Composites Science and Technology 68(2008)3285-3292 Contents lists available at ScienceDirect Composites Science and Technology ELSEVIER journalhomepagewww.elsevier.com/locate/compscitech Measurement and calculation of thermal residual stress in fiber reinforced ceramic matrix composites Hui mei* National Key Laboratory of Thermostructure Composite Materials, Materials Science, Northwestern Polytechnical University, 547 P.O. Box, XIan, Shaanxi 710072, PR China ARTICLE IN F O ABSTRACT Article history: Received 29 January 2008 (C/SiC)and silicon carbide fiber(SiC/SiC) were completely investigated. Thermal residual stress in the C/ Accepted 20 August 2008 Sic was quantified by three different methods of experimental measurement, analytical calculation, and Available online 28 August 2008 heoretical prediction, and then compared with that in the Sic/SiC. Good agreement between these meth- ds was observed and their applicability to the present composite systems was validated. Relationships between the thermal residual stress state and macroscopic mechanical properties of the composites(e.g, A Ceramic matrix composites the first matrix cracking stress)are discusse B Mechanical property e 2008 Elsevier Ltd. All rights reserved. C Residual stress 1 Introduction (not only material surface)during mechanical loading attract more considerable attention, mainly because of its strong influence on Continuous fiber reinforced ceramic matrix composites(CMcs) the macroscopic tensile stress-strain response and of potential re currently considered for applications as structural materials in improvement of mechanical properties of these materials once th aerospace and other industries since they retain the advanta completely understanding the significant TRS. In this regard, Steen ges of ceramics while providing an enhanced damage tolerance [ et al.8-9] pre esents apply method to qu Generally, ceramic matrix composites are fabricated at high tify the residual stress state in continuous fiber ceramic matrix temperature, i.e. typically 900-1100C of the chemical vapor composites. The method consists of a novel interpretation of the infiltration(CVi) processing of Sic or C-matrix composites [2-3 results of tensile tests and offers the advantage that the initial (e.g, C/SiC, SiC/SiC and C/C, etc. ) Thus, thermal residual stresses residual stresses as well as their evolution with temperature and (TRS)are often generated in the composites upon cooling from pro- with applied loading can be determined. Evans et al. [10-11devel cessing to room temperatures due to extensive mismatch of the oped an analytical methodology to correlate the misfit stress with coefficients of thermal expansion( CTEs) between the constituents the unload/reload hysteresis and permanent strain with emphasis (fiber, interphase and matrix) on the interfacial properties. Then the tRS can be estimated as the are misfit stress multiplied by the volume-averaged stiffness coeffi scopic mechanical behavior of CMCs by determining the cient. However, these reported methods have not yet been com- states of the constituents(compressive or tensile stresses) pared systematically when applied to a specified composite, and omposites and forming the damage to the composites in also no description involving tRS comparison of the two composite to release themselves(matrix cracking, fiber-matrix debonding ). systems reinforced with different fibers applied to these methods Accordingly, estimation of TRs is a very important issue for the can be found in the recent literature. development and application of advanced CMCs. X-ray diffraction For this purpose, the present studies focus on investigation on (XRD) is considered as the most traditionally used technique for thermal residual stresses in two Sic-ceramic matrix composite sys- is only suited to the measurement of TRS in very small areas of (Sic/SiC). Three different methods of experimental measurement, the surface of polycrystalline materials in a very fine scale. More- analytical calculation, and theoretical prediction were conducte over, TRS in the fibres can usually not be analysed since they are to quantify thermal residual stress in the C/SiC, and then the ob- only partly crystalline and amorphous to diffraction methods [7]. tained results were compared with that in the SiC/ SiC Agreement Comparatively, axial trs behaviors of as a whole CMc material between and applicability of these methods to the present com- posite systems were concerned. Relationships between the tr TeL:+862988494616;fax:+862988494620. state and macroscopic mechanical properties of the composite (e.g. first matrix cracking stress)are discussed. S-see front matter o 2008 Elsevier Ltd. All rights reserved
Measurement and calculation of thermal residual stress in fiber reinforced ceramic matrix composites Hui Mei * National Key Laboratory of Thermostructure Composite Materials, Materials Science, Northwestern Polytechnical University, 547 P.O. Box, Xi’an, Shaanxi 710072, PR China article info Article history: Received 29 January 2008 Received in revised form 2 July 2008 Accepted 20 August 2008 Available online 28 August 2008 Keywords: A. Ceramic matrix composites B. Mechanical property C. Residual stress abstract In this study, thermal residual stresses in two SiC-ceramic matrix composites reinforced with carbon fiber (C/SiC) and silicon carbide fiber (SiC/SiC) were completely investigated. Thermal residual stress in the C/ SiC was quantified by three different methods of experimental measurement, analytical calculation, and theoretical prediction, and then compared with that in the SiC/SiC. Good agreement between these methods was observed and their applicability to the present composite systems was validated. Relationships between the thermal residual stress state and macroscopic mechanical properties of the composites (e.g., the first matrix cracking stress) are discussed. 2008 Elsevier Ltd. All rights reserved. 1. Introduction Continuous fiber reinforced ceramic matrix composites (CMCs) are currently considered for applications as structural materials in both aerospace and other industries since they retain the advantages of ceramics while providing an enhanced damage tolerance [1]. Generally, ceramic matrix composites are fabricated at high temperature, i.e. typically 900–1100 C of the chemical vapor infiltration (CVI) processing of SiC or C-matrix composites [2–3] (e.g., C/SiC, SiC/SiC and C/C, etc.). Thus, thermal residual stresses (TRS) are often generated in the composites upon cooling from processing to room temperatures due to extensive mismatch of the coefficients of thermal expansion (CTEs) between the constituents (fiber, interphase and matrix). TRS are known to have a significant influence on the macroscopic mechanical behavior of CMCs by determining the stress states of the constituents (compressive or tensile stresses) in the composites and forming the damage to the composites in order to release themselves (matrix cracking, fiber-matrix debonding). Accordingly, estimation of TRS is a very important issue for the development and application of advanced CMCs. X-ray diffraction (XRD) is considered as the most traditionally used technique for characterizing residual stresses in CMC materials [4–6]. However, it is only suited to the measurement of TRS in very small areas of the surface of polycrystalline materials in a very fine scale. Moreover, TRS in the fibres can usually not be analysed since they are only partly crystalline and amorphous to diffraction methods [7]. Comparatively, axial TRS behaviors of as a whole CMC material (not only material surface) during mechanical loading attract more considerable attention, mainly because of its strong influence on the macroscopic tensile stress–strain response and of potential improvement of mechanical properties of