《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_Matrix crack evolution in SiC fiber/glass matrix cross-ply laminates

Part A: applied scienc and manufacturing ELSEVIER Composites: Part A 30(1999)593-597 Matrix crack evolution in Sic fiber/glass matrix cross-ply laminates Nobuo Takeda", Manami Kiriyama Center for Collaborative Research(CCR). The University of Tokyo, 4-6-1 Komba, Meguro-ku, Tokyo 153, Japan Matrix crack evolution was studied for SiC fiber-reinforced glass-matrix cross-ply laminates. A novel in situ SEM(scanning electron microscope)observation was conducted to measure the fiber/matrix debonding and sliding in 0 plies using specimens with parallel micro- lines printed on the surfaces. Interfacial debondings were found to grow intermittently as the applied stress increased. The debonding length distribution depends on the number of 90 plies as well as the type of damage modes. An analytical model for the matrix crack evolution was proposed using the energy balance calculation based on Kuo and Chou(Kuo ws, Chou Tw. Multiple cracking of unidirectinal and cross-ply ceramic matrix composites. J Am Ceram Soc 1995: 78(3): 745-755), with the modification of including the effects of damage mode interaction as well as Poisson contraction in the debonded regions. The predicted evolution agrees well with the experimental one C1999 Elsevier Science Ltd. All rights reserved Keywords: Glass matrix composites; Matrix crack evolution; Micro-line 1. Introduction sed to measure the overall sequence of matrix cracking, and a novel in situ SEM/micro-line technique was used to Knowledge of matrix crack evolution is important for the quantify the fiber/matrix debonding and sliding behavior in development of fiber-reinforced ceramic matrix composites 0%plies. Then, a modified analytical model based on Kuo CMC)[1]. In particular, it is necessary to study the and Chou [10] was proposed and the theoretical prediction sequence of such microscopic damages up to the final frac- was compared with the experimental results ture to ensure the damage tolerance capability. Many studies some tensile properties of glass or glass-ceramic matrix composite laminates were experimentally obtained [2, 3]. 2. 1. Material The matrix crack growth criterion was studied for SiC/ glass-ceramic unidirectional laminates using fracture SiC (Nicalon", Nippon Carbon) fiber-reinforced borosi- mechanics[4]. The fiber/matrix interfacial properties were licate glass(Pyrex7740, Corning)matrix composites were also studied extensively [5, 6]. A full statistical treatment of fabricated by Nippon Carbon. Fibers coated with approxi- the matrix crack evolution and associated stress-strain mately 70 nm thick carbon layer were used to fabricate behaviors has been conducted recently [7]. The damage laminates by impregnating fiber cross-plies with glass evolution in cross-ply laminates is, however, more complex powder slurry and hot-pressing them at 1100oC for than in unidirectional ones since the matrix cracks occur 10 min. The stacking configuration was [03/90m./03](m both C°and90° plies8-10 1, 2, 3)and the nominal fiber volume fraction Vr was 0.36 Although cross-ply or woven laminates are most impor- The average thickness of a unidirectional ply was 0.2 mm, tant in practical applications of CMC, the microscopic which resulted in the total thickness ranging from 1. 4 mm damage evolution has not been well characterized yet. (m= I)to 1. 8(m= 3) The purpose of the present study is to characterize damage sequences in SiC fiber-reinforced glass-matrix cross-ply 2.2. Replica and in situ SEM/micro-line techniques laminates both experimentally and theoretically from a micro-mechanical viewpoint. A replica technique was 0.4 mm/min using polished specimens of 5 mm in width Corresponding author. Tel /fax: +81-3-3481-4476 e-mail: takeda a and 25 mm in gage length. Tests were stopped intermittently at several loading stages to take replicas of the damage by 1359-835X/99/S- see front matter @1999 Elsevier Science Ltd. All rights reserved P:S1359-835X(98)00155-9

