Composites Science and Technology 58(1998)409-418 PIl:S0266-3538(97)00139-5 0266353898s1900 CARBON-FIBER-REINFORCED YMAS GLASS-CERAMIC. MATRIX COMPOSITES-IV THERMAL RESIDUAL STRESSES AND FIBER/MATRIX INTERFACES Valerie Bianchi. a Paul Goursat* erik menessier @LMCTS, ESA CNRS 6015, Faculte des sciences, 123 avenue Albert Thomas, 87060 Limoges Cedex, france bCeramigues et Composites, BP 7, 65460 Bazet, france ( Received 21 November 1996; revised 14 July 1997; accepted 17 July 1997) Abstract mation of an interphase which is likely to control the matrix reinforced with continuous carbon fiber uted by hot-pressing exhibit different fructure Se apri deflection and propagation of cracks and the frictional sliding of fibers. Physico-chemical reactions can also lead to wider interfacial separation and changes in frac- according to the sintering thermal cycle. The thermal ture strength The purpose of this paper is to determine the role mismatch in coefficients of thermal expansion and the played by physico-chemical reactions and thermal thermomechanical characteristics of both fibers and residual stresses in determining the strength of the fihe matrix. An ultrasonic technique is used to determine the matrix interface and to predict the composite behavior. An microcracking in the matrix. The infuence of the materials is to follow changes in Young s modulus with ature. First, an ultrasonic technique has beer between the fibers and the matrix on the nature and the used to determine the temperatures at which thermal strength of the fiber/matrix interface is discussed. -C 1998 residual stresses are higher than the matrix strength and Elsevier Science Lid. All rights reserved nduce microcracking in the matrix, which is expected to occur on cooling during the fabrication of composites Keywords: A. ccramic-matrix composites, A. carbon Sccond, thermal residual stresses have bccn cstimat fibres, B. fibre/matrix bond, C. residual stress, D. non- by a model which takes into account the thermoelastic destructive testing anisotropy of carbon fibers. To achieve this goal, the coefficients of thermal expansion(CTE) of carbon fibers were calculated from those of the matrices and the 1 INTRODUCTION composites Thermal conditions in the fabrication process of cat bon- fiber-reinforced YMAS-matrix composites have 2 EXPERIMENTAL PROCEDURES been shown to play a dominant role in the fracture behavior of these composites, which depends strongly 2.1 Young s modulus on the nature and strength of the interfacial fiber matrix The knowledge of material clastic constants allows the bond. 2 The interface must be weak enough to allow calculation of the elastic moduli, which express the energy dissipation by frictional sliding of the fibers in macroscopic proportionality between stress and strain the matrix blocks. The strength of the interface is cor- Elastic constants, which are related to interatomic related with the thermomechanical properties of both potential and have an intrinsic character, can allow the constituents and to the physico-chemical reactions monitoring of certain structural changes in materials, between them. Indeed, residual stresses, caused by the such as glass crystallization and phase transitions thermal expansion mismatch between the fibers and the Moreover, the Youngs modulus of a heterogeneous matrix, can lead to cohesion or debonding of the inter- material is related to the volume fraction and the mor face, which raises or lowers the ultimate strength and phology of each constituent, to the porosity fraction fluences the fracture type. Physico-chemical reactions and geometry, 6 to the cracking direction of the material between the fibers and the matrix can induce the for- and its volume fraction Measurement of the propagation time of an ultra- *To whom correspondence should be addressed sonic wave in a material offers a means of evaluating the
