《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_Al2O3-SiC-34

f MATERIALIA Pergamon Acta mater.49(2001)3553-3563 www.elsevier.com/locate/actamat TEMPERATURE DEPENDENCE OF CRACK WAKE BRIDGING STRESSES IN A SIC-WHISKER-REINFORCED ALUMINA G.R. SARRAFl-NOUR and T w. COYLET Department of Materials Science and Engineering, University of Toronto, 184 College St, Toronto, oN, Canada M5S 3F4 Received 12 July 2000: received in revised form 8 June 2001: accepted 8 June 2001) Abstract-The crack face bridging behavior of a SiC-whisker-reinforced alumina composite was charac rized between room temperature and 1400oC in air. The bridging relations of the material were deconvoluted from the chevron-notched specimen R-curves by employing the fracture mechanics weight function method and assuming that pullout bridging was the dominant bridging mechanism. The results indicated that the maximum bridging stress decreased linearly with increasing temperature while the distribution of the bridging tresses appeared to shift towards larger crack opening displacements. The former trend was found to good agreement with literature data on the temperature dependence of residual stresses measured in sim omposites, while the latter agreed with the observation of an increasing whisker pullout length in such s with increasing temperature. In agreement with previous studies of this material, some crack- one between 1000C and 1300C, no influence from the microcrack zone on the bridging stresses was detected. 200/ Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Fracture fracture toughness; Crack wake bridging stress 1 INTRODUCTION operating in the crack wake zone T>1200.C. In contrast to these studies It is now well-known that when incorporated in a cer- made in other research works [10,11] imic matrix, strong ceramic whiskers can improve the strong toughening component due tor of as high as four relative to the monolithic matrix microcrack zone, and crack branching [12], in the material[1-3]. Various toughening mechanisms con- composite at T>1200 C with no mention of any R- sidered as contributing to the improved fracture curve behavior. One reason for the inconsistency of resistance of the composite material include crack these results may be the sensitivity of the fra acture deflection, microcracking, and crack-wake bridging behavior of the composite and the operative toughen mechanisms the latter has widely been accepted to be of the material: predominantly effects associated with composite [4-7 of the whisker/matrix interface [15-18] Previous studies of the fracture behavior of Sic. Crack-wake-bridging behavior of monolithic and whisker-reinforced alumina based on R-curve reinforced ceramics is frequently studied by measurements concluded a strong crack wake bridg- employing R-curve measurements, with the observed e hg component in the toughening of the material at behavior commonly discussed based on the rate and that crack wake toughen- [46,8,9, 19-21]. However, a major deficiency ing mechanisms dominated the fracture resistance of inherent to such inherent to such evaluations is the strong dependence the composite; however, the active mechanism was the r suggested to change from a predominantly frontal specimen/crack and the type of loading, making the zone(microcracking) type at low temperatures to one results obtained by using different crack geometries essentially incomparable. In spite of numerous studie on the fracture and R-curve behavior of sic-whisker addressed. reinforced alumina composites, there are only few Coyle) studies dealing directly with the characterization of 1359-6454/01/20.00 O 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved P:S1359-6454(01)00244-0

Acta mater. 49 (2001) 3553–3563 www.elsevier.com/locate/actamat TEMPERATURE DEPENDENCE OF CRACK WAKE BRIDGING STRESSES IN A SiC-WHISKER-REINFORCED ALUMINA G. R. SARRAFI-NOUR and T. W. COYLE† Department of Materials Science and Engineering, University of Toronto, 184 College St., Toronto, ON, Canada M5S 3E4 ( Received 12 July 2000; received in revised form 8 June 2001; accepted 8 June 2001 ) Abstract—The crack face bridging behavior of a SiC-whisker-reinforced alumina composite was charac￾terized between room temperature and 1400°C in air. The bridging relations of the material were deconvoluted from the chevron-notched specimen R-curves by employing the fracture mechanics weight function method and assuming that pullout bridging was the dominant bridging mechanism. The results indicated that the maximum bridging stress decreased linearly with increasing temperature while the distribution of the bridging stresses appeared to shift towards larger crack opening displacements. The former trend was found to be in good agreement with literature data on the temperature dependence of residual stresses measured in similar composites, while the latter agreed with the observation of an increasing whisker pullout length in such composites with increasing temperature. In agreement with previous studies of this material, some crack-tip toughening due to a microcrack damage zone formed around the crack-tip by diffusional cavitation could be observed at T
1000°C. Although the material exhibited toughening by both a microcrack zone and a bridging zone between 1000°C and 1300°C, no influence from the microcrack zone on the bridging stresses was detected.  2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Fracture & fracture toughness; Crack wake bridging stress 1. INTRODUCTION It is now well-known that when incorporated in a cer￾amic matrix, strong ceramic whiskers can improve the fracture resistance of the resulting composite by a fac￾tor of as high as four relative to the monolithic matrix material [1–3]. Various toughening mechanisms con￾sidered as contributing to the improved fracture resistance of the composite material include crack deflection, microcracking, and crack-wake bridging by the reinforcement. Amongst these toughening mechanisms the latter has widely been accepted to be responsible for the observed R-curve behavior in the composite [4–7]. Previous studies of the fracture behavior of SiC￾whisker-reinforced alumina based on R-curve measurements concluded a strong crack wake bridg￾ing component in the toughening of the material at temperatures beyond 1000°C [8]. Further studies [6, 9] arrived at the conclusion that crack wake toughen￾ing mechanisms dominated the fracture resistance of the composite; however, the active mechanism was suggested to change from a predominantly frontal zone (microcracking) type at low temperatures to one † To whom all correspondence should be addressed. E-mail address: coyle@ecf.utoronto.ca (T. W. Coyle) 1359-6454/01/$20.00  2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S13 59-6454(01)00244-0 operating in the crack wake zone (bridging) at T
1200°C. In contrast to these studies, observations made in other research works [10, 11] supported a strong toughening component due to a frontal microcrack zone, and crack branching [12], in the composite at T
1200°C with no mention of any R￾curve behavior. One reason for the inconsistency of these results may be the sensitivity of the fracture behavior of the composite and the operative toughen￾ing mechanisms to the details of the microstructure of the material: predominantly effects associated with whisker surface morphology [13, 14] and the nature of the whisker/matrix interface [15–18]. Crack-wake-bridging behavior of monolithic and reinforced ceramics is frequently studied by employing R-curve measurements, with the observed behavior commonly discussed based on the rate and the amount of the rise of the R-curve, for example [4–6, 8, 9, 19–21]. However, a major deficiency inherent to such evaluations is the strong dependence of the R-curves on the geometry of test specimen/crack and the type of loading, making the results obtained by using different crack geometries essentially incomparable. In spite of numerous studies on the fracture and R-curve behavior of SiC-whisker￾reinforced alumina composites, there are only few studies dealing directly with the characterization of

3554 SARRAFI-NOUR and COYLE- CRACK WAKE BRIDGE bridging behavior in this material [22, 23]. A main objective in this work was to characterize the bridging stress and its variation with temperature in a Sic- whisker-reinforced alumina between room tempera ture and 1400C. For this purpose, a hybrid experimental/numerical scheme was employed which utilized the R-curves obtained from chevron-notched xure test specimens of the composite to deconvol ute the distribution of the bridging stresses as function of crack opening displacement at various tempera 2. EXPERIMENTAL PROCEDURES 2. 1. Material and specimen preparation Fig. 1. Schematic of the fracture plane of a chevron notch The SiC-whisker-reinforced composite material ed in this study was a commercial cutting tool gra material( Grade wG-300, Greenleaf Corp, Saeger Series) with a cross-head speed of 50 um/min. The town, PA)and contained 33 vol. of Sic-whiskers flexure test fixture was made from various grades of spersed in an alumina matrix. The composite pow- SiC conforming to the specifications given in ASTM cess. The material is hot-pressed uniaxially in the minimum of three specimens(most of the tests were shape of plates, which are virtually of full density. conducted using four or five specimens per test Most of the SiC-whiskers have a diameter between condition)was used at each of the test temperatures I and I um and aspect ratios of 10-100. The alum- ambient, 800oC, 1000C, 1200 C, 1300C and ina matrix grain size ranges between I and 5 Hm. 1400C under air atmosphere. The heating schedule The microstructure of the material shows preferred of the fracture tests at elevated temperatures consisted orientation of the Sic-whiskers within the plane nor- of heating the specimen to the test temperature at mal to the hot-pressing axis. In addition, whisker-rich 15C/min, soaking for 20 min to achieve temperature and whisker-poor regions, typically 30-50 um in size, equilibrium in the furnace and loading the samples to due to reinforcement clustering typical of whisker- failure followed by cooling to room temperature at reinforced composites can be observed in the 15C/min. The loading-point compliance of the speci material. The composite material is of high purity and mens during the fracture test was determined by mea- erain boundaries and whisker/matrix interfaces [11, of the specimens and correlating it with the load-point 4]. Such a clean interface between the SiC-whiskers displacement through an analytical relation[25, 26) and the alumina matrix makes this composite an The differential displacement was measured between excellent model material to study the temperature dependence of the bridging stresses. The absence of points, each located at 15 mm from either side of the an(amorphous)second phase at the interface in this central measuring point on the specimen, using a sin- from a boundary phase with increasing temperature. [27. The test setup arrangement and the displacement The composite test specimens were received from measuring device were schematically shown else- manufacturer in the form of machined rectangular where[26]. The accuracy of the loading-point co flexure specimens with length(L)45-47 mm, width pliance measurements on the chevron-notched speci (W)5.00 mm and depth(B)of 4.00 mm. The width mens by employing this method was verified both numerI ally using three-dimensional finite element, pressing axis. A chevron-notch was cut into the test FE, analysis and experimentally by conducting con specimens using a 300-um-thick diamond cut-off trolled fracture tests on test specimens of materials wheel such that both the resulting crack-plane and the with a flat R-curve behavior at room and elevated crack propagation direction were parallel to the hot- temperatures [26] The chey hematically in Fig. 1, had an initial depth RESULTS adw=0.32 and a final depth a /W=l 3.1.R-cu 2. 2. Controlled fracture test The were calculated from the load-dis- fracture tests were conducted under thre raceme es using standard fracture mechanics nding load and displacement control conditions on procedure on the compliance measurement ervo-hydraulic testing machine (Instron 8500 method [4]. For this purpose, the required cor