Matrix crack evolution in SiC fiber/glass matrix cross-ply laminates Nobuo Takeda*, Manami Kiriyama Center for Collaborative Research (CCR), The University of Tokyo, 4-6-1 Komba, Meguro-ku, Tokyo 153, Japan Abstract Matrix crack evolution was studied for SiC fiber-reinforced glass-matrix cross-ply laminates. A novel in situ SEM (scanning electron microscope) observation was conducted to measure the fiber/matrix debonding and sliding in 08 plies using specimens with parallel micro￾lines printed on the surfaces. Interfacial debondings were found to grow intermittently as the applied stress increased. The debonding length distribution depends on the number of 908 plies as well as the type of damage modes. An analytical model for the matrix crack evolution was proposed using the energy balance calculation based on Kuo and Chou (Kuo WS, Chou TW. Multiple cracking of unidirectinal and cross-ply ceramic matrix composites. J Am Ceram Soc 1995;78(3):745–755), with the modification of including the effects of damage mode interaction as well as Poisson contraction in the debonded regions. The predicted evolution agrees well with the experimental one. q 1999 Elsevier Science Ltd. All rights reserved. Keywords: Glass matrix composites; Matrix crack evolution; Micro-line 1. Introduction Knowledge of matrix crack evolution is important for the development of fiber-reinforced ceramic matrix composites (CMC) [1]. In particular, it is necessary to study the sequence of such microscopic damages up to the final frac￾ture to ensure the damage tolerance capability. Many studies have been devoted to modelling the damage process in unidirectional, cross-ply and woven CMC. For example, some tensile properties of glass or glass–ceramic matrix composite laminates were experimentally obtained [2, 3]. The matrix crack growth criterion was studied for SiC/ glass–ceramic unidirectional laminates using fracture mechanics [4]. The fiber/matrix interfacial properties were also studied extensively [5,6]. A full statistical treatment of the matrix crack evolution and associated stress–strain behaviors has been conducted recently [7]. The damage evolution in cross-ply laminates is, however, more complex than in unidirectional ones since the matrix cracks occur in both 08 and 908 plies [8–10]. Although cross-ply or woven laminates are most impor￾tant in practical applications of CMC, the microscopic damage evolution has not been well characterized yet. The purpose of the present study is to characterize damage sequences in SiC fiber-reinforced glass–matrix cross-ply laminates both experimentally and theoretically from a micro-mechanical viewpoint. A replica technique was used to measure the overall sequence of matrix cracking, and a novel in situ SEM/micro-line technique was used to quantify the fiber/matrix debonding and sliding behavior in 08 plies. Then, a modified analytical model based on Kuo and Chou [10] was proposed and the theoretical prediction was compared with the experimental results. 2. Experiments 2.1. Materials SiC (Nicalone, Nippon Carbon) fiber-reinforced borosi￾licate glass (Pyrexe7740, Corning) matrix composites were fabricated by Nippon Carbon. Fibers coated with approxi￾mately 70 nm thick carbon layer were used to fabricate laminates by impregnating fiber cross-plies with glass powder slurry and hot-pressing them at 11008C for 10 min. The stacking configuration was [03/90m/03] (m ˆ 1, 2, 3) and the nominal fiber volume fraction Vf was 0.36. The average thickness of a unidirectional ply was 0.2 mm, which resulted in the total thickness ranging from 1.4 mm (m ˆ 1) to 1.8 (m ˆ 3). 2.2. Replica and in situ SEM/micro-line techniques Tensile tests were conducted at a cross-head speed of 0.4 mm/min using polished specimens of 5 mm in width and 25 mm in gage length. Tests were stopped intermittently at several loading stages to take replicas of the damage by Composites: Part A 30 (1999) 593–597 1359-835X/99/$ - see front matter q 1999 Elsevier Science Ltd. All rights reserved. PII: S1359-835X(98)00155-9 * Corresponding author. Tel./fax: 181-3-3481-4476; e-mail: takeda@ compmat.rcast.u-tokyo.ac.jp

