《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_High-temperature creep of a bi-directional, continuous-SiC-fiber-reinforced glass-ceramic composite

SEI TERIALS ENGE& ENGIEERN ELSEVIER Materials Science and Engineering A300(2001)68-79 www.elsevier.com/locate/msea High-temperature creep of a bi-directional continuous-SiC-fiber-reinforced glass-ceramic composite B.G. Nair a, *, R F. Cooper a, M.E. Plesha b Materials Science Program, Unirersity of Wisconsin-Madison Madison, WI 53706, US.A Department of Nuclear Engineering and Engineering Physics, Unirersity of wisconsin-Madison Madison, WI 53706, US.A Received 9 May 2000: received in revised form 6 September 2000 Abstract The ' off-axis, high-temperature compression creep behavior of bidirectionally(2D, 0/90) reinforced CAS-l/SiC(Nicalon fiber) composites was studied experimentally in the stress-temperature regime of 1275-1325.C and 15-50 MPa. The results indicated that the overall, high-T rheologic response of the 2D composites was intermediate to the properties of ID composites with fiber orientations corresponding to the constituent plies in the 2D material. This behavior strongly suggested that the 2D material behaved as an isostrain laminate during creep. A simple analysis, treating the 2D material as a three-phase laminate, where the constituent plies were assigned the viscoelastic properties of the corresponding ID materials and separated by thin layers of unreinforced matrix, fit the experimental data. In the case of 2D composites with the plies misoriented at 20 and 70%to the applied stress(20/-700composites), however, microstructural study suggested that growth of cracks in directions perpendic ular to the applied stress due to the poisson effect would have made a significant contribution to the bulk strain. Hence, such crack growth acts as a limitation to the universal applicability of the laminate model. c 2001 Elsevier Science B v. All rights Keywords: Ceramic composite: Fiber-reinforced; Bidirectional; Creep; Modeling: Laminate 1. Introduction limited by their creep, fracture and fatigue properties at high temperatures. Multidirectional fiber reinforcement is often sug While fracture properties of 2D ceramic composites gested as a possible solution to the anisotropic mechan- have been studied in some detail [1, 2 ], high-temperature observe creep is not commonly considered as a limiting factor (D) ceramic composites. Conventional wisdom sug for their applicability. This is primarily due to a ten- gests that a simple, multi-ply, symmetrical, bidirection- to overestimate the creep performance of 2D ally reinforced (2D, 0/90)composite would exhibit composites based on experiments conducted in ge superior, near-isotropic, inplane mechanical properties ometries that maximize the creepresistance offered by as compared to ID composites. However, a detailed the reinforcing fibers, e.g. tensile creep experiments with investigation of the mechanical properties of such 2D the direction of the applied stress parallel to one set of composites as a function of misorientation of the ap- reinforcing fibers 3-5] or flexural creep experiments plied load with respect to the fiber reinforcement has where one set of fibers are parallel to the direction of not been undertaken. At the typical operating condi- the maximum principal stress [6-8]. In these loading tions of high temperature and low differential stress. geometries, a large portion of the load is transferred to the possible application of 2D composite components is the fibers and so the steady-state creep response of the composite strain rates result(typically less than 10-8 Corresponding author. present address: Energ y Tecnolgy Divi: s-). Our work on the creep of unidirectionally rein- +1-630-2524193;fax:+1-630-2523604 forced (ID) composites [9-11] suggests, however, that E-mail address: bgnair@pop.et anl. gov(B.G. Nair ). the 'off-axis' geometry might be the real limiti 0921-5093/01/s- see front matter o 2001 Elsevier Science B.V. All rights reserved PI:S0921-509300)01778-0

Materials Science and Engineering A300 (2001) 68–79 High-temperature creep of a bi-directional, continuous-SiC-fiber-reinforced glass-ceramic composite B.G. Nair a,*, R.F. Cooper a , M.E. Plesha b a Materials Science Program, Uni6ersity of Wisconsin-Madison Madison, WI 53706, USA b Department of Nuclear Engineering and Engineering Physics, Uni6ersity of Wisconsin-Madison Madison, WI 53706, USA Received 9 May 2000; received in revised form 6 September 2000 Abstract The ‘off-axis’, high-temperature compression creep behavior of bidirectionally (2D, 0/90°) reinforced CAS–II/SiC (Nicalon® fiber) composites was studied experimentally in the stress–temperature regime of 1275–1325°C and 15–50 MPa. The results indicated that the overall, high-T rheologic response of the 2D composites was intermediate to the properties of 1D composites with fiber orientations corresponding to the constituent plies in the 2D material. This behavior strongly suggested that the 2D material behaved as an isostrain laminate during creep. A simple analysis, treating the 2D material as a three-phase laminate, where the constituent plies were assigned the viscoelastic properties of the corresponding 1D materials and separated by thin layers of unreinforced matrix, fit the experimental data. In the case of 2D composites with the plies misoriented at 20 and 70° to the applied stress (20/–70° composites), however, microstructural study suggested that growth of cracks in directions perpendic￾ular to the applied stress due to the Poisson effect would have made a significant contribution to the bulk strain. Hence, such crack growth acts as a limitation to the universal applicability of the laminate model. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Ceramic composite; Fiber-reinforced; Bidirectional; Creep; Modeling; Laminate www.elsevier.com/locate/msea 1. Introduction Multidirectional fiber reinforcement is often sug￾gested as a possible solution to the anisotropic mechan￾ical properties observed in unidirectionally reinforced (1D) ceramic composites. Conventional wisdom sug￾gests that a simple, multi-ply, symmetrical, bidirection￾ally reinforced (2D, 0/90°) composite would exhibit superior, near-isotropic, inplane mechanical properties as compared to 1D composites. However, a detailed investigation of the mechanical properties of such 2D composites as a function of misorientation of the ap￾plied load with respect to the fiber reinforcement has not been undertaken. At the typical operating condi￾tions of high temperature and low differential stress, the possible application of 2D composite components is limited by their creep, fracture and fatigue properties at high temperatures. While fracture properties of 2D ceramic composites have been studied in some detail [1,2], high-temperature creep is not commonly considered as a limiting factor for their applicability. This is primarily due to a ten￾dency to overestimate the creep performance of 2D composites based on experiments conducted in ge￾ometries that maximize the creepresistance offered by the reinforcing fibers, e.g. tensile creep experiments with the direction of the applied stress parallel to one set of reinforcing fibers [3–5] or flexural creep experiments where one set of fibers are parallel to the direction of the maximum principal stress [6–8]. In these loading geometries, a large portion of the load is transferred to the fibers and so the steady-state creep response of the composite is rate-limited by creep of the fibers low composite strain rates result (typically less than 10−8 s−1 ). Our work on the creep of unidirectionally rein￾forced (1D) composites [9–11] suggests, however, that the ‘off-axis’ geometry might be the real limiting case * Corresponding author. Present address: Energy Technology Divi￾sion, Argonne National Laboratory, Argonne, IL 60439, USA. Tel.: +1-630-2524193; fax: +1-630-2523604. E-mail address: bgnair@pop.et.anl.gov (B.G. Nair). 0921-5093/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S0921-5093(00)01778-0