3554 SARRAFI-NOUR and COYLE: CRACK WAKE BRIDGE bridging behavior in this material [22, 23]. A main objective in this work was to characterize the bridging stress and its variation with temperature in a SiC￾whisker-reinforced alumina between room tempera￾ture and 1400°C. For this purpose, a hybrid experimental/numerical scheme was employed which utilized the R-curves obtained from chevron-notched flexure test specimens of the composite to deconvol￾ute the distribution of the bridging stresses as function of crack opening displacement at various tempera￾tures. 2. EXPERIMENTAL PROCEDURES 2.1. Material and specimen preparation The SiC-whisker-reinforced composite material used in this study was a commercial cutting tool grade material (Grade WG-300, Greenleaf Corp., Saeger￾town, PA) and contained 33 vol.% of SiC-whiskers dispersed in an alumina matrix. The composite pow￾der preparation is a proprietary powder blending pro￾cess. The material is hot-pressed uniaxially in the shape of plates, which are virtually of full density. Most of the SiC-whiskers have a diameter between 0.1 and 1 µm and aspect ratios of 10–100. The alum￾ina matrix grain size ranges between 1 and 5 µm. The microstructure of the material shows preferred orientation of the SiC-whiskers within the plane nor￾mal to the hot-pressing axis. In addition, whisker-rich and whisker-poor regions, typically 30–50 µm in size, due to reinforcement clustering typical of whisker￾reinforced composites can be observed in the material. The composite material is of high purity and generally exhibits no or very little glass phase at the grain boundaries and whisker/matrix interfaces [11, 24]. Such a clean interface between the SiC-whiskers and the alumina matrix makes this composite an excellent model material to study the temperature dependence of the bridging stresses. The absence of an (amorphous) second phase at the interface in this material avoids complicating behavior that may arise from a boundary phase with increasing temperature. The composite test specimens were received from the manufacturer in the form of machined rectangular flexure specimens with length (L) 45–47 mm, width (W) 5.00 mm and depth (B) of 4.00 mm. The width (W) of the test specimens was parallel to the hot￾pressing axis. A chevron-notch was cut into the test specimens using a 300-µm-thick diamond cut-off wheel such that both the resulting crack-plane and the crack propagation direction were parallel to the hot￾pressing axis. The chevron notch geometry, shown schematically in Fig. 1, had an initial depth a0/W = 0.32 and a final depth a1/W = 1. 2.2. Controlled fracture test Fracture tests were conducted under three-point￾bending load and displacement control conditions on a servo-hydraulic testing machine (Instron 8500 Fig. 1. Schematic of the fracture plane of a chevron notch. Series) with a cross-head speed of 50 µm/min. The flexure test fixture was made from various grades of SiC conforming to the specifications given in ASTM C1211-92 and had a lower-span-distance of 40 mm. A minimum of three specimens (most of the tests were conducted using four or five specimens per test condition) was used at each of the test temperatures: ambient, 800°C, 1000°C, 1200°C, 1300°C and 1400°C under air atmosphere. The heating schedule of the fracture tests at elevated temperatures consisted of heating the specimen to the test temperature at 15°C/min, soaking for 20 min to achieve temperature equilibrium in the furnace and loading the samples to failure followed by cooling to room temperature at 15°C/min. The loading-point compliance of the speci￾mens during the fracture test was determined by mea￾suring a differential displacement on the tensile face of the specimens and correlating it with the load-point displacement through an analytical relation [25, 26]. The differential displacement was measured between the center-point of the specimen and two reference points, each located at 15 mm from either side of the central measuring point on the specimen, using a sin￾gle linear variable displacement transducer, LVDT [27]. The test setup arrangement and the displacement measuring device were schematically shown else￾where [26]. The accuracy of the loading-point com￾pliance measurements on the chevron-notched speci￾mens by employing this method was verified both numerically using three-dimensional finite element, FE, analysis and experimentally by conducting con￾trolled fracture tests on test specimens of materials with a flat R-curve behavior at room and elevated temperatures [26]. 3. RESULTS 3.1. R-curves The R-curves were calculated from the load–dis￾placement curves using standard fracture mechanics procedure based on the compliance measurement method [4]. For this purpose, the required com-

SARRAFI-NOUR and COYLE- CRACK WAKE BRIDGE 3555 pliance-crack length relation for the chevron-notched lowing a similar methodology, a procedure was specimen was calculated by employing a three- recently developed to obtain the distribution of brid dimensional FE solution [28, 29] obtained for the ing tractions from R-curves measured using chevron- same specimen geometry under four-point flexure notched flexure specimens [28]. The method allows load condition and modifying the solution to allow the deconvolution of a bridging relation from th for the change in the span-to-width ratio. (The com- measured R-curve by performing an iterative analysis pliance of the chevron-notched specimen under three- on the R-curve data which incorporates the inter- point flexure condition and without any crack was rela lations between the fracture mechanics weight func- obtained by using a simplified three-dimensional tion, stress intensity factor, and crack opening dis finite element model composed of -600 linear placement, and an implicit assumption of a dominant elements. pullout bridging mechanism. The analysis procedure, Typical R-curves calculated from the load-dis- as described in detail previously [28], involves fittir placement curves of the specimens fractured at vari- the right-hand side of the following equation to the ous temperatures are shown in Fig. 2. A fully con- R-curve obtained using a chevron-notched specimen trolled crack propagation regime could not be achieved in the tests conducted at room temperature due to the strong run-arrest 14, 20] nature of the crack owth behavior of the composite at room tempera- I+/=. ture. As can be seen from the r-curve results at room ∑c(a-xy temperature(Fig. 2, left), on many occasions an unstable crack growth/re-initiation preceded the crack arrest point. Since unstable crack propagation is not a condition in favor of formation of bridging where Kr is the fracture resistance of the material whiskers/ligaments in the crack wake, a continuous measured by an external observer during the course R-curve representing the true shielding contribution of stable crack propagation, Ktip is the stress intensity of the crack wake could not be obtained for the test factor at the crack tip which would be equal to K specimens at room temperature. The run-arrest the initial value of the fracture resistance or the tough- behavior was particularly visible around the ness of the material in the absence of any crack wake maximum load of the load-displacement curves at contributions, and Kbr is the stress intensity factor due room temperature and significantly diminished with to crack wake bridging. The function h of the inte- increasing temperature above 800C grand is the fracture mechanics weight function for 3. 2. Deconvolution of the bridging stresses from the the wake tractions in the appropriate chevron-notched specimen geometry [33] and the polynomial function within the square brackets is the expansion of the ett and collaborators have described a method- unknown bridging stress, o in the crack length, a ology for analysing R-curves arising from the crack and position, x, co-ordinates. Iterative analysis of th wake bridging process in ceramics based on the frac- R-curve data using equation(1) yields the coef- ture mechanics weight function method [30-32]. Fol- ficients, Ci, of the unknown bridging stress function 105 9.5 95 8.5 E8.5 7.5 7.5 6.5 5.5 040.50.60.70.80.9 0.3040.50.60.70.80.9 a/ in equation(1)