N Takeda, M. Kiriyama/Composites: Part A 30(1999)593-597 Matrix C地 Ply Matrix Crack Matrix Crack ll 90"Ply (a)[0390103],E=0.25% (a)"Sky 200x 100pm 今:计 Matrix Crack (a)[03902/03],E=0.20% Fig. 1. Photographs of replicas showing cracks under tensile load (b) using polyacetate films. Matrix crack evolution in both 0 and 90 plies was quantitatively measured by observing Fig. 2. In situ SEM photographs of fiber/matrix sliding on specimen surfaces with printed micro-lines. replicas through an optical microscope after the tests The in situ SEM/micro-line technique has been estab- lished recently to quantitatively measure the microscopic pattems in CMC cross-ply laminates are matrix cracks forced composites under loading [ll], and is used here for generating in both 0 and 90 plies. Matrix cracks penetrat ing into both 0 and 90 plies are dominant in [0, 901/031 brittle matrix composites. Parallel micro-lines were printed laminates. However, matrix cracks only existing in 0 plies on the parallel-sided specimen surfaces by a photo-lithogra shy technique. Micro-line patterns of l um in width and 3 can also be observed more often from the earlier loading or 5 um in gap were used on specimens in the same sizes as stage as the number of 90 plies increases. The following those used in the replica observation. The printed specimens experimental formula can be obtained by fitting all experi- mental data were loaded at the same cross-head speed inside a SEM with a servo-hydraulic loading stage as well as a temperate control unit. Two-dimensional distribution of fiber/matrix =p2.390m+189 interfacial debonding and sliding in 0 plies, in particular where the matrix crack densities or the numbers of cracks was observed and measured quantitatively as a function of per unit length in the tensile direction in 0 and 90 plies are the stress level. Photographs were taken at various loading denoted by PI and p2, respectively ages and fed into a computer as digital images, and then the relative displacement was digitally measured. The reso- lution in the displacement is 0.02 um in the present study. 3.2. In situ observation of interfacial debonding and sliding Fig. 2 shows in situ SEM photographs of a damage state 3. Experimental results near a 0 matrix crack among matrix cracks penetrating into both 0 and 90 plies. x and Ar are defined as the distance 3. 1. Initiation and growth of matrix cracks from a crack in the direction of the given tensile stress and the relative displacement or sliding of a micro-line Fig. 1 presents photographs of replicas, which show respectively. Ld is defined as the debonding length on a

using polyacetate films. Matrix crack evolution in both 08 and 908 plies was quantitatively measured by observing replicas through an optical microscope after the tests. The in situ SEM/micro-line technique has been estab￾lished recently to quantitatively measure the microscopic deformation and interfacial damage evolution in fiber-rein￾forced composites under loading [11], and is used here for brittle matrix composites. Parallel micro-lines were printed on the parallel-sided specimen surfaces by a photo-lithogra￾phy technique. Micro-line patterns of 1 mm in width and 3 or 5 mm in gap were used on specimens in the same sizes as those used in the replica observation. The printed specimens were loaded at the same cross-head speed inside a SEM with a servo-hydraulic loading stage as well as a temperate control unit. Two-dimensional distribution of fiber/matrix interfacial debonding and sliding in 08 plies, in particular, was observed and measured quantitatively as a function of the stress level. Photographs were taken at various loading stages and fed into a computer as digital images, and then the relative displacement was digitally measured. The reso￾lution in the displacement is 0.02 mm in the present study. 3. Experimental results 3.1. Initiation and growth of matrix cracks Fig. 1 presents photographs of replicas, which show matrix cracks under tensile load. Characteristic damage patterns in CMC cross-ply laminates are matrix cracks generating in both 08 and 908 plies. Matrix cracks penetrat￾ing into both 08 and 908 plies are dominant in [03/901/03] laminates. However, matrix cracks only existing in 08 plies can also be observed more often from the earlier loading stage as the number of 908 plies increases. The following experimental formula can be obtained by fitting all experi￾mental data, r1 ˆ r …1:390m11:889† 2 × 1024 …1† where the matrix crack densities or the numbers of cracks per unit length in the tensile direction in 08 and 908 plies are denoted by r 1 and r 2, respectively. 