B G. Nair et al. /Materials Science and Engineering 4300(2001)68-79 for such 2D composites. In ID ceramic matrix com- tial transient due to load transfer from the matrix to the posites with a distinctly thin(<O I um) viscoelastic fibers, leading to steady-state creep that is rate limited nterface separating the fiber and matrix, the loading by flow of the fibers. As o increases, the shear forces at geometry that produces the highest strain-rate is one the fiber-matrix interface increase, these result in a hat optimizes slip at the interface, i.e. that have fibers substantial contribution to the bulk composite strain by oriented at approximately 45 to the applied stress, or. interface sliding (or, depending on the composite sys- Thus, it is of fundamental interest to extend the study tem, interphase filow). The contribution due to this of fiber-orientation effects to the creep deformation of relative displacement at the interface is maximized at 2D composites and so investigate the feasibility of 45. However, geometrical constraints dictate that modeling high-T creep of these materials the matrix would still be rate-limiting as slip at the The specific rheologic response of the individual plies interphase must be accommodated by matrix shear in 2D composites depends on the stress-distribution flow. Further increase in op results in a high plasticity developed in the composite at steady state. Thus, the e.g. von Mises) potential le matrix around the recognition of a suitable paradigm that describes the fibers, leading to matrix flow around the fibers. This is elastic flow of 2D composites is predicated on under- accompanied by cavitation at the fiber-matrix interface standing how the stresses are partitioned between the due to the development of tensile tractions normal to various plies. This line of thought leads to the question the interface of whether a 2D composite could behave as a simple The present work focuses on characterizing the hi twophase laminate with each ply behaving as a thin temperature, low-differential-stress rheology of 2D(O/ section of a ID composite. In the remainder of this 90, cross-ply) laminates in off-axis loading geometries paper, any reference to 2D composites should be con- and comparing/contrasting their response with the case sidered to be meant for composites with 0/90o fiber for ID reinforcement. As a necessary requirement for reinforcement unless otherwise mentioned 2D composite specimens for the creep study under composites with an identical matrix composition. Be- taken here are designed such that the applied stress, a1 cause, the matrix chemical composition, phase distribu is parallel to the planes defined by the fiber directions in tion and morphology(and hence it is viscoelastic both sets of plies. These 2D specimens can be charac rheology) were different from that of the composites terized by a misorientation angle, y, which is the acute used in our previous experimental work [9], these ID angle between the direction of the applied stress and the composite baseline experiments also provided addi- set of plies is thus misoriented at(y-90%) from the oped earli cation to the Id rheological model devel- orientation of any one set of fibers(Fig. la); the other loading direction. Similarly, in ID composites, off-axis geometry can be characterized by a misorientation an- 2. Experimental design and procedure gle, o (Fig. 1b). Characterizing flow in 2D composites requires an analysis of their behavior in the context of low-well-understood creep behavior of ID composites; 2.1. Material specifications possible that fiber orientations in the 2D material The materials used in this study were Sic fiber orrespond behaviorally with ID material, i.e. with =vand90°一ψ. For ID composites with~0°,the Nicalon)-reinforced calcium aluminosilicate com- rheologic response is characterized by a significant ini posites fabricated and supplied by Coming, Inc. Both the bidirectionally reinforced(2D) and unidirectionally reinforced(ID)composite sheets were fabricated by uniaxial hot-pressing of prepreg plies at 1350C and 90°v 15 MPa [12]. Both ID and 2D materials consisted of 16 plies, each with a fiber volume fraction, Vr, of 0.3 the 2D composite had a [o/90s(sy D)lay-up The matrix was an anorthite-based glassceramic(Com- ing Code CAS-Il) with a grain-size of 3 um. The estimated oxide composition of the CAS-II matrix based on X-ray fluorescence spectroscopy (XRAL Labs, Ont., Canada)is shown in Table 1. X-ray diffrac tion of powder specimens indicated that the primary phases were anorthite (Cao: Al,O3: 2SiO2) and mullite (ALO3: 2SiO2 ): a calculation based on peak intensities Fig.1.Specimen geometry for off-axis'compression creep exp: indicated 85% anorthite and 11% mullite by weight ments.(a) 2D composites: The outer ply ()is cut away to reveal its complementary ply (D);(b) ID composites Electron-microprobe analysis(Cameca SX51) showed

B.G. Nair et al. / Materials Science and Engineering A300 (2001) 68–79 69 for such 2D composites. In 1D ceramic matrix com￾posites with a distinctly thin (B0.1 mm) viscoelastic interface separating the fiber and matrix, the loading geometry that produces the highest strain-rate is one that optimizes slip at the interface, i.e. that have fibers oriented at approximately 45° to the applied stress, s1. Thus, it is of fundamental interest to extend the study of fiber-orientation effects to the creep deformation of 2D composites and so investigate the feasibility of modeling high-T creep of these materials. The specific rheologic response of the individual plies in 2D composites depends on the stress-distribution developed in the composite at steady state. Thus, the recognition of a suitable paradigm that describes the inelastic flow of 2D composites is predicated on under￾standing how the stresses are partitioned between the various plies. This line of thought leads to the question of whether a 2D composite could behave as a simple twophase laminate with each ply behaving as a thin section of a 1D composite. In the remainder of this paper, any reference to 2D composites should be con￾sidered to be meant for composites with 0/90° fiber reinforcement unless otherwise mentioned. 2D composite specimens for the creep study under￾taken here are designed such that the applied stress, s1 is parallel to the planes defined by the fiber directions in both sets of plies. These 2D specimens can be charac￾terized by a misorientation angle, c, which is the acute angle between the direction of the applied stress and the orientation of any one set of fibers (Fig. 1a); the other set of plies is thus misoriented at (c−90°) from the loading direction. Similarly, in 1D composites, off-axis geometry can be characterized by a misorientation an￾gle, 8 (Fig. 1b). Characterizing flow in 2D composites requires an analysis of their behavior in the context of now-well-understood creep behavior of 1D composites; it is possible that fiber orientations in the 2D material correspond behaviorally with 1D material, i.e. with 8=c and 90°−c. For 1D composites with 80°, the rheologic response is characterized by a significant ini￾tial transient due to load transfer from the matrix to the fibers, leading to steady-state creep that is rate limited by flow of the fibers. As 8 increases, the shear forces at the fiber-matrix interface increase, these result in a substantial contribution to the bulk composite strain by interface sliding (or, depending on the composite sys￾tem, interphase flow). The contribution due to this relative displacement at the interface is maximized at 845°. However, geometrical constraints dictate that the matrix would still be rate-limiting as slip at the interphase must be accommodated by matrix shear flow. Further increase in 8 results in a high plasticity (e.g. von Mises) potential in the matrix around the fibers, leading to matrix flow around the fibers. This is accompanied by cavitation at the fiber-matrix interface due to the development of tensile tractions normal to the interface. The present work focuses on characterizing the high￾temperature, low-differential-stress rheology of 2D (0/ 90°, cross-ply) laminates in off-axis loading geometries and comparing/contrasting their response with the case for 1D reinforcement. As a necessary requirement for such a comparison, experiments were done on 1D composites with an identical matrix composition. Be￾cause, the matrix chemical composition, phase distribu￾tion and morphology (and hence it is viscoelastic rheology) were different from that of the composites used in our previous experimental work [9], these 1D composite baseline experiments also provided addi￾tional verification to the 1D rheological model devel￾oped earlier. 2. Experimental design and procedure 2.1. Material specifications The materials used in this study were SiC fiber (Nicalon)-reinforced, calcium aluminosilicate com￾posites fabricated and supplied by Coming, Inc. Both the bidirectionally reinforced (2D) and unidirectionally reinforced (1D) composite sheets were fabricated by uniaxial hot-pressing of prepreg plies at 1350°C and 15 MPa [12]. Both 1D and 2D materials consisted of 16 plies, each with a fiber volume fraction, Vf , of 0.3; the 2D composite had a [0/90°]4S (symmetrical) lay-up. The matrix was an anorthite-based glassceramic (Com￾ing Code CAS-II) with a grain-size of 3 mm. The estimated oxide composition of the CAS-II matrix based on X-ray fluorescence spectroscopy (XRAL Labs, Ont., Canada) is shown in Table 1. X-ray diffrac￾tion of powder specimens indicated that the primary phases were anorthite (CaO:Al2O3:2SiO2) and mullite (3Al2O3:2SiO2); a calculation based on peak intensities indicated 85% anorthite and 11% mullite by weight. Electron-microprobe analysis (Cameca SX51) showed Fig. 1. Specimen geometry for ‘off-axis’ compression creep experi￾ments. (a) 2D composites: The outer ply (I) is cut away to reveal its complementary ply (II); (b) 1D composites.