SARRAFI-NOUR and COYLE: CRACK WAKE BRIDGE 3555 pliance–crack length relation for the chevron-notched specimen was calculated by employing a three￾dimensional FE solution [28, 29] obtained for the same specimen geometry under four-point flexure load condition and modifying the solution to allow for the change in the span-to-width ratio. (The com￾pliance of the chevron-notched specimen under three￾point flexure condition and without any crack was obtained by using a simplified three-dimensional finite element model composed of
600 linear elements.) Typical R-curves calculated from the load–dis￾placement curves of the specimens fractured at vari￾ous temperatures are shown in Fig. 2. A fully con￾trolled crack propagation regime could not be achieved in the tests conducted at room temperature due to the strong run–arrest [4, 20] nature of the crack growth behavior of the composite at room tempera￾ture. As can be seen from the R-curve results at room temperature (Fig. 2, left), on many occasions an unstable crack growth/re-initiation preceded the crack arrest point. Since unstable crack propagation is not a condition in favor of formation of bridging whiskers/ligaments in the crack wake, a continuous R-curve representing the true shielding contribution of the crack wake could not be obtained for the test specimens at room temperature. The run–arrest behavior was particularly visible around the maximum load of the load–displacement curves at room temperature and significantly diminished with increasing temperature above 800°C. 3.2. Deconvolution of the bridging stresses from the R-curve Fett and collaborators have described a method￾ology for analysing R-curves arising from the crack wake bridging process in ceramics based on the frac￾ture mechanics weight function method [30–32]. Fol￾Fig. 2. R-curves from the composite specimens at room temperature (left) and at elevated temperatures (right). The solid curves included with the elevated temperature R-curve data are plotted using the best-fit coefficients in equation (1). lowing a similar methodology, a procedure was recently developed to obtain the distribution of bridg￾ing tractions from R-curves measured using chevron￾notched flexure specimens [28]. The method allows the deconvolution of a bridging relation from the measured R-curve by performing an iterative analysis on the R-curve data which incorporates the inter￾relations between the fracture mechanics weight func￾tion, stress intensity factor, and crack opening dis￾placement, and an implicit assumption of a dominant pullout bridging mechanism. The analysis procedure, as described in detail previously [28], involves fitting the right-hand side of the following equation to the R-curve obtained using a chevron-notched specimen: KR Ktip Kbr (1) Ko
a a0 h(x,a)i j3 i,j 0 Cij·aj (ax) i dx where KR is the fracture resistance of the material measured by an external observer during the course of stable crack propagation, Ktip is the stress intensity factor at the crack tip which would be equal to Ko, the initial value of the fracture resistance or the tough￾ness of the material in the absence of any crack wake contributions, and Kbr is the stress intensity factor due to crack wake bridging. The function h of the inte￾grand is the fracture mechanics weight function for the wake tractions in the appropriate chevron-notched specimen geometry [33] and the polynomial function within the square brackets is the expansion of the unknown bridging stress, sbr, in the crack length, a, and position, x, co-ordinates. Iterative analysis of the R-curve data using equation (1) yields the coef- ficients, Cij, of the unknown bridging stress function

3556 SARRAFI-NOUR and COYLE- CRACK WAKE BRIDGE and the initial value of fracture toughness of the curve while simultaneously minimizing the follow- material, Ko(if not determined through indeper experiments) The displacement of the crack walls due to the closure bridging tractions, Sn can be obtained fol ∑(oD)a-(oG))=min lowing Rice's relation between the stress intensity factor, K, crack opening displacement, 8, and th weight function, h[341 where obS)ai is the magnitude of the calculated bridging stress at the crack opening 8 for the crack H do length a; and is an average bridging stress (2)calculated over a range of the crack lengths, including 7, at the same crack opening displacement Analysis of the r-curves of the composite speci mens tested at different temperatures by using the where H is an appropriate elastic modulus(equal to procedures described allowed deconvolution of the E and E=E/(1-v), with v being the Poisson's bridging relation and K, from the R-curve results. As ratio, under the plane stress and plane strain con- discussed previously [26], the Ko obtained through the ditions, respectively ) By employing the integral form analysis procedure describes the crack tip toughness from the bridging stresses could be calculated once from crack wake shielding processes. Therefore, it the coefficients Ci were known should be viewed as containing the contributions from any other toughening mechanisms operative in the material, including the toughness of the matrix, Or=F2 co h(x, o h(x', a' a (3) Typical fit curves to the R-curves and the resulting bridging relations obtained from the analysis of th yade R-curves of the composite material at various tem peratures are shown in Figs 2 and 3, respectively. Due to the strong influence of the run-arrest behavior on the shape of the R-curves of the composites at room In equation(3)x represents the co-ordinate at which temperature, these R-curves were not used in the the crack opening displacement is to be determined, analysis. However, the minimum value of kg that x'is the co-ordinate where the(bridging)stress o is occurred after multiple run-arrests and at long crack acting, and a' is a running integration variable. The lengths was assumed as the initial value of fracture total crack surface displacement can be obtained by toughness, Ko. The magnitude of the bridging stress the superposition of the crack surface displacements in the composite at room temperature was estimated The former displacement could be determined The plane-strain elastic modulus of the composite numerically by using finite element analysis [28 The bridging relation is finally obtained by correl displacement fields was determined from the speci- ating the total crack surface displacements and the magnitude of the bridging stress through the crack ength and position co-ordinates, a and x. It should 15 be noted that a bridging relation calculated through 800°c the analysis procedure is valid only if the resulting 1000°C Oh vs. 8 for various crack lengths are self-consistent, respect to COD is independent of the crack length. In oo order to help converge to such solutions during the iteration analysis a number of constraints imposed on the bridging stress function representing the expansion of the bridging stress in the crack co ordinate system [28]. These constraints were selected based on the fundamentals of the(pullout) bridging mechanism. Further experience with this procedure indicated that the constraints introduced could not of the procedure to a dis crack opening displacement, 28 [um] tribution of bridging stresses leading to a self-consist ent bridging relation under all circumstances. In some crack op isplacement obtained from the analysis of the cases, it was necessary to fit equation(I)to the R- R-curve SiC-whisker-reinforced alumina composite

3556 SARRAFI-NOUR and COYLE: CRACK WAKE BRIDGE and the initial value of fracture toughness of the material, Ko (if not determined through independent experiments). The displacement of the crack walls due to the closure bridging tractions, dbr, can be obtained fol￾lowing Rice’s relation between the stress intensity factor, K, crack opening displacement, d, and the weight function, h [34]: h H K ∂d ∂a (2) where H is an appropriate elastic modulus (equal to E and E = E/(1n2 ), with n being the Poisson’s ratio, under the plane stress and plane strain con￾ditions, respectively). By employing the integral form of equation (2) the crack wall displacements arising from the bridging stresses could be calculated once the coefficients Cij were known: dbr 1 E i j3 i,j 0 Cij
a x h(x,a)
a a0 h(x,a)(a (3) x) i aj dxda In equation (3) x represents the co-ordinate at which the crack opening displacement is to be determined, x is the co-ordinate where the (bridging) stress s is acting, and a is a running integration variable. The total crack surface displacement can be obtained by the superposition of the crack surface displacements due to the applied load and due to the bridging stress. The former displacement could be determined numerically by using finite element analysis [28]. The bridging relation is finally obtained by correl￾ating the total crack surface displacements and the magnitude of the bridging stress through the crack length and position co-ordinates, a and x. It should be noted that a bridging relation calculated through the analysis procedure is valid only if the resulting sbr vs. d for various crack lengths are self-consistent, i.e., the distribution of the bridging stresses with respect to COD is independent of the crack length. In order to help converge to such solutions during the iteration analysis a number of constraints were imposed on the bridging stress function representing the expansion of the bridging stress in the crack co￾ordinate system [28]. These constraints were selected based on the fundamentals of the (pullout) bridging mechanism. Further experience with this procedure indicated that the constraints introduced could not guarantee the convergence of the procedure to a dis￾tribution of bridging stresses leading to a self-consist￾ent bridging relation under all circumstances. In some cases, it was necessary to fit equation (1) to the R￾curve while simultaneously minimizing the follow￾ing relation: (sbr(d)ai sbr(d)) 2 min (4) where sbr(d)ai is the magnitude of the calculated bridging stress at the crack opening d for the crack length ai and sbr(d)
is an average bridging stress calculated over a range of the crack lengths, including ai , at the same crack opening displacement. Analysis of the R-curves of the composite speci￾mens tested at different temperatures by using the procedures described allowed deconvolution of the bridging relation and Ko from the R-curve results. As discussed previously [26], the Ko obtained through the analysis procedure describes the crack tip toughness of the material in the absence of any contributions from crack wake shielding processes. Therefore, it should be viewed as containing the contributions from any other toughening mechanisms operative in the material, including the toughness of the matrix, at the crack tip. Typical fit curves to the R-curves and the resulting bridging relations obtained from the analysis of the R-curves of the composite material at various tem￾peratures are shown in Figs 2 and 3, respectively. Due to the strong influence of the run-arrest behavior on the shape of the R-curves of the composites at room temperature, these R-curves were not used in the analysis. However, the minimum value of KR that occurred after multiple run–arrests and at long crack lengths was assumed as the initial value of fracture toughness, Ko. The magnitude of the bridging stress in the composite at room temperature was estimated differently and will be discussed later on in the paper. The plane-strain elastic modulus of the composite material required for the calculation of crack opening displacement fields was determined from the speci￾Fig. 3. Distribution of the bridging stresses as a function of crack opening displacement obtained from the analysis of the R-curves of the SiC-whisker-reinforced alumina composite.