these materials once completely understanding the significant TRS. In this regard, Steen et al. [8–9] presents an alternative easy-to-apply method to quantify the residual stress state in continuous fiber ceramic matrix composites. The method consists of a novel interpretation of the results of tensile tests and offers the advantage that the initial residual stresses as well as their evolution with temperature and with applied loading can be determined. Evans et al. [10–11] developed an analytical methodology to correlate the misfit stress with the unload/reload hysteresis and permanent strain with emphasis on the interfacial properties. Then the TRS can be estimated as the misfit stress multiplied by the volume-averaged stiffness coeffi- cient. However, these reported methods have not yet been compared systematically when applied to a specified composite, and also no description involving TRS comparison of the two composite systems reinforced with different fibers applied to these methods can be found in the recent literature. For this purpose, the present studies focus on investigation on thermal residual stresses in two SiC-ceramic matrix composite systems reinforced with carbon fiber (C/SiC) and silicon carbide fiber (SiC/SiC). Three different methods of experimental measurement, analytical calculation, and theoretical prediction were conducted to quantify thermal residual stress in the C/SiC, and then the obtained results were compared with that in the SiC/SiC. Agreement between and applicability of these methods to the present composite systems were concerned. Relationships between the TRS state and macroscopic mechanical properties of the composites (e.g. first matrix cracking stress) are discussed. 0266-3538/$ - see front matter 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2008.08.015 * Tel.: +86 29 88494616; fax: +86 29 88494620. E-mail address: phdhuimei@yahoo.com. Composites Science and Technology 68 (2008) 3285–3292 Contents lists available at ScienceDirect Composites Science and Technology journal homepage: www.elsevier.com/locate/compscitech
H Mei/Composites Science and Technology 68(2008)3285-3292 2. Experimental procedures tooling and further coated with Sic by I-CVi under the same condi tions(final coating thickness 50 um). The specimens had a gage- 2.1. Material preparation section volume of approximately 25 8x 3 mm. To avoid surface damage of the specimen during the tensile tests, the specimen The C/Sic composites used in this investigation were processed edges were protected by bonding two pairs of Aluminum tab by isothermal chemical vapor infiltration( CVl)of SiC into woven (see Fig. 3) 0°90° fiber performs at~1000° The classical CVI SiC processing methodology has been described elsewhere [12]. The preforms 2.2. Mechanical tests were made from 1KT-300 carbon fibers and fiber volume contents of the as-processed composites was about 40 voL %. Fiber architec- Both monotonic tensile and periodic unloading-reloading tests tures of the as-received composite panels are shown in Fig. la and were conducted at room temperature on a servohydraulic load- (microstructures in this study were observed with a scanning frame( Model 8801, Instron Ltd, High Wycombe, England) with electron microscope, SEM, Hitachi S-2700, Tokyo, Japan). The mag- a loading rate of 0.06 mm/min. The monotonic tensile tests were ified surface observation of the crossover fiber bundles indicate eal-time monitored by the acoustic emission technique(Model the deposition morphology of the Cvi-Sic matrix. As is typical of MICRo-80D, Physical Acoustic Corp, NJ, USA). The cyclic unload lultiple-ply composites, not all plies(X-Y planes)were perfectly ing-reloading tests were preformed wit an Incremen igned in the Z-direction of the panels( Fig. 1a). SEM views of loading of 20 MPa per cycle up to final rupture. To the polished composites exhibit porosity present in the as-pro- the effect of Trs on the macroscopic mechanical respons cessed CVI C/SiC, including the inter-bundle pores in Fig. 2a and ferent CMC composites, a 2D Hi-Nicalon Sic composite with the the inter-filament pores in Fig. 2b. The TEM observation of the same 0 90 Sic fiber(Nippon Carbon Co., Tokyo, Japan)architec- upper-left picture in Fig. 2b shows that in the as-processed com- tures was used to conduct the same unloading-reloa posite, the carbon fibers were uniformly coated with the PyC inter references. The used 2D SiC/SiC composite proce hase(200 nm)and then the column nanocrystals of Sic matrix rently with the previou opposites vertically grew on the soft PyC interphase I-CVI technology. SEM micrographs in Fig. 4 present the eu. The bulk density and porosity of the infiltrated composite pan- fiber architectures and the constituent microstructures is 2.2 g/cm and 13% in average, respectively As shown in Fig 3. fiber, Pyc interphase(200 nm)and CVI-SiC matrix in the 2D tensile specimens were machined from the panels using diamond Sic/Sic composite Fig 1. SEM micrographs showing the fiber architectures of the 2D C/ sic composite prepared by Cvl (a)3D view and (b) top view. The magnified observation indicating the morphology of the CVI-SiC matrix. b Fig. 2. Micrographs showing porosity present in the virgin 2D C/SiC. (a)inter-bundle pores and(b) inter- filament pores. The TEM observation indicating the constituen and CVI-SiC matrix
2. Experimental procedures 2.1. Material preparation The C/SiC composites used in this investigation were processed by isothermal chemical vapor infiltration (CVI) of SiC into woven 0/90 fiber performs at 1000 C. The classical CVI SiC processing methodology has been described elsewhere [12]. The preforms were made from 1 K T-300 carbon fibers and fiber volume contents of the as-processed composites was about 40 vol.%. Fiber architectures of the as-received composite panels are shown in Fig. 1a and b (microstructures in this study were observed with a scanning electron microscope, SEM, Hitachi S-2700, Tokyo, Japan). The magnified surface observation of the crossover fiber bundles indicates the deposition morphology of the CVI-SiC matrix. As is typical of multiple-ply composites, not all plies (X–Y planes) were perfectly aligned in the Z-direction of the panels (Fig. 1a). SEM views of the polished composites exhibit porosity present in the as-processed CVI C/SiC, including the inter-bundle pores in Fig. 2a and the inter-filament pores in Fig. 2b. The TEM observation of the upper-left picture in Fig. 2b shows that in the as-processed composite, the carbon fibers were uniformly coated with the PyC interphase (200 nm) and then the column nanocrystals of SiC matrix vertically grew on the soft PyC interphase. The bulk density and porosity of the infiltrated composite panels is 2.2 g/cm3 and 13% in average, respectively. As shown in Fig. 3, tensile specimens were machined from the panels using diamond tooling and further coated with SiC by I-CVI under the same conditions (final coating thickness 50 lm). The specimens had a gagesection volume of approximately 25 8 3 mm3 . To avoid surface damage of the specimen during the tensile tests, the specimen edges were protected by bonding two pairs of Aluminum tabs (see Fig. 3). 2.2. Mechanical tests Both monotonic tensile and periodic unloading-reloading tests were conducted at room temperature on a servohydraulic loadframe (Model 8801, Instron Ltd., High Wycombe, England) with a loading rate of 0.06 mm/min. The monotonic tensile tests were real-time monitored by the acoustic emission technique (Model MICRO-80D, Physical Acoustic Corp., NJ, USA). The cyclic unloading-reloading tests were preformed with an incremental step loading of 20 MPa per cycle up to final rupture. To compare the effect of TRS on the macroscopic mechanical response of different CMC composites, a 2D Hi-Nicalon/SiC composite with the same 0/90 SiC fiber (Nippon Carbon Co., Tokyo, Japan) architectures was used to conduct the same unloading–reloading tests as references. The used 2D SiC/SiC composite processed concurrently with the previous C/SiC composites under the same I-CVI technology. SEM micrographs in Fig. 4 present the woven fiber architectures and the constituent microstructures of SiC fiber, PyC interphase (200 nm) and CVI-SiC matrix in the 2D SiC/SiC composite. Fig. 1. SEM micrographs showing the fiber architectures of the 2D C/SiC composite prepared by CVI, (a) 3D view and (b) top view. The magnified observation indicating the morphology of the CVI-SiC matrix. Fig. 2. Micrographs showing porosity present in the virgin 2D C/SiC, (a) inter-bundle pores and (b) inter-filament pores. The TEM observation indicating the constituent microstructures of carbon fiber, PyC interphase and CVI-SiC matrix. 3286 H. Mei / Composites Science and Technology 68 (2008) 3285–3292