ELSEVIER Composites Science and Technology 58 (1998) 409418 9 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain PII: SO266-3538(97)00139-5 0266-3538/98 $19.00 CARBON-FIBER-REINFORCED YMAS GLASS-CERAMICMATRIX COMPOSITES-IV. THERMAL RESIDUAL STRESSES AND FIBER/MATRIX INTERFACES Valirie Bianchi,” Paul GoursaF* & Erik MCnessierb “LMCTS, ESA CNRS 6015, Faculte des Sciences, 123 avenue Albert Thomas, 87060 Limoges Cedex, France bCPramiques et Composites, BP 7, 65460 Bazet, France (Received 21 November 1996; revised 14 July 1997; accepted 17 July 1997) Abstract Unidirectional composites consisting of a glass-ceramic matrix reinforced with continuous carbon fibers, fabricated by hot-pressing, exhibit d@erent fracture behavior according to the sintering thermal cycle. The thermal residual stresses in composites are determined from the mismatch in coeficients of thermal expansion and the thermomechanical characteristics of both fibers and matrix. An ultrasonic technique is used to determine the temperature at which, on cooling, residual stresses induce microcracking in the matrix. The influence of the mechanical stresses and physico-chemical reactions between the fibers and the matrix on the nature and the strength of thefiberlmatrix interface is discussed. -0 1998 Elsevier Science Ltd. All rights reserved Keywords: A. ceramic-matrix composites, A. carbon fibres, B. fibre/matrix bond, C. residual stress, D. nondestructive testing 1 INTRODUCTION Thermal conditions in the fabrication process of carbon-fiber-reinforced YMAS-matrix composites have been shown to play a dominant role in the fracture behavior of these composites,’ which depends strongly on the nature and strength of the interfacial fiber/matrix bond.2 The interface must be weak enough to allow energy dissipation by frictional sliding of the fibers in the matrix blocks. The strength of the interface is correlated with the thermomechanical properties of both constituents and to the physico-chemical reactions between them. Indeed, residual stresses, caused by the thermal expansion mismatch between the fibers and the matrix, can lead to cohesion or debonding of the interface, which raises or lowers the ultimate strength and influences the fracture type. Physico-chemical reactions between the fibers and the matrix can induce the for- *To whom correspondence should be addressed. 409 mation of an interphase which is likely to control the deflection and propagation of cracks and the frictional sliding of fibers. Physico-chemical reactions can also lead to wider interfacial separation and changes in fracture strength. The purpose of this paper is to determine the roles played by physico-chemical reactions and thermal residual stresses in determining the strength of the fiber/ matrix interface and to predict the composite behavior. An appropriate way to detect structural changes in materials is to follow changes in Young’s modulus with temperature.3 First, an ultrasonic technique has been used to determine the temperatures at which thermal residual stresses are higher than the matrix strength and induce microcracking in the matrix, which is expected to occur on cooling during the fabrication of composites.’ Second, thermal residual stresses have been estimated by a model which takes into account the thermoelastic anisotropy of carbon fibers. To achieve this goal, the coefficients of thermal expansion (CTE) of carbon fibers were calculated from those of the matrices and the composites. 2 EXPERIMENTAL PROCEDURES 2.1 Young’s modulus The knowledge of material elastic constants allows the calculation of the elastic moduli, which express the macroscopic proportionality between stress and strain. Elastic constants, which are related to interatomic potential and have an intrinsic character, can allow the monitoring of certain structural changes in materials, such as glass crystallization and phase transitions.4 Moreover, the Young’s modulus of a heterogeneous material is related to the volume fraction and the morphology of each constituent,’ to the porosity fraction and geometry,6 to the cracking direction of the material and its volume fraction.’ Measurement of the propagation time of an ultrasonic wave in a material offers a means of evaluating the
410 V, Bianchi et al material elastic properties. This technique is described aI fiber transverse CTE in a previous papct The composites were treated in an argon gas flow uH fiber major Poissons coefficient, vertical and tubular electric furnace which could be matrix Poissons coefficient heated to 1550C, with the temperature being controlled E fiber longitudinal Youngs modulus near to the sample by a Pt/Pt-Rh 10% thermocouple matrix Youngs modulus Linear heating and cooling rates of 5. minwere Vm- Vr matrix and fiber volume fractions used. The furnace pressure can be controlled from 10-2 to 1000 hPa. The sample temperature and the transdu Measurements of af, af