B G. Nair et al. Materials Science and Engineering 4300 (2001)68-79 Table I Composition of CAS-lI Estimated by X-Ray Fluorescence (i.e. constant-stress)tests were performed, based on the assumption of constant-volume deformation, pre- Oxide Mol%b cision adjustments were made to the total load ap- plied to the specimen; these adjustments accompanied each inelastic strain increment of 0.001. The tempera- 16.9 ture was controlled and monitored during a test using a type-C(alloy w/w-26% Re) thermocouple located 2 mm from the center of the specimen. The accu- As,O, racy of the temperature measurement is 1C, the drift in temperature during any experiment was also X-ray fluorescence spectroscopy(XRAL Labs, Hamilton, Ont less than±1°C Two DCDTs connected in series were used to mon- itor the displacement of the top-piston during traces of free silica(Sio2) and very small particles test;analog-to-digital conversion and data storage <0.2 um) of zircon (ZrSiO4)finely distributed were done with a personal computer. The data collec throughout the matrix tion rate was between one and six readings per The mean diameter of the Nicalon Sic fibers is minute depending on the strain rate displayed by in- 15 um. The fibers in the composite are fully crys- dividual specimens. Given the length of the speci allized with a very fine grain-size of 1.5 nm mens, the apparatus could easily resolve strain rates [13, 14]. The fiber-matrix interface in these composites as low as 10-8s-l little drift in the room tempera- consists of two planar (i.e. cylindrical sheath) inter- ture aided the resolution. A typical displacement-time phases, one of graphite against the fiber and the plot obtained from a creep experiment on a 2D com other of amorphous calcium aluminosilicate contact- posite specimen(40/-500, 1275oC)is shown in Fig ng the matrix. These interphases, each <100 nn 2a. At each level of stress, the specimen is allowed to thick, are formed by a fiber oxidation/displacement reach a nominal steady shown in the strain- action at the interface during composite pro- rate versus strain plot of the same experiment shown cessing [13]. The densities of both the 2D and Id in Fig. 2b. Fig. 2c and d show similar plots for a ID composites were estimated directly by precise mass composite specimen(=400, T=1300oC and dimensional measurements of polished, rectangu lar specimens. The 2D composites had a density of 2.3. Data analysis 2.57g cm; the ID materials density was 2.64 g cm-3 For individual segments of an experiment, the in- elastic creep data were fit by a regression analysis to 2. 2. Experimental methodology the Burgers solid model so as to discern the steady state strain-rate at each level of applied stress, the All experimental specimens had nominal dimensions functional form employed was 3×3×6 mm and were cut from composite sheets using a diamond saw with one pair of 3 x 6 mm a[t-t]= K exp[ -A(t-t)]+Ess(t-t) (1) faces being parallel to the component plies. The di where e[t-t] is the inelastic strain, with t denoting mensions of each test specimen were precisely mea- the starting time at each particular level of an, and Ess sured with a micrometer after polishing each of the is the steady-state strain-rate. The first (negative-expo- faces to 600 grit. 2D composite specimens with a sur- nential) term describes the transient strain at each face-ply misorientation angle y(Fig. la)are referred level of applied stress. The constant K is a geometric to as y /(y-90%) specimens. The 2D specimens, for factor that defines the load-transfer characteristics of our purposes, can be considered to have 90 symme- the composite for a given fiber orientation(); it is a try:a y/(y-90%) specimen is expected to have iden- function of the modulii of elasticity of the fiber(E) tical mechanical properties as(90%-y)/-y specimen and matrix(Em), the respective Poisson ratios (ur and neglecting end effects. For this study, 0/-90%, 20/-70 Um) and the volume fraction of the fibers (va and 40/-50 2D specimens were prepared. ID com- Error bars for the creep data were estimated base posite specimens were made with =0, 20, 40, 50, 70 on the uncertainty in temperature ( 1C). The ind 90 orientations(Fig. Ib) activation energy for creep in these composites is rela High-temperature deformation experiments were tively high; as such, the possible error in cal performed on a dead-weight compression apparatus culation of steady-state strain-rate due to temperature controlled atmosphere of flowing Ar(gauge pres- uncertainty was greater by far than any systemat tIc sure flow rate 30 cm min-). The error related to measurement of the creep displace apparatus is described in detail elsewhere [15]. Creep ment

70 B.G. Nair et al. / Materials Science and Engineering A300 (2001) 68–79 Table 1 Composition of CAS-II Estimated by X-Ray Fluorescence Oxide Mol.% Wt.%a b SiO2 39.8 47.7 21.716.9CaO 28.5Al2O3 40.3 2 1.32.3ZrO 0.4MgO 0.7 0.10.3As2O3 a X-ray fluorescence spectroscopy (XRAL Labs, Hamilton, Ont.). b Calculated from weight-percent data. (i.e. constant-stress) tests were performed, based on the assumption of constant-volume deformation, pre￾cision adjustments were made to the total load ap￾plied to the specimen; these adjustments accompanied each inelastic strain increment of 0.001. The tempera￾ture was controlled and monitored during a test using a type-C (alloy W/W-26% Re) thermocouple located 2 mm from the center of the specimen. The accu￾racy of the temperature measurement is 91°C; the drift in temperature during any experiment was also less than 91°C. Two DCDTs connected in series were used to mon￾itor the displacement of the top-piston during a creep test; analog-to-digital conversion and data storage were done with a personal computer. The data collec￾tion rate was between one and six readings per minute depending on the strain rate displayed by in￾dividual specimens. Given the length of the speci￾mens, the apparatus could easily resolve strain rates as low as 10−8 s−1 ; little drift in the room tempera￾ture aided the resolution. A typical displacement-time plot obtained from a creep experiment on a 2D com￾posite specimen (40/–50°; 1275°C) is shown in Fig. 2a. At each level of stress, the specimen is allowed to reach a nominal steady-state as shown in the strain￾rate versus strain plot of the same experiment shown in Fig. 2b. Fig. 2c and d show similar plots for a 1D composite specimen (8=40°, T=1300°C). 2.3. Data analysis For individual segments of an experiment, the in￾elastic creep data were fit by a regression analysis to the Burgers solid model so as to discern the steady￾state strain-rate at each level of applied stress, the functional form employed was o[t−t]=K exp[−A(t−t)]+o; ss(t−t) (1) where o[t−t] is the inelastic strain, with t denoting the starting time at each particular level of s1, and o; ss is the steady-state strain-rate. The first (negative-expo￾nential) term describes the transient strain at each level of applied stress. The constant K is a geometric factor that defines the load-transfer characteristics of the composite for a given fiber orientation(s); it is a function of the modulii of elasticity of the fiber (Ef ) and matrix (Em), the respective Poisson ratios (6f and 6m) and the volume fraction of the fibers (Vf ). Error bars for the creep data were estimated based on the uncertainty in temperature (91°C). The activation energy for creep in these composites is rela￾tively high; as such, the possible error in cal￾culation of steady-state strain-rate due to temperature uncertainty was greater by far than any systematic error related to measurement of the creep displace￾ment. traces of free silica (SiO2) and very small particles (B0.2 mm) of zircon (ZrSiO4) finely distributed throughout the matrix. The mean diameter of the Nicalon SiC fibers is 15 mm. The fibers in the composite are fully crys￾tallized with a very fine grain-size of 1.5 nm [13,14]. The fiber-matrix interface in these composites consists of two planar (i.e. cylindrical sheath) inter￾phases, one of graphite against the fiber and the other of amorphous calcium aluminosilicate contact￾ing the matrix. These interphases, each 100 nm thick, are formed by a fiber oxidation/displacement reaction at the interface during composite pro￾cessing [13]. The densities of both the 2D and 1D composites were estimated directly by precise mass and dimensional measurements of polished, rectangu￾lar specimens. The 2D composites had a density of 2.57 g cm−3 ; the 1D material’s density was 2.64 g cm−3 . 2.2. Experimental methodology All experimental specimens had nominal dimensions 3×3×6 mm and were cut from composite sheets using a diamond saw with one pair of 3×6 mm faces being parallel to the component plies. The di￾mensions of each test specimen were precisely mea￾sured with a micrometer after polishing each of the faces to 600 grit. 2D composite specimens with a sur￾face-ply misorientation angle c (Fig. 1a) are referred to as c/(c−90°) specimens. The 2D specimens, for our purposes, can be considered to have 90° symme￾try; a c/(c−90°) specimen is expected to have iden￾tical mechanical properties as (90°−c)/–c specimen neglecting end effects. For this study, 0/–90°, 20/–70° and 40/–50° 2D specimens were prepared. 1D com￾posite specimens were made with 8=0, 20, 40, 50, 70 and 90° orientations (Fig. 1b). High-temperature deformation experiments were performed on a dead-weight compression apparatus in a controlled atmosphere of flowing Ar (gauge pres￾sure +100 Pa; flow rate 30 cm3 min−1 ). The apparatus is described in detail elsewhere [15]. Creep