H Mei/Composites Science and Technology 68(2008)3285-3292 and the ae counts enlarged with increasing inelastic strain at stress 80 mm higher than 50 MPa Theonset"strain(obtained from extrapola- ion of the initial high-rate aE energy to the abscissa for this strain in Fig. 5, see Ref [13])is round 0.05% Multiple matrix cracking and 8 mm interface debonding resulted in macroscopic nonlinear mechanical response leading to this aE activity. the slope of the tensile curve Fiber architectures continuously decreases as the stress increases between 50 an 150 MPa. Above 150 MPa, with a sudden reduction in AE energy the stress-strain relationship turns into apparent linearity up to 3 mm final fracture at stress of 250.60 MPa and strain of 0.65% g. 3. Geometry and dimensions of the tensile test pieces. 3.2. Reloading-unloading behaviors Fig 6 presents the hysteresis loop evolutions of the 2D C/Sic 3. Results and discussion composites during the loading-unloading-reloading cycle tests. It can be seen from this figure that the loading curve in each loop was mostly linear to the stress level of the preceding step and then became nonlinear, following the envelope which is basically iden- > Fig. 5 gives a typical stress-strain curve of 2D C/SiC composite tical to the monotonic tensile stress-strain curve shown in Fig 5. mple with corresponding acoustic emission(AE)signals during The nonlinear monotonic tensile testing. The AE energy below proportional limit schematically depicted in Fig. 7. The inelastic strain E upon loading stress of omc =50 MPa was small, that above the proportional limit includes the sliding strain, es. that arises from the matrix crack obviously became large, indicating that the onset of significant opening caused by interface debonding/sliding, and the thermal propagation and multiplication of the as-processed matrix micro- misfit relief strain er caused by relief of the misfit strain. The elastic cracks correlated closely to the proportional limit stress. After strain, ee, represents the reversible strain upon unloading. The total the initiation period, the accumulated AE energy increased rapidly strain a at each peak applied stress p is thus b SiC matrix Fig 4. SEM micrographs showing(a)the woven 0/90 fiber architectures and (b) the constituent micro res of Hi-Nicalon SiC fiber, Pyc interphase and CVI-SiC matrix Time(s) 0300600900120015001800 250 Linearity 6x105 195 175 AE energy 155 3155555 1x10° 00010203040.50.60.7 (%) Fig. 5. Typical monotonic tensile stress-strain curve of the 2D C/Sic composite with the associated acoustic emission response
3. Results and discussion 3.1. Monotonic tensile behaviors Fig. 5 gives a typical stress–strain curve of 2D C/SiC composite sample with corresponding acoustic emission (AE) signals during monotonic tensile testing. The AE energy below proportional limit stress of rmc = 50 MPa was small, that above the proportional limit obviously became large, indicating that the onset of significant propagation and multiplication of the as-processed matrix microcracks correlated closely to the proportional limit stress. After the initiation period, the accumulated AE energy increased rapidly and the AE counts enlarged with increasing inelastic strain at stress higher than 50 MPa. The ‘‘onset” strain (obtained from extrapolation of the initial high-rate AE energy to the abscissa for this strain in Fig. 5, see Ref. [13]) is round 0.05%. Multiple matrix cracking and interface debonding resulted in macroscopic nonlinear mechanical response leading to this AE activity. The slope of the tensile curve continuously decreases as the stress increases between 50 and 150 MPa. Above 150 MPa, with a sudden reduction in AE energy the stress–strain relationship turns into apparent linearity up to final fracture at stress of 250.60 MPa and strain of 0.65%. 3.2. Reloading–unloading behaviors Fig. 6 presents the hysteresis loop evolutions of the 2D C/SiC composites during the loading–unloading–reloading cycle tests. It can be seen from this figure that the loading curve in each loop was mostly linear to the stress level of the preceding step and then became nonlinear, following the envelope which is basically identical to the monotonic tensile stress–strain curve shown in Fig. 5. The nonlinear phenomena associated with matrix cracking are schematically depicted in Fig. 7. The inelastic strain ei upon loading includes the sliding strain, es, that arises from the matrix crack opening caused by interface debonding/sliding, and the thermal misfit relief strain eT caused by relief of the misfit strain. The elastic strain, ee, represents the reversible strain upon unloading. The total strain e* at each peak applied stress rp is thus 120 mm Fiber architectures Aluminum tab 3 mm 8 mm 80 mm Fig. 3. Geometry and dimensions of the tensile test pieces. Fig. 4. SEM micrographs showing (a) the woven 0/90 fiber architectures and (b) the constituent microstructures of Hi-Nicalon SiC fiber, PyC interphase and CVI-SiC matrix in the 2D SiC/SiC composite. Fig. 5. Typical monotonic tensile stress–strain curve of the 2D C/SiC composite with the associated acoustic emission response. H. Mei / Composites Science and Technology 68 (2008) 3285–3292 3287
H Mei/Composites Science and Technology 68(2008)3285-3292 250 Table 1 The experimental and calculational results of the parameters in the loading unloading-reloading cycle tests 200 p(MPa) fe(% Ep(GPa) b(MPa 0.30.02038000822 0286 241.1 00160922166 044340011590055930011509269 150 068230.0220900903200208488.54 8240.101470030460.1319300333683.6 0.13022 0.170130.042347881 0217130.048517208 3497 2D C/SiC 14180.20150062870.2643700528367.0 0.331700 298840.099890.398730.085855845 50 10203.50345750.117110462860.0960055.48-53.26 11223.70398690.1364305351201100952 0.00.1020.30.40.50.6 Strain(%) hysteresis loops of the 2D C/SiC composites with ding cycles ②≌oEo0 050500 200250 Peak applied stress(MPa) relief strain fr of the 2D C/SiC composites obtained upon unloading, along with the secant modulus of the hysteresis loop, as a function of the applied stress. material s modulus along with an extension of inelastic residual strains Ei. Camus et al. [14 pointed out that the inelastic residual Fig.7. Schematic of hysteresis loop with elastic strain and inelastic strain in a c/sic strains in CMCs may be attributed to the interaction of several phe- naterial system during the reloading-unloading cycles. nomena: (i)the release of axial residual stresses (i.e. parallel to the ε*=+ε=斷r+B5+le loading direction) present in the composite from processing: (11) partial irreversible sliding arising from the various energy dissipa The thermal misfit relief strain er depends upon the elastic stiffness, tive frictional mechanisms: and (iii)a mechanical impediment of Ep, of the damaged material and can be written as complete crack closure possibly related to fiber roughness and or the contact between