3.2. In situ observation of interfacial debonding and sliding Fig. 2 shows in situ SEM photographs of a damage state near a 08 matrix crack among matrix cracks penetrating into both 08 and 908 plies. x and Dx are defined as the distance from a crack in the direction of the given tensile stress and the relative displacement or sliding of a micro-line, respectively. Ld is defined as the debonding length on a 594 N. Takeda, M. Kiriyama / Composites: Part A 30 (1999) 593–597 Fig. 1. Photographs of replicas showing cracks under tensile load. Fig. 2. In situ SEM photographs of fiber/matrix sliding on specimen surfaces with printed micro-lines

Takeda, M. Kiriyama/Composites: Part A 30(1999)593-59 595 0.4 0.4 y-a-173.6(MPa) 0.3 -195.2(MPa) 日 o213.1(MPa) V…2473(MPa) 10010 x(um) 0 o…z0=0.1725(mm) Fig. 3. Relative interfacial displacement as a function of distance from 0.1 crack tip at0°90° interface(O90y03]) fiber/matrix interface. The region of fiber/matrix debonding 20-1001020 is found at the interface where Ax=0 ig. 3 shows some representative results of Ar as func- Fig. 4. Distribution of relative interfacial displacement at different tions of x and the stress level at the o%/90% interface in stances =o in the thickness direction from 0/90interface(0y/903/03 903/03] specimens. For the sequence of debonding and slid Ocp=183.9 MPa).(a)Crack penetrating both 0 and 90 plies, (b) Isolated ing at x <o, La was almost the same, even when the applied crack in o plies. stress g increased from 173.6 to 195.2 MPa. while the rela tive displacement or sliding, Ax, increased especially near interaction between different modes [8, 10]. Shear-lag the crack tip. Approximately 3 um increase in Ly was found analysis was used to obtain the stress transfer both at the by the stress level of 213.1 MPa, but no increase was 0/90 interfaces and fiber/matrix interfaces in 0 plies. In observed at 230. 1 MPa, while Ar increased near the crack this study, the stress distribution is modified, considering the tip. A remarkable increase in Ld was found again at Poisson contraction in debonded regions in 0 plies as noted 247.3 MPa. In summary, it can be concluded that the in the Ar measurement. Thus, in debonded regions, the stress increases. The derivative of A xlx increases near the axial stress in a fiber or is given by shear stress To and the dobonding tip with increasing applied stress. This is due to the relaxation in residual thermal stress as well as the dor __ 2To (2) decrease in interfacial friction Fig 4 shows the distribution of Ax at several distances =o where ro is the fiber radius. To is determined assuming the from the 0/90 interface in the thickness direction. Fig 4a is Coulomb friction as for matrix cracks penetrating into both 0 and 90 plies, and Fig 4b for cracks only existing in 0 plies In the case of Fig T0=-(+吓) (3) 4a, both Ly and Ax decrease with increasing =o, except near where u is the coefficient of friction, and o and pare the 07 /90 interface. This is presumably due to fiber misa normal stresses in the radial direction at the interface due ignment and interlaminar shear stress. In the case of Fig. to thermal expansion mismatch and Poisson contraction b, on the other hand, both Ld and x are almost independent effects, respectively. the friction occurs when oc+ap<o on =0. In both cases, Ax is almost zero at the specimen The debonding length Ld in modes 3 and 5 was predicted surface (E0=0.6 mm) suming that the shear stress distribution in the thickness in 0 plies is linear. Displacements of fibers and matrix in debonded regions in 0 plies(uf and um) were related with 4. Theoretical approach the average displacements in 0 and 90 plies which were calculated from the shear-lag analysis, assuming a proper 4. 1. Stress analysis and debonding length prediction geometric similarity rule. The details of the stress analysis and debonding length prediction are found in Ref [121 Kuo [8 classified the cracking states in a cross-ply laminate into five damage modes, as shown in Fig. 5, and 4.2. Energy balance criterion for matrix crack evolution theoretically derived the critical stress for each mode based on the energy balance criterion, without considering the The observed damages were classified into 13 patterns