B G. Nair et al. Materials Science and Engineering 4300(2001)68- 2D:40/50 1275°c T:366 (a) 3 0 TIme TIme(h) 25F2D:409/50° 1Dφ=40° T=1275°c .50 T=1300c 5.7B 6.0 +;3Mm MPa 25 MPa 6.5 0 1.6 2.0 Strain (% Fig. 2. Typical creep responses of 2D and ID composite specimens. (a)and(b), strain vs time and strain-rate vs strain, respectively, for 40/-50o 2 D composite at I275°C.(c)and(d), same representation forφ=40° ID composite at1300°C 2.4.Optical microscopy 3. Experimental results Optical microscopy specimens were prepared from 3.1. 2D Composite creep experime h the deformed and undeformed 2D composite creep specimens. In an effort to study the creep-induced The composite creep data was evaluated relative to cavitation at the fiber-matrix interface as well as other the standard, semi-empirical equation for steady-state similar damage, all specimens were sectioned such that cre ep[161 one set of fibers was perpendicular to the plane of observation(the(y-90) ply)and the other parallel Es=Coiexpl-se (the y ply) To avoid possible variations in observed microstructure due to variations in specimen prepara- where a is the applied stress, Oapp is the apparent tion, the 2D specimens were ground and polished activation energy for composite creep and T is the lultaneously, on the same polishing block Polishing absolute temperature. The data for creep of CAS-Il was done to l-um diamond paste. For ID specimens Cr 2D composites are presented in Figs. 3 and 4.At ll sectioning was done such that the fibers were per- constant temperature, Ess increased with the 40/-50o pendicular to the plane of observation. The microstruc- composites showed the highest strain-rates. For exam- tures were recorded using a digital camera(Pixera PVc ple, at 1300%C, the steady-state strainrate for the 40/- 100C); image enhancement and analysis was performed 50 composite under a stress of 40 MPa wa using OPTIMAS software(FSI Automation, Bothell, approximately two orders of magnitude higher than WA that for the 0/-90 composite(Fig. 3b). Both the

B.G. Nair et al. / Materials Science and Engineering A300 (2001) 68–79 71 Fig. 2. Typical creep responses of 2D and 1D composite specimens. (a) and (b), strain vs time and strain-rate vs strain, respectively, for 40/–50° 2D composite at 1275°C. (c) and (d), same representation for 8=40° 1D composite at 1300°C. 2.4. Optical microscopy Optical microscopy specimens were prepared from both the deformed and undeformed 2D composite creep specimens. In an effort to study the creep-induced cavitation at the fiber-matrix interface as well as other similar damage, all specimens were sectioned such that one set of fibers was perpendicular to the plane of observation (the (c−90°) ply) and the other parallel (the c ply). To avoid possible variations in observed microstructure due to variations in specimen prepara￾tion, the 2D specimens were ground and polished simultaneously, on the same polishing block. Polishing was done to 1-mm diamond paste. For 1D specimens, all sectioning was done such that the fibers were per￾pendicular to the plane of observation. The microstruc￾tures were recorded using a digital camera (Pixera PVC 100C); image enhancement and analysis was performed using OPTIMAS software (FSI Automation, Bothell, WA). 3. Experimental results 3.1. 2D Composite creep experiments The composite creep data was evaluated relative to the standard, semi-empirical equation for steady-state creep [16]: o; ss=Cs1 n exp−Qapp RT  (2) where s1 is the applied stress, Qapp is the apparent activation energy for composite creep and T is the absolute temperature. The data for creep of CAS-II/ SiCf 2D composites are presented in Figs. 3 and 4. At constant temperature, o; ss increased with c: the 40/–50° composites showed the highest strain-rates. For exam￾ple, at 1300°C, the steady-state strainrate for the 40/– 50° composite under a stress of 40 MPa was approximately two orders of magnitude higher than that for the 0/–90° composite (Fig. 3b). Both the

B G. Nair et al. Materials Science and Engineering 4300 (2001)68-79 40/-500 and the 20/-700 composites showed non-New- tonian creep behavior with n increasing from about 2 at 2D 1275° c to about3atl300°C.Theo/-90°spec showed Newtonian behavior in the temperature range 200-+0/m0 1300-1325C. Fig. 4 illustrates the variation of @a with -a, for specimens with different values of y. The 1500 0/-90o composites had an activation energy of about 480 k mol-I. The increase in n with t for othe 。1000 loading configurations (y+O) results in @app having a 500 very strong dependence on the applied stress; @ a 2D 4. Variation of Oapp with for 2D T〓1275c different values of y 8.0 increased from 650 to 1400 kJ mol- for 40/ and from x 1500 to 2400 kj mol 20/-70° composites. 3. 2. Creep experiments on ID composites and on the 20°/70";n=21 unreinforced CAS- matrix 1.5 A comparison of the creep data of y(y-90%)2D Log F-o.(MPa) composite specimens to the data for ID composites with y and p=(90%-p) is presented in Fig. 5 4.5F2D For all values of y, the values of n for 2D composites are intermediate to those for the ID composites, where pp corresponds to either y or(90-y) As such a result suggests an application of laminate theory to the under tanding of 2D behavior, it is nessasary to provide here comprehensive results for the ID material -65 Creep data for ID composite specimens with differ ent values of at 1300 and 1275C are shown in Fig 6a and b respectively. For =0, the observed theol- v0"/90°;n=13 ogy was Newtonian (n A 1). For specimens with values 1112131.41.51.61.718 of op ranging from 40 to 90, n was consistently between Log I-o, (MPa)l 1.9 and 2.7 in the temperature range 1275-1300oC. Fig 7 shows the variation of @app with applied stress for vanous specimen ge metre es. For off-axis'geometries with (p=20-90, @app was significantly higher(> 1000 kJ mol-)than for =0(@app 400-440 kJ mol-) 1300°c The behavior of specimens with 20, both in 。1275°c terms of stress and temperature sensitivity is in striking 6.0 contrast to the general trend. The p= 20 specimens displayed the highest values of n for ID composites Further. n decreased from 5.3 at 1300oc to 3.6 at 1325C(Fig. 8). @app decreased from 2200 kJ mol-I at -a1=20 MPa to 900 kJ mol- at -a1=40 MPa(Fig. 7) Fig.9 illustrates the dependence of iss on at 1275 DEgrees and 1300oC. The =50 specimens consistently dis- Fig3.Stress/strain-rate relationships for 2D composites as a function played the highest strain-rates at all temperatures and of v(a)1275oC:(b)1300C(c) Strain-rate as a function of y for a stresses- at 1300C and 40 MPa, the steady-state constant stress of 40 MPa(the 0/90 data point is extrapolated based strain-rate for p= 50 was two orders of magnitude Eq.(1) higher than the strain-rate of the on-axis, =0 speci