SARRAFI-NOUR and COYLE- CRACK WAKE BRIDGE 3557 400 300 山200 100 400 80012001600 Temperature [C] Fig. 4. Variation of the plane-strain elastic modulus of the SiC-whisker-reinforced alumina composite calculated from the measured initial compliance of the chevron-notched flexure test specimens. The error bars represent the scatter range of the data from three to five individual test specimens This work Yu and Kobayashi[22] Linear fit(data from this work 15 10 40080012001600 1600 TICI Fig. 5. Variation of (a) the maximum value of the bridging stress, and (b) the initial value of the fracture toughness, in the Sic-whisker-reinforced alumina composite as a function of temperature men compliance. For this se,the compliance 4. DISCUSSION values determined from the slope of the linear seg- 4.1. Bridging stress ment of the load-displacement curves from the chev on-notched flexure specimens were compared with The variation of the maximum bridging stress in the calculated compliance from the finite element sol- the composite with temperature is shown in Fig. 5(a) ution to yield the modulus value. These modulus Although the results of R-curve tests at room tem- results are presented in Fig. 4 perature could not be used in the analysis to calculate Variation of the maximum bridging stress from the the bridging relations, a maximum bridging stress of bridging relations(Fig. 3)and the initial value of the --23 MPa estimated through a linear extrapolation of fracture toughness deconvoluted from the R-curve the results from this work to room temperature results are shown in Figs 5(a)and(b), respectively. appeared to be in good agreement with the bridging As described earlier the K, values determined through stress values reported previously for a 30 vol % SIC the analysis include the contribution from any tough- whisker-reinforced alumina [22, 23 ning mechanism operative at the tip of the crack and The linear dependence of the maximum bridging should not be viewed as an indicator of the toughness stress on temperature, suggested by the data shown in of the alumina matrix alone Fig. 5(a), is consistent with the mechanics of pullo

SARRAFI-NOUR and COYLE: CRACK WAKE BRIDGE 3557 Fig. 4. Variation of the plane-strain elastic modulus of the SiC-whisker-reinforced alumina composite calculated from the measured initial compliance of the chevron-notched flexure test specimens. The error bars represent the scatter range of the data from three to five individual test specimens. Fig. 5. Variation of (a) the maximum value of the bridging stress, and (b) the initial value of the fracture toughness, in the SiC-whisker-reinforced alumina composite as a function of temperature. men compliance. For this purpose, the compliance values determined from the slope of the linear seg￾ment of the load–displacement curves from the chev￾ron-notched flexure specimens were compared with the calculated compliance from the finite element sol￾ution to yield the modulus value. These modulus results are presented in Fig. 4. Variation of the maximum bridging stress from the bridging relations (Fig. 3) and the initial value of the fracture toughness deconvoluted from the R-curve results are shown in Figs 5(a) and (b), respectively. As described earlier the Ko values determined through the analysis include the contribution from any tough￾ening mechanism operative at the tip of the crack and should not be viewed as an indicator of the toughness of the alumina matrix alone. 4. DISCUSSION 4.1. Bridging stress The variation of the maximum bridging stress in the composite with temperature is shown in Fig. 5(a). Although the results of R-curve tests at room tem￾perature could not be used in the analysis to calculate the bridging relations, a maximum bridging stress of
23 MPa estimated through a linear extrapolation of the results from this work to room temperature appeared to be in good agreement with the bridging stress values reported previously for a 30 vol.% SiC￾whisker-reinforced alumina [22, 23]. The linear dependence of the maximum bridging stress on temperature, suggested by the data shown in Fig. 5(a), is consistent with the mechanics of pullout

3558 SARRAFI-NOUR and COYLE- CRACK WAKE BRIDGE bridging In the absence of a viscous interfacial film, t which can give rise to a strong non-linear behavior at the sliding interface between the pullout SiC-whis ker and the alumina matrix with increasing tempera ture. the closure stress exerted on the crack surfaces due to the bridging tractions produced by the pullout process, opo, can be written [71 Fig. 6. Examples of the post-fracture observations of face of the chevron notch a wheref is the fraction of the whiskers participating perature(left), and a specin a test at I300°C in the pullout process, t is the frictional shear resist- ance of the debonded interface between the whiskers and the matrix, and lpo, d, and 28 are whisker pullout length, whisker diameter and total crack opening dis- the same temperature domain the thermal residual lacement(assuming 8 is the displacement of one stresses vary by almost three-orders-of-magnitude in side of the crack relative to the crack plane), respect- SiC-reinforced alumina composites [3840]. In the ively. In a real composite system both and Ipo are absence of quantitative data on the variation of the istributed statistically as a result of the size distri- interfacial friction coefficient with temperature in the bution of the(pullout)whiskers. The interfacial shear composite, it may be assumed that such variations resistance can be expressed in terms of an interfacial would be small if no amorphous phase is present at friction coefficient, u, and the radial component the interface. Consequently, variation of t with tem- (compressive),o, of thermal residual stress at the perature would be similar to that for the residual SiC-whisker/alumina matrix interface [7, 351 stresses and, therefore, would dominate the change in magnitude of the bridging stress as described by t=po,=p△a△T (6) equation(5) Comparison between the temperature dependence where is a function of the elastic properties and strains/stresses measured for SiC-whisker-reinforced volume fractions of both whiskers and matrix, Aa is alumina composites by Majumdar et al. [38] and Bal the thermal expansion mismatch between matrix and lard et al. [39], as shown in Fig. 7, also shows excel whiskers, and AT is the temperature difference lent agreement. For a better graphical presentation between the environment and the temperature below and an easier ison amongst different data, the which the thermal residual stresses can no longer be stress/strain results presented in Fig. 7 have been ne relaxed by the creep process malized over their values at room temperature. Based The observed response of the bridging behavior of the material to temperature can be discussed based on the temperature dependence of Lpo, t andf in equa- 1.2 ● SiCW-A| umina tions(4)and(5). It has been commonly observed that the pullout length of SiC-whisker increases with 日e3(SCw)[39] increasing temperature [6, 36). This behavior can be radial stress(whisker)[38] attributed to the increase in extent of the interfacial axial stress(whisker)[38] 0.8 debonding with increasing temperature due to linear fit to SiCw E33 reduction of the residual clamping force exerted on 20.6 the whiskers by the alumina matrix with increasing temperature. An example of the increase of the pul- 50.4 lout length of the SiC-whiskers in the composite with Increasing test temperature is shown in Fig. 6 0.2 F linear fit to the bridging Previous works 6, 36] have indicated that the vari- stress results ation of the whisker pullout length between room temperature and 1300 C is about a factor of 3. Within Fig. 7. Comparison between the temperature dependence of the A non-linear behavior of the bridging stresses with thermal residual stresses in Sic- whisker-reinforced ncreasing temperature observed by the authors in a SiC- composites [38, 39] with that from the bridgin omposite has been discussed and correlated to the presence of an amorphous interphase of the residual strain was determined parallel to the hot- n the composite [37] pressing axis in the sample coordinate

