Availableonlineatwww.sciencedirect.cor ° Science Direct CERAMICS INTERNATIONAL ELSEVIER Ceramics International 34(2008)1857-1865 www.elsevier.com/locate/ceramint Study of the resistance to crack propagation in alumina by acoustic emission S. Bouras . l. zerizer. f gheldane. M.t. bouazza. B. bouzabata Laboratoire des Materiaux Avances, Universite de Annaba, B P. 12, 23000 Annaba, algeria Received 7 March 2006: received in revised form 4 February 2007; accepted 29 June 2007 Available online 19 August 2007 Abstract The resistance to crack propagation or R-curve effect is still extensively studied in polycrystalline ceramic materials. This effect is shown in the literature by the increase of the stress intensity factor K versus crack extension, or by the decrease of crack velocity versus Ki under flexure tests. We have studied this fracture resistance by using the acoustic emission and the hertzian indentation technique. It was found that the acoustic emission count rate decreases, like crack velocity in conditions of sub-critical crack growth before the failure is reached. Two specimen of alumina, respectively with small and coarse grains, were tested. a high crack extension resistance is obtained for coarse-grained alumina Mechanisms of crack bridging and crack shielding are responsible for the R-curve effect. These mechanisms are also operating during cyclic loading. The resistance to crack propagation increases more and more after each cycle. Also we obtain R-curve effect during static loading On the other hand, toluene or silicone oil corrosive environment delays the crack propagation. But water medium has a reverse effect and the apparent toughness is reduced in this case. C 2007 Elsevier Ltd and Techna Group S r.l. All rights reserved. Keywords: Hertzian indentation; Acoustic emission; Crack extension; R-curve; Sub-critical growth; Alumina 1. Introduction roughness of the fracture surfaces permits physical contact between them as long as the crack does not open too much 1.I. Resistance to crack propagation: R-curve effect 1. 2. Sub-critical crack growth Ceramic brittleness is due to pre-existent micro-cracks which propagate unstably until the failure occurs. Som The sub-critical crack growth is one of the most frequent to stable crack propagation. In this case, the material toughness propagation modes in ceramics. It occurs under stress lower is no longer constant but increases with the crack extension than the critical stress for fracture. Slow crack growth is most The increase of fracture resistance with crack extension suitably described by a relation between the crack velocity V under stable crack growth is due to energy-consuming effects and the stress intensity factor K, in a KrV diagram(Fig. 1).In such as micro-cracking [ crack ramification, bridging by closely on K. For intermediate stresses or stage I, the grains (21, crack shielding by a damaged zone, plastic propagation continues with constant speed. At high stresses, the called r-curve behavior and is associated with the stress intensity factor KI: additional energy is necessary for a crack to depends on the chemical environment, on the loading mode 3] propagate until failure occurs, because of residual compressive and on the initial flaw size [4], but is independent of the stresses appearing in the crack wake and tending to close it. The specimen geometry The catastrophic fracture of a component occurs at the critical value Kic. Klo is a threshold limit [5] below which no crack growth appears. It permits us to define a safety domain for the specimen 2-8842/34.00@ 2007 Elsevier Ltd and Techna Group S.r.L. All rights reserved 10.1016 1-ceramint.2007.06015
Study of the resistance to crack propagation in alumina by acoustic emission S. Bouras *, I. Zerizer, F. Gheldane, M.T. Bouazza, B. Bouzabata Laboratoire des Mate´riaux Avance´s, Universite´ de Annaba, B.P. 12, 23000 Annaba, Algeria Received 7 March 2006; received in revised form 4 February 2007; accepted 29 June 2007 Available online 19 August 2007 Abstract The resistance to crack propagation or R-curve effect is still extensively studied in polycrystalline ceramic materials. This effect is shown in the literature by the increase of the stress intensity factor KI versus crack extension, or by the decrease of crack velocity versus KI under flexure tests. We have studied this fracture resistance by using the acoustic emission and the Hertzian indentation technique. It was found that the acoustic emission count rate decreases, like crack velocity in conditions of sub-critical crack growth before the failure is reached. Two specimen of alumina, respectively with small and coarse grains, were tested. A high crack extension resistance is obtained