72 B.G. Nair et al. / Materials Science and Engineering A300 (2001) 68–79 40/–50° and the 20/–70° composites showed non-New￾tonian creep behavior with n increasing from about 2 at 1275°C to about 3 at 1300°C. The 0/–90° specimens showed Newtonian behavior in the temperature range 1300–1325°C. Fig. 4 illustrates the variation of Qapp with −s1 for specimens with different values of c. The 0/–90° composites had an activation energy of about 480 kJ mol−1 . The increase in n with T for other loading configurations (c"0) results in Qapp having a very strong dependence on the applied stress; Qapp Fig. 4. Variation of Qapp with −s1 for 2D composite specimens for different values of c. Fig. 3. Stress/strain-rate relationships for 2D composites as a function of c. (a) 1275°C; (b) 1300°C. (c) Strain-rate as a function of c for a constant stress of 40 MPa (the 0/90° data point is extrapolated based on Eq. (1)). increased from 650 to 1400 kJ mol−1 for 40/–50° compsites and from 1500 to 2400 kJ mol−1 for 20/–70° composites. 3.2. Creep experiments on 1D composites and on the unreinforced CAS-II matrix A comparison of the creep data of c(c−90°) 2D composite specimens to the data for 1D composites with 8=c and 8=(90°−c) is presented in Fig. 5. For all values of c, the values of n for 2D composites are intermediate to those for the 1D composites, where 8 corresponds to either c or (90°−c). As such a result suggests an application of laminate theory to the under￾standing of 2D behavior, it is nessasary to provide here comprehensive results for the 1D material. Creep data for 1D composite specimens with differ￾ent values of 8 at 1300 and 1275°C are shown in Fig. 6a and b respectively. For 8=0°, the observed theol￾ogy was Newtonian (n1). For specimens with values of 8 ranging from 40 to 90°, n was consistently between 1.9 and 2.7 in the temperature range 1275–1300°C. Fig. 7 shows the variation of Qapp with applied stress for various specimen geometries. For ‘off-axis’ geometries with 8=20–90°, Qapp was significantly higher (\1000 kJ mol−1 ) than for 8=0° (Qapp400–440 kJ mol−1 ). The behavior of specimens with 8=20°, both in terms of stress and temperature sensitivity is in striking contrast to the general trend. The 8=20° specimens displayed the highest values of n for 1D composites. Further, n decreased from 5.3 at 1300°C to 3.6 at 1325°C (Fig. 8). Qapp decreased from 2200 kJ mol−1 at −s1=20 MPa to 900 kJ mol−1 at −s1=40 MPa (Fig. 7). Fig. 9 illustrates the dependence of o; ss on 8 at 1275 and 1300°C. The 8=50° specimens consistently dis￾played the highest strain-rates at all temperatures and stresses — at 1300°C and 40 MPa, the steady-state strain-rate for 8=50° was two orders of magnitude higher than the strain-rate of the on-axis, 8=0° speci-

B G. Nair et al. Materials Science and Engineering 4300(2001)68- men and more than three times that for = 90. Fur- At 1300%C. 30% of the inelastic strain was recovered thermore, a misorientation of just 200 from the loading for a =0 specimen on dropping the level of stress direction causes an increase in Ess by a factor of 30 over down to x3 MPa at the conclusion of a stress-stepped the on-axis case test. For off-axis geometries, =20 composites showed the highest strain-recovery(- 14% of inelastic 5.5}T=1300°c strain)after such a stress drop. For all other orienta tions. the recovered strain was minimal and could not be estimated accurately due to noise in displacement Fig. 10 shows data for the creep of the unreinforced CAS-II matrix material. The data indicates a clear transition from Newtonian (n= 1)rheology at low stress(-0,15 MPa) to a non-Newtonian (n>2) rheology at higher stresses. Q for matrix creep increased from x 900 kJ mol-l at 15 mPa to about 1080 kJ ol- at 35 MPa 3.3. Optical microscopy Log F-o, MPa) Optical micrographs for undeformed and deformed 2D composite specimens are presented in Fig. Ila-d 55}T=1300°c Fig. lla shows the microstructure of the undeformed (b) 2D material. Some intrinsic damage (i.e. as created in the composite fabrication process) in the form of a 1D:φ=20° network of randomly oriented matrix microcracks most of which are under 100 um in length, is present Such a network of cracks was also seen in the deformed 2D composite specimens; tthe 0/-90(Fig 1lb)and the 40/-50(Fig llc)composites had microstructures very similar to that of the undeformed composite. However, visual study of these micrographs suggested that the length of cracks(in the 90 and 50 plies)in the direction deformed composites as compared to the undeformed 13 1.6 composite- a few cracks of length as high as 400 um Log F-o (MPa)l in the direction of the applied stress. There was no significant increase in the number of cracks, however, (c) suggesting that the existing pre-cracks from the unde 50T=1300°c formed composite must have elongated in the direction of the compressive stress during creep. There was very little creep-induced cavitation at the fiber-matrix inter- face in the 50 or 90 plies as compared to ID com- posites with =40-90. The 20/-70% com however, showed a very different microstructure(Fig I ld)as compared to the other orientations. The mi- crostructure was characterized by very long crack (600-800 um long in some cases)that originate in the 70 plies and eventually get deflected toward the 20o l 1.6 4. Discussion Fig. 5. Comparison of creep data at 1300C of 2D composite creep data to ID data for specimens with o=y and(90-y):(a)0/-90 The ometry in (b)20/-70°,(c)40/-50° experiments enforces an isostrain condition on the