fiber/matrix interface. The region of fiber/matrix debonding is found at the interface where Dx ± 0. Fig. 3 shows some representative results of Dx as func￾tions of x and the stress level at the 08/908 interface in [03/ 903/03] specimens. For the sequence of debonding and slid￾ing at x , 0, Ld was almost the same, even when the applied stress s increased from 173.6 to 195.2 MPa, while the rela￾tive displacement or sliding, Dx, increased especially near the crack tip. Approximately 3 mm increase in Ld was found by the stress level of 213.1 MPa, but no increase was observed at 230.1 MPa, while Dx increased near the crack tip. A remarkable increase in Ld was found again at 247.3 MPa. In summary, it can be concluded that the debonding grows intermittently, not gradually as the applied stress increases. The derivative of Dx/x increases near the dobonding tip with increasing applied stress. This is due to the relaxation in residual thermal stress as well as the decrease in interfacial friction. Fig. 4 shows the distribution of Dx at several distances z0 from the 08/908 interface in the thickness direction. Fig. 4a is for matrix cracks penetrating into both 08 and 908 plies, and Fig. 4b for cracks only existing in 08 plies. In the case of Fig. 4a, both Ld and Dx decrease with increasing z0, except near the 08/908 interface. This is presumably due to fiber misa￾lignment and interlaminar shear stress. In the case of Fig. 4b, on the other hand, both Ld and x are almost independent on z0. In both cases, Dx is almost zero at the specimen surface (z0 ˆ 0.6 mm). 4. Theoretical approach 4.1. Stress analysis and debonding length prediction Kuo [8] classified the cracking states in a cross-ply laminate into five damage modes, as shown in Fig. 5, and theoretically derived the critical stress for each mode based on the energy balance criterion, without considering the interaction between different modes [8,10]. Shear-lag analysis was used to obtain the stress transfer both at the 08/908 interfaces and fiber/matrix interfaces in 08 plies. In this study, the stress distribution is modified, considering the Poisson contraction in debonded regions in 08 plies as noted in the Dx measurement. Thus, in debonded regions, the relationship between the interfacial shear stress t 0 and the axial stress in a fiber sf is given by dsf dx ˆ 2 2t0 r0 …2† where r0 is the fiber radius. t 0 is determined assuming the Coulomb friction as t0 ˆ 2m…sc 1 sp† …3† where m is the coefficient of friction, and sc and sp are normal stresses in the radial direction at the interface due to thermal expansion mismatch and Poisson contraction effects, respectively. the friction occurs when sc 1 sp , 0. The debonding length Ld in modes 3 and 5 was predicted assuming that the shear stress distribution in the thickness in 08 plies is linear. Displacements of fibers and matrix in debonded regions in 08 plies (uf and um) were related with the average displacements in 08 and 908 plies which were calculated from the shear-lag analysis, assuming a proper geometric similarity rule. The details of the stress analysis and debonding length prediction are found in Ref. [12]. 4.2. Energy balance criterion for matrix crack evolution The observed damages were classified into 13 patterns, N. Takeda, M. Kiriyama / Composites: Part A 30 (1999) 593–597 595 Fig. 3. Relative interfacial displacement as a function of distance from crack tip at 08/908 interface ([03/903/03]). Fig. 4. Distribution of relative interfacial displacement at different distances z0 in the thickness direction from 08/908 interface. ([03/903/03], s CP ˆ 183.9 MPa). (a) Crack penetrating both 08 and 908 plies, (b) Isolated crack in 08 plies

