《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_fiber19Fracture behaviour of 2D-weaved, silica–silica.pdf_大学文库

Availableonlineatwww.sciencedirect.com BCIENCEODIRE。T Engineering Fracture Mechanics ELSEVIER Engineering Fracture Mechanics 71(2004)2589-2605 www.elsevier.com/locate/engfracm fracture behaviour of 2D-weaved. silica-silica continuous fibre-reinforced ceramic-matrix composites(CFCS) N. Eswara Prasad", Sweety Kumari, S.v. Kamat, M. Vijayakumar, G. Malakondaiah Defence Metallurgical Research laboratory, PO Kanchanbagh, Hyderabad 500058, India Received 18 February 2003: received in revised form 29 January 2004: accepted 24 February 2004 Abstract Significantly improved fracture resistance (in terms of fracture toughness and fracture energy) can be imparted to monolithic ceramics by adopting composite design methodology based on fibre reinforcement technology. The present paper describes the fracture behaviour of one such fibre- reinforced material, namely the silica-silica based continuous fibre-reinforced, ceramic-matrix composite(CFCC)in two orthogonal notch orientations of crack divider and crack arrester orientations. Different fracture resistance parameters have been evaluated to provide a quantitative treatment of the observed fracture behaviour. From this study, it has been concluded that the overall fracture resistance of the CFCC is best reflected by total fracture energy release rate Je), which parameter encompasses most of the fracture events/processes. The Je values of the composite are found to be more than an order of magnitude higher than the energy values corresponding to the plane strain fracture toughness (Ko, derived from Kle, the plane strain fracture toughness)and >200% higher than elastic-plastic fracture toughness (ie). Apart from this, the composite is found to exhibit high degree of anisotropy in the fracture resistance and also, a significant variation in the relative degree of shear component with crack extension. g 2004 Elsevier Ltd. All rights reserved Keywords: Continuous fibre 2D silica-silica composites: Fracture behaviour and modes of failure; Fracture resistance; Total fracture energy release rate; R-curve behaviour 1. Introduction Ceramic materials have assumed significant technological importance as structural materials because the newer design and development methodologies, adopting fibre reinforcements, have resulted in enhancement of the fracture resistance of monolithic ceramics by several fold [1-6]. Among various ceramic materi- als, amorphous silica uniquely combines different properties to suit several select technological applications Corresponding author.Tel:+91-40-24340051;fax:+91-40-24340683/4341439 E-mailaddresses:nep(@dmrl.ernet.in,neswarap@rediffmail.com(N.EswaraPrasad) 0013-7944/S. see front matter 2004 Elsevier Ltd. All rights reserved doi: 10. 1016/j-engfracmech 2004.02.005

Fracture behaviour of 2D-weaved, silica–silica continuous fibre-reinforced, ceramic–matrix composites (CFCCs) N.Eswara Prasad *, Sweety Kumari, S.V. Kamat, M.Vijayakumar, G.Malakondaiah Defence Metallurgical Research Laboratory, PO Kanchanbagh, Hyderabad 500058, India Received 18 February 2003; received in revised form 29 January 2004; accepted 24 February 2004 Abstract Significantly improved fracture resistance (in terms of fracture toughness and fracture energy) can be imparted to monolithic ceramics by adopting composite design methodology based on fibre reinforcement technology.The present paper describes the fracture behaviour of one such fibre-reinforced material, namely the silica–silica based continuous fibre-reinforced, ceramic–matrix composite (CFCC) in two orthogonal notch orientations of crack divider and crack arrester orientations.Different fracture resistance parameters have been evaluated to provide a quantitative treatment of the observed fracture behaviour.From this study, it has been concluded that the overall fracture resistance of the CFCC is best reflected by total fracture energy release rate (Jc), which parameter encompasses most of the fracture events/processes.The Jc values of the composite are found to be more than an order of magnitude higher than the energy values corresponding to the plane strain fracture toughness (JKQ, derived from KIc, the plane strain fracture toughness) and >200% higher than elastic–plastic fracture toughness (JIc).Apart from this, the composite is found to exhibit high degree of anisotropy in the fracture resistance and also, a significant variation in the relative degree of shear component with crack extension. 2004 Elsevier Ltd.All rights reserved. Keywords: Continuous fibre 2D silica–silica composites; Fracture behaviour and modes of failure; Fracture resistance; Total fracture energy release rate; R-curve behaviour 1. Introduction Ceramic materials have assumed significant technological importance as structural materials because the newer design and development methodologies, adopting fibre reinforcements, have resulted in enhancement of the fracture resistance of monolithic ceramics by several fold [1–6].Among various ceramic materials, amorphous silica uniquely combines different properties to suit several select technological applications * Corresponding author.Tel.: +91-40-24340051; fax: +91-40-24340683/4341439. E-mail addresses: nep@dmrl.ernet.in, neswarap@rediffmail.com (N. Eswara Prasad). 0013-7944/$ - see front matter 2004 Elsevier Ltd.All rights reserved. doi:10.1016/j.engfracmech.2004.02.005 Engineering Fracture Mechanics 71 (2004) 2589–2605 www.elsevier.com/locate/engfracmech