microcrack lips slightly removed from their 2) initial positions, resulting in increased stiffnesses at the lower end of the loops once unloading In the present case of the 2D C SiC composite, narrow hysteresis loops in Fig. 6 account for negli- 3) gible frictional sliding whereas crack closure impediment effects are nearly absent. Thus, the inelastic strain ai is in large part as- cribed to the contribution from the release of axial residual stres- Below the stress level of the preceding step, the top portion of ses. It can be actually seen from Fig. 8 that at lower stresses each loading curve exhibits apparent linearity and Ep is obtained below 150 MPa the thermal misfit relief strain er of the 2D C/Sic from the linear fitting of the top linear portion, which can be called composites is closely superposed with the inelastic strain =p. At steady secant modulus(SSM)of each hysteresis loop. In this condi- higher stresses above 150 MPa, however, the sliding strain as is ion, thermal misfit relief strain Er can be determined directly from unavoidable to occur with gradually increasing applied stress. the abscissa coordinates of the intersection point by extrapolation resulting in slight deviation of the thermal misfit relief strain Er of the compliance slopes(Ep) from the inelastic strain a Table 1 and Fig. 8 show changes in the elastic strain ce, inelas The loading curve of each hysteresis loop is alike with the tic strain Ei and thermal misfit relief strain ar of the 2D C/Sic monotonic tensile curve of the composite containing cracks: a composites obtained upon unloading, along with the SSM Ep of small elastic deformation occurs upon initial reloading, followed each hysteresis loop, as a function of the applied stress. Obviously, by a nonlinear behavior with partial irreversible sliding and finally the peak applied stress increases the SSM Ep diminishes whereas the slip zone stops at the debond tip accompanied by establish the elastic strain ee, inelastic strain a and thermal misfit relief ment of a large linear response of the whole composite system un strain Er increase Periodic loading/unloading cycles can introduce til the preceding stress level approaches. Fig. 9 illustrates typical damage into the CMC, which exhibits a progressive decrease of the tangent modulus changes calculated directly from the slopes of
e ¼ ei þ ee ¼ eT þ es þ ee ð1Þ The thermal misfit relief strain eT depends upon the elastic stiffness, Ep, of the damaged material and can be written as eT ¼ e rp Ep ð2Þ and es þ ee ¼ rp Ep ð3Þ Below the stress level of the preceding step, the top portion of each loading curve exhibits apparent linearity and Ep is obtained from the linear fitting of the top linear portion, which can be called steady secant modulus (SSM) of each hysteresis loop. In this condition, thermal misfit relief strain eT can be determined directly from the abscissa coordinates of the intersection point by extrapolation of the compliance slopes (Ep). Table 1 and Fig. 8 show changes in the elastic strain ee, inelastic strain ei and thermal misfit relief strain eT of the 2D C/SiC composites obtained upon unloading, along with the SSM Ep of each hysteresis loop, as a function of the applied stress. Obviously, as the peak applied stress increases the SSM Ep diminishes whereas the elastic strain ee, inelastic strain ei and thermal misfit relief strain eT increase. Periodic loading/unloading cycles can introduce damage into the CMC, which exhibits a progressive decrease of the material’s modulus along with an extension of inelastic residual strains ei. Camus et al. [14] pointed out that the inelastic residual strains in CMCs may be attributed to the interaction of several phenomena: (i) the release of axial residual stresses (i.e. parallel to the loading direction) present in the composite from processing; (ii) partial irreversible sliding arising from the various energy dissipative frictional mechanisms; and (iii) a mechanical impediment of complete crack closure possibly related to fiber roughness and/or the contact between microcrack lips slightly removed from their initial positions, resulting in increased stiffnesses at the lower end of the loops once unloading. In the present case of the 2D C/ SiC composite, narrow hysteresis loops in Fig. 6 account for negligible frictional sliding whereas crack closure impediment effects are nearly absent. Thus, the inelastic strain ei is in large part ascribed to the contribution from the release of axial residual stresses. It can be actually seen from Fig. 8 that at lower stresses below 150 MPa the thermal misfit relief strain eT of the 2D C/SiC composites is closely superposed with the inelastic strain ei. At higher stresses above 150 MPa, however, the sliding strain es is unavoidable to occur with gradually increasing applied stress, resulting in slight deviation of the thermal misfit relief strain eT from the inelastic strain ei. The loading curve of each hysteresis loop is alike with the monotonic tensile curve of the composite containing cracks: a small elastic deformation occurs upon initial reloading, followed by a nonlinear behavior with partial irreversible sliding and finally the slip zone stops at the debond tip accompanied by establishment of a large linear response of the whole composite system until the preceding stress level approaches. Fig. 9 illustrates typical tangent modulus changes calculated directly from the slopes of Fig. 6. Tensile stress/strain hysteresis loops of the 2D C/SiC composites with interrupted unloading/reloading cycles. Fig. 7. Schematic of hysteresis loop with elastic strain and inelastic strain in a C/SiC material system during the reloading–unloading cycles. Table 1 The experimental and calculational results of the parameters in the loading– unloading–reloading cycle tests n rp (MPa) ee (%) ei (%) e * (%) eT (%) Ep (GPa) b (MPa) 1 20.3 0.02038 0.00822 0.0286 0.00686 93.57 6.42 2 41.1 0.04434 0.01159 0.05593 0.01150 92.69 10.66 3 61.5 0.06823 0.02209 0.09032 0.02084 88.54 18.45 4 82.4 0.10147 0.03046 0.13193 0.03336 83.62 27.90 5 100.7 0.13022 0.03991 0.17013 0.04234 78.81 33.37 6 121.5 0.16963 0.0475 0.21713 0.04851 72.08 34.97 7 141.8 0.2015 0.06287 0.26437 0.05283 67.03 35.41 8 162.6 0.25067 0.08103 0.3317 0.06885 61.89 42.62 9 182.8 0.29884 0.09989 0.39873 0.08585 58.45 50.18 10 203.5 0.34575 0.11711 0.46286 0.09600 55.48 53.26 11 223.7 0.39869 0.13643 0.53512 0.11009 52.65 57.97 Fig. 8. Development of the elastic strain ee, inelastic strain ei and thermal misfit relief strain eT of the 2D C/SiC composites obtained upon unloading, along with the secant modulus of the hysteresis loop, as a function of the applied stress. 3288 H. Mei / Composites Science and Technology 68 (2008) 3285–3292