and am with a vertical dilat cer signals were recorded simultaneously by a computer. ometer (Setaram TMA 92), in a neutral atmosphere. Because of errors in the material density(20.5%), the with linear heating and cooling rates of 3 up to from the phase displacement owing to coupling with the For this, the experimental curves of relative mipid or sample length(20-1%), the propagation time resulting 1000 C, should therefore allow calculation of aa wave guide(sl.5%)and the changes in density and versus temperature were approximated by a third-order CtE which were taken into account, the uncertainty in the Youngs modulus value is *4%. Several parameters can affect the accuracy of the impulse propagation. such △L =A+Br+C72+D73 as the ratio between the sizes of the heterogeneities and ple dimensions. Techniques based on a temporal signal At a time t,(AL/Lo) and(AL/Lo) can be differ- analysis can then become imprecise. The implementa- entiated to obtain af(T)and af(n), and thus ai(n)and tion of a owever allowed an af(T). a(T)and a' (n) can then be integrated to obtain improvement in the measurement of propagation delays (△L/Lo)and(△L/ Lo)i backed with the following by intercorrelation techniques. boundary conditions. 2.2 Coefficients of thermal expansion (△LLo)(T=20°C)=0 If the fiber/matrix bonding is strong and the poisson ratios of both fibers and matrix are equal, Schapery shows that the rule of mixtures can be applied to the (△L/Lo{(=1000eas case of the cte of a unidirectional. continuous-fibe (△L/Lo):(7=1000° C)Td composite a=“m2mm+E 2. 3 Determination of residual thermal stresses Em Vm+EVr Because of the high ratio of fiber length to diameter in continuous-fiber-reinforced materials, these composites When the Poisson s ratios are different, which is the can be represented by two semi- infinite concentric usual case, the author shows that eqn(1)is still a good cylinders with radii a and b( Fig. 1). 1.2 From this approximation. representation of a composite, Hsueh and Becher have For isotropic fibers, the transverse CTE of the com- developed a model -itself a simplified version of the posite is model previously proposed by Mikata and Toya4 allowing the determination of the thermal stresses ;, oI af=(1+Vm )am Im +(+vidaVr-(vm Vm+v vr) d om in composites and their influence on the expansion (2) For Kevlar- fiber composites, Rojstaczer et al. have considered the anisotropic thermoelasticity of the fiber (1+Vm)Vm +a Vr+vir Vr-(vm Vm +vl vr)ai The following nomenclature has been used(the matrix is taken to be isotropic composite longitudinal cte. omposite transverse CtE, fiber longitudinal CTE Fig. I, Schematic illustration of the composite cylinder model
410 I/. Biunchi et al material elastic properties. This technique is described in a previous paper.3 The composites were treated in an argon gas flow in a vertical and tubular electric furnace which could be heated to 155O”C, with the temperature being controlled near to the sample by a Pt/Pt-Rh 10% thermocouple. Linear heating and cooling rates of 5”Cmin’ were used. The furnace pressure can be controlled from lop2 to 1000 hPa. The sample temperature and the transducer signals were recorded simultaneously by a computer. Because of errors in the material density (~0.5%) the sample length (Z O.l%), the propagation time resulting from the phase displacement owing to coupling with the wave guide (Z 1.5%) and the changes in density and CTE which were taken into account, the uncertainty in the Young’s modulus value is * 4%. Several parameters can affect the accuracy of the impulse propagation, such as the ratio between the sizes of the heterogeneities and the ultrasonic wavelength, and insufficiently large sample dimensions. Techniques based on a temporal signal analysis can then become imprecise. The implementation of a frequency analysis, however, allowed an improvement in the measurement of propagation delays by intercorrelation techniques.x 2.2 Coefficients of thermal expansion If the fiber/matrix bonding is strong and the Poisson’s ratios of both fibers and matrix are equal, Schapery” shows that the rule of mixtures can be applied to the case of the CTE of a unidirectional, continuous-fiber composite: When the Poisson’s ratios are different, which is the usual case, the author shows that eqn (1) is still a good approximation. For isotropic fibers, the transverse CTE of the composite is: For Kevlar-fiber composites, Rojstaczer et ~11.