N. Eswara Prasad et al. Engineering Fracture Mechanics 71(2004) 2589-2605 [7-10). These properties include, high melting point combined with high thermal shock resistance and xcellent thermal as well as electrical insulating properties [8, 10]. However, the mechanical properties of lica material in the monolithic form are far from acceptable levels. Silica, in its bulk form, has low strength (both tensile and flexural) and extremely low fracture toughness as compared to several structural ceramic materials [8]; thus, needing significant improvements so that it can be accepted for any structural application. One of the means of achieving improved mechanical properties is by using either two-or three- dimensional(designated commonly as 2D- and 3D, respectively) networks of continuous fibres as rein- forcements to the ceramic-matrix material leading to newer structural materials, known as"continuous fibre-reinforced, ceramic-matrix composites(CFCCs)". Numerous studies have been conducted in the last two decades on the fibre/whisker toughening of this class of ceramics. These studies have been compre- hensively reviewed by Evans [2] as well as by Becher [4] and later, by Faber [6]. However, to the best of our knowledge, there are no fracture toughness/energy studies reported so far for the silica-silica CFCCs During the fracture process of a CFCC, various events/developments take place in the three regions of the fracture, namely the wake of the crack, at the crack tip and finally in the region of process zone ahead of the crack tip These influence the net enhancements in the fracture resistance of a CFCC. They include some or most of the following [2, 3, 5 1. Local increase in the stress level with the application of external loading 2. relative displacement of matrix/interface elements 3. matrix microcracking, leading to matrix failure(with or without significant crack path meandering, i.e rack deflection and/or branching) 4. debonding of matrix/fibre interface(with or without significant frictional forces), fibre pull-out and fibre breakage in the crack tip process zone, 6. frictional sliding of the fibres along the matrix/fibre interfaces, 7. loss of residual strain energy These processes/stages, schematically shown in Fig. 1, result in significant energy dissipation through frictional events in the wake and process zones, acoustic emission and fibre debonding, pull-out and breakage. Contributions from these stages of crack tip and fibre reinforcements interactions, with or ULL-oUT FRIC TIONAL DISSIPATION ENERGY DISSIPATED ACOUSTIC WAVES MATRIX CRACK RESIDUA SURFACES STRESS-FREE LOSS OF RESIDUAL Fig. l. Schematic showing various events and processes of crack bridging mechanism in fibre-reinforced composites(from Ref. 2). Note that the crack extension process essentially involves matrix microcracking, fibre/matrix debonding, fibre fracture and fibre pull

[7–10].These properties include, high melting point combined with high thermal shock resistance and excellent thermal as well as electrical insulating properties [8,10].However, the mechanical properties of silica material in the monolithic form are far from acceptable levels.Silica, in its bulk form, has low strength (both tensile and flexural) and extremely low fracture toughness as compared to several structural ceramic materials [8]; thus, needing significant improvements so that it can be accepted for any structural application.One of the means of achieving improved mechanical properties is by using either two- or threedimensional (designated commonly as 2D- and 3D-, respectively) networks of continuous fibres as reinforcements to the ceramic–matrix material leading to newer structural materials, known as ‘‘continuous fibre-reinforced, ceramic–matrix composites (CFCCs)’’.Numerous studies have been conducted in the last two decades on the fibre/whisker toughening of this class of ceramics.These studies have been comprehensively reviewed by Evans [2] as well as by Becher [4] and later, by Faber [6].However, to the best of our knowledge, there are no fracture toughness/energy studies reported so far for the silica–silica CFCCs. During the fracture process of a CFCC, various events/developments take place in the three regions of the fracture, namely the wake of the crack, at the crack tip and finally in the region of process zone ahead of the crack tip.These influence the net enhancements in the fracture resistance of a CFCC.They include some or most of the following [2,3,5]: 1.Local increase in the stress level with the application of external loading, 2.relative displacement of matrix/interface elements, 3. matrix microcracking, leading to matrix failure (with or without significant crack path meandering, i.e., crack deflection and/or branching), 4.debonding of matrix/fibre interface (with or without significant frictional forces), 5.fibre pull-out and fibre breakage in the crack tip process zone, 6.frictional sliding of the fibres along the matrix/fibre interfaces, 7.loss of residual strain energy. These processes/stages, schematically shown in Fig.1, result in significant energy dissipation through frictional events in the wake and process zones, acoustic emission and fibre debonding, pull-out and breakage.Contributions from these stages of crack tip and fibre reinforcements interactions, with or Fig.1.Schematic showing various events and processes of crack bridging mechanism in fibre-reinforced composites (from Ref.[2]). Note that the crack extension process essentially involves matrix microcracking, fibre/matrix debonding, fibre fracture and fibre pullout. 2590 N. Eswara Prasad et al. / Engineering Fracture Mechanics 71 (2004) 2589–2605