H Mei/Composites Science and Technology 68(2008)3285-3292 3289 Table 2 Parameters and values used in calculation 70 ng s modulus of matrix Volume fraction of matrix 亏65 fraction of c fber 60 160 MPa (axial) C fber radit Coefficient related to weave b 200 MPa Interface sliding stress for C/SiC MPa 100 150 Processing temperature Youngs modulus of Sic fiber ￥ Ptvaican unloading -reloading cues. calcuated om tne reloading curves cTE of sic fil SiC fber radius Interface sliding stress for SiC/SiC MPa loading curves of several unloading-reloading loops. It is clear that the tangent modulus of the composite at each loading cycle de- CTE, coefficient of thermal expansion. creases with increasing reloading stress up to the final distinctive steady state (i.e. SSM), which indicating that the top linear behav or with no sliding indeed exists for the present composite system Both initial modulus and final SSM of the composite at each hyster- esis loop decrease as the peak applied stress increases such as from 160 160 MPa. 180 MPa to 200 MPa. E=iEV, 3.3. Experimental measurement of TRs According to Steen and Camus [8, 14, the axial residual stress state at a given temperature and for a given composite specimen can be determined directly from the coordinates of that commor intersection point by extrapolation of the compliance slopes of the top linear portion at each reloading-unloading loop As shown in Fig. 7, these compliance slopes happen to meet at a single point O(Er, or)localized in the compression domain. Specifically, if the -0.30.2-0.10.00.10.20.30.40.50.60.7 matrix of the composite is in residual compression, the intersection of the regression lines of the reloading-unloading loops lies in the positive stress-strain quadrant(I quadrant ) and if the matrix of Fig 10. Typical step-loading curves of 2D C/Sic showing the intersection point of gative stress-strain quadrant(ll quadrant). In the present C/ stress-strain quadrant ons the composite is in residual tension, the intersection lies in the tive unloading-reloading loops in the negative SiC, below the processing temperature of 1000C the Sic matrix is in residual tensile stress whereas the carbon fiber reinforcement ite specimen at the last hysteresis loop(see Table 1).This so-called is in residual compressive stress since the SiC matrix normally has 'EVe line was also plotted in the Fig. 7. Above this line all the com- greater CTE than the axial carbon fiber(see Table 2). As a result, liance slopes can intersect at the origin point O and the envelop the C/sic materials have a pre-cracked as-received condition due to tensile curve of the composite(defined as tensile mastercurve by to the residual tensile stress state in the brittle SiC matrix once Steen)exhibits large nonlinear phenomena associated with time- cooled down from the processing temperature and the speci dependent matrix cracking. The intersection of the tensile master- intersection for indication of the axial residual stress state local- curve with this line indicates that a saturated matrix cracking state The lower-right solid straight line through the origin o in illustrated in Fig. 7) and the longitudinal 90 fibers in the load direc final failure with the minimum modulus cracks. High modulus fibers and bundles now bore the global load- Ep=ErVE (4) in a completely cracked matrix, leading to macroscopic"stiffen- ing"phenomenon and linear stress-strain relationship of the fibers where Ef and Vf denote the modulus and volume fraction of the with"some slope recovery". The tensile mastercurve with"slo intact fibers oriented in the direction of loading. The parameter i recovery"continuously climbs up along with Emin line until the is defined as a modified coefficient related to fiber woven architec fibres failure occurs leading to a decrease in the value of Vr and then ture of the composite perform, and here it is equal to 0.5 because final rupture of the composite is coming. The"stiffening"phenom- only one half of the fibers(longitudinal fibers) in 2D [0 /90]C/ enon and linear stress-strain response of the composite prior to Sic has a contribution to the modulus of the whole composite in rupture caused by the solely load bearing fibers were also observed the loading direction. Using the data listed in Table 2 and Eq (4). by the other researchers [15-17]. Fig 2a in a previously reported the minimum modulus of the composite approximates to 46 GPa, work by Mei et al. [18 indicated this behavior of the 2D C/Sic which is slightly lower than the SSM Ep of 52.65 GPa of the compos- composite In the present study, however, this phenomenon could
loading curves of several unloading–reloading loops. It is clear that the tangent modulus of the composite at each loading cycle decreases with increasing reloading stress up to the final distinctive steady state (i.e., SSM), which indicating that the top linear behavior with no sliding indeed exists for the present composite system. Both initial modulus and final SSM of the composite at each hysteresis loop decrease as the peak applied stress increases such as from 160 MPa, 180 MPa to 200 MPa. 3.3. Experimental measurement of TRS According to Steen and Camus [8,14], the axial residual stress state at a given temperature and for a given composite specimen can be determined directly from the coordinates of that common intersection point by extrapolation of the compliance slopes of the top linear portion at each reloading-unloading loop. As shown in Fig. 7, these compliance slopes happen to meet at a single point O0 (er,rr) localized in the compression domain. Specifically, if the matrix of the composite is in residual compression, the intersection of the regression lines of the reloading–unloading loops lies in the positive stress–strain quadrant (I quadrant); and if the matrix of the composite is in residual tension, the intersection lies in the negative stress–strain quadrant (III quadrant). In the present C/ SiC, below the processing temperature of 1000 C the SiC matrix is in residual tensile stress whereas the carbon fiber reinforcement is in residual compressive stress since the SiC matrix normally has a greater CTE than the axial carbon fiber (see Table 2). As a result, the C/SiC materials have a pre-cracked as-received condition due to the residual tensile stress state in the brittle SiC matrix once cooled down from the processing temperature and the special intersection for indication of the axial residual stress state localized in the III quadrant in Fig. 10. The lower-right solid straight line through the origin O0 in Fig. 10 represents an elastic behavior of the composite before the final failure with the minimum modulus Emin p ¼ kEfVf ð4Þ where Ef and Vf denote the modulus and volume fraction of the intact fibers oriented in the direction of loading. The parameter k is defined as a modified coefficient related to fiber woven architecture of the composite perform, and here it is equal to 0.5 because only one half of the fibers (longitudinal fibers) in 2D [0/90] C/ SiC has a contribution to the modulus of the whole composite in the loading direction. Using the data listed in Table 2 and Eq. (4), the minimum modulus of the composite approximates to 46 GPa, which is slightly lower than the SSM Ep of 52.65 GPa of the composite specimen at the last hysteresis loop (see Table 1). This so-called ‘EfVf line’ was also plotted in the Fig. 7. Above this line all the compliance slopes can intersect at the origin point O0 and the envelope to tensile curve of the composite (defined as tensile mastercurve by Steen) exhibits large nonlinear phenomena associated with timedependent matrix cracking. The intersection of the tensile mastercurve with this line indicates that a saturated matrix cracking state is reached (this stress is called matrix crack saturation stress rs as illustrated in Fig. 7) and the longitudinal 90 fibers in the load direction were completely bridged by the transverse saturated matrix cracks. High modulus fibers and bundles now bore the global loading in a completely cracked matrix, leading to macroscopic ‘‘stiffening” phenomenon and linear stress–strain relationship of the fibers with ‘‘some slope recovery”. The tensile mastercurve with ‘‘slope recovery” continuously climbs up along with Emin p line until the fibres failure occurs leading to a decrease in the value of Vf and then final rupture of the composite is coming. The ‘‘stiffening” phenomenon and linear stress-strain response of the composite prior to rupture caused by the solely load bearing fibers were also observed by the other researchers [15–17]. Fig. 2a in a previously reported work by Mei et al. [18] indicated this behavior of the 2D C/SiC composite. In the present study, however, this phenomenon could Table 2 Parameters and values used in calculation Parameter Symbol Value Units Porosity of composite P 13 % Young’s modulus of matrix Em 350 GPa Volume fraction of matrix Vm 60 % CTE* of SiC matrix am 4.6 106 /K Young’s modulus of C fiber Ef 230 GPa Volume fraction of C fiber Vf 40 % CTE of C fiber af 0 (axial) 106 /K 10 (radial) C fiber radius R 3.5 lm Coefficient related to weave k 0.5 Crack spacing before failure d 150–160 lm Interface sliding stress for C/SiC s 6 MPa Room temperature To 298 K Processing temperature Tp 1273 K Matrix fracture energy Cm 6 J/m2 Young’s modulus of SiC fiber Ef 200 GPa Volume fraction of SiC fiber Vf 40 % CTE of SiC fiber af 4.6 106 /K SiC fiber radius R 7 lm Interface sliding stress for SiC/SiC s 20 MPa * CTE, coefficient of thermal expansion. Fig. 10. Typical step-loading curves of 2D C/SiC showing the intersection point of the regression lines of consecutive unloading–reloading loops in the negative stress–strain quadrant. Fig. 9. Typical tangent modulus change curves calculated from the reloading curves of several typical unloading–reloading cycles. H. Mei / Composites Science and Technology 68 (2008) 3285–3292 3289