3558 SARRAFI-NOUR and COYLE: CRACK WAKE BRIDGE bridging. In the absence of a viscous interfacial film,† which can give rise to a strong non-linear behavior at the sliding interface between the pullout SiC-whis￾ker and the alumina matrix with increasing tempera￾ture, the closure stress exerted on the crack surfaces due to the bridging tractions produced by the pullout process, spo, can be written [7]: spo f4t (lpo2d) dw (5) where f is the fraction of the whiskers participating in the pullout process, t is the frictional shear resist￾ance of the debonded interface between the whiskers and the matrix, and lpo, dw and 2d are whisker pullout length, whisker diameter and total crack opening dis￾placement (assuming d is the displacement of one side of the crack relative to the crack plane), respect￾ively. In a real composite system both f and lPo are distributed statistically as a result of the size distri￾bution of the (pullout) whiskers. The interfacial shear resistance can be expressed in terms of an interfacial friction coefficient, m, and the radial component (compressive), sr, of thermal residual stress at the SiC-whisker/alumina matrix interface [7, 35]: t msr m a T (6) where  is a function of the elastic properties and volume fractions of both whiskers and matrix, a is the thermal expansion mismatch between matrix and whiskers, and T is the temperature difference between the environment and the temperature below which the thermal residual stresses can no longer be relaxed by the creep process. The observed response of the bridging behavior of the material to temperature can be discussed based on the temperature dependence of lpo, t and f in equa￾tions (4) and (5). It has been commonly observed that the pullout length of SiC-whisker increases with increasing temperature [6, 36]. This behavior can be attributed to the increase in extent of the interfacial debonding with increasing temperature due to reduction of the residual clamping force exerted on the whiskers by the alumina matrix with increasing temperature. An example of the increase of the pul￾lout length of the SiC-whiskers in the composite with increasing test temperature is shown in Fig. 6. Previous works [6, 36] have indicated that the vari￾ation of the whisker pullout length between room temperature and 1300°C is about a factor of 3. Within † A non-linear behavior of the bridging stresses with increasing temperature observed by the authors in a SiC￾platelet-reinforced alumina composite has been discussed and correlated to the presence of an amorphous interphase in the composite [37]. Fig. 6. Examples of the post-fracture observations of the pul￾lout length in the SiC-whisker-reinforced alumina on the sur￾face of the chevron notch: a specimen from a test at room tem￾perature (left), and a specimen from a test at 1300°C (right). Bar=1 µm. the same temperature domain the thermal residual stresses vary by almost three-orders-of-magnitude in SiC-reinforced alumina composites [38–40]. In the absence of quantitative data on the variation of the interfacial friction coefficient with temperature in the composite, it may be assumed that such variations would be small if no amorphous phase is present at the interface. Consequently, variation of t with tem￾perature would be similar to that for the residual stresses and, therefore, would dominate the change in magnitude of the bridging stress as described by equation (5). Comparison between the temperature dependence of the maximum bridging stress and the residual strains/stresses measured for SiC-whisker-reinforced alumina composites by Majumdar et al. [38] and Bal￾lard et al. [39], as shown in Fig. 7, also shows excel￾lent agreement. For a better graphical presentation and an easier comparison amongst different data, the stress/strain results presented in Fig. 7 have been nor￾malized over their values at room temperature. Based Fig. 7. Comparison between the temperature dependence of the thermal residual stresses in SiC-whisker-reinforced alumina composites [38, 39] with that from the bridging stresses obtained in the present work. Note that the e33 [39] component of the residual strain was determined parallel to the hot￾pressing axis in the sample coordinate.

SARRAFI-NOUR and COYLE- CRACK WAKE BRIDGE 3559 on the bridging stress results shown in Fig. 5(a)and maximum bridging stress, o, of 23 MPa were calcu- the linear fit to the data, the stress free temperature lated by employing the numerical scheme described for the composite was estimated to be 1345C, in previously [45]. Some of the calculated R-curves are agreement with estimated values of 1350@C [38] and compared with the initial portion of an R-curve from 70±130°C[39 a test at room temperature in Fig. 8. As can be seen An earlier investigation in the SiC-fiber/glass sys- the experimental data shown in Fig. 8 appears to be tem using single-fiber push-through tests found a lin- in a reasonable agreement with the R-curves calcu- ear dependence on temperature for both debonding lated for K,=5.8-5.9 MPa.m 2 and 8. 0.5 um and frictional shear stresses at a lower temperature Although the toughening contributions arising from through the viscous flow process 141]. Therefore, a thus crack-geometry-dependent arguments, it may be linear dependence on AT for t in equations (5)and evaluated independent of the crack geometry by cal- (6)in the SiC-whisker-reinforced alumina system is culating the energy dissipated by the bridging process to be expected unless variation of u with temperature(bridging work), i.e. the integral of the constitutive is highly non-linear. Previous examinations [10, ll, bridging relation or the area under the obS)curve 24] of the SiC-whisker/alumina interfaces in the com- However, we note that an accurate evaluation of such posite material studied here found essentially no a fracture resistance indicator should address the residual second or amorphous phase in such regions. crack opening displacement domain of interest(this Consequently, an anomalous behavior due to the reintroduces implicitly the crack-scale dependence of not poe g of this interface at high temperatures is the toughening arising from the bridging mechanism) Nevertheless, the integrals of the bridging relations Based on the maximum room temperature bridging obtained( Fig. 3)are shown in Fig 9 as a function of high temperature results, R-curves were calculated for that the contribution of the bridging zone ao stress of -23 MPa determined by extrapolation of the temperature. Not unexpectedly, the results indicat comparison with the room temperature results. For toughening of the composite decreased with increas- this purpose the estimated value of the bridging stress ing temperature between 800 C and 1300oC. Due to was considered as the characteristic stress, oo, in the lack of similar data from room temperature tests, such exponential bridging relation [31] an assessment could not be reliably extended to th (6)=exp( (7)4.2. Crack tip toughness The bridging stress results presented in Figs 5(a) and 9 unequivocally indicated that the toughe where do is a characteristic crack opening displace ment. This exponential bridging relation, derived ana lytically from the strain softening bridging relation proposed by Mai and Lawn [42] by taking into 7.[°4 point-bend test specimen Rt account the effect of a statistical distribution of the size of the bridging grains, has been used previously lithic alumina materials/30, 31, 32, 43]. It also agrees f to describe the bridging behavior of various mono- with the experimental observations of Steinbrech et o al. [44]on alumina, which indicated that the critical 26.5 crack opening displacement for the bridging elements to disengage from the matrix was about one-quarter of the active grain size. Our use of this relation to 8=0.5 calculate the room temperature R-curve of the com 0=23MP{---8-025m posite was based on the similarity of the tail-off behavior of this relation and those calculated from the 5.5 elevated temperature R-curves, and the assumption 0.3040.50.60.7080.9 that it would thus give rise to a similar level of the shielding stress intensity factor. Based on the micro- length at room temperature was considered to be the assumption of an exponential bridging relation, equation about one whisker diameter and, therefore, the para- (7), with characteristic displacements of 0. 25 and 0.5 um on a meter 8, was estimated to be 0. 25-0.5 um Using such maximum bridging stress of 23 MPa. The onset value of the values for 8, and K,=5.5-6.3 MPa. m'n the r- calculated curves at a/l=0.32 indicates the value of K used curves that would arise during propagation of the a test specimen under four-point bending condition and prior crack in the chevron-notched test specimen for a