for coarse-grained alumina. Mechanisms of crack bridging and crack shielding are responsible for the R-curve effect. These mechanisms are also operating during cyclic loading. The resistance to crack propagation increases more and more after each cycle. Also we obtain R-curve effect during static loading. On the other hand, toluene or silicone oil corrosive environment delays the crack propagation. But water medium has a reverse effect and the apparent toughness is reduced in this case. # 2007 Elsevier Ltd and Techna Group S.r.l. All rights reserved. Keywords: Hertzian indentation; Acoustic emission; Crack extension; R-curve; Sub-critical growth; Alumina 1. Introduction 1.1. Resistance to crack propagation: R-curve effect Ceramic brittleness is due to pre-existent micro-cracks which propagate unstably until the failure occurs. Some technical ceramics exhibit a crack growth resistance that leads to stable crack propagation. In this case, the material toughness is no longer constant but increases with the crack extension. The increase of fracture resistance with crack extension under stable crack growth is due to energy-consuming effects such as micro-cracking [1], crack ramification, bridging by grains [2], crack shielding by a damaged zone, plastic deformation, or phase transformation. This phenomenon is called R-curve behavior and is associated with the stress intensity factor KI: additional energy is necessary for a crack to propagate until failure occurs, because of residual compressive stresses appearing in the crack wake and tending to close it. The roughness of the fracture surfaces permits physical contact between them as long as the crack does not open too much. 1.2. Sub-critical crack growth The sub-critical crack growth is one of the most frequent propagation modes in ceramics. It occurs under stress lower than the critical stress for fracture. Slow crack growth is most suitably described by a relation between the crack velocity V and the stress intensity factor KI in a KI–V diagram (Fig. 1). In stage I, at low applied stresses, the crack velocity depends closely on KI. For intermediate stresses or stage II, the propagation continues with constant speed. At high stresses, the velocity becomes again very sensitive to KI in the stage III. V depends on the chemical environment, on the loading mode [3] and on the initial flaw size [4], but is independent of the specimen geometry. The catastrophic fracture of a component occurs at the critical value KIC. KI0 is a threshold limit [5] below which no crack growth appears. It permits us to define a safety domain for the specimen. www.elsevier.com/locate/ceramint Ceramics International 34 (2008) 1857–1865 * Corresponding author. 0272-8842/$34.00 # 2007 Elsevier Ltd and Techna Group S.r.l. All rights reserved. doi:10.1016/j.ceramint.2007.06.015
l858 S. Bouras et al./Ceramics Intemational 34(2008)1857-1865 Fig. 1. Crack velocity as a function of applied stress intensity factor (Krv diagram). In the stage I, the growth rate is controlled by a corrosion K,(MPam) reaction at the crack tip. The variation of v versus KI Fig. 2. Sub-critical crack growth under constant load with natural cracks or a described by the following law: macro-crack 191 V=AK ( where Kappl=oYais applied by external load and AKI is the contribution of the reinforcement mechanisms The R-curve where A and n are constants that characterize the material and effect compensates the effect of the sub-critical growth. This its environment respectively has been shown on alumina and zirconia by fett and munz In the stage Il, the growth rate is controlled by the diffusion [10, 11)using flexure tests under constant load. The authors of corrosive species towards the crack tip [6,7] reported the KrV diagram(Fig. 2)that shows a minimum In the stage Ill, governed also by a similar law as relation(1), velocity when K,increases he driving force is higher and the failure is imminent This Observations of brittle crystalline solids in the transmission stage is due to different mechanisms: thermally activated electron microscope by Lawnet al [14], Hockey and Wiederhom growth, growth controlled by a dislocation process, etc. [7, 8]. [15], Hockey and Lawn [16] have revealed inter-facial misfit Different sub-critical growth behaviors due to an R-curve dislocations which form when crack interfaces rebond effect have been observed in the case of a macro-crack imperfect registry, but no evidence for crack tip plasticity. It is (initiated from a notch in bending) or of natural flaws(pores, this absence of plasticity which explains why the static fatigue inclusions, etc 3,]. This R-curve effect, with a decrease limit of glasses and ceramics corresponds to equilibrium