B.G. Nair et al. / Materials Science and Engineering A300 (2001) 68–79 73 men and more than three times that for 8=90°. Fur￾thermore, a misorientation of just 20° from the loading direction causes an increase in o; ss by a factor of 30 over the on-axis case. At 1300°C, 30% of the inelastic strain was recovered for a 8=0° specimen on dropping the level of stress down to 3 MPa at the conclusion of a stress-stepped test. For off-axis geometries, 8=20° composites showed the highest strain-recovery (14% of inelastic strain) after such a stress drop. For all other orienta￾tions, the recovered strain was minimal and could not be estimated accurately due to noise in displacement data. Fig. 10 shows data for the creep of the unreinforced CAS-II matrix material. The data indicates a clear transition from Newtonian (n=1) rheology at low stress (−s115 MPa) to a non-Newtonian (n\2) rheology at higher stresses. Q for matrix creep increased from 900 kJ mol−1 at 15 MPa to about 1080 kJ mol−1 at 35 MPa. 3.3. Optical microscopy Optical micrographs for undeformed and deformed 2D composite specimens are presented in Fig. 11a–d. Fig. 11a shows the microstructure of the undeformed 2D material. Some intrinsic damage (i.e. as created in the composite fabrication process) in the form of a network of randomly oriented matrix microcracks, most of which are under 100 mm in length, is present. Such a network of cracks was also seen in the deformed 2D composite specimens; tthe 0/–90° (Fig. 11b) and the 40/–50° (Fig. 11c) composites had microstructures very similar to that of the undeformed composite. However, visual study of these micrographs suggested that the length of cracks (in the 90 and 50° plies) in the direction of the applied stress was somewhat higher in these deformed composites as compared to the undeformed composite — a few cracks of length as high as 400 mm in the direction of the applied stress. There was no significant increase in the number of cracks, however, suggesting that the existing pre-cracks from the unde￾formed composite must have elongated in the direction of the compressive stress during creep. There was very little creep-induced cavitation at the fiber-matrix inter￾face in the 50 or 90° plies as compared to 1D com￾posites with 8=40–90°. The 20/–70° composites however, showed a very different microstructure (Fig. 11d) as compared to the other orientations. The mi￾crostructure was characterized by very long cracks (600–800 mm long in some cases) that originate in the 70° plies and eventually get deflected toward the 20° plies. 4. Discussion The specimen geometry in the 2D composite creep experiments enforces an isostrain condition on the plies. Fig. 5. Comparison of creep data at 1300°C of 2D composite creep data to 1D data for specimens with 8=c and (90−c); (a) 0/–90°; (b) 20/–70°, (c) 40/–50°.

G. Nair et al. / Materials Science and Engineering 4300(2001)68- -5.0 (a) D 55T=1300°c 7.0 中=50°;n25 -7H■φ=70°;n=26 1.01.112 31.4151.61.7 Loga1MPa〕 -.0 ID -5.5 T=1275c -6.0 6.5 90;n=20 75 8.0 L.01.1 1.51.61.7 Fig. 6. Stress/strain-rate relationships for ID composites as a function of o, (a)1300C;(b)1275.C. ID 1200 =20° Fig. 7. Variation of Capp with -a, for different values of p in ID composites

74 B.G. Nair et al. / Materials Science and Engineering A300 (2001) 68–79 Fig. 6. Stress/strain-rate relationships for 1D composites as a function of 8, (a) 1300°C; (b) 1275°C. Fig. 7. Variation of Qapp with −s1 for different values of 8 in 1D composites

B G. Nair et al. Materials Science and Engineering 4300 (2001)68-79 The fact that the creep results presented in Fig. 5 indicate the 2D material, a necessary first step is to understand intermediate behavior of the 2D material compared to the significance of the results for the ID composite orresponding ID specimen suggests that the 2D com- posite behaves as a laminate, i. e. the applied stress 4.1. ID Composite rheology distributed among the constituent plies, based on the effective viscosities of each. To investigate the possibility The inelastic response of the present CAS-II/SiCr ID of laminate theory to composites displayed behavioral trends that were pre- dictable based on our earlier experimental work on a similar anorthite-matrix/SiCr composite [10]. The previ- 5F1D:=20° ous study, which emphasized only off-axis loading with cp>30%, demonstrated(a) the maximum strain rate n=3.7 occurring for 50 and(b) substantial stress and orientation effects on the apparent activation energy, results qualitatively identical to those presented here for similar values of cp in Figs. 6, 7 and 9. The previous data n=53 were analyzed by the articulation of three modes of T=1325°c inelastic response [15] that were defined /identified by the -8.5 T=1300°c strain/strain-rate effects of specific components of the stress tensor -(1)the load-transfer(LT)mode for the 16 normal-stress component parallel to the fibers, (2)the Log F-a. (MPa) transverse-shear(TS)mode for the normal-stress compo- nent perpendicular to the fibers and ( 3)the longitudinal- Fig. 8. Stressstrain-rate relationships for 9=20 ID specimens at shear(LS)mode for the shear-stress component parallel to the fibers (and its complementary component, required for equilibrium). In the LT mode of deformation, stress ID is continuously transferred from the matrix to the fiber -o1 =40 MPa as deformation proceeds In the ts mode, deformation primarily occurs by shear flow of the matrix around the -6.0 fibers resulting in very little improvement in creep properties over the unreinforced matrix. The terminology used for these modes of deformation is based on our previous work [15]. Both the LT and the TS modes of deformation have been studied in detail previously in ID T=1275°c ceramic composites [6, 17]. Application of the mode analysis to the off-axis-loading ID composite flow is 8.0 analogous to the use of the Levy-Mises flow rules in continuum plasticity. From this analysis, and from p Degree knowing the structure and resultant flow behavior of the Fig. 9. Strain-rate as a function of o for ID specimens deformed at fiber-matrix interface(flow on the thin, amorphous -O,=40 MPa silicate interlayer), one realizes that considerable, tem perature-sensitive sliding can occur on the interface Matrix Unreinforced) Thus, a substantial magnitude for the LS component of the applied stress (e.g. x45%) promotes significant 1300°c displacement across the interface (modeling suggests 1310°c some 40%/ of the accumulated strain results from interfa- 1310° cial displacement when x 40-500), which turn. affects greatly the state of stress in the matrix [18]. The result overall is both the optimization of steady-state D5.0 strain rate at =50%(it is the TS component that moves 3.0 the maximum away from =45%)as well as(because of the temperature sensitivity of the interface response) the dramatic, high apparent activation energy for composite Log F-C,(MPa) New in these ID composite experiments (i studied experimentally previously) is the data for com- 10. Steady-state creep response of unreinforced CAS.lI matri pression creep with p=0 and 20. The steady-state flow

B.G. Nair et al. / Materials Science and Engineering A300 (2001) 68–79 75 The fact that the creep results presented in Fig. 5 indicate intermediate behavior of the 2D material compared to corresponding 1D specimen suggests that the 2D com￾posite behaves as a laminate, i.e. the applied stress is distributed among the constituent plies, based on the effective viscosities of each. To investigate the possibility of a straight forward application of laminate theory to the 2D material, a necessary first step is to understand the significance of the results for the 1D composite. 4.1. 1D Composite rheology The inelastic response of the present CAS-II/SiCf 1D composites displayed behavioral trends that were pre￾dictable based on our earlier experimental work on a similar anorthite-matrix/SiCf composite [10]. The previ￾ous study, which emphasized only off-axis loading with 8]30°, demonstrated (a) the maximum strain rate occurring for 8=50° and (b) substantial stress and orientation effects on the apparent activation energy, results qualitatively identical to those presented here for similar values of 8 in Figs. 6, 7 and 9. The previous data were analyzed by the articulation of three modes of inelastic response [15] that were defined/identified by the strain/strain-rate effects of specific components of the stress tensor — (1) the load-transfer (LT) mode for the normal-stress component parallel to the fibers, (2) the transverse-shear (TS) mode for the normal-stress compo￾nent perpendicular to the fibers and (3) the longitudinal￾shear (LS) mode for the shear-stress component parallel to the fibers (and its complementary component, required for equilibrium). In the LT mode of deformation, stress is continuously transferred from the matrix to the fiber as deformation proceeds. In the TS mode, deformation primarily occurs by shear flow of the matrix around the fibers resulting in very little improvement in creep properties over the unreinforced matrix. The terminology used for these modes of deformation is based on our previous work [15]. Both the LT and the TS modes of deformation have been studied in detail previously in ID ceramic composites [6,17]. Application of the mode analysis to the off-axis-loading 1D composite flow is analogous to the use of the Levy-Mises flow rules in continuum plasticity. From this analysis, and from knowing the structure and resultant flow behavior of the fiber-matrix interface (flow on the thin, amorphous silicate interlayer), one realizes that considerable, tem￾perature-sensitive sliding can occur on the interface. Thus, a substantial magnitude for the LS component of the applied stress (e.g. 845°) promotes significant displacement across the interface (modeling suggests some 40% of the accumulated strain results from interfa￾cial displacement when 840–50°), which, in turn, affects greatly the state of stress in the matrix [18]. The result overall is both the optimization of steady-state strain rate at 8=50° (it is the TS component that moves the maximum away from 8=45°) as well as (because of the temperature sensitivity of the interface response) the dramatic, high apparent activation energy for composite flow. New in these 1D composite experiments (i.e. not studied experimentally previously) is the data for com￾pression creep with 8=0 and 20°. The steady-state flow Fig. 8. Stress/Strain-rate relationships for 8=20° 1D specimens at 1300 and 1325°C. Fig. 9. Strain-rate as a function of 8 for 1D specimens deformed at −s1=40 MPa. Fig. 10. Steady-state creep response of unreinforced CAS-II matrix.