N. Eswara Prasad et al. Engineering Fracture Mechanics 71(2004)2589-2605 without the contributions from matrix fracture events. have led to unified models for the fracture resistance in materials that exhibit crack bridging [2-6]. The toughening in these cases of crack bridging is essentially due to ductile or brittle reinforcements. In the case of present CFCCs, it is the later that makes contri butions to the toughening. In the present paper, the fracture behaviour of a two-dimensional (2D) silica fibre-reinforced, silica matrix composite is presented and discussed. Various parameters of fracture resistance have been used to quantify the fracture resistance of the material. These include, the plane strain fracture toughness(Kl) elastic-plastic fracture toughness (ic) and total fracture energy release rate (e). Also reported and dis- cussed are the effects of notch orientation and notch depth on the fracture resistance in these composites. 2. Experimental details he two-dimensionally weaved silica fibre preforms are vacuum impregnated using colloidal silica Ition precursor to provide the matrix for the silica-silica continuous fibre-reinforced, ceramic-matrix composites (referred to as"silica-silica CFCC"or simply"CFCC"). The interconnected network of capillaries in the preforms facilitates solution impregnation, thus providing uniform matrix for the CFCC After infiltration, the CFCC is dried and during this drying process, water content of the matrix gel solution is gradually removed. These dried CFCCs are then sintered to impart interparticle bonding and in turn, this Facilitates load transfer from the matrix to the fibre and vice-versa There are no standard test procedures for the evaluation of fracture toughness/energy of ceramic materials, especially for the advanced ceramic composites such as CFCCs. However, several studies have been reported in the recent past which describe in detail the procedures adopted for and the fracture behaviour observed of the monolithic ceramics and ceramic-matrix composites, including CFCCs(see Refs. [11-18] for details and a summary of these details in Ref [19D. Since ceramic materials exhibit brittle fracture, the AsTM Standard E-399, describing the standard practice for the evaluation of plane strain fracture toughness of metallic materials [20], can conveniently be adopted to determine the fracture oughness of these materials. However, since the CfCCs also exhibit limited extent of non-linear fracture, the J-integral technique once again developed for metallic materials(fundamentals and standard practices described in Refs. [21-23] and [24], respectively) also applies equally Single edge notch beam(SENB)specimens of 8 mm thickness, 10 mm width and a span length of 40 mm were used. The fracture toughness/energy was evaluated in two notch orientations, namely (i)crack divider orientation, in which the notch is along the orientation of the plies in the thickness direction and (ii)crack arrester orientation, in which the notch is perpendicular to the orientation of the plies in the thickness direction(the third orientation of crack delamination could not be studied because of specimen size limi tations). In both cases, notch is perpendicular to the longitudinal plies Notches of varied length were introduced using 0.3 mm thick diamond wafer blades, mounted on a standard Isomet cutting machine. A specially designed jig was used to obtain straight notches by moving the job across the cutting plane. The notches thus introduced were found to have a finite root radius, p, typically of the order of 160 um. The p values were determined by Delta TM 35 x-y profile projector. The notch root radii. either in the crack divider or crack arrester orientation were found to be similar. The crack lengths were maintained in the range of 0.35 to 0. 7 times the specimen width. Among these, specimens with crack lengths in the range specified by the ASTM standard E-399[20](0.45-0.55 times the specimen width) were only considered for the determination of Klc values. The other specimens with large lengths were employed essentially to determine the work of fracture [25], which results will be reported separately. The fracture energy determined from the load-displacement data were used to determine the elastic-plastic fracture toughness, JIe and the total fracture energy release rate, Jc. The later two fracture resistance parameters are based on J-integral [21]