cracks in velocity, is well observed at the start of the macro-crack and to the true Griffith criterion growth and tends towards saturation(Fig. 2). When the driving force becomes closer to KIc and the propagation rate quickly 1.3. Acoustic emission increases. the behavior becomes similar to that of natural cracks The acoustic emission(A E )designates all manifestation of The r-curve effect in alumina was studied by Fett and Munz acoustic waves whose source is within a material undergoing a [10-12]. The KrV curves for macro-cracks show an initial structural modification induced by an applied mechanical load decrease followed by an increase of velocity up to a When an irreversible energy release occurs, a part is catastrophic failure. A similar behavior has been observed transformed emitted stress wave that can be detected by Steinbrech [13]. The driving force at the sharp crack tip [14], with an appropriate sensor from th In the polycrystalline ceramic materials, the sub-critical stress intensity factor"Kappl, by the stress shielding effect due crack growth, essentially intergranular, is one of the sources of to the crack surface interaction In the coarse-grained alumina A.E. Because of the microstructure (rigid grain, porosity studied by the authors(grain size is about 20 um), the shielding inclusions, etc. the crack tip is irregular and the growth occurs process is essentially bridging of the crack surfaces by by sequential steps along the tip. An A E event corresponds at each step. The A E. method must be highly sensitive and the The effective stress intensity factor at the crack tip, Ktip, may sensor, even distant from the source, detects the source event be written as Therefore, it is not necessary to localize the source The interest is to acquire data about emissive events and to YV-ldde (2) relate them to their origin mechanisms
In the stage I, the growth rate is controlled by a corrosion reaction at the crack tip. The variation of V versus KI is described by the following law: V ¼ AKn I (1) where A and n are constants that characterize the material and its environment respectively. In the stage II, the growth rate is controlled by the diffusion of corrosive species towards the crack tip [6,7]. In the stage III, governed also by a similar law as relation (1), the driving force is higher and the failure is imminent. This stage is due to different mechanisms: thermally activated growth, growth controlled by a dislocation process, etc. [7,8]. Different sub-critical growth behaviors due to an R-curve effect have been observed in the case of a macro-crack (initiated from a notch in bending) or of natural flaws (pores, inclusions, etc.) [3,9–11]. This R-curve effect, with a decrease in velocity, is well observed at the start of the macro-crack growth and tends towards saturation (Fig. 2). When the driving force becomes closer to KIC and the propagation rate quickly increases, the behavior becomes similar to that of natural cracks. The R-curve effect in alumina was studied by Fett and Munz [10–12]. The KI–V curves for macro-cracks show an initial decrease followed by an increase of velocity up to a catastrophic failure. A similar behavior has been observed by Steinbrech [13]. The driving force at the sharp crack tip [14], ‘‘tip stress intensity factor’’ Ktip, differs from the ‘‘applied stress intensity factor’’ Kappl, by the stress shielding effect due to the crack surface interaction. In the coarse-grained alumina studied by the authors (grain size is about 20 mm), the shielding process is essentially bridging of the crack surfaces by interlocking grains. The effective stress intensity factor at the crack tip, Ktip, may be written as Ktip ¼ Kappl DKI (2) where Kappl = sYa1/2 is applied by external load and DKI is the contribution of the reinforcement mechanisms. The R-curve effect compensates the effect of the sub-critical growth. This has been shown on alumina and zirconia by Fett and Munz [10,11] using flexure tests under constant load. The authors reported the KI–V diagram (Fig. 2) that shows a minimum in velocity when KI increases. Observations of brittle crystalline solids in the transmission electron microscope by Lawn et al.[14], Hockey andWiederhorn [15], Hockey and Lawn [16] have revealed inter-facial misfit dislocations which form when crack interfaces rebond in imperfect registry, but no evidence for crack tip plasticity. It is this absence of plasticity which explains why the static fatigue limit of glasses and ceramics corresponds to equilibrium cracks and to the true Griffith criterion. 