N. Takeda, M. Kiriyama/Composites: Part 4 30(1999)593-597 mode 3 mode 5 mode 5 Fig. 5. Classification of damage states in brittle matrix cross-ply laminates (after Kuo [8)). considering the neighbouring damage modes In Pattern 12 shown in Fig. 6, for example, mode 5 damage occurs between existing mode 3 and mode 5 damages. Each damage pattern can be divided into one or more repeated elements. For one crack in each repeated element, AU is defined as a function of Ld, crack spacing s, and applied Pattern No, 12 tress oCP. Fig. 6. An example of schematic representation of cracking sequence △U(σcp,L,s)=W-Uan where W is work done by an external load and Ual is the sum of energy terms following formula, ∑(△y=∑(△U) where subscripts i and f denote before and after the damage growth, respectively. The summention is made over al Uc+ Udb+Us+ Uf+ Um+U cracks in the repeated unit Ue is crack surtace energy, Uab. intertacial debonding 4.3. Comparison behveen theoretical prediction and and AUm are strain energies in fibers and matrix in 0 plies, respectively. AU2 is strain energy in 90 plies. The energy The above balance criterion can predict matrix crack terms in Eq(6)are written as evolution in cross-ply laminates. Because matrix cracks 26V6 normally initiate at yarns in 90 plies (yarn density Laya I yarn/mm), the initial crack density was assumed to be 10/cm, while surface energies of fiber/matrix debonding and matrix cracking in 0 plies, ym and yab, were to be Us Total 2.5 J/m- and 0.8 J/m, respectively. Table 1 shows the bVe ole I (odx Probabilistic prediction of cracking process Stacking Crack density Cracking Critical Debonding (on)2 configuration after cracking mode stress length of new (MPa) cracks(um) U2 (o2)2dx mode 1 254 mode mode 5 mode 1 where 2b and 2d are total thickness of 0 and 90 plies, mode 65.59 respectively. Er, Em, and E2 are Youngs modulus of fiber mode matrix, and 90 ply, respectively 0390303]10 mode 1 & o From the energy balance within each repeated unit before mode 3 228 77 after a damage growth, such as in Fig. 6, the critical mode 6547 stress for such damage growth can be determined using the mode 5 6547

considering the neighbouring damage modes. In Pattern 12 shown in Fig. 6, for example, mode 5 damage occurs between existing mode 3 and mode 5 damages. Each damage pattern can be divided into one or more repeated elements. For one crack in each repeated element, DU is defined as a function of Ld, crack spacing s, and applied stress s CP. DU…sCP; Ld;s† ˆ W 2 Uall …4† where W is work done by an external load and Uall is the sum of energy terms. W ˆ …b 1 d† sCP Ef Zs 0 sf dx …5† Uall ˆ Uc 1 Udb 1 Us 1 Uf 1 Um 1 U2 …6† Uc is crack surface energy, Udb interfacial debonding energy, and Us energy loss due to interfacial friction. DUf and DUm are strain energies in fibers and matrix in 08 plies, respectively. DU2 is strain energy in 908 plies. The energy terms in Eq. (6) are written as, Udb ˆ 2bVf r0 Ldgdb; Us ˆ 2bVf r0 ZLd 0 t0…Duf 2 Dum† dx; Uf ˆ bVf 2Ef Zs 0 …sf† 2 dx Um ˆ bVm 2Em Zs 0 …sf m† 2 dx; U2 ˆ d 2E2 Zs 0 …sf 2† 2 dx …7† where 2b and 2d are total thickness of 08 and 908 plies, respectively. Ef, Em, and E2 are Young’s modulus of fiber, matrix, and 908 ply, respectively. From the energy balance within each repeated unit before and after a damage growth, such as in Fig. 6, the critical stress for such damage growth can be determined using the following formula, X…DU† i # X…DU† f …8† where subscripts i and f denote before and after the damage growth, respectively. The summention is made over all cracks in the repeated unit. 4.3. Comparison between theoretical prediction and experiments The above balance criterion can predict matrix crack evolution in cross-ply laminates. Because matrix cracks normally initiate at yarns in 908 plies (yarn density, 1 yarn/mm), the initial crack density was assumed to be 10/cm, while surface energies of fiber/matrix debonding and matrix cracking in 08 plies, g m and gdb, were to be 2.5 J/m2 and 0.8 J/m2 , respectively. Table 1 shows the 596 N. Takeda, M. Kiriyama / Composites: Part A 30 (1999) 593–597 Fig. 5. Classification of damage states in brittle matrix cross-ply laminates (after Kuo [8]). Fig. 6. An example of schematic representation of cracking sequence (Pattern #12). Table 1 Probabilistic prediction of cracking process Stacking configuration Crack density after cracking (/cm) Cracking mode Critical stress (MPa) Debonding length of new cracks (mm) [03/901/03] 20 mode 1 254 — 40 mode 5 295 65.60 80 mode 5 295 65.60 [03/902/03] 20 mode 1 239 — 40 mode 5 272 65.59 80 mode 5 272 65.59 [03/903/03] 10 mode 1 227 — 20 mode 3 228 25.77 40 mode 5 255 65.47 80 mode 5 255 65.47