292 not be seen because the tested composite sample ruptured at Ep- opening displacement)model. The axial residual stress in matrix 52.65 GPa before e= 46 GPa can be analytically expressed by 10 The intersection coordinates(Er, Or), as shown in Fig. 7, can be simply calculated by using arbitrary two pairs of ogous trian- tEVA+正E (10) gles,eg,△ORG~△FHG,as and the misfit stress, oT, can be extracted from the permanent strain E 11(ie the inelastic strain ai defined in Fig. 7) Thus ing to Eq(3), the TRS Or can be linearly expressed as a gT (Ep-+2 function of TR strain in each reloading-unloading loop I -) or=Eper+b where the SSM Ep is given by where R is the fiber radius, E and Em are the Young 's modulus of the composite and matrix, E is the modulus of the composite contain- ing(see Fig. 7). Vm is the tion of the matrix and t is interface sliding stress, and d is the and the intercept b is given by matrix crack spacing. The coefficients a, bi(appear in Eq. (11)were defined by Hutchinson and jensen [19] b=Epbr=EpE”-Gp (8) Fig 11 is the theoretical predictions of the permanent strain Ej as function of the peak applied stress op with three different level of and the known parameters such as the total strain g'and the peak ap- misfit stress o of 70, 100 and 150 MPa by using the Eq (11)and the plied stress ap. Table 1 gives the values of all the parameters for the data listed in Tables 1 and 2. The detailed analysis and calculation I hysteresis loops of the tested 2D C/SiC composite specimen. It procedure related to the misfit stress of the presently tested 2D C/ should be noted that the line determined by the Eq (6)just denotes SiC composite can be found in another paper by Wang et al. [201 the fitting line of the top linear portion of each hysteresis loop, e.g. It is clear from Fig. 11 that the theoretical prediction of the perm line O,Fin Fig. 7. Fig. 10 plotted all the 11 lines(dashed line)together nent strain ei perfectly matches the experimental results when o is with the periodic loading/unloading stress-strain curves. Evidently, equal to 100 MPa. Through the data in Table 2 and Eq (10), analy these compliance slopes are found to nearly intersect in a single ically calculated value of the trs of the tested 2D C/Sic materials oint o(Er, or), which can be termed"thermal-residual-stress-free containing matrix cracks and interface sliding is 136.71 MPa, which origin( 14. It can be easily calculated out by solving the coordinates of all the 55 intersections of the 11 lines(C1= 55)as E 3100 MPa 后012 0=150 MPa According to the data in Table 1, the tRstress and strain could be easy to be obtained by using Matlab" programming: Er=-012+0.04% 13084+34.53 MPa. all the calculational results of the 55 intersections of the 11 lines are listed in table 3 3.4. Analytical calculation of trs considering matrix cracking and interfacial sliding Evans and his colleagues [10-11 developed analytical formulas Peak maximum stress(MPa) for the calculation of TRS of LdE(large debond energy) materials considering matrix cracking and interface sliding, mainly based Fig. 11. Accumulation of residual strains with applied stress. Misfit stress can be on the analysis of interface inelastic deformation and CoD(crack obtained by fitting them with difterent values on fixed >h Table 3 Calculational coordinates of all the 55 intersections of the 11 lines 020-173.66 167.85 0.09-108.38 0.12 -1323 L3-0.0 -019-16983L25-0.13-135.56L39-0.10-116 45 -014-14277128010-12001n-012-12937159-00-10183210-013-13803 010-118.54L10-0.10-117.6 0.18 178.22 11-12739L210-0.11-12386 0.10-10915L5-0.12-12383L310-0.13-14219 12-12950L2 0.13-13421L47-0.07 03-5889Ls,11-0.21-207.77 -013-13886L35-0.14-139.82L49-0.09-10597 0.09103.16L9n-0.29-281.29 0.19-16758L 0.12 0-0.09-108.60L1 0.14-129.3 Thermal residual strain and stress(AVE* STDEV) 2513084±345Ma Ly denotes the intersection of lines i andj
not be seen because the tested composite sample ruptured at Ep = 52.65 GPa before Emin p = 46 GPa. The intersection coordinates (er,rr), as shown in Fig. 7, can be simply calculated by using arbitrary two pairs of analogous triangles, e.g., DO’RG DFHG, as rr rp ¼ er þ eT es þ ee ð5Þ Thus, according to Eq. (3), the TRS rr can be linearly expressed as a function of TR strain in each reloading–unloading loop n: rr ¼ Eper þ b ð6Þ where the SSM Ep is given by Ep ¼ rp es þ ee ð7Þ and the intercept b is given by b ¼ EpeT ¼ Epe rp ð8Þ The SSM Ep and the intercept b are now obtained by the linear fitting and the known parameters such as the total strain e* and the peak applied stress rp. Table 1 gives the values of all the parameters for the 11 hysteresis loops of the tested 2D C/SiC composite specimen. It should be noted that the line determined by the Eq. (6) just denotes the fitting line of the top linear portion of each hysteresis loop, e.g. line O’F in Fig. 7. Fig. 10 plotted all the 11 lines (dashed line) together with the periodic loading/unloading stress–strain curves. Evidently, these compliance slopes are found to nearly intersect in a single point O0 (er,rr), which can be termed ‘‘thermal-residual-stress-free” origin [14]. It can be easily calculated out by solving the coordinates of all the 55 intersections of the 11 lines (C2 11 ¼ 55) as, rr ¼ E1 p . . . E11 p 2 6 6 6 4 3 7 7 7 5 er þ b1 . . . b11 2 6 6 4 3 7 7 5 ð9Þ According to the data in Table 1, the TR stress and strain could be easy to be obtained by using Matlab programming: er = 0.12 ± 0.04%, and rr = 130.84 ± 34.53 MPa. All the calculational results of the 55 intersections of the 11 lines are listed in Table 3. 3.4. Analytical calculation of TRS considering matrix cracking and interfacial sliding Evans and his colleagues [10–11] developed analytical formulas for the calculation of TRS of LDE (large debond energy) materials considering matrix cracking and interface sliding, mainly based on the analysis of interface inelastic deformation and COD (crack opening displacement) model. The axial residual stress in matrix can be analytically expressed by [10] rm r ¼ Em EmVm þ kEfVf rT ð10Þ and the misfit stress, rT , can be extracted from the permanent strain ei [11] (i.e., the inelastic strain ei defined in Fig. 7) rT ¼ ð 1 Ep 1 E Þ 2 8 b2ð1a1VfÞ 2R 4dsEmV2 f ð 1 Ep 1 EÞ Erp 1 Ep ei rp ð11Þ where R is the fiber radius, E and Em are the Young’s modulus of the composite and matrix, E* is the modulus of the composite containing matrix cracks upon unloading (see Fig. 7). Vm is the volume fraction of the matrix and s is interface sliding stress, and d is the matrix crack spacing. The coefficients ai, bi (appear in Eq. (11)) were defined by Hutchinson and Jensen [19]. Fig. 11 is the theoretical predictions of the permanent strain ei as a function of the peak applied stress rp with three different level of misfit stress rT of 70, 100 and 150 MPa by using the Eq. (11) and the data listed in Tables 1 and 