1.3. Acoustic emission The acoustic emission (A.E.) designates all manifestation of acoustic waves whose source is within a material undergoing a structural modification induced by an applied mechanical load. When an irreversible energy release occurs, a part is transformed in an emitted stress wave that can be detected with an appropriate sensor. In the polycrystalline ceramic materials, the sub-critical crack growth, essentially intergranular, is one of the sources of A.E. Because of the microstructure (rigid grain, porosity inclusions, etc.) the crack tip is irregular and the growth occurs by sequential steps along the tip. An A.E. event corresponds at each step. The A.E. method must be highly sensitive and the sensor, even distant from the source, detects the source event. Therefore, it is not necessary to localize the source. The interest is to acquire data about emissive events and to relate them to their origin mechanisms. Fig. 1. Crack velocity as a function of applied stress intensity factor (KI–V diagram). Fig. 2. Sub-critical crack growth under constant load with natural cracks or a macro-crack [9]. 1858 S. Bouras et al. / Ceramics International 34 (2008) 1857–1865
S. Bouras et al. /Ceramics Intemational 34(2008)1857-1865 859 200 > lV Time(s) 200400600800100012001400160018002000 uL「Luu Fig. 3. Burst type signal: amplitude crest to crest. When the source liberates an energy pulse, the correspond ing signal of A E is of burst type(Fig 3). This signal is easily Fig 4. Numbering of arks of an acoustic emission salvo nguished from the ground noise because of its high amplitude. The signal contains some information concerning is loaded by a spherical indenter of radius R, a circular crack of the source phenomenon. radius ro, forms a minimum critical load Pcro is slightly Crack propagation is the result of successive jumps of superior to the radius a of the contact zone between the ball and localized parts of the crack front. Each crack jump(an ark) is the material. As the load increases, the crack propagates both at the source of acoustic emission. A group of arks represents a the surface over a circle around the contact zone, and in depth as crack that emits an event(a salvo). Each salvo is represented by a conical shape crack of length c [20]. " See Electronic Annex 1 an acoustic emission peak in the curves amplitude-time. The in the online version of this article". This method needs the events count rate, dN/dt, is a correct image of the average crack presence of natural initial flaws at the surface of the sample growth rate. It is related to the stress intensity factor by a similar Upon attaining a critical""Griffith configuration", a favourably equation as relation(1). located flaw runs around the contact to form a surface ring Previous works [17, 18] have already shown that the events crack. The faws, introduced by polishing, are Griffith elliptic count rate exhibits the same functional dependence on K as defects with a front curve and become sharp crack after a does the slow crack velocity. Evans and Linzer [17]showed that lifetime [21-24 the relationship between the events count rate dN/dt and the Using spheres, flat punches and peeling, Maugis and time-to-failure can be effectively used for the failure prediction. Barquins [25] and Maugis [26] studied the equilibrium, healin However, this prediction needs a well-characterized material and the propagation of sub-critical Griffith cracks according to and a well-defined low-level emission. Khuri et al. [ 19] used the loss of the elasticity at the crack tip in elastic solids, glasses acoustic surface wave techniques on polished ceramics for and ceramics. The edge of the contact area can be considered as detecting and characterizing surface cracks and also to predict an interface crack tip in mode I such that the system is the same failure. Our experimental conditions of A E are close to those for a notched solid with an imposed crack path Maugis has also used by Evans and Linzer. In fact, the time-to-failure can be widely evoked the Griffith criterion at the crack tip local measured by AE In the present work, the acoustic emission is detected by a Bruel Kjaer piezoelectric transducer of frequency range 200- band filter >200 kHz, gain 40 dB), and an amplifier(variable gain from 0 to 50 dB with a filter of 200 kHz to 2 MHz)are used. After amplification, the signal is memorised in a home made counter. The number of times that it overpasses a given fixed threshold V* above the noise level (Fig. 4), is recorded as counts N. The counts can be cumulative(cumulative counts: M) Y initial crack or initialized at regular intervals(count rate: dN/dt: number of arks by unit of time) 14. Hertzian indentation In our work, the A E technique is used to follow the changes in cracks propagation dynamics in a Hertzian indentation loading. The Hertzian indentation(Fig. 5) is a mechanical Fig. 5 ics of the Hertzian contact: a contact radius; ro crack radiu haracterization method. When a brittle material plane surface the surface; c crack length in depth; R ball radius; P indentation load