‘~’ have considered the anisotropic thermoelasticity of the fiber: The following nomenclature has been used (the matrix is taken to be isotropic): CY y composite longitudinal CTE, o; composite transverse CTE, or fiber longitudinal CTE, I a( fiber transverse CTE, om matrix CTE. ‘& fiber major Poisson’s coefficient, 2 matrix Poisson’s coefficient, EL fiber longitudinal Young’s modulus, matrix Young’s modulus, V,. V’ matrix and fiber volume fractions. Measurements of a:, cry and CX, with a vertical dilatometer (Setaram TMA 92) in a neutral atmosphere, with linear heating and cooling rates of 3°C min ’ up to lOOO”C, should therefore allow calculation of of and of. For this, the experimental curves of relative expansion versus temperature were approximated by a third-order polynomial: AL -=A+BT+CT2$DT’ &I (4) At a time t, (AL/Lo): and (AL/Lo): can be differentiated to obtain c+ 7’) and $( 7’), and thus of( 7) and o:(7). c1f(7’) and of(7’) can then be integrated to obtain (AL/Lo); and (AL/Lo); backed with the following boundary conditions: (Af&)f;,( T = 20°C) = 0 (5) (AW&(T= lOOO”C),,,,,,,,, = WILdftV = lOOO”%,,,,,,,, (6) 2.3 Determination of residual thermal stresses Because of the high ratio of fiber length to diameter in continuous-fiber-reinforced materials, these composites can be represented by two semi-infinite concentric cylinders with radii a and h (Fig. l).“,‘2 From this representation of a composite, Hsueh and Becher” have developed a model&itself a simplified version of the model previously proposed by Mikata and Toya14-- allowing the determination of the thermal stresses ci, af and cm in composites and their influence on the expansion 7 Fig. I. Schematic illustration of the composite cylinder model
Carbon fiber-reinforced yMas glass-ceramic-matrix composites--IV 411 behavior, where a; is the interfacial radial stress and 3 RESULTS and gm are thc axial strcsscs in the fibcr and the matrix The authors considered the case of isotropic fibers. In 3.1 fracture behavior of the composites the present work, the model has therefore been extended Pitch-based and PAN-based carbon-fiber-reinforced for the case of a composite without an interphase, to YMAS-matrix composites were hot-pressed in the 950- take into account the thermoelastic anisotropy of the 1250C temperature range which had been previously carbon fibers. For polar coordinates (r, 0, z), the stresses defined from the microstructural study of the matrix. I6 in the fiber, f and of, are equal to the interfacial stress, Several hot-pressing conditions were applied to the pre pregs in order to determine the most suitable thermal cycle for the highest bending fracture strength. Table 1 o=o=0 7) summarizes the nomenclature used and shows the main results for a fiber volume fraction of 0. 35. 1.2 When the temperature changes, strains are expressed by For P25 carbon-fiber composites, the ultimate bend two components, the elastic component and a second ing strength is about 440 MPa and the fracture is alway hich represents thermal free strains. 5 controlled with fiber extraction lengths of about 100 um The strains in the fiber are then written as except for the composites P10 and Pll which exhibit fiber debondings I mm in length. This change agrees Er=a AT+/Ef-(vo! /E! +ve 0 /E)(8) with that of the distance between microcracks and sug- El=aAT+o,/Ef-vrgoi/Ef+vfo /E! )(9) In the case of T400H carbon-fiber composites, the mechanical behavior is modified for each sintering con aAT+o/E-(v0./Ef+Uoi/)(10) dition, the ultimate bending strength varying between 300 and 1100 MPa and the distance between micro- reasons ure=vr, cracks from 95 to 550 um. Composite Tl, hot-pressed Ef= Ef, uf /E=o/ef and af Therefore eqns when the glass is insufficiently viscous, presents a non- (8)(10)can be simplified brittle fracture owing to the casy extraction of non- In the same way, and knowing that I5 impregnated bundles of fibers, the other fibers breaking with no pull-out. For the other composites, the fiber oa2(b2-r2) extractions are about 100 um in length and the fracture is brittle, except for the composite t7 in which some bundles of fibers are pulled out in the delamination planes (b2+r2) 3.2 Changes in Young s modulus with temperature Changes in Youngs modulus with temperature were we can write the strains in the matrix, em, eg and em followed on P25 and T400H