acoustic Corporation, 8000 SPARTAN AT Users Manual, PAC, NJ, USA, 1988. 13. Pappas, Y. Z., Markopoulos, Y. Z. and Kostopoulos, V., Failure mechanisms analysis of 2-D carbon/carbon using acoustic emission monitoring. NDT&E Int., 1998, 31, 157± 163. 14. Korotzis, D. T., Vellios, L. and Kostopoulos, V., On the viscoelastic response of composite laminates (Viscoelastic Lamination Theory). J. of Mech. of Time Dep. Mat., submitted. Fatigue damage accumulation in 3-D SiC/SiC composites 215