B G. Nair et al. Materials Science and Engineering 4300(2001)68- 40 P1 50°Ply os(v) Ply :3:1-90Ply 70 Ply -O Cos(y) Fig. 11. Optical micrographs of 2D composites. The deformed composites were crept at 1300C,(a) Undefortned specimen. The network of randomly oriented microcracks are a result of processing; they are probably introduced by thermal stress accompanying cooling of the hot-pressed material,(b)Cross-section of 90o plies of a 0/-90o specimen, 2- 1. 5%,(c) Cross-section of 50 plies of a 40/-500 specimen, 2- 6%;(d) for op=0(which isolates the LT mode)displays rate- specimens, must be less than x 27 for this to be the limitation by the creep of the Nicalon fibers -a simple case. Thus, such fiber bending would be expected only rule-of-mixtures calculation indicates that, having all of in composites with small, non-zero values of At higher he applied load carried by the fibers, the data-both stresses, the frictional forces at the contact area between absolute rate and activation energy -are fully consis the specimen and platens are higher, translation of the tent with previously published data and analysis for ends of the specimen is less efficient. This situation results creep, in a similarly reducing environment, of fully in fixing of the ends of individual fibers, causing bending crystallized Nicalon fiber [19, 20)(which is the condition at high levels of stress. Since greater elastic displacement of the fibers in our material, see Section 3) is possible in the bending mode at the same level of stress, c The behavior of the =20 specimen is in marked lesser and lesser number of fibers contribute to the overall ontrast to the expected and uniform trends seen in composite creepresistance, fiber bending could cause specimens with higher values of The decrease in much higher overall strain-rates as the matrix carries a stress-exponent with temperature-l varies from 5.3 at greater share of the load. Thus, the onset of fiber bending, 1300C to 3. 7 at 1325C-was a unique occurrence in and the resulting impact on ss could be the cause of the our studies of ID composites. Further, this magnitude high apparent n in these composites. The magnitude of for n is much higher than at the other orientations. absolute strain-rates for (=20 are consistent with this Microstructural observations of deformed interpretation; at 1300oC, Ess is comparable to =0at revealed no signs of crack initiation or growth that could =20 MPa indicative of fiber creep and toφ=90° have been one cause for a high value of n. The data are at -g=40 MPa indicative of matrix flow consistent, though, with the onset of elastic bending of Analysis of the variation of recovered strain(Eg) with the fibers at the higher stress levels in our experiments is useful in assessing the contribution of the fibers In these specimens, there are a significant number of the overall creepresistance of ID composites. The on-axis fibers running end to end; given the dimensions of our geometry is most conducive to accumulation of stored elastic energy in the fibers during creep and hence, it was It should also be noted that, for the same temperature and not surprising to see the highest eR for =00 composites differential stress, the creep resistance of crystallized Nicalon fiber (ER%). The recovered strain is still significant at some 10-times greater than that of the CAS-ll matrix(cf. Fig. 62 (for =0, normalizedwith respectto stress)and Fig. 10). Thus, for pp=20(ER -14%)suggesting some load-transfer to the the modeling of high-T, low-o, off-axis creep in these composite fibers. At higher values of the stored elastic energy in materials, it is a physically defensible simplification to assume the the fibers is minimal and correspondingly the recovered fibers as elastic [9, 18]. strain was irresolvable

76 B.G. Nair et al. / Materials Science and Engineering A300 (2001) 68–79 Fig. 11. Optical micrographs of 2D composites. The deformed composites were crept at 1300°C, (a) Undefortned specimen. The network of randomly oriented microcracks are a result of processing; they are probably introduced by thermal stress accompanying cooling of the hot-pressed material, (b) Cross-section of 90° plies of a 0/–90° specimen, o1.5%, (c) Cross-section of 50° plies of a 40/–50° specimen, o6%; (d) Cross-section of 70° plies 20/–70° specimen, o6%. for 8=0° (which isolates the LT mode) displays rate￾limitation by the creep of the Nicalon fibers — a simple rule-of-mixtures calculation indicates that, having all of the applied load carried by the fibers, the data — both absolute rate and activation energy — are fully consis￾tent with previously published data and analysis for creep, in a similarly reducing environment, of fully crystallized Nicalon fiber [19,20] (which is the condition of the fibers in our material, see Section 3)1 . The behavior of the 8=20° specimen is in marked contrast to the expected and uniform trends seen in specimens with higher values of 8. The decrease in stress-exponent with temperature-n varies from 5.3 at 1300°C to 3.7 at 1325°C — was a unique occurrence in our studies of 1D composites. Further, this magnitude for n is much higher than at the other orientations. Microstructural observations of deformed specimens revealed no signs of crack initiation or growth that could have been one cause for a high value of n. The data are consistent, though, with the onset of elastic bending of the fibers at the higher stress levels in our experiments. In these specimens, there are a significant number of fibers running end to end; given the dimensions of our specimens, 8 must be less than 27° for this to be the case. Thus, such fiber bending would be expected only in composites with small, non-zero values of 8. At higher stresses, the frictional forces at the contact area between the specimen and platens are higher, translation of the ends of the specimen is less efficient. This situation results in fixing of the ends of individual fibers, causing bending at high levels of stress. Since greater elastic displacement is possible in the bending mode at the same level of stress, lesser and lesser number of fibers contribute to the overall composite creepresistance, fiber bending could cause much higher overall strain-rates as the matrix carries a greater share of the load. Thus, the onset of fiber bending, and the resulting impact on o; ss could be the cause of the high apparent n in these composites. The magnitude of absolute strain-rates for 8=20° are consistent with this interpretation; at 1300°C, o; ss is comparable to 8=0° at −s=20 MPa indicative of fiber creep and to 8=90° at −s=40 MPa, indicative of matrix flow. Analysis of the variation of recovered strain (oR) with 8 is useful in assessing the contribution of the fibers to the overall creepresistance of 1D composites. The on-axis geometry is most conducive to accumulation of stored elastic energy in the fibers during creep and hence, it was not surprising to see the highest oR for 8=0° composites (oR30%). The recovered strain is still significant at 8=20° (oR14%) suggesting some load-transfer to the fibers. At higher values of 8, the stored elastic energy in the fibers is minimal and correspondingly the recovered strain was irresolvable. 1 It should also be noted that, for the same temperature and differential stress, the creep resistance of crystallized Nicalon fiber is some 103 -times greater than that of the CAS-II matrix (cf. Fig. 6a (for 8=0°, normalizedwith respectto stress) and Fig. 10). Thus, for the modeling of high-T, low-s, off-axis creep in these composite materials, it is a physically defensible simplification to assume the fibers as elastic [9,18].