carbon-fiber-reinforced Because of the boundary conditions: e=Eg when YMAS-matrix composites in order to determine the r=a, er=em and 2F:=0+m=[/(r-1)Jo the temperature at which microcracks appear in the matrix stresses o, d, and om are writter On cooling after hot pressing, stresses induced by the thermal expansion mismatch between the fibers and o,=[(a-s)am +sa -! ] AT/qr-ps) (11) the matrix vary with the maximum temperature used for fabrication, since the stresses of, om and o, depend = ro+ T/( account the temperature parameter, the composites hot a=[vr/(r-d)la (13) pressed at low temperature (TI and P3), such that the natrix is kept vitreous, were submitted to different hermal cycles during which their Youngs modulus with was recorded. The first thermal cycle was intended to allow observation of variations in the Young's modulus P=(1-v)/Ef 4 Vm/Em+(1/Em).(1+ vr)(1-vr) on cooling when the matrix is vitreous, whcrcas the (14) second thermal cycle allowed these variations to be observed when the matrix has crystallized(Al2O3+M q=m/Em+(u3,/E!)·(1-v)/v(15) Al2O 4+ cordierite+a and B Y2 Si2O,). 16 The exact maximum temperature to be applied during the youngs r=2v/(-1)·w/Em-2u E(16) modulus measurement to allow the microcracks close up while keeping the matrix vitreous was deter- mined from preliminary tests on the Youngs modulus 1)/(vE)-1/Em
Carbon-jiber-reinforced YMAS glass-ceramic-matrix composites-IV 411 behavior, where oi is the interfacial radial stress and of and a!” are the axial stresses in the fiber and the matrix. The authors considered the case of isotropic fibers. In the present work, the model has therefore been extended for the case of a composite without an interphase, to take into account the thermoelastic anisotropy of the carbon fibers. For polar coordinates (rJ,z), the stresses in the fiber, r~f and ci, are equal to the interfacial stress, fYi:15 c7,F = 0; = rJj (7) When the temperature changes, strains are expressed by two components, the elastic component and a second which represents thermal free strainsI The strains in the fiber are then written as: EL = CYLAT + ai/Ef, - (VS,ai/G + &a,f/<) (9) Es = a!fAT+ ai/e - (&Di/Ef, + Vf:ci/g) (10) For symmetry reasons, v;, = vFZ, vi0 = &, vf, = vir, ,$ = .I$, vg/e = vf,/l$ and af = I$. Therefore eqns (8)-( 10) can be simplified. In the same way, and knowing that:15 0; = a2(b2 - r*) r2(b2 _ a2) Oi and 0; = - a2 (b2 + r’) rz(b2 _ a2) ai we can write the strains in the matrix, ET, EZ; and E;. Because of the boundary conditions: E: = E: when r=a 3 EL = ~1f and cFZ = 0 =+- a: =[Vfi(Vf-l)]af, the stresses oi, a: and c,” are written: ai = [(q - s)% + SCY~ - qa:] . A T/(qr - PS) 0: = [(r -p)cum - r(YF + pat] . A T/(qr - ps) of = [Vf/(Vf - w; with: P = (1 - &)IEE + &n/E, + (l/E,) . (1 + Vf)/(l 4 = hnl& + (4,/q . (1 - Vf)/Vf r = 2Vf/(Vf - 1) . v,/E, - 2v~,/.!$ .s = (Vf - l)/(V&) - l/E,,, (11) (12) (13) Vf) (14) (15) (16) (17) 3 RESULTS 3.1 Fracture behavior of the composites Pitch-based and PAN-based carbon-fiber-reinforced YMAS-matrix composites were hot-pressed in the 950- 1250°C temperature range which had been previously defined from the microstructural study of the matrix.‘,‘6 Several hot-pressing conditions were applied to the prepregs in order to determine the most suitable thermal cycle for the highest bending fracture strength.’ Table 1 summarizes the nomenclature used and shows the main results for a fiber volume fraction of 0.35.‘*2 For P25 carbon-fiber composites, the ultimate bending strength is about 440 MPa and the fracture is always controlled with fiber extraction lengths of about 100 pm, except for the composites PlO and Pll which exhibit fiber debondings 1 mm in length. This change agrees with that of the distance between microcracks and suggests the weakening of the fiber/matrix interface. In the case of T400H carbon-fiber composites, the mechanical behavior is modified for each sintering condition, the ultimate bending strength varying between 300 and 1 lOOMPa and the distance between microcracks from 95 to 550 pm. Composite Tl, hot-pressed when the glass is insufficiently viscous, presents a nonbrittle fracture owing to the easy extraction of nonimpregnated bundles of fibers, the other fibers breaking with no pull-out. For the other composites, the fiber extractions are about 100 pm in length and the fracture is brittle, except for the composite T7 in which some bundles of fibers are pulled out in the delamination planes. 