SARRAFI-NOUR and COYLE: CRACK WAKE BRIDGE 3559 on the bridging stress results shown in Fig. 5(a) and the linear fit to the data, the stress free temperature for the composite was estimated to be
1345°C, in agreement with estimated values of 1350°C [38] and 1470±130°C [39]. An earlier investigation in the SiC-fiber/glass sys￾tem using single-fiber push-through tests found a lin￾ear dependence on temperature for both debonding and frictional shear stresses at a lower temperature range where the glass matrix could not deform through the viscous flow process [41]. Therefore, a linear dependence on T for t in equations (5) and (6) in the SiC-whisker-reinforced alumina system is to be expected unless variation of m with temperature is highly non-linear. Previous examinations [10, 11, 24] of the SiC-whisker/alumina interfaces in the com￾posite material studied here found essentially no residual second or amorphous phase in such regions. Consequently, an anomalous behavior due to the softening of this interface at high temperatures is not possible. Based on the maximum room temperature bridging stress of
23 MPa determined by extrapolation of the high temperature results, R-curves were calculated for comparison with the room temperature results. For this purpose the estimated value of the bridging stress was considered as the characteristic stress, so, in the exponential bridging relation [31]: s(d) soexp( d do ) (7) where do is a characteristic crack opening displace￾ment. This exponential bridging relation, derived ana￾lytically from the strain softening bridging relation proposed by Mai and Lawn [42] by taking into account the effect of a statistical distribution of the size of the bridging grains, has been used previously to describe the bridging behavior of various mono￾lithic alumina materials [30, 31, 32, 43]. It also agrees with the experimental observations of Steinbrech et al. [44] on alumina, which indicated that the critical crack opening displacement for the bridging elements to disengage from the matrix was about one-quarter of the active grain size. Our use of this relation to calculate the room temperature R-curve of the com￾posite was based on the similarity of the tail-off behavior of this relation and those calculated from the elevated temperature R-curves, and the assumption that it would thus give rise to a similar level of the shielding stress intensity factor. Based on the micro￾scopic observations of this work and those reported in previous investigations [6, 9, 36], the whisker pullout length at room temperature was considered to be about one whisker diameter and, therefore, the para￾meter d, was estimated to be 0.25–0.5 µm. Using such values for do, and Ko = 5.5–6.3 MPa.m1/2, the R￾curves that would arise during propagation of the crack in the chevron-notched test specimen for a maximum bridging stress, so, of 23 MPa were calcu￾lated by employing the numerical scheme described previously [45]. Some of the calculated R-curves are compared with the initial portion of an R-curve from a test at room temperature in Fig. 8. As can be seen, the experimental data shown in Fig. 8 appears to be in a reasonable agreement with the R-curves calcu￾lated for Ko = 5.8–5.9 MPa.m1/2 and do
0.5 µm. Although the toughening contributions arising from a bridging zone are tied into the R-curve effects, and thus crack-geometry-dependent arguments, it may be evaluated independent of the crack geometry by cal￾culating the energy dissipated by the bridging process (bridging work), i.e. the integral of the constitutive bridging relation or the area under the sbr(d) curve. However, we note that an accurate evaluation of such a fracture resistance indicator should address the crack opening displacement domain of interest (this reintroduces implicitly the crack-scale dependence of the toughening arising from the bridging mechanism). Nevertheless, the integrals of the bridging relations obtained (Fig. 3) are shown in Fig. 9 as a function of temperature. Not unexpectedly, the results indicate that the contribution of the bridging zone to the toughening of the composite decreased with increas￾ing temperature between 800°C and 1300°C. Due to lack of similar data from room temperature tests, such an assessment could not be reliably extended to the room temperature condition. 4.2. Crack tip toughness The bridging stress results presented in Figs 5(a) and 9 unequivocally indicated that the toughening Fig. 8. Comparison of an experimentally measured R-curve for the SiC-whisker-reinforced alumina at room temperature with the R-curves calculated for the same specimen geometry based the assumption of an exponential bridging relation, equation (7), with characteristic displacements of 0.25 and 0.5 µm on a maximum bridging stress of 23 MPa. The onset value of the calculated curves at a/W = 0.32 indicates the value of Ko used in each calculation. The experimental data were obtained from a test specimen under four-point bending condition and prior to crack instability.

3560 SARRAFI-NOUR and COYLE- CRACK WAKE BRIDGE the same procedure. No evidence of any microcrack like features could be identified in the reference sam ple. Further microscopic observations on the speci mens from fracture tests at higher temperatures indi cated that the length of these microcracks increased E with increasing temperature. The increase of the microcrack length apparently caused a transition from shielding to amplification conditions at th crack tip [ll resulting in the trend observed for th crack tip toughness results in Fig. 5(b) Since the R-curves of the composite were analyzed based on an a priori assumption of wake dominated 0 bridging toughening, the question arises as to th 1200 1600 possible influence of the microcrack zone on the curve behavior beyond its contribution to the crack tip Temperature [oc] toughness In the other words, it may be questioned if Fig. 9. The work done by the bridging stresses as a func the microcrack zone of the type observed here con- of temperature obtained from the integral of the bridging tributed to the observed R-curve behavior. As shown relations(Fig 3)deconvoluted from the R-curves by the data of Fig. Il, the composite material exhib- ited a fat R-curve behavior at 1400%C. at least withir the crack length range that could be estimated from contributions due to the bridging mechanism in the the compliance measurements. At the same time, the diminished with increasing temperature. fracture toughness of the com he initial value of the fracture toughness as obtained ture appeared be higher than the Ko, estimated for the through the analysis of the R-curves(Fig. 5(b))how- material at room temperature due to the presence of ever, showed improvements at high temperatures the microcrack zone. In addition, it is also noteworthy relative to its value at ambient temperature that the chevron notch fracture toughness calculated A previous study of this SiC-whisker-reinforced from the maximum load achieved during the fracture alumina by Han and Suresh [10] indicated that the test and the minimum value of the geometric function material was susceptible to the formation of a for the chevron-notched specimen(horizontal dash- microcrack zone around the crack tip at elevated tem- dotted line shown along each of the R-curves in peratures. The toughening contributions arising from Fig. 11)agreed well with its value on the measured the elevated temperature microcrack zone have been R- discussed by Han et al. [ Il] based on the microcrack- We also compared the temperature dependence of toughening model from Ortiz [46]. The microcrack our K, results with the toughness values reported by zone of this type was found to arise from the coalesc- Han et al. [11] as shown in Fig. 12. The fracture ence of interfacial cavities formed ahead of the crack toughness results from [11] were obtained using four- tip [ll] due to the large local stress field in this point flexure straight-through notched specimens that region. It was also found [10, Il that the cavities had been precracked (precrack length <200 um) by initiated at the interface between SiC-whiskers and cyclic fatigue loading using over 10 compression- alumina matrix grains as a result of an oxidation reac- compression cycles. When developed under a cyclic tion at the interface at high temperatures closure loading, bridges are worn out as a result of the Evidence for the presence of the interfacial cavi- fatigue loading condition [47, 48] leaving the wake of tation at high temperatures in the specimens studied the precrack virtually traction free. In addition, it was in this work could be found by microscopic examin- reported in [ll] that no indication of stable crack ations of the specimens broken at 1200 C and growth was observed during the fracture testing of the 1300oC. For this purpose, broken test specimens from specimens up to 1200C, indicating that no bridging controlled fracture tests described in Section 2.2 were region had been developed in the wake by any further cut normal to the fracture surface and along the direc- stable extension of the precrack. As a result, the tion of the crack growth. The plane normal to the toughness values determined in such tests incorpor fracture surface was then carefully polished to a mir- ated only the toughening contributions confined to the ror finish using various diamond polishing-media and crack tip region. However, the investigators [ll] did the region adjacent to the fracture surface was not feel confident in excluding the possibility of observed using a field emission SEM. Examples of stable extension of the precrack prior to the achieve these observations showing microcrack formation in ment of the maximum load in their fracture tests at a specimen from the fracture test at 1200.C are 1300-1500C and, hence, calculated an apparent frac- presented in Fig. 10. To verify that the observed fea- ture toughness in this temperature range by using the tures shown in Fig. 10 were not an artifact from the maximum load from the fracture test and the precrack sample preparation procedures, one of the samples length measured at room temperature before the frac- broken at room temperature was prepared following ture test. Given that dependenc

3560 SARRAFI-NOUR and COYLE: CRACK WAKE BRIDGE Fig. 9. The work done by the bridging stresses as a function of temperature obtained from the integral of the bridging relations (Fig. 3) deconvoluted from the R-curves. contributions due to the bridging mechanism in the composite diminished with increasing temperature. The initial value of the fracture toughness as obtained through the analysis of the R-curves (Fig. 5(b)) how￾ever, showed improvements at high temperatures relative to its value at ambient temperature. A previous study of this SiC-whisker-reinforced alumina by Han and Suresh [10] indicated that the material was susceptible to the formation of a microcrack zone around the crack tip at elevated tem￾peratures. The toughening contributions arising from the elevated temperature microcrack zone have been discussed by Han et al. [11] based on the microcrack￾toughening model from Ortiz [46]. The microcrack zone of this type was found to arise from the coalesc￾ence of interfacial cavities formed ahead of the crack tip [11] due to the large local stress field in this region. It was also found [10, 11] that the cavities initiated at the interface between SiC-whiskers and alumina matrix grains as a result of an oxidation reac￾tion at the interface at high temperatures. Evidence for the presence of the interfacial cavi￾tation at high temperatures in the specimens studied in this work could be found by microscopic examin￾ations of the specimens broken at 1200°C and 1300°C. For this purpose, broken test specimens from controlled fracture tests described in Section 2.2 were cut normal to the fracture surface and along the direc￾tion of the crack growth. The plane normal to the fracture surface was then carefully polished to a mir￾ror finish using various diamond polishing-media and the region adjacent to the fracture surface was observed using a field emission SEM. Examples of these observations showing microcrack formation in a specimen from the fracture test at 1200°C are presented in Fig. 10. To verify that the observed fea￾tures shown in Fig. 10 were not an artifact from the sample preparation procedures, one of the samples broken at room temperature was prepared following the same procedure. No evidence of any microcrack￾like features could be identified in the reference sam￾ple. Further microscopic observations on the speci￾mens from fracture tests at higher temperatures indi￾cated that the length of these microcracks increased with increasing temperature. The increase of the microcrack length apparently caused a transition from crack tip shielding to amplification conditions at the crack tip [11], resulting in the trend observed for the crack tip toughness results in Fig. 5(b). Since the R-curves of the composite were analyzed based on an a priori assumption of wake dominated bridging toughening, the question arises as to the possible influence of the microcrack zone on the R￾curve behavior beyond its contribution to the crack tip toughness. In the other words, it may be questioned if the microcrack zone of the type observed here con￾tributed to the observed R-curve behavior. As shown by the data of Fig. 11, the composite material exhib￾ited a flat R-curve behavior at 1400°C, at least within the crack length range that could be estimated from the compliance measurements. At the same time, the fracture toughness of the composite at this tempera￾ture appeared be higher than the Ko, estimated for the material at room temperature due to the presence of the microcrack zone. In addition, it is also noteworthy that the chevron notch fracture toughness calculated from the maximum load achieved during the fracture test and the minimum value of the geometric function for the chevron-notched specimen (horizontal dash– dotted line shown along each of the R-curves in Fig. 11) agreed well with its value on the measured R-curve. We also compared the temperature dependence of our Ko results with the toughness values reported by Han et al. [11] as shown in Fig. 12. The fracture toughness results from [11] were obtained using four￾point flexure straight-through notched specimens that had been precracked (precrack length 200 µm) by cyclic fatigue loading using over 106 compression– compression cycles. When developed under a cyclic closure loading, bridges are worn out as a result of the fatigue loading condition [47, 48] leaving the wake of the precrack virtually traction free. In addition, it was reported in [11] that no indication of stable crack growth was observed during the fracture testing of the specimens up to 1200°C, indicating that no bridging region had been developed in the wake by any further stable extension of the precrack. As a result, the toughness values determined in such tests incorpor￾ated only the toughening contributions confined to the crack tip region. However, the investigators [11] did not feel confident in excluding the possibility of stable extension of the precrack prior to the achieve￾ment of the maximum load in their fracture tests at 1300–1500°C and, hence, calculated an apparent frac￾ture toughness in this temperature range by using the maximum load from the fracture test and the precrack length measured at room temperature before the frac￾ture test. Given that dependence on the