When the source liberates an energy pulse, the corresponding signal of A.E. is of burst type (Fig. 3). This signal is easily distinguished from the ground noise because of its high amplitude. The signal contains some information concerning the source phenomenon. Crack propagation is the result of successive jumps of localized parts of the crack front. Each crack jump (an ark) is the source of acoustic emission. A group of arks represents a crack that emits an event (a salvo). Each salvo is represented by an acoustic emission peak in the curves amplitude-time. The events count rate, dN/dt, is a correct image of the average crack growth rate. It is related to the stress intensity factor by a similar equation as relation (1). Previous works [17,18] have already shown that the events count rate exhibits the same functional dependence on K1 as does the slow crack velocity. Evans and Linzer [17] showed that the relationship between the events count rate dN/dt and the time-to-failure can be effectively used for the failure prediction. However, this prediction needs a well-characterized material and a well-defined low-level emission. Khuri et al. [19] used acoustic surface wave techniques on polished ceramics for detecting and characterizing surface cracks and also to predict failure. Our experimental conditions of A.E. are close to those used by Evans and Linzer. In fact, the time-to-failure can be measured by A.E. In the present work, the acoustic emission is detected by a Bru¨el & Kjær piezoelectric transducer of frequency range 200– 300 kHz with a 2–3 mV ground noise. A preamplifier (passband filter >200 kHz, gain 40 dB), and an amplifier (variable gain from 0 to 50 dB with a filter of 200 kHz to 2 MHz) are used. After amplification, the signal is memorised in a home made counter. The number of times that it overpasses a given fixed threshold V* above the noise level (Fig. 4), is recorded as counts N. The counts can be cumulative (cumulative counts: N) or initialized at regular intervals (count rate: dN/dt: number of arks by unit of time). 1.4. Hertzian indentation In our work, the A.E. technique is used to follow the changes in cracks propagation dynamics in a Hertzian indentation loading. The Hertzian indentation (Fig. 5) is a mechanical characterization method. When a brittle material plane surface is loaded by a spherical indenter of radius R, a circular crack of radius r0, forms a minimum critical load PCr0 is slightly superior to the radius a of the contact zone between the ball and the material. As the load increases, the crack propagates both at the surface over a circle around the contact zone, and in depth as a conical shape crack of length c [20]. ‘‘See Electronic Annex 1 in the online version of this article’’. This method needs the presence of natural initial flaws at the surface of the sample. Upon attaining a critical ‘‘Griffith configuration’’, a favourably located flaw runs around the contact to form a surface ring crack. The flaws, introduced by polishing, are Griffith elliptic defects with a front curve and become sharp crack after a lifetime [21–24]. Using spheres, flat punches and peeling, Maugis and Barquins [25] and Maugis [26] studied the equilibrium, healing and the propagation of sub-critical Griffith cracks according to the loss of the elasticity at the crack tip in elastic solids, glasses and ceramics. The edge of the contact area can be considered as an interface crack tip in mode I such that the system is the same for a notched solid with an imposed crack path. Maugis has also widely evoked the Griffith criterion at the crack tip local conditions. Fig. 3. Burst type signal: amplitude crest to crest. Fig. 4. Numbering of arks of an acoustic emission salvo. Fig. 5. Schematics of the Hertzian contact: a contact radius; r0 crack radius at the surface; c crack length in depth; R ball radius; P indentation load. S. Bouras et al. / Ceramics International 34 (2008) 1857–1865 1859