3.2 Changes in Young’s modulus with temperature Changes in Young’s modulus with temperature were followed on P25 and T400H carbon-fiber-reinforced YMAS-matrix composites in order to determine the temperature at which microcracks appear in the matrix. On cooling after hot-pressing, stresses induced by the thermal expansion mismatch between the fibers and the matrix vary with the maximum temperature used for fabrication, since the stresses uf, brn and bi depend on the temperature variation.’ In order to take into account the temperature parameter, the composites hotpressed at low temperature (Tl and P3), such that the matrix is kept vitreous, were submitted to different thermal cycles during which their Young’s modulus was recorded. The first thermal cycle was intended to allow observation of variations in the Young’s modulus on cooling when the matrix is vitreous, whereas the second thermal cycle allowed these variations to be observed when the matrix has crystallized (A1203 + MgA1204+ cordierite + c( and p Y2Si207).“‘6 The exact maximum temperature to be applied during the Young’s modulus measurement to allow the microcracks to close up while keeping the matrix vitreous was determined from preliminary tests on the Young’s modulus equipment
412 V. Bianchi et al Table 1. Main characteristics of P25/YMAS and T400H/YMAS composites, interfacial debonding(od)and shear(r)stresses Ref. Fiber Densification Crystallization Crack spacing fracture Fracture nterfacial Interfacial shear conditions(C/h) conditions(C/h) strength(MPa) debonding stress t(M stress, od(MPa) 950 245⊥65 440土60 P3P25 P4P25 105005 PS P25 1050/1 455±7 178±48 050/1.5 P7P25 1050/6 P8P25 l100/ P9P25 1150f P10P25 10500.5 12500.5 士180 Pl1 P25 10501 1250/15 ±270 59±33 1-0±0-7 TI T400H 950/l 95±25 300士 controlled 1322±258 108±337 T2 T400H 520±70 lcss controlled I137±167 363±8-0 T3 T400H 190±35 670±35 brittle T4T400H100/1 330±85 770±10 TS T400H 450±1201100±30 769±285 167±8-8 T6 400H 1050/1 1250/1.5 550±l50570±35 ess brittle 846+162 204±111 apitch-based carbon fibers from thorne PPAN-based carbon fibers from toray (a)and(b) present the relative variation of Indccd, since the coefficient of thermal expansion of the the apparent longitudinal Youngs modulus of a P25/ glass is slightly higher than that of the ceramic matrix, YMAS composite. During the heat treatment, thethe thermal stresses induced by this thermal expansion modulus decreases linearly, This regular and reversible mismatch are greater for a smaller temperature variation evolution is observed for the major part of the materi Is.fRom 860 C, the softening of the glass allows 3. 3 Coefficients of thermal expansion of the carbon matrix microcracks to close and explains the apparent fibers increase of the modulus. As the temperature is increased In order to evaluate the residual thermal stresses in the again [Fig. 2(b)], it is the crystallization of the glass composites from the model that is developed above, the which causes the second rise of the Young,s modulus. coefficients of thermal expansion of the fibers must be The temperature was maintained for I h at 1050C to determined The CTEs of the matrix' and the compo- reproduce the sintering therinal cycle of the coinposite, sites were measured in a vertical dilatometer(Set but the growth of crystals is observed to be a slow pro- TMA 92), under a flow of argon, with a linear heating cess compared with the crystallization of the glass On and cooling rate of 3 C min- and were fitted with cooling of the crystallized composite [Fig. 2(b)] the polynomial laws. Two identical thermal cycles were modulus is stable until a temperature of 625C, after carried out successively in order to verify the accuracy which it decreases rapidly, this temperature seemingly of the measurements corresponding to the onset of microcracking. The end of igure 4(a)and(b) present the relative expansion the curve is drawn as a dotted line: the progressive curves for the composites P5 and T3(crystallized matri decohesion between the sample and the wave guide 000c and show the differenc cannot be avoided. For the vitreous composite existing between the longitudinal and transverse CtEs cracks are closed and the glass becomes rigid again. a(5.0x10 6C and a,=10.4x10Cn values are [ Fig. 2(a)), the modulus increases on cooling: micro For the range 50 to 1000C, the