SARRAFI-NOUR and COYLE- CRACK WAKE BRIDGE 3561 pullo 1.0 kv x13 0K 2.31 1.gkv×5g,ek"''台ig'n the vic adjacent to the fracture surface, FS, with the microcrack damage indicated by the arrow within the marked region(left) and higher the same microcrack(right) Note that the micrographs show the cross section normal to the fracture surface, FS, which extends into the ane of the 11 11 T14s30 o This work 10 0 Han, Waren and Suresh(pre- 9 △T14532 E 9 the notch tip precrack length 2 up to200 um)[111 三 6 5 80012001600 30.40.50.60.70.80.9 Fig.11.Flat R-curve behavior from multiple specimens of the obtained for the Sic-whisker-reinforced alumina composite by Han et al. [11 and K, values determined in this work The vertical narrow dash-double-dotted line designated by value of the geometric function for the chevron-notched speci- men geometry employed in the fracture test. The horizontal both the microcrack and the whisker-bridging pro- large-dash-dotted lines correspond to the fracture toughness cesses were concurrently operative calculated from the maximum load achieved in the fracture Despite a good agreement at T.C 124, 49 rom the analysis scheme employed in this work Microscopic observation of the fracture surface of the within the temperature range 1000-1300oC where composite specimens also revealed that

SARRAFI-NOUR and COYLE: CRACK WAKE BRIDGE 3561 Fig. 10. An example of the observation of microcracks in the vicinity of the fracture surface in the SiC-whisker (bright phase) reinforced alumina (dark phase) composite sample from the controlled fracture test at 1200°C: low-magnification image of a region adjacent to the fracture surface, FS, with the microcrack damage indicated by the arrow within the marked region (left) and higher magnification view of the same microcrack (right). Note that the micrographs show the cross section normal to the fracture surface, FS, which extends into the plane of the image. Fig. 11. Flat R-curve behavior from multiple specimens of the SiC-whisker-reinforced alumina composite tested at 1400°C in air. The vertical narrow dash–double-dotted line designated by Ymin marks the crack length corresponding to the minimum value of the geometric function for the chevron-notched speci￾men geometry employed in the fracture test. The horizontal large-dash–dotted lines correspond to the fracture toughness calculated from the maximum load achieved in the fracture testing of each of the specimens and the Ymin value. crack/specimen geometry is inherent to R-curve behavior in ceramic materials, one would expect that the Ko evaluations of the present work would be dif￾ferent from those reported in [11] if the microcrack zone formed at elevated temperatures possessed R￾curve characteristics. On the contrary, a good agree￾ment could be found between our results and those from [11] up to 1200°C (Fig. 12), albeit a microcrack zone was found in our specimens at 1200°C. In addition, an R-curve contribution from the microcrack zone formed at elevated temperatures would have lead to anomalous bridging stress results from the analysis scheme employed in this work within the temperature range 1000–1300°C where Fig. 12. Comparison between the fracture toughness results obtained for the SiC-whisker-reinforced alumina composite by Han et al. [11] and Ko values determined in this work. both the microcrack and the whisker-bridging pro￾cesses were concurrently operative. Despite a good agreement at T1200°C, the results from higher temperatures appeared to be significantly different. One possibility for this behavior could be the dependence of the crack-tip damage zone forma￾tion on the oxidation reaction at the interface [11], which in turn may be sensitive to the local impurity level. This may vary from one batch of the material to another leading to a different magnitude of tough￾ening and its dependence on temperature. Another possibility for the difference in the results could be the healing of the pre-cracks in an oxidizing atmos￾phere giving rise to a higher apparent toughness. Creep studies have found significantly faster oxi￾dation kinetics for the SiC-whisker-reinforced alum￾ina composite heated in air at T 1300°C [24, 49]. Microscopic observation of the fracture surface of the composite specimens also revealed that for the same

3562 SARRAFL-NOUR and COYLE: CRACK WAKE BRIDGE test duration, only samples tested at T>1300C had In agreement with a previous study, a microcrack a continuous glassy layer on the fracture surfaces. zone was found to lead to the improvement of th e-cracked n of the material for a crack-tip tough T>1000°C. prolonged duration to such oxidizing conditions may However, the results here did not indicate of any R cause healing of the pre-crack through joining of the curve contributions from the microcrack zone; the crack surfaces by the oxidation products (glass material showed a flat R-curve at 1400C with a frac- phase). A recent fracture toughness round robin test ture toughness in excess of the crack-tip toughness at arried out on silicon nitride also suggested such heal- room temperature by about 20%. The elevated-tem- ng processes as a cause for higher fracture toughness perature microcrack zone also did not appear to measured on pre-cracked specimens when tested in impart any visible influence on the bridging stresses air atmosphere [50]. In fact, post-fracture microscopic when it occurred concurrently with the bridging examination of the sic-whisker-reinforced alumina mechanism This conclusion was drawn based on the omposite material in the present study indicated evi- absence of an anomalous behavior in the bridging dence of such behavior Cracks branched off the main stress results between 1000%C and 1300C crack in the specimens tested at T21300C were found to be filled by a glassy phase, which was con- Acknowledgements-The authors sidered to be the product of the oxidation of the Sic Choll K. Jun and Greenleaf Corpora acknowledge Dr phase. The crack grown in a chevron-notched speci- generously providing the specimens gerton, PA for this work men, however, is protected from such crack-healing effects as a sharp and virgin crack tip is produced in the specimen in situ during the actual fracture test. REFERENCES In summary, the results of our R-curve analysi show no indication of a contribution of the Am. Ceram. Soc., 1988, 71(12), 1050 microcrack zone to the R-curve behavior, only to an 2. Sajgalik, P. and Dusza, J, J. Eur. Ceram. Soc., 1989, 5, increase in Ko. The increase in Ko seen in the present study is in agreement with previous work at tempera- 3. Campbell, G. H, Ruhle, M, Dalgleish, B J and Evan A.G.,J. Am. ceram.Soc.,190,73(3),521 tures up to 1200 C. Above 1200oC the discrepancy 4. Jenkins, M G, Kobayashi, A.S., White, K.W. and Bradt, with the previous study is likely due to crack healing R.C., J. Am. Ceram Soc., 1987, 78(6), 393 in that study 5. Krause. R. F. Jr. Fuller, E. R. and Rhodes, J. F.J. Am. Ceran.Soc,1990,73(3),559 5 CONCLUSIONS H. Hasselman, D. Munz, M. Sakai and v. Ya. Shevchenko Fracture Mechanics of Ceramics, Vol 9. Plenum Press, The distribution of the bridging stresses as a fur New York, 1992, p. 147 ion of crack opening displacement was deconvoluted 7. Becher, P F, Hsueh, C -H, Alexander, K.B. and Sun, from the R-curves of a 33 vol% SiC-whisker reinforced alumina composite as a function of tem-8. Jenkins, M. G, Kobayashi,A R C, Eng. Fract. Mech, 1988, 30(4),505 perature between800° C and I300°Ci maximum bridging stress was found to decrease lin- 74(9),2280 early with increasing temperature, yielding a zero 10. Han, L x and Suresh, S, J. Am. Ceram. Soc., 1989 value at <%C. Extrapolation of these bridging 11. Han, Warren, R and Suresh, S, Acta metall. mater. stress results to the room temperature condition gave 992,402)259 an estimated value of about 23 MPa for the maximum 12 Hansson, T, Swan, A. H and Warren, R, J. Eur. Ceram. bridging stress. This was found to be in good agree Soc.1994.13.427 ment with the maximum bridging stress results 13. Akatsu, T, Tanabe, Y, Matsuura, S, Yamada, M. Ishii H, Munakata, M. and Y asuda, E.J. Ce determined at room temperature in previous works Soc. Jpn, 1991,99(5,431 a similar composite material. Comparison between 14. Akatsu, T. and Suda, E, Ceram. Trans. the temperature dependence of the maximum bridging 15. Tiegs, T.N., in Ceramic stresses determined in our work with those of the The amerrd Interni ceram. Eng. Sci. Proc, 1992 thermal residual strains/stresses of the Sic-whisker 16. Qi, D. and Coyle,R.T phase in SiC-whisker-reinforced alumina composites 3(9-10),678 from other investigations showed a very good agree- 17. Steyer, T E. and Faber, K. T, Ceram. Eng. Sci.Proc. ment between the results. This indicated the domi- 1992, 13(9-10), 669 nance of the thermal residual stresses in the evoluti 18. Braski D. N. and Alexander. K. B.J. Mater. Res. 199 of the bridging stresses in the composite and was 0(4),1016 19. Ohji, T, Goto, Y. and Tsuge, A.,J. Am. Ceram. Soc. line with the mechanics of the bridging process in 991,74(4),739. whisker-reinforced composite. This indicated the rad- 20. Steyer, T. E and Faber, K.T.,J.Am. Cera 1995 ial thermal residual stress on the sic-whiskers as the 8(10),2673 dominant variable imparting temperature effects on Ohji, T, Shigegaki, Y, Miyajima, T. and Kanzaki, S,J. the bridging stresses when the whisker/matrix inter- 22. Yu, C. T and Kobayashi, A.S., Ceram. Eng. Sci. Proc. ce was free of 993,14(7-8),273