The mechanism of cone crack initiation and propagation is Physique et de Physique des Materiaux)laboratory ell understood by using the Hertz-Huber stress tensor and from an alumina powder(99.9% purity). Sintered at 1550C fracture mechanics [24, 27-30). Sneddon [31] has given the under an applied uniaxial load of 40 MPa, the resulting stress field grain size is between 2 and 10 um. The second material In brittle materials, the Hertzian crack is catastrophically (Fig. 6b), an industrial alumina provided by Desmarquet produced in a very short time. However, in materials exhibing Ceramiques et Techniques(code AF997,99.8%purity),has an R-curve effect, the crack occurs progressively as loading been sintered at 1600C ending in coarse grains with sizes proceeds: small cracks are initiated from random flaws to form between 5 and 20 um. relatively deep circle arc that coalesce in a circular crack at the urface, and in a conical crack in depth 32] The critical value Pc corresponding to the final unstable crack extension is determined by the A.E. event of the highe amplitude. The crack jumps occurring before reaching P( oduce acoustic emission events of small amplitudes The A.E. monitoring is then a tool for following the resistance to crack propagation step by step. It can also be used to determine the fracture surface energy and the toughness by using classical theories of the Hertzian indentation [29, 30, 33-41 Initial flaws of a chosen size are introduced by using a polishing paper of a specific abrasion grit size[21,32]. The balls used in the present work have the following characteristics emented carbide 94WC-6Co, density: 15 g/cm, hardness 1550 Hv, E=630 GPa, U=0.22, radius from I to 14 mm. They have been provided by CIMAP-France 2. Description of the materials We studied two alumina ceramics. The first material has been processed by G.E. MPP.M( Groupe d' Etudes de Metallurgie y200 Fig. 7. Stages of a circular fissure formation. Laboratory alumina(small Fig. 6. Microstructure of alumina:(a) elaborated in laboratory (small grains) grains); grit size 3 um: (a) Pmax=700N, R=4 mm; (b)Pmax=950N, and(b) industrial alumina(coarse grains R=8mm:(c)Pmax= 1350N, R=3 mm
The mechanism of cone crack initiation and propagation is well understood by using the Hertz–Huber stress tensor and fracture mechanics [24,27–30]. Sneddon [31] has given the stress field. In brittle materials, the Hertzian crack is catastrophically produced in a very short time. However, in materials exhibing an R-curve effect, the crack occurs progressively as loading proceeds: small cracks are initiated from random flaws to form relatively deep circle arc that coalesce in a circular crack at the surface, and in a conical crack in depth [32]. The critical value PC corresponding to the final unstable crack extension is determined by the A.E. event of the highest amplitude. The crack jumps occurring before reaching PC produce acoustic emission events of small amplitudes. The A.E. monitoring is then a tool for following the resistance to crack propagation step by step. It can also be used to determine the fracture surface energy and the toughness by using classical theories of the Hertzian indentation [29,30,33–41]. Initial flaws of a chosen size are introduced by using a polishing paper of a specific abrasion grit size [21,32]. The balls used in the present work have the following characteristics: cemented carbide 94WC–6Co, density: 15 g/cm3 , hardness: 1550 Hv, E = 630 GPa, v ¼ 0:22, radius from 1 to 14 mm. They have been provided by CIMAP-France. 2. Description of the materials We studied two alumina ceramics. The first material has been processed by G.E.M.P.P.M (Groupe d’Etudes de Me´tallurgie Physique et de Physique des Mate´riaux) laboratory (Fig. 6a) from an alumina powder (99.9% purity). Sintered at 1550 8C under an applied uniaxial load of 40 MPa, the resulting grain size is between 2 and 10 mm. The second material (Fig. 6b), an industrial alumina provided by Desmarquet Ce´ramiques et Techniques (code AF997, 99.8% purity), has been sintered at 1600 8C ending in coarse grains with sizes between 5 and 20 mm. Fig. 6. Microstructure of alumina: (a) elaborated in laboratory (small grains) and (b) industrial alumina (coarse grains). Fig. 7. Stages of a circular fissure formation. Laboratory alumina (small grains); grit size 3 mm: (a) Pmax = 700 N, R = 4 mm; (b) Pmax = 950 N, R = 8 mm; (c) Pmax = 1350 N, R = 3 mm. 1860 S. Bouras et al. / Ceramics International 34 (2008) 1857–1865
S. Bouras et al. /Ceramics intemational 34(2008)1857-1865 3. Results The acoustic activity recorded before reaching Pc(Fig 9) similar to the A.E. activity shown on the left of the higher event Under Hertzian indentation loading, the circular and conical observed in Fig. 8. These acoustic signals obtained during racks do not occur immediately. They are formed gradually by ding below the critical load are linked to sub-critical crack progression and propagation of the initial crack(Fig. 7) until propagation. In fact, this A.E. activity has already been shown the formation of a complete circle whichever the used loading by Nadeau [42] as caused by the interaction between the node(monotonous, static, or cyclic). This effect is due to an moving crack and defects on