Takeda, M. Kiriyama/Composites: Part A 30(1999)593-59 using specimens with parallel micro-lines printed on the heoretical Prediction urfaces. Interfacial debonding was found to grow intermit △口 tently as the applied stress increased. The debonding length distribution depended on the number of 90 plies as well as the type of damage modes. Based on the above microscopic observation, an analytical model for damage growth was proposed using the energy balance calculation based on Kuo and Chou [101, with the modification of including the effects of the interaction between different damage modes as well as the Poisson contraction in debonded regions. The 0100200300 predicted damage sequence agreed reasonably well with the experimental one, although further improvement is neces Applied Stress(MPa) sary for better prediction Fig. 7. Comparison between predicted and experimental overall crack References predicted evolution of matrix cracks for each laminate configuration. The initial crack was always in mode 1 [1 Marshall DB, Evans AG. Failure mechanisms in ceramic-fiber/o followed by several cracks at the earlier loading mic-matrix composites. J Am Ceram Soc 1985: 68(5): 225-231 [2] Prewo KM. Tension and flexural strength of silicon carbide fibre- stage. The following damage evolution depended on the reinforced glass ceramics. J Mater Sci 1986; 21: 3590-3600 type of laminate configuration, although the final saturated 3] Prewo KM. Carbon fibre reinforced glass matrix composite: tension crack density was similar. As expected in the microscopic and flexural properties. J Mater Sci 1988 23: 2745-2752 observations that revealed the interfacial debonding always 4 Budiansky B, Hutchinson JW occurred when cracks appear in 0 plies, the present analysis reinforced ceramics. J Mech Phys Solids 1986, 34(2): 167-18 5] Marshall DB, Oliver wC. Measurement of interfacial mechanical predicted only modes 1, 3, and 5 could occur in the present properties in fiber-reinforced ceramic composites. J Am Ceram So material system 987;70(8:542-548. Fig. 7 shows the overall crack density as a function of the [6 Hsueh CH. Matrix cracking with frictional bridging fibres in contin- applied stress. The theoretical prediction agrees well with ic composites. Part 2: Cracking due to residual stres- the experimental results, although the former provides steeper ses. J Mater sci199530:4793-4800. [7 Ahn BK, Curtin WA. Strain and hysteresis by stochastic matrix crack increase than the latter in the large crack density region ing in ceramic matrix composites. J Mech Phys Solids 1997; 45: 177- 8]Kuo wS Damage of multi-directionally reinforced ceramic-matrix 5 Conclusions Matrix crack evolution was studied for SiC fiber-rein 9 Karandikar P, Chou Tw. Characterization and forced glass matrix composite [0, 90,031(m=1, 2, 3) acking and elastic moduli changes in Nicalon-CAS composites Compos Sci Technol 1993: 46: 253-264 cross-ply laminates. Characteristic damage patterns were (10) Kuo wS, Chou TW. Multiple cracking of unidirectinal and cross-ply matrix cracks generating in both 0 and 90 plies Matrix ceramic matrix composites. J Am Ceram Soc 1995: 78(3):745-755 cracks penetrating into both 0 and 90 plies were dominant [11] Takeda N, Nizuma H, Ogihama S, Kobayashi A. Application of in[03/901/03]laminates, while matrix cracks only existing in micro-line/grid methods to temperature-dependent microscopic 0 plies were also observed more often from the earlier deformation and damage in CFRP laminates. Exp Mech ading stage as the number of 90 plies increased. A 1997;37(2:182-187 novel in situ sem observation was conducted to measure [12] Takeda N, Kiriyama M. Modeling of microscopic damage sequence in SiC fiber reinforced glass matrix cross-ply laminates, 1998 the fiber/matrix interfacial debonding and sliding in 0 pli (submitted)