2. The detailed analysis and calculation procedure related to the misfit stress of the presently tested 2D C/ SiC composite can be found in another paper by Wang et al. [20]. It is clear from Fig. 11 that the theoretical prediction of the permanent strain ei perfectly matches the experimental results when rT is equal to 100 MPa. Through the data in Table 2 and Eq. (10), analytically calculated value of the TRS of the tested 2D C/SiC materials containing matrix cracks and interface sliding is 136.71 MPa, which Table 3 Calculational coordinates of all the 55 intersections of the 11 lines Li,j * er rr Li,j er rr Li,j er rr Li,j er rr Li,j er rr L1,2 0.20 173.66 L2,4 0.19 167.85 L3,7 0.09 108.38 L4,11 0.12 122.50 L6,11 0.13 132.39 L1,3 0.20 170.71 L2,5 0.15 148.00 L3,8 0.09 111.55 L5,6 0.08 98.52 L7,8 0.12 130.78 L1,4 0.19 169.83 L2,6 0.13 135.56 L3,9 0.10 116.15 L5,7 0.05 77.45 L7,9 0.13 140.79 L1,5 0.16 154.10 L2,7 0.10 118.54 L3,10 0.10 117.62 L5,8 0.07 90.60 L7,10 0.13 138.03 L1,6 0.14 142.77 L2,8 0.10 120.01 L3,11 0.12 129.37 L5,9 0.09 101.83 L7,11 0.18 178.22 L1,7 0.11 127.00 L2,9 0.11 123.15 L4,5 0.11 118.10 L5,10 0.09 106.11 L8,9 0.14 151.78 L1,8 0.11 127.39 L2,10 0.11 123.86 L4,6 0.10 109.15 L5,11 0.12 123.83 L8,10 0.13 142.19 L1,9 0.12 129.50 L2,11 0.13 134.21 L4,7 0.07 91.98 L6,7 0.03 58.89 L8,11 0.21 207.77 L1,10 0.12 129.66 L3,4 0.19 168.10 L4,8 0.08 98.72 L6,8 0.06 86.28 L9,10 0.12 131.70 L1,11 0.13 138.86 L3,5 0.14 139.82 L4,9 0.09 105.97 L6,9 0.09 103.16 L9,11 0.29 281.29 L2,3 0.19 167.58 L3,6 0.12 126.50 L4,10 0.10 108.83 L6,10 0.09 108.60 L10,11 0.14 129.31 Thermal residual strain and stress (AVE ± STDEV) er ¼ 0:12 0:04% rr ¼ 130:84 34:53 MPa * Li,j denotes the intersection of lines i and j. Fig. 11. Accumulation of residual strains with applied stress. Misfit stress can be obtained by fitting them with different values on fixed Ri. 3290 H. Mei / Composites Science and Technology 68 (2008) 3285–3292
H Mei/Composites Science and Technology 68(2008)3285-3292 corresponds extremely well with both experimental result of loops in order to compare difference of TRS state in different CMCs. et al. [14]. In the present C/SiC, the Sic matrix is in residual tensile stress-free"origin o basically approaches the zero point o of p 30.84 MPa as measured above and of 140 MPa reported by Camus Using the method described in Section 3.3, thethermal-resio down from the processing temperature to room temperature. If tic strain still observed in Fig. 12. The models expressed by eqs the composite is applied to a compressive stress that is just equal(10)and(12)also give the zero value for the trs of the tested to TRS of 136.71 MPa, these processing-induced matrix microcracks 2D SiC/SiC composite because the Sic fibers have the nearly same should close completely and the residual tensile stress in matrix CTE as the Sic matrix( thermal misfit stress is equal to zero) would disappear immediately (reduce to zero ). At this time, the zero The applied stresses at which the loop width is zero provide point 0 of the external applied stress would be translated to now initial estimates of the onset stress for matrix cracking. As shown thermal-residual-stress-free"origin O. Thus, the whole properties in Fig. 12, the first matrix cracking stress omc of the tested sic/Sic of t dramatically. Consequently, composite approximates to 150 MPa. As expected, this parameter the trs is a key factor for improvement of the composite property. property was approximatively promoted 100 MPa in contrast to the C/Sic (only 50 MPa as measured in Fig. 5 by AE monitoring ). 3.5. Theoretical prediction of TRS with ideal interfacial bond and non- Obviously, the processing-induced TRS has a significant influence cracked matnⅸ on the first matrix cracking stress. The greater the tRs in the composites, the less the first matrix cracking stress and the Consider a composite with ideal interf nd and without any poorer the whole properties of the composites. Normally the first matrix cracks associated with relief of RS from processing matrix cracking stress can be predicted by the classical ACK mod- temperature to room temperature, the axial residual stress in a el based on steady-state matrix crack and constant sliding stress t non-cracked matrix then can be classically estimated by [21]J ErVe (12) ∫6EvE2r (13 where am and af refer to the linear cte of the matrix and fiber pectively t, and to are the processing temperature and opera- where I m is the matrix fracture energy, r the fiber radius. Using the tion temperature Using the data listed in Table 2, the axial residual data listed in Table 2 and Eq(13), the first matrix cracking stress of tress in non-cracked matrix gives 282.06 MPa, which should be the the c/Sic and Sic Sic composites are 41. 25 MPa and 155.58 MPa theoretical maximum TRS in matrix prior to relief and much higher Suming the misfit stress a'=100 MPa for C/Sic and O MPa for matrix cracks and interface sliding. However, the stiffness Em of the agreement with above expermendlos al predictions exhibit good cracking and interface sliding oo results, validating the preceding analysis and then applicability of ur, which in turn causes decrease and partial relief of the trs. those methods to the present composite systems. omparatively, the"regression line intersection"method is rel ative simple and rapid to obtain TRS and easy to identify the com- 4. Conclusions pressive or tensile state of TRs in the composites for engineering applications, whereas the analytical formula and theoretical model are either cumbersome with too many unknown parameters or ite systems stresses in two Sic-ceramic matrix compos d with carbon fiber(C/Sic)and silicon car impractical with too ideal assumption. Fortunately, the model of bide fiber ere completely investigated. Thermal Eq(12)can be further improved by modifying the matrix stiffness residual stress of.84+34.53 MPa in the 2D C/Sic was deter to reflect matrix cracking and interface debonding. mined by solving the geometric intersection points of the regres- 3.6. Comparison of Trs with a SiC/SiC system sion lines of consecutive unloading/reloading hysteresis loops. This experimentally measured result corresponded extremely curves of 2D Hi-Nicalon/SiC composites within several hysteresis and was severely less than the theoretical maximum TRS of 282.06 MPa in the composites with ideal interface bond and non-cracked matrix. In contrast to the C/Sic, the sic/Sic appar ently yielded a negligible trs(close to zero value)because the Sic fibers have the nearly same Cte as the SiC matrix that cause thermal misfit stress was equal to zero. Compared with the al lytical formula and theoretical models, the"regression line inter section"method is relatively simple and rapid to obtain tRS and easy to identify the compressive or tensile state of trs in the composites for engineering applications. The thermal residual D Hi-Nicalon/Sic stress has a significant influence on improvement in the proper ties of the composites. The less the thermal residual stress in the 0 composites, the greater the first matrix cracking stress and more the whole properties of the composite can be promoted -0.160.000.160.320.480.64 Acknowledgements Strain(% Financial support for this work was provided by the Natural Fig. 12. Example of unloading-reloading curves of 2D Hi-Nicalon/SiC composi Science Foundation of China(Contract No. 90405015)and the National Young Elitists Foundation(Contract No. 50425208 ). The