surfa increase of the crack propagation resistance(R-curve effect When a crack is initiated at a favourable flaw, it propa Fig. 7 shows the various steps of formation of a circular along a certain proportion of the length of a circle of radius ro fissure resulting from loading up to the loads of 700 N(Fig. 7a), (partial circular crack), at the surface. Its radius does not change 950N(Fig. 7b), and 1350N(Fig. 7c) followed by an with the increase of the load And by further loading, the partial unloading. The AE activity for the load of 1450n higher circular crack will grow by following the same path of radius ro. than Pc is given in Fig. 8. The crest amplitude value of the in conformity with the Hertzian stress field highest A.E. peak corresponding to the critical load Pc, given The number n of a.e. events increases under the effect of by the relation dB=20 logIo V+ 60 [32], where V is the the increasing applied load, first slowly, then quickly as the recorded voltage, is 57 dB. This event peak recorded at 580 s unstable propagation and the failure become imminent corresponds to the closing of the partial circle as observed (Fig. 10). And below Pc, the events count rate decreases ( Fig. 7c) because of small A.E. activity(Fig. 11)revealing an increase of the R-curve effect. This change in events count rate qualitatively similar to the variation of crack velocity if one assumes that each AE to a step of a crack 1200 900 0 0.3 20040060080010001200 Time(s) Fig 8. Acoustic emission during loading up to a load Pmax(1450 N)higher than Fig. 10. Typical A.E. events count as a function of load(Pmax=750N) Pc. Laboratory alumina(small grains); grit Laboratory alumina(small grains); grit size 3 um; R=3 mm. Alumina with small grains 10001200 Time(s) Laboratory alumina(small grains): grit size 3 um; R=3mm.wer than Pc. Fig. 11. Events count rate until a load below the critical load Pc Fig. 9. Acoustic emission for loading up to a load of 820N lowe (Pmax=750N
3. Results Under Hertzian indentation loading, the circular and conical cracks do not occur immediately. They are formed gradually by progression and propagation of the initial crack (Fig. 7) until the formation of a complete circle whichever the used loading mode (monotonous, static, or cyclic). This effect is due to an increase of the crack propagation resistance (R-curve effect). Fig. 7 shows the various steps of formation of a circular fissure resulting from loading up to the loads of 700 N (Fig. 7a), 950 N (Fig. 7b), and 1350 N (Fig. 7c) followed by an unloading. The AE activity for the load of 1450 N higher than PC is given in Fig. 8. The crest amplitude value of the highest A.E. peak corresponding to the critical load PC, given by the relation dB = 20 log10 V + 60 [32], where V is the recorded voltage, is 57 dB. This event peak recorded at 580 s corresponds to the closing of the partial circle as observed (Fig. 7c). The acoustic activity recorded before reaching PC (Fig. 9) is similar to the A.E. activity shown on the left of the higher event observed in Fig. 8. These acoustic signals obtained during loading below the critical load are linked to sub-critical crack propagation. In fact, this A.E. activity has already been shown by Nadeau [42] as caused by the interaction between the moving crack and defects on surface. When a crack is initiated at a favourable flaw, it propagates along a certain proportion of the length of a circle of radius r0 (partial circular crack), at the surface. Its radius does not change with the increase of the load. And by further loading, the partial circular crack will grow by following the same path of radius r0, in conformity with the Hertzian stress field. The number N of A.E. events increases under the effect of the increasing applied load, first slowly, then quickly as the unstable propagation and the failure become imminent (Fig. 10). And below PC, the events count rate decreases because of small A.E. activity (Fig. 11) revealing an increase of the R-curve effect. This change in events count rate is qualitatively similar to the variation of crack velocity if one assumes that each A.E. event corresponds to a step of a crack Fig. 8. Acoustic emission during loading up to a load Pmax (1450 N) higher than PC. Laboratory alumina (small grains); grit size 3 mm; R = 4 mm. Fig. 9. Acoustic emission for loading up to a load of 820 N lower than PC. Laboratory alumina (small grains); grit size 3 mm; R = 3 mm. Fig. 10. Typical A.E. events count as a function of load (Pmax = 750 N). Laboratory alumina (small grains); grit size 3 mm; R = 3 mm. Fig. 11. Events count rate until a load below the critical load PC (Pmax = 750 N). S. Bouras et al. / Ceramics International 34 (2008) 1857–1865 1861