without the contributions from matrix fracture events, have led to unified models for the fracture resistance in materials that exhibit crack bridging [2–6].The toughening in these cases of crack bridging is essentially due to ductile or brittle reinforcements.In the case of present CFCCs, it is the later that makes contributions to the toughening. In the present paper, the fracture behaviour of a two-dimensional (2D) silica fibre-reinforced, silica– matrix composite is presented and discussed.Various parameters of fracture resistance have been used to quantify the fracture resistance of the material.These include, the plane strain fracture toughness (KIc), elastic–plastic fracture toughness (JIc) and total fracture energy release rate (Jc).Also reported and discussed are the effects of notch orientation and notch depth on the fracture resistance in these composites. 2. Experimental details The two-dimensionally weaved silica fibre preforms are vacuum impregnated using colloidal silica solution precursor to provide the matrix for the silica–silica continuous fibre-reinforced, ceramic–matrix composites (referred to as ‘‘silica–silica CFCC’’ or simply ‘‘CFCC’’).The interconnected network of capillaries in the preforms facilitates solution impregnation, thus providing uniform matrix for the CFCC. After infiltration, the CFCC is dried and during this drying process, water content of the matrix gel solution is gradually removed.These dried CFCCs are then sintered to impart interparticle bonding and in turn, this facilitates load transfer from the matrix to the fibre and vice-versa. There are no standard test procedures for the evaluation of fracture toughness/energy of ceramic materials, especially for the advanced ceramic composites such as CFCCs.However, several studies have been reported in the recent past which describe in detail the procedures adopted for and the fracture behaviour observed of the monolithic ceramics and ceramic–matrix composites, including CFCCs (see Refs.[11–18] for details and a summary of these details in Ref.[19]).Since ceramic materials exhibit brittle fracture, the ASTM Standard E-399, describing the standard practice for the evaluation of plane strain fracture toughness of metallic materials [20], can conveniently be adopted to determine the fracture toughness of these materials.However, since the CFCCs also exhibit limited extent of non-linear fracture, the J-integral technique once again developed for metallic materials (fundamentals and standard practices described in Refs.[21–23] and [24], respectively) also applies equally. Single edge notch beam (SENB) specimens of 8 mm thickness, 10 mm width and a span length of 40 mm were used.The fracture toughness/energy was evaluated in two notch orientations, namely (i) crack divider orientation, in which the notch is along the orientation of the plies in the thickness direction and (ii) crack arrester orientation, in which the notch is perpendicular to the orientation of the plies in the thickness direction (the third orientation of crack delamination could not be studied because of specimen size limitations).In both cases, notch is perpendicular to the longitudinal plies. Notches of varied length were introduced using 0.3 mm thick diamond wafer blades, mounted on a standard Isomet cutting machine.A specially designed jig was used to obtain straight notches by moving the job across the cutting plane.The notches thus introduced were found to have a finite root radius, q, typically of the order of 160 lm.The q values were determined by Delta TM 35 x–y profile projector.The notch root radii, either in the crack divider or crack arrester orientation, were found to be similar.The crack lengths were maintained in the range of 0.35 to 0.7 times the specimen width. Among these, specimens with crack lengths in the range specified by the ASTM standard E-399 [20] (0.45–0.55 times the specimen width) were only considered for the determination of KIc values.The other specimens with larger crack lengths were employed essentially to determine the work of fracture [25], which results will be reported separately.The fracture energy determined from the load–displacement data were used to determine the elastic–plastic fracture toughness, JIc and the total fracture energy release rate, Jc.The later two fracture resistance parameters are based on J-integral [21]. N. Eswara Prasad et al. / Engineering Fracture Mechanics 71 (2004) 2589–2605 2591

N. Eswara Prasad et al. Engineering Fracture Mechanics 71(2004)2589-2605 DISPLACEMENT (6) g. 3. of hd nosa isee ct ak etah wit d sng me ewa dta in otsr at the rmsisteanae u ihespecckeas ter an e tation length (grven It can be seen from these curves that increase in crack length decreases maximum load attained prior to the commencement of crack extension. The load initially increases linearly with the displacement in all the cases.This corresponds to the stage in which the specimen largely experiences elastic stresses. Followed by his stage, the crack extension takes place. This is reflected in nonlinear increase in the load with dis- placement followed by noticeable drop in the load with further increase in the displacement. The load- displacement curves show distinctly different characteristics at this stage of crack extension in the two notch orientations The material in the crack divider orientation shows a steep, but continuous fall in the load with increase in the displacement(Fig. 2). Such a behaviour is seen in specimens with lower crack lengths(a) and(b)in Fig. 2 with a/W=0.32 and 0.44, respectively). This clearly indicates gradual extension of the crack front However, higher crack length specimens in this notch orientation((c)and(d)in Fig. 2 with a/W=0.56 and 0.65, respectively) do not show such steep load drop. Instead, these specimens show near-saturation in the variation of load with displacement, up to a displacement of 800 um. In this case, the fibre bundles undergo significant bending without breakage and crack extension essentially occurs along fibre/matrix interface. On the other hand, the specimens in the crack arrester orientation show distinct and sudden load drops with crack extension(shown as A1 B1, A2B2 etc, in the curves(a),()and(c)of Fig 3). Again, at large crack lengths(a/W=0.64, case(c)in Fig 3)the specimen shows gradual load drop with displacement Such a behaviour is attributable to the change in the nature of crack extension. As shown schematically in ne specimens in the crack arrester orientation show complete mode I(tensile) fracture dominant fibre bundle breakage leading to relatively insignificant crack extension along the fibre/matrix interface when the crack lengths are smaller(a/w<0.45). As crack length increases, the extent of crack extension along the fibre/matrix interface also increases, leading to significant extent of'H'and'Tcracking (Fig 4b). This results in mode I crack extension in the initial stages and a mixed mode fracture in the later stages, comprising mode I and mode II (in-plane shear or sliding) components. This occurs in case of specimens with a/W values in the range 0.55-0.6. At still higher crack lengths(cases(c)and(d)in Fig. 2 and (c)in Figs. 3 and 4), the crack extension occurs essentially in mode II with interply shearing being the