predicted evolution of matrix cracks for each laminate configuration. The initial crack was always in mode 1, followed by several mode 1 cracks at the earlier loading stage. The following damage evolution depended on the type of laminate configuration, although the final saturated crack density was similar. As expected in the microscopic observations that revealed the interfacial debonding always occurred when cracks appear in 08 plies, the present analysis predicted only modes 1, 3, and 5 could occur in the present material system. Fig. 7 shows the overall crack density as a function of the applied stress. The theoretical prediction agrees well with the experimental results, although the former provides steeper increase than the latter in the large crack density region. 5. Conclusions Matrix crack evolution was studied for SiC fiber-rein￾forced glass matrix composite [03/90m/03] (m ˆ 1, 2, 3) cross-ply laminates. Characteristic damage patterns were matrix cracks generating in both 08 and 908 plies. Matrix cracks penetrating into both 08 and 908 plies were dominant in [03/901/03] laminates, while matrix cracks only existing in 08 plies were also observed more often from the earlier loading stage as the number of 908 plies increased. A novel in situ SEM observation was conducted to measure the fiber/matrix interfacial debonding and sliding in 08 plies using specimens with parallel micro-lines printed on the surfaces. Interfacial debonding was found to grow intermit￾tently as the applied stress increased. The debonding length distribution depended on the number of 908 plies as well as the type of damage modes. Based on the above microscopic observation, an analytical model for damage growth was proposed using the energy balance calculation based on Kuo and Chou [10], with the modification of including the effects of the interaction between different damage modes as well as the Poisson contraction in debonded regions. The predicted damage sequence agreed reasonably well with the experimental one, although further improvement is neces￾sary for better prediction. References [1] Marshall DB, Evans AG. Failure mechanisms in ceramic–fiber/cera￾mic–matrix composites. J Am Ceram Soc 1985;68(5):225–231. [2] Prewo KM. Tension and flexural strength of silicon carbide fibre￾reinforced glass ceramics. J Mater Sci 1986;21:3590–3600. [3] Prewo KM. Carbon fibre reinforced glass matrix composite: tension and flexural properties. J Mater Sci 1988;23:2745–2752. [4] Budiansky B, Hutchinson JW, Evans AG. Matrix fracture in fiber￾reinforced ceramics. J Mech Phys Solids 1986;34(2):167–189. [5] Marshall DB, Oliver WC. Measurement of interfacial mechanical properties in fiber-reinforced ceramic composites. J Am Ceram Soc 1987;70(8):542–548. [6] Hsueh CH. Matrix cracking with frictional bridging fibres in contin￾uous fibre ceramic composites. Part 2: Cracking due to residual stres￾ses. J Mater Sci 1995;30:4793–4800. [7] Ahn BK, Curtin WA. Strain and hysteresis by stochastic matrix crack￾ing in ceramic matrix composites. J Mech Phys Solids 1997;45:177– 209. [8] Kuo WS. Damage of multi-directionally reinforced ceramic–matrix composites. PhD Dissertation, University of Delaware, Newark, DE, 1992. [9] Karandikar P, Chou TW. Characterization and modeling of micro￾cracking and elastic moduli changes in Nicalon-CAS composites. Compos Sci Technol 1993;46:253–264. [10] Kuo WS, Chou TW. Multiple cracking of unidirectinal and cross-ply ceramic matrix composites. J Am Ceram Soc 1995;78(3):745–755. [11] Takeda N, Niizuma H, Ogihama S, Kobayashi A. Application of micro-line/grid methods to temperature-dependent microscopic deformation and damage in CFRP laminates. Exp Mech 1997;37(2):182–187. [12] Takeda N, Kiriyama M. Modeling of microscopic damage sequence in SiC fiber reinforced glass matrix cross-ply laminates, 1998 (submitted). N. Takeda, M. Kiriyama / Composites: Part A 30 (1999) 593–597 597 Fig. 7. Comparison between predicted and experimental overall crack densities