m From 700 C, the modulus decrease suggests the begin Because of the presence of matrix microcracks in the ning of microcracking composites, on heating, the measurement of the long The same phenomena are observed with T400H/ itudinal CtE of the composites is likely to correspond YMAS composites [Fig. 3(a) and (b)]. A variation of to the longitudinal CTE of the fibers. When the sinter- about 30C is noted and can be attributed to variations ing temperature(1050 C) is reached, the microcracks in the fabrication of the matrix On cooling, the mod- should be a priori closed up, so that, on cooling down to ulus is observed to be stable until 300C for the crystal- the temperature at which thermal stresses induce lized composite and until 575@C for the glassy sample. microcracking in the matrix, the CTEs of the fibers can For the P25 and T400H composites, microcracking be calculated from those of the matrix and the compo appears in the glass matrix at higher temperature. sites. This suggests that, in this temperature range which
412 V. Bianchi et al. Table 1. Main characteristics of PZS/YMAS and T4OOH/YMAS composites,2 interfacial debonding (nd) and shear (t) stresses Ref. Fiber Densification Crystallization Crack spacing Fracture Fracture Interfacial lnterfacial shear conditions (“C/h) conditions (“C/h) (w) PI P25” 95oi I P2 P25 970/l P3 P25 lOOO/ 1 P4 P25 lO50/0~5 P5 P25 1050/l P6 P25 lO5Ojl lO5Ojl~S P7 P25 lO5Ojl 1050/S P8 P25 I loo/l P9 P25 1150/l PI0 P25 lO5OjO.5 125OjO.5 PI1 P25 1050/l 125Oil.5 Tl T400Hh T2 T400H T3 T400H T4 T400H T5 T400H T6 T400H T7 T400H 950/I 1 ooo/ I 1050/l 1100/1 ll5Ojl 12001 I 1050/l 1250/1.5 “Pitch-based carbon fibers from Thornel. ‘PAN-based carbon fibers from Torayca. 245 * 65 600& 180 lOOO*270 95*25 lOOi 190*35 33Oi85 450* 120 4ooZt 110 550* 150 Figure 2(a) and (b) present the relative variation of the apparent longitudinal Young’s modulus of a P25/ YMAS composite. During the heat treatment, the modulus decreases linearly. This regular and reversible evolution is observed for the major part of the materials.” From 860°C the softening of the glass allows matrix microcracks to close and explains the apparent increase of the modulus. As the temperature is increased again [Fig. 2(b)], it is the crystallization of the glass which causes the second rise of the Young’s modulus. The temperature was maintained for 1 h at 1050°C to reproduce the sintering thermal cycle of the composite, but the growth of crystals is observed to be a slow process compared with the crystallization of the glass. On cooling of the crystallized composite [Fig. 2(b)] the modulus is stable until a temperature of 625°C after which it decreases rapidly, this temperature seemingly corresponding to the onset of microcracking. The end of the curve is drawn as a dotted line; the progressive decohesion between the sample and the wave guide cannot be avoided. For the vitreous composite [Fig. 2(a)], the modulus increases on cooling: microcracks are closed and the glass becomes rigid again. From 700°C the modulus decrease suggests the beginning of microcracking. The same phenomena are observed with T400H/ YMAS composites [Fig. 3(a) and (b)]. A variation of about 30°C is noted and can be attributed to variations in the fabrication of the matrix. On cooling, the modulus is observed to be stable until 300°C for the crystallized composite and until 575°C for the glassy sample. For the P25 and T400H composites, microcracking appears in the glass matrix at higher temperature. strength (MPa) type debonding stress r (MPa) stress, od (MPa) (Push-in-test)’ 440 & 60 controlled 300*45 controlled 520 * 70 less controlled 670* 35 brittle 77oi 105 1100*300 760 * 65 570135 less brittle 455 f 73 17.814-8 59*33 I .o * 0.7 1322*258 108 * 33.7 11371167 36.3 Z!Z 8.0 769 f 285 16,7+8.8 846i 162 20.4 i- I 1. I Indeed, since the coefficient of thermal expansion of the glass is slightly higher than that of the ceramic matrix, the thermal stresses induced by this thermal expansion mismatch are greater for a smaller temperature variation. 