It can be seen from these curves that increase in crack length decreases maximum load attained prior to the commencement of crack extension.The load initially increases linearly with the displacement in all the cases.This corresponds to the stage in which the specimen largely experiences elastic stresses.Followed by this stage, the crack extension takes place.This is reflected in nonlinear increase in the load with displacement followed by noticeable drop in the load with further increase in the displacement.The load– displacement curves show distinctly different characteristics at this stage of crack extension in the two notch orientations. The material in the crack divider orientation shows a steep, but continuous fall in the load with increase in the displacement (Fig.2).Such a behaviour is seen in specimens with lower crack lengths ((a) and (b) in Fig.2 with a=W ¼ 0:32 and 0.44, respectively). This clearly indicates gradual extension of the crack front. However, higher crack length specimens in this notch orientation ((c) and (d) in Fig.2 with a=W ¼ 0:56 and 0.65, respectively) do not show such steep load drop. Instead, these specimens show near-saturation in the variation of load with displacement, up to a displacement of 800 lm.In this case, the fibre bundles undergo significant bending without breakage and crack extension essentially occurs along fibre/matrix interface.On the other hand, the specimens in the crack arrester orientation show distinct and sudden load drops with crack extension (shown as A1B1, A2B2 etc., in the curves (a), (b) and (c) of Fig. 3). Again, at large crack lengths (a=W ¼ 0:64, case (c) in Fig.3) the specimen shows gradual load drop with displacement. Such a behaviour is attributable to the change in the nature of crack extension.As shown schematically in Fig.4a, the specimens in the crack arrester orientation show complete mode I (tensile) fracture with predominant fibre bundle breakage leading to relatively insignificant crack extension along the fibre/matrix interface when the crack lengths are smaller (a=W < 0:45).As crack length increases, the extent of crack extension along the fibre/matrix interface also increases, leading to significant extent of ‘H’ and ‘T ’ cracking (Fig.4b).This results in mode I crack extension in the initial stages and a mixed mode fracture in the later stages, comprising mode I and mode II (in-plane shear or sliding) components.This occurs in case of specimens with a=W values in the range 0.55–0.6. At still higher crack lengths (cases (c) and (d) in Fig. 2 and (c) in Figs.3 and 4), the crack extension occurs essentially in mode II with interply shearing being the Fig.3.Load–displacement data obtained during the evaluation of fracture resistance using specimens with varied crack length (given in terms of the normalised crack length with specimen width) in case of the material in the ‘‘crack arrester’’ orientation. N. Eswara Prasad et al. / Engineering Fracture Mechanics 71 (2004) 2589–2605 2593

N. Eswara Prasad et al. Engineering Fracture Mechanics 71(2004)2589-2605 (a) PLY BREAKING- MODE I b】T’AND" H CRACK|NG MIXED MODE I/II (C) INTERPLY SHEAR-MODE II Fig 4. Schematic figure showing the nature of crack extension in the crack arrester orientation when the specimen crack length is raried significantly. (a)Short crack lengths(a/w0.6). Note the increasing extent of mode II fracture component with increasing crack length values. principal fracture event. The associated fibre bundle fracture is negligible(notice the very small sudden load drop(s)shown as A1 BI in Fig 3c) 3. 2. Plane strain fracture toughness (Klc) The plane strain fracture toughness(Klc)of the 2D silica-silica CFCC material was evaluated in the crack divider and crack arrester orientations according to the astm standard E-399 [20]. Specimens of varied crack length have been used for the determination of fracture toughness Figs 2 and 3 show the basic data of the load variation with displacement for the specimens in the two notch orientations. Table 1 provides the details of the specimens and the data derived from these fracture toughness tests. Though the specimens with varied a/W were tested, data corresponding to specimens with a/w values in the range of 0.45-0.55, as specified by ASTM standard E-399 [19], were only used to arrive at Klc. The values of K, and Ko derived for each test are also listed in Table 1. These data in Table l show that the material exhibits valid Kmax/Ko values(<1. 1)only when the crack lengths are smaller(a/W<0.44). At higher crack lengths. the material exhibits limited extent of stable crack extension, which yielded Kmax/ Ko values that are in excess of 1. 1. In view of these observations, the Ko values derived from specimens with a/w of 0.44 and 0.56 in the crack divider orientation and 0.52 in the crack arrester orientation(note only a small variation in the Ko values between different test specimens, see data in Table 1) are considered to yield valid KI Under such conditions, the CFCC material exhibits a significantly higher fracture toughness value in the crack divider orientation as compared to the crack arrester orientation. An average value of 2.03 MPavm (corresponding to the crack lengths of a/W of 0.44 and 0.56)obtained for the crack divider orientation is ore than 100% higher than the value obtained in the crack arrester orientation(Klc=0.98 MPa vm) econdly, the value of conditional fracture toughness(Ko) decreases significantly with increase in the crack length, especially in the crack divider orientation. This is due to the change in fracture mode. At higher