3562 SARRAFI-NOUR and COYLE: CRACK WAKE BRIDGE test duration, only samples tested at T 1300°C had a continuous glassy layer on the fracture surfaces. Exposing a pre-cracked specimen of the material for a prolonged duration to such oxidizing conditions may cause healing of the pre-crack through joining of the crack surfaces by the oxidation products (glass phase). A recent fracture toughness round robin test carried out on silicon nitride also suggested such heal￾ing processes as a cause for higher fracture toughness measured on pre-cracked specimens when tested in air atmosphere [50]. In fact, post-fracture microscopic examination of the SiC-whisker-reinforced alumina composite material in the present study indicated evi￾dence of such behavior. Cracks branched off the main crack in the specimens tested at T 1300°C were found to be filled by a glassy phase, which was con￾sidered to be the product of the oxidation of the SiC phase. The crack grown in a chevron-notched speci￾men, however, is protected from such crack-healing effects as a sharp and virgin crack tip is produced in the specimen in situ during the actual fracture test. In summary, the results of our R-curve analysis show no indication of a contribution of the microcrack zone to the R-curve behavior, only to an increase in Ko. The increase in Ko seen in the present study is in agreement with previous work at tempera￾tures up to 1200°C. Above 1200°C the discrepancy with the previous study is likely due to crack healing in that study. 5. CONCLUSIONS The distribution of the bridging stresses as a func￾tion of crack opening displacement was deconvoluted from the R-curves of a 33 vol.% SiC-whisker￾reinforced alumina composite as a function of tem￾perature between 800°C and 1300°C in air. The maximum bridging stress was found to decrease lin￾early with increasing temperature, yielding a zero value at
1400°C. Extrapolation of these bridging stress results to the room temperature condition gave an estimated value of about 23 MPa for the maximum bridging stress. This was found to be in good agree￾ment with the maximum bridging stress results determined at room temperature in previous works on a similar composite material. Comparison between the temperature dependence of the maximum bridging stresses determined in our work with those of the thermal residual strains/stresses of the SiC-whisker phase in SiC-whisker-reinforced alumina composites from other investigations showed a very good agree￾ment between the results. This indicated the domi￾nance of the thermal residual stresses in the evolution of the bridging stresses in the composite and was in line with the mechanics of the bridging process in a whisker-reinforced composite. This indicated the rad￾ial thermal residual stress on the SiC-whiskers as the dominant variable imparting temperature effects on the bridging stresses when the whisker/matrix inter￾face was free of an amorphous second phase. In agreement with a previous study, a microcrack zone was found to lead to the improvement of the crack-tip toughness in the composite at T
1000°C. However, the results here did not indicate of any R￾curve contributions from the microcrack zone; the material showed a flat R-curve at 1400°C with a frac￾ture toughness in excess of the crack-tip toughness at room temperature by about 20%. The elevated-tem￾perature microcrack zone also did not appear to impart any visible influence on the bridging stresses when it occurred concurrently with the bridging mechanism. This conclusion was drawn based on the absence of an anomalous behavior in the bridging stress results between 1000°C and 1300°C. Acknowledgements—The authors wish to acknowledge Dr. Choll K. Jun and Greenleaf Corporation, Saegertown, PA for generously providing the specimens used in this work. REFERENCES 1. Becher, P. F., Hsueh, C., Angelini, P. and Tiegs, T. N., J. Am. Ceram. Soc., 1988, 71(12), 1050. 2. Sajgalik, P. and Dusza, J., J. Eur. Ceram. Soc., 1989, 5, 321. 3. Campbell, G. H., Ruhle, M., Dalgleish, B. J. and Evans, A. G., J. Am. Ceram. Soc., 1990, 73(3), 521. 4. Jenkins, M. G., Kobayashi, A. S., White, K. W. and Bradt, R. C., J. Am. Ceram. Soc., 1987, 78(6), 393. 5. Krause, R. F. Jr., Fuller, E. R. and Rhodes, J. F., J. Am. Ceram. Soc., 1990, 73(3), 559. 6. Guazzone, L. and White, K. W., in, ed. R. C. Bradt, D. P. H. Hasselman, D. Munz, M. Sakai and V. Ya. Shevchenko. Fracture Mechanics of Ceramics, Vol. 9. Plenum Press, New York, 1992, p. 147. 7. Becher, P. F., Hsueh, C. -H., Alexander, K. B. and Sun, E. Y., J. Am. Ceram. Soc., 1996, 79(2), 298. 8. Jenkins, M. G., Kobayashi, A. S., White, K. W. and Bradt, R. C., Eng. Fract. Mech., 1988, 30(4), 505. 9. White, K. W. and Guazzone, L., J. Am. Ceram. Soc., 1991, 74(9), 2280. 10. Han, L. X. and Suresh, S., J. Am. Ceram. Soc., 1989, 72(7), 1233. 11. Han, L. X., Warren, R. and Suresh, S., Acta metall. mater., 1992, 40(2), 259. 12. Hansson, T., Swan, A. H. and Warren, R., J. Eur. Ceram. Soc., 1994, 13, 427. 13. Akatsu, T., Tanabe, Y., Matsuura, S., Yamada, M., Ishii, H., Munakata, M. and Yasuda, E., J. Ceram. Soc. Jpn., 1991, 99(5), 431. 14. Akatsu, T. and Ysuda, E., Ceram. Trans., 1998, 99, 295. 15. Tiegs, T. N., in Ceramic Materials and Components for Engines, 3rd International Symposium, ed. V. J. Tennery. The American Ceramic Society, 1989, p. 937. 16. Qi, D. and Coyle, R. T., Ceram. Eng. Sci. Proc., 1992, 13(9-10), 678. 17. Steyer, T. E. and Faber, K. T., Ceram. Eng. Sci. Proc., 1992, 13(9-10), 669. 18. Braski, D. N. and Alexander, K. B., J. Mater. Res., 1995, 10(4), 1016. 19. Ohji, T., Goto, Y. and Tsuge, A., J. Am. Ceram. Soc., 1991, 74(4), 739. 20. Steyer, T. E. and Faber, K. T., J. Am. Ceram. Soc., 1995, 78(10), 2673. 21. Ohji, T., Shigegaki, Y., Miyajima, T. and Kanzaki, S., J. Am. Ceram. Soc., 1997, 80(4), 991. 22. Yu, C. T. and Kobayashi, A. S., Ceram. Eng. Sci. Proc., 1993, 14(7-8), 273