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 com￾plete 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 emis￾sion 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 e€ect of fatigue on both e€ective dynamic modulus of elasticity and the relative loss factor (damping coecient) 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 trig￾gered 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 fati￾gue 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 ¯ex￾ural vibration experiment were secured unchanged. Then, the specimen was exposed again to free ¯ex￾ural vibration and its response was monitored. An A/D board (National Instrument 2000) with 2.5 mV sensitivity and maximum sampling fre￾quency 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 spec￾trum 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 dis￾cussed.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 di€erential 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 ˆ 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 ˆ 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 sti€ness matrix Dc ‰ Š: Dc xx is account as the complex bending sti€ness of the 3 D SiC/SiC along the loading direction according to the analysis presented else￾where.14 Assuming harmonic time dependence eqn (1) obtains the form @4wc …x† @x4 ÿ !2 a2 c wc …x† ˆ 0 …3† Fatigue damage accumulation in 3-D SiC/SiC composites 209