N. Eswara Prasad et al. Engineering Fracture Mechanics 71(2004)2589-2605 Table l Plane strain fracture toughness (KIc, MPa ym) data of the 2D silica-silica CFCC material f(a/w) Po and p (a) Crack divider orientation 123 9.76 7.23 3.12and0.32 234and246 2.15and2.26 993 4.39and0.44 205and206 2.43aand24 994 5.60and0.56 .25 89 and 101 1.63a and 1.84 7.26 6.35and0.65 4.63 52 and 58 1.36andl52 (b) Crack arrester orientation 7.74 7.53 58and66.5 0.78and0.89 23456 7.59 8.95 06and0.403 2.15 58 and 60 0.84and0.87 9.1 53 and 60 0.98aand1.10 976 4.84and0. 3.5 33 and 0.72and0.86 4.9and0.64 37 and 49 theo Decimen width, in mm; B-specimen thickness, in mm; L-specimen span length(fixed value of 40 mm); Pg--conditional load for nset of fracture, in N; Pmar-maximum load in the load-displacement curve, in N; Ko-conditional fracture toughness, in MPa vm; Kmar-maximum stress intensity factor, in MPa vm. Valid Klc. crack lengths, as discussed in the previous section, the fracture mode gradually changes to predominant shear, involving mode II (in-plane shear or sliding) fracture components. This is true for both test orien tations 3.3. Elastic-plastic fracture toughness (JIc) The procedure suggested by Landes and Begley [23] and the ASTM standard E-813 [24] provide details of the latest standard practice for the determination of elastic-plastic fracture toughness, Jic. Alternatively, another widely accepted methodology, again suggested by Landes and Begley [22], can also be employed for Jie determination. Both these methodologies are based on Rice proposed J-integral [21]. The later proce- dure principally involves the determination of fracture energy o) from the energy absorbed in the fracture process(Eini, area under the load-displacement, usually the displacement considered here corresponds to the load line) by specimens with different crack lengths, up to either a constant displacement or a constant load. In the present case, the load-displacement data given in Figs. 2 and 3 are used to calculate the energy for the crack initiation(Eini), which event is assumed to occur at the displacements corresponding to the peak load. Eini values thus determined are used to calculate the fracture energy, Jo as [21, 22 o=△Emn/B(△a), where(AEini)is the difference in the fracture energies(corresponding to peak loads in the load displacement curves)of two specimens with different initial crack lengths(their difference is Aa). The values of Jo, determined from the load-displacement curves in crack divider and crack arrester orientations, are shown as a function of crack length in Fig. 5. As to be expected, the material shows constant values of o in the crack divider(1.36 kJ/m")and crack arrester(0.66 kJ/m")orientations. The scatter in o values is higher for crack arrester orientation as compared to the crack divider orientation. However, all these values were found to satisfy the validity conditions and hence, can be termed as elastic-plastic fracture toughness, JIc of the CFCc As stated above, the lc corresponds to the peak load (assumed to correspond to the crack initiation) and ence would encompass only those fracture events that occur in the CFCC material before or up to the

crack lengths, as discussed in the previous section, the fracture mode gradually changes to predominant shear, involving mode II (in-plane shear or sliding) fracture components.This is true for both test orientations. 3.3. Elastic–plastic fracture toughness (JIc) The procedure suggested by Landes and Begley [23] and the ASTM standard E-813 [24] provide details of the latest standard practice for the determination of elastic–plastic fracture toughness, JIc.Alternatively, another widely accepted methodology, again suggested by Landes and Begley [22], can also be employed for JIc determination.Both these methodologies are based on Rice proposed J-integral [21].The later procedure principally involves the determination of fracture energy (JQ) from the energy absorbed in the fracture process (Eini, area under the load–displacement, usually the displacement considered here corresponds to the load line) by specimens with different crack lengths, up to either a constant displacement or a constant load.In the present case, the load–displacement data given in Figs.2 and 3 are used to calculate the energy for the crack initiation (Eini), which event is assumed to occur at the displacements corresponding to the peak load. Eini values thus determined are used to calculate the fracture energy, JQ as [21,22]: JQ ¼ DEini=BðDaÞ; ð1Þ where (DEini) is the difference in the fracture energies (corresponding to peak loads in the load displacement curves) of two specimens with different initial crack lengths (their difference is Da).The values of JQ, determined from the load–displacement curves in crack divider and crack arrester orientations, are shown as a function of crack length in Fig.5.As to be expected, the material shows constant values of JQ in the crack divider (1.36 kJ/m2) and crack arrester (0.66 kJ/m2) orientations.The scatter in JQ values is higher for crack arrester orientation as compared to the crack divider orientation.However, all these values were found to satisfy the validity conditions and hence, can be termed as elastic–plastic fracture toughness, JIc of the CFCC. As stated above, the JIc corresponds to the peak load (assumed to correspond to the crack initiation) and hence would encompass only those fracture events that occur in the CFCC material before or up to the Table 1 Plane strain fracture toughness (KIc, MPa pm) data of the 2D silica–silica CFCC material Specimen no. WB a and a=W f ða=W Þ PQ and Pmax KQ and Kmax (a) Crack divider orientation 1 9.76 7.23 3.12 and 0.32 1.6 234 and 246 2.15 and 2.26 2 9.93 7.54 4.39 and 0.44 2.22 205 and 206 2.43a and 2.43 3 9.94 7.17 5.60 and 0.56 3.25 89 and 101 1.63a and 1.84 4 9.76 7.26 6.35 and 0.65 4.63 52 and 58 1.36 and 1.52 (b) Crack arrester orientation 1 7.76 7.60 2.52 and 0.325 1.62 70 and 74 0.86 and 0.90 2 7.74 7.53 2.7 and 0.35 1.73 58 and 66.5 0.78 and 0.89 3 7.59 8.95 3.06 and 0.403 2.15 58 and 60 0.84 and 0.87 4 7.68 9.13 4.0 and 0.52 2.84 53 and 60 0.98a and 1.10 5 7.61 9.76 4.84 and 0.58 3.5 33 and 40 0.72 and 0.86 6 7.67 9.89 4.9 and 0.64 4.43 37 and 49 0.99 and 1.3 W ––specimen width, in mm; B––specimen thickness, in mm; L––specimen span length (fixed value of 40 mm); PQ––conditional load for the onset of fracture, in N; Pmax––maximum load in the load–displacement curve, in N; KQ––conditional fracture toughness, in MPa pm; Kmax––maximum stress intensity factor, in MPa pm. a Valid KIc. N. Eswara Prasad et al. / Engineering Fracture Mechanics 71 (2004) 2589–2605 2595