B G. Nair et al. /Materials Science and Engineering 4300(2001)68-79 4.2. 2D Composite rheology 900-y) yielded strain-rates significantly different (too low) from those observed for the 2D specimens experi Creep behavior of the 0/-90% 2D composites is con- mentally. Microstructural investigation of undeformed trolled by creep of fibers in the 0 plies- values of n 2D composites, however, suggests that there are very ind Oapp for 0/-90o composites correspond well with few areas where direct contact between the fibers of the data available for of fully crystallized adjacent plies is seen. Rather, a discrete layer of matrix Nicalon"fibers [ 19, 20] and also with our data for creep material exists between the plies. This layer is of thick of lD composites with =00. If all the applied stress ness a 10-50 um(cf Fig. 13a), which is about 5-25% arried by the fibers in the 0o plies, the expected strain of the thickness of the individual plies. Thus, it is rate for the stresses employed in our experiments reasonable to assume that this matrix layer acts as a 10-7s, which compares very favorably with the third lamellar constituent in the composite and observed strain-rates for the 0/-90o composite tributes to the bulk creep strain according to its The creep behaviors of 40/-50 and 20/700 composites effective viscosity. are strikingly similar, although the 40/-50% composites Fig. 12 presents a highly simplified schematic of a show much higher strain-rates in the temperature range 2-ply section of the 2D composite along with the inter 1275-1300oC. The strong dependence of gnn on G,, spersed layers of unreinforced matrix. The constitutive and the unusually high values of ann observed bear equations for the rheology of each of the plies and the testament to an increase in the matrix von-Mises poten- manx layer at constant temperature can De exp tials with temperature due to thermally activated vis- cous flow of the interphase [15]. At higher differentia stresses, the expected flow mechanism of the matrix non-Newtonian(n- 3)dislocation creep [21, 22]. Thus, In addition to these three constitutive equations, for constant al, more volume of the matrix exhibits Isostrain conditions demand that, at steady state, the dislocation creep at a higher T, resulting in a higher strain-rates in all three plies are the same A straightforward application of laminate theory to where the three terms correspond to the steady-state he rheology of 2D material, with each of the plies strain-rates of the two sets of plies and the unreinforced characterized as having the viscoelastic properties of matrix, respectively. Finally, if the thickness of each set the corresponding ID composites(i.e, with o=y and of plies is d (cf Fig. 12), equilibrium imposes the following constraint 2am+(d-a)ow+(d-a)ow-90-y where om, oy and o(v-goo)are the partitioned stresses in the matrix layer and the two sets of constituent plies y90° respectively. Numerical solution of these equations em- ploying different values of a with the viscosity of this layer being that of the unreinforced matrix nicely fit the data for 2D composites using a 20-30 um for the 0/-90 and 20/-70 composites and a 30-40 um for the 40/-500 composites(see Fig. 13). As this result is consistent with the microstructural observations. the analysis seems to support the initial assumptions, spe- cifically regarding the behavior of the 2D composite a plastic laminate. Similar behavior has been observed in glass-fiber-reinforced polymers [23], where axis composites with an orientation v/-y(fibers in adjacent plies not perpendicular to each other except for when y= 45%) had creep compliances similar to that of unidirectional composites with =y, which indi- cates that the plies behaved as ID composite sections The presence of a network of matrix microcracks Fig 12 Highly simplified schematic of the lamellar structure of a 2D some questions regarding the applicability of the simple composite. The matrix regions included at the ends are to model described above. A study of the literature ever suggests that such a network of microcracks

B.G. Nair et al. / Materials Science and Engineering A300 (2001) 68–79 77 4.2. 2D Composite rheology Creep behavior of the 0/–90° 2D composites is con￾trolled by creep of fibers in the 0° plies — values of n and Qapp for 0/–90° composites correspond well with the data available for creep of fully crystallized Nicalon® fibers [19,20] and also with our data for creep of 1D composites with 8=0°. If all the applied stress is carried by the fibers in the 0° plies, the expected strain￾rate for the stresses employed in our experiments is 10−7 s−1 , which compares very favorably with the observed strain-rates for the 0/–90° composite. The creep behaviors of 40/–50 and 20/70° composites are strikingly similar, although the 40/–50° composites show much higher strain-rates in the temperature range 1275–1300°C. The strong dependence of Qapp on s1, and the unusually high values of Qapp observed bear testament to an increase in the matrix von-Mises poten￾tials with temperature due to thermally activated vis￾cous flow of the interphase [15]. At higher differential stresses, the expected flow mechanism of the matrix is non-Newtonian (n3) dislocation creep [21,22]. Thus, for constant s1, more volume of the matrix exhibits dislocation creep at a higher T, resulting in a higher ‘average’ n. A straightforward application of laminate theory to the rheology of 2D material, with each of the plies characterized as having the viscoelastic properties of the corresponding 1D composites (i.e., with 8=c and 90°−c) yielded strain-rates significantly different (too low) from those observed for the 2D specimens experi￾mentally. Microstructural investigation of undeformed 2D composites, however, suggests that there are very few areas where direct contact between the fibers of adjacent plies is seen. Rather, a discrete layer of matrix material exists between the plies. This layer is of thick￾ness a10–50 mm (cf. Fig. 13a), which is about 5–25% of the thickness of the individual plies. Thus, it is reasonable to assume that this matrix layer acts as a third lamellar constituent in the composite and con￾tributes to the bulk creep strain according to its own effective viscosity. Fig. 12 presents a highly simplified schematic of a 2-ply section of the 2D composite along with the inter￾spersed layers of unreinforced matrix. The constitutive equations for the rheology of each of the plies and the matrix layer at constant temperature can be expressed as o; ss=Csn (3) In addition to these three constitutive equations, isostrain conditions demand that, at steady state, the strain-rates in all three plies are the same: o; c=o; (c−90$) =o; m (4) where the three terms correspond to the steady-state strain-rates of the two sets of plies and the unreinforced matrix, respectively. Finally, if the thickness of each set of plies is d (cf Fig. 12), equilibrium imposes the following constraint: 2asm+(d−a)sc+(d−a)s(c−90$) =2ds1 (5) where sm, sc and s(c−90°) are the partitioned stresses in the matrix layer and the two sets of constituent plies, respectively. Numerical solution of these equations em￾ploying different values of a with the viscosity of this layer being that of the unreinforced matrix nicely fit the data for 2D composites using a20–30 mm for the 0/–90 and 20/–70° composites and a30–40 mm for the 40/–50° composites (see Fig. 13). As this result is consistent with the microstructural observations, the analysis seems to support the initial assumptions, spe￾cifically regarding the behavior of the 2D composite as a plastic laminate. Similar behavior has been observed in glass-fiber-reinforced polymers [23], where 2D off￾axis composites with an orientation c/–c (fibers in adjacent plies not perpendicular to each other except for when c=45°) had creep compliances similar to that of unidirectional composites with 8=c, which indi￾cates that the plies behaved as 1D composite sections. The presence of a network of matrix microcracks in the as-fabricated, undeformed 2D composites raises some questions regarding the applicability of the simple model described above. A study of the literature, how￾ever, suggests that such a network of microcracks could Fig. 12. Highly simplified schematic of the lamellar structure of a 2D composite. The matrix regions included at the ends are to ensure symmetry.