corresponds extremely well with both experimental result of 130.84 MPa as measured above and of 140 MPa reported by Camus et al. [14]. In the present C/SiC, the SiC matrix is in residual tensile stress leading to opening microcracks in the materials once cooled down from the processing temperature to room temperature. If the composite is applied to a compressive stress that is just equal to TRS of 136.71 MPa, these processing-induced matrix microcracks should close completely and the residual tensile stress in matrix would disappear immediately (reduce to zero). At this time, the zero point O of the external applied stress would be translated to now ‘‘thermal-residual-stress-free” origin O’. Thus, the whole properties of the composite would be promoted dramatically. Consequently, the TRS is a key factor for improvement of the composite property. 3.5. Theoretical prediction of TRS with ideal interfacial bond and noncracked matrix Consider a composite with ideal interface bond and without any matrix cracks associated with relief of the TRS from processing temperature to room temperature, the axial residual stress in a non-cracked matrix then can be classically estimated by rm r ¼ Em kEfVf kEfVf þ EmVm ðaf amÞðTo TpÞ ð12Þ where am and af refer to the linear CTE of the matrix and fiber, respectively. Tp and To are the processing temperature and operation temperature. Using the data listed in Table 2, the axial residual stress in non-cracked matrix gives 282.06 MPa, which should be the theoretical maximum TRS in matrix prior to relief and much higher than the above experimental and calculational results that consider matrix cracks and interface sliding. However, the stiffness Em of the matrix decreases once the matrix cracking and interface sliding occur, which in turn causes decrease and partial relief of the TRS. Comparatively, the ‘‘regression line intersection” method is relative simple and rapid to obtain TRS and easy to identify the compressive or tensile state of TRS in the composites for engineering applications, whereas the analytical formula and theoretical model are either cumbersome with too many unknown parameters or impractical with too ideal assumption. Fortunately, the model of Eq. (12) can be further improved by modifying the matrix stiffness to reflect matrix cracking and interface debonding. 3.6. Comparison of TRS with a SiC/SiC system Fig. 12 presents a typical example of unloading–reloading curves of 2D Hi-Nicalon/SiC composites within several hysteresis loops in order to compare difference of TRS state in different CMCs. Using the method described in Section 3.3, the ‘‘thermal-residualstress-free” origin O0 basically approaches the zero point O of the external applied stress although there is a little irreversible inelastic strain still observed in Fig. 12. The models expressed by Eqs. (10) and (12) also give the zero value for the TRS of the tested 2D SiC/SiC composite because the SiC fibers have the nearly same CTE as the SiC matrix (thermal misfit stress is equal to zero). The applied stresses at which the loop width is zero provide initial estimates of the onset stress for matrix cracking. As shown in Fig. 12, the first matrix cracking stress rmc of the tested SiC/SiC composite approximates to 150 MPa. As expected, this parameter property was approximatively promoted 100 MPa in contrast to the C/SiC (only 50 MPa as measured in Fig. 5 by AE monitoring). Obviously, the processing-induced TRS has a significant influence on the first matrix cracking stress. The greater the TRS in the composites, the less the first matrix cracking stress and the poorer the whole properties of the composites. Normally, the first matrix cracking stress can be predicted by the classical ACK model based on steady-state matrix crack and constant sliding stress s [21], rmc ¼ 6EfV2 f sE2 Cm ð1 VfÞRE2 m ( )1=3 rT ð13Þ where Cm is the matrix fracture energy, R the fiber radius. Using the data listed in Table 2 and Eq. (13), the first matrix cracking stress of the C/SiC and SiC/SiC composites are 41.25 MPa and 155.58 MPa (Assuming the misfit stress rT = 100 MPa for C/SiC and 0 MPa for SiC/SiC), respectively. These theoretical predictions exhibit good agreement with above experimental observations and calculational results, validating the preceding analysis and then applicability of those methods to the present composite systems. 4. Conclusions Thermal residual stresses in two SiC-ceramic matrix composite systems reinforced with carbon fiber (C/SiC) and silicon carbide fiber (SiC/SiC) were completely investigated. Thermal residual stress of 130.84 ± 34.53 MPa in the 2D C/SiC was determined by solving the geometric intersection points of the regression lines of consecutive unloading/reloading hysteresis loops. This experimentally measured result corresponded extremely well with the analytically calculated TRS of 136.71 MPa in the C/SiC material containing matrix cracking and interface sliding, and was severely less than the theoretical maximum TRS of 282.06 MPa in the composites with ideal interface bond and non-cracked matrix. In contrast to the C/SiC, the SiC/SiC apparently yielded a negligible TRS (close to zero value) because the SiC fibers have the nearly same CTE as the SiC matrix that cause thermal misfit stress was equal to zero. Compared with the analytical formula and theoretical models, the ‘‘regression line intersection” method is relatively simple and rapid to obtain TRS and easy to identify the compressive or tensile state of TRS in the composites for engineering applications. The thermal residual stress has a significant influence on improvement in the properties of the composites. The less the thermal residual stress in the composites, the greater the first matrix cracking stress and the more the whole properties of the composite can be promoted. Acknowledgements Financial support for this work was provided by the Natural Science Foundation of China (Contract No. 90405015) and the National Young Elitists Foundation (Contract No. 50425208). The Fig. 12. Example of unloading–reloading curves of 2D Hi-Nicalon/SiC composites within several hysteresis loops. H. Mei / Composites Science and Technology 68 (2008) 3285–3292 3291
H Mei/Composites Science and Technology 68(2008)3285-3292 authors also gratefully acknowledge the program for Changjiang 110] Vagaggini E, Domergue JM, Evans AG. Relationships Scholars and Innovative Research Team in University(PCSirT) ips c eawrencomysoesits References nts and the constituent properties of ceramic matrix composites: tudy on unidirectional materials. J 995;78(10):2721-31 [2] Naslain R. Lamon J. Pailler R, Bourrat X, Guette A, Langlais F. Micro/ [13 Morscher GN. Stress-dependent matrix cracking in 2D woven SiC-fiber infiltrated Sic matrix composites. Comp Sci Technol [3] Mei H, Cheng LF, Zhang LT, Xu YD. Modeling the effects of thermal and [14] Camus G, Guillaumat L, Baste S Development of damage in a 2D woven C/Sic mechanical load cycling on a C/SiC composite in oxygen/ argon mixtures. composite under mechanical loading: I mechanical characterization. Comp Sci 3-72. rmal residual stresses in ceramic matrix composites [15] Wang M, Laird C Characterization of microstructure and tensile behavior of a model and finite element analysis. Acta Metall Mater Mater1996:44(4):1371-87 95:43(6):2241-53 [16 Cady C, Heredia properties of several In JL Ther <perimental results for model materials. Acta [17] Wang M, Laird C. Tension-tension fatigue of a cross-woven C/SiC composite Mater Sci Eng 1997: A230: 171-82. [7] Broda M, Pyzalla A, Reimers w. X-ray analysis of residual stresses in C/Sic [19] Hucthinson JW. Jensen H. Models of fiber de g and pull-out mposites Appl Composite Mater 1999: 6: 51-66. 8] Steen M. Tensile mastercurve of ceramic matrix composites: significance and [20] Wang yo. Zhang Lr. cheng LF. Mei h. mia jo. Characterization of tensile 0 ons for modeling. Mat1912024、 fabricated by chemical vapor infiltration. Mater Sci Eng A 2007. doi:10 10161 red and fibre-reinforced composites: Proceedings Research Workshop, Kiev, Ukraine: Netherlands: 2-6 Science and technology press, Teddington, UK, 1971. p 15-8
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