2596 N. Eswara Prasad et al. Engineering Fracture Mechanics 71(2004) 2589-2605 E 1.5 Crack Divider Orientation J.=1.36kJm2 Crack arrester orie Crack Length(a Fig. 5. Variation of elastic-plastic fracture toughness o) with crack length for the CFCC in crack divider and crack arrester ori- event that the material undergoes first fibre bundle fracture. As discussed earlier, these events include matrix microcracking and fibre/matrix debonding: but, do not include the fibre bundle failure and fibre pull-out. However, it is well accepted now that the last two events too contribute significantly to the overall fracture resistance of CFCC materials and the energy absorbed during these two processes is also con siderable. Hence, an alternative method of total (elastic-plastic) fracture energy release rate is adopted to evaluate the fracture resistance that accounts for all the fracture events of the present material( described in details in the next section). Hence, the Jie values evaluated and reported in the present section are valid materials' fracture resistance properties; however, they are conservative in nature 3.4. Total fracture energy release rate (e) Li and coworkers [26-29] have successfully extended the J-integral concept to brittle materials, first for concrete materials and later for inhomogeneous and discontinuous materials, a preliminary review of which was provided by Mai [30]. Later, these methodologies were successfully employed for CFCCs by Li and coworkers themselves [29]and Nair and Wang 31]. Homogeneous materials exhibit a parabolic decrease in the stress with radial distance (r) from the crack tip(Fig. 6a). Such a gradual decrease in the stress denotes stable crack extension, which is one of the basic requirements for applying J-integral. The discontinuous, heterogeneous CFCCs also exhibit such crack tip stress singularity. But these materials, in addition, exhibit events of unstable crack extension. This is despite the fact that the material, in general, exhibits parabolic decrease in the stress with radial distance, r(Fig. 6b). Each of the load excursions and sudden load drops in the failure of a fibre bundle and the subsequent load excursion is due to gradual build up of the local stref o ig. 6b represent the local crack tip fracture event. A sudden load drop in the crack tip stress level is due In such cases, the overall or global fracture energy (a or the total fracture energy release rate, Je)represents the fracture resistance of the material

event that the material undergoes first fibre bundle fracture.As discussed earlier, these events include matrix microcracking and fibre/matrix debonding; but, do not include the fibre bundle failure and fibre pull-out.However, it is well accepted now that the last two events too contribute significantly to the overall fracture resistance of CFCC materials and the energy absorbed during these two processes is also considerable.Hence, an alternative method of total (elastic–plastic) fracture energy release rate is adopted to evaluate the fracture resistance that accounts for all the fracture events of the present material (described in details in the next section).Hence, the JIc values evaluated and reported in the present section are valid materials’ fracture resistance properties; however, they are conservative in nature. 3.4. Total fracture energy release rate (Jc) Li and coworkers [26–29] have successfully extended the J-integral concept to brittle materials, first for concrete materials and later for inhomogeneous and discontinuous materials, a preliminary review of which was provided by Mai [30].Later, these methodologies were successfully employed for CFCCs by Li and coworkers themselves [29] and Nair and Wang [31].Homogeneous materials exhibit a parabolic decrease in the stress with radial distance (r) from the crack tip (Fig.6a).Such a gradual decrease in the stress denotes stable crack extension, which is one of the basic requirements for applying J-integral.The discontinuous, heterogeneous CFCCs also exhibit such crack tip stress singularity.But these materials, in addition, exhibit events of unstable crack extension.This is despite the fact that the material, in general, exhibits parabolic decrease in the stress with radial distance, r (Fig.6b).Each of the load excursions and sudden load drops in Fig.6b represent the local crack tip fracture event.A sudden load drop in the crack tip stress level is due to the failure of a fibre bundle and the subsequent load excursion is due to gradual build up of the local stress. In such cases, the overall or global fracture energy (Ja or the total fracture energy release rate, Jc) represents the fracture resistance of the material. 0.5 1.0 1.5 2.0 2 5 Crack Length (a), mm Elastic Plastic Fracture Toughness (JQ), k /m2 3 4 6 7 Crack Divider Orientation Crack Arrester Orientation JIc= 0.66 k /m2 J JIc= 1.36 k /m2 J J Fig.5.Variation of elastic–plastic fracture toughness (JQ) with crack length for the CFCC in crack divider and crack arrester orientations. 2596 N. Eswara Prasad et al. / Engineering Fracture Mechanics 71 (2004) 2589–2605

2598 N. Eswara Prasad et al. Engineering Fracture Mechanics 71(2004) 2589-2605 This is the case in the present CFCC materials. As stated earlier, the increasing contributions from mode Il or in-plane shear fracture during mode I fracture toughness evaluation using specimens of varied crack length, require the adoption of such an energy concept. Li and coworkers [29] have clearly shown that the total fracture energy release rate(they referred to this parameter as the global or over-all fracture energy elease rate, J, and we designate this term as /c, the(critical) total fracture energy release rate; see Fig. 6c) corresponding to the far field loading for discontinuous CFCCs and is given as Jc=jb+ where b is the energy consumed by the development of fracture process zone and tip can be obtained from the stress intensity factor at the crack tip, Ktip using the equation K The overall fracture energy release rate c)could be obtained from [31, 32](using an equation similar to (1): J={-(△Em/Aa)}/B AEfr/Aa is the slope of the linear regression curve fit between the total energy for fracture(Err)and the crack length(a). The Aa here is actually the difference in the crack lengths(such as ay-ay or a3 -ai, where aj, ay and a] correspond to the initial crack lengths of different specimens) but not crack extension. Once the two terms of Jc and Jtip are calculated individually, the third term Jb can be computed from Eq(2) The procedure involved for the evaluation of Jc is illustrated schematically in Fig. 7. Specimens of varied crack length(three crack lengths, al, a2 and a3, in which a1 a2 a3 as in the present case of crack arrester orientation) are pulled in tension in ramp control. These values of (Efr) vary with the chosen value of displacement(6, in this case 81, 82, and d3(and 81<82<83)as shown in Fig. 7). Ideally, the displacement value is chosen in such a way that it encompasses all the events that significantly influence the fracture process and hence, reflected in the determined total fracture energy release rate In the present study, three grossly different displacement values(81, 82, and 83)are chosen for the evaluation of J e. The first chosen value of the displacement(S1) essentially encompasses the elastic region and in this case even the peak load 616 DISPLACEMENT 61 load-displacement curves showing the procedure adopted for the evaluation of total fracture energy release rate

This is the case in the present CFCC materials.As stated earlier, the increasing contributions from mode II or in-plane shear fracture during mode I fracture toughness evaluation using specimens of varied crack length, require the adoption of such an energy concept.Li and coworkers [29] have clearly shown that the total fracture energy release rate (they referred to this parameter as the global or over-all fracture energy release rate, Ja and we designate this term as Jc, the (critical) total fracture energy release rate; see Fig.6c) corresponding to the far field loading for discontinuous CFCCs and is given as Jc ¼ Jb þ Jtip; ð2Þ where Jb is the energy consumed by the development of fracture process zone and Jtip can be obtained from the stress intensity factor at the crack tip, Ktip using the equation: Jtip ¼ K2 tipð1 m2 Þ=E: ð3Þ The overall fracture energy release rate (Jc) could be obtained from [31,32] (using an equation similar to (1)): Jc ¼ fðDEfr=DaÞg=B: ð4Þ DEfr=Da is the slope of the linear regression curve fit between the total energy for fracture (Efr) and the crack length (a).The Da here is actually the difference in the crack lengths (such as a2 a1 or a3 a1; where a1, a2 and a3 correspond to the initial crack lengths of different specimens) but not crack extension.Once the two terms of Jc and Jtip are calculated individually, the third term Jb can be computed from Eq.(2). The procedure involved for the evaluation of Jc is illustrated schematically in Fig.7.Specimens of varied crack length (three crack lengths, a1, a2 and a3, in which a1 < a2 < a3 as in the present case of crack arrester orientation) are pulled in tension in ramp control.These values of (Efr) vary with the chosen value of displacement (d, in this case d1, d2, and d3 (and d1 < d2 < d3) as shown in Fig.7).Ideally, the displacement value is chosen in such a way that it encompasses all the events that significantly influence the fracture process and hence, reflected in the determined total fracture energy release rate.In the present study, three grossly different displacement values (d1, d2, and d3) are chosen for the evaluation of Jc.The first chosen value of the displacement (d1) essentially encompasses the elastic region and in this case even the peak load Fig.7.Representative load–displacement curves showing the procedure adopted for the evaluation of total fracture energy release rate (Jc). 2598 N. Eswara Prasad et al. / Engineering Fracture Mechanics 71 (2004) 2589–2605

《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_fiber19Fracture behaviour of 2D-weaved, silica–silica

《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_fiber19Fracture behaviour of 2D-weaved, silica–silica