3.3 Coefficients of thermal expansion of the carbon fibers In order to evaluate the residual thermal stresses in the composites from the model that is developed above, the coefficients of thermal expansion of the fibers must be determined. The CTEs of the matrix’ and the composites were measured in a vertical dilatometer (Setaram TMA 92) under a flow of argon, with a linear heating and cooling rate of 3”Cmin’ and were fitted with polynomial laws. Two identical thermal cycles were carried out successively in order to verify the accuracy of the measurements. Figure 4(a) and (b) present the relative expansion curves for the composites P5 and T3 (crystallized matrix composites) up to 1000°C and show the difference existing between the longitudinal and transverse CTEs. For the range 50 to lOOO”C, the mean values are c$ = 5.0x 10-6”C-’ and CX; = 10.4x 10-6”C-‘. Because of the presence of matrix microcracks in the composites, on heating, the measurement of the longitudinal CTE of the composites is likely to correspond to the longitudinal CTE of the fibers. When the sintering temperature (105O’C) is reached, the microcracks should be a priori closed up, so that, on cooling down to the temperature at which thermal stresses induce microcracking in the matrix, the CTEs of the fibers can be calculated from those of the matrix and the composites. This suggests that, in this temperature range which
Carbon-fiber-reinforced Ymas glass-cerc 413 00501o020300400507008090010 015 A200300400506070800 0010001100 Temperature(°C Temperature°C Fig. 2. Relative variation Fig. 3. Relative variation of the apparent longitudinal Youngs modulus(ultrasonic lue)in a P25-fiber-rein- Young's modulus (ultrasonic technique)in a T400H-fiber forced YMAS-matrix composit he matrix is kept vitr reinforced YMAS-matrix composite when the matrix is kept eous(a)and when the matrix is crystallized(b) vitreous(a)and when the matrix is crystallized(b) has been approximately determined by the ultrason be made owing to the lack of studies on these fibers. It technique, the CTEs of the fibers should be equivalent, can only be noted that the orders of magnitude and the whatever the conditions of calculation are shape of the relative expansion curves are close to the The elastic data used for the calculations are sum- results obtained for other fibers sometimes obtained marized in Table 2. The value for the Poisson's ratio vf with other techniques.21-23 Nevertheless, if our calcula of the P25 fiber, since no result exists in the literature tions had been carried out without considering that was based on other results obtained for pitch-based af=af, the results would have been different but still fibers, even though their textures are different.18-21 In credible, except at low temperature 24.25 the same way, the value for the T400H fiber was also chosen to equal 0.2, on the hasis of manufacturer's data 3. 4 Calculation of the thermal residual stresses and results obtained for T300 fiber, which has a texture The thermal residual stresses have been calculated for a similar to that of the T400H I fiber volume fraction of 0.35 in three cases The results of the calculations [eqns(1)and and (3) Ising the assumption that af=ai are shown in Fig. 5 1. on cooling from 800 to 20C for a vitreous matrix ind Table 3. a great difference is seen between the [composites equivalent to the composites P3 and longitudinal and transverse CTEs of the carbon fibers TI; Figs 6(a)and Fig. 71(a)] since, above 800C, as could be foreseen from their textures. No compar the dilatometric curve has shown that the stresses ison between our results and those of other authors can n still be relaxed: 24 Table 2. Elastic data for the matrix, and the p25 and T400H carbon fibers YMAS matrix T400H fiber En=157 GPa Poissons ratio m=0.29 =02
Carbon-jber-reinforced YMAS glass-ceramic-matrix composites-IV 413 ?(x1 400 500 600 700 800 Tempemlure (“C) Tempemture (“C) Temperature (“C) (b) Fig. 2. Relative variation of the apparent longitudinal Fig. 3. Relative variation of the apparent longitudinal Young’s modulus (ultrasonic technique) in a PZS-fiber-rein- Young’s modulus (ultrasonic technique) in a T400H-fiberforced YMAS-matrix composite when the matrix is kept vitr- reinforced YMAS-matrix composite when the matrix is kept eous (a) and when the matrix is crystallized (b). vitreous (a) and when the matrix is crystallized (b). has been approximately determined by the ultrasonic technique, the CTEs of the fibers should be equivalent, whatever the conditions of calculation are. The elastic data used for the calculations are summarized in Table 2. The value for the Poisson’s ratio uf, of the P25 fiber, since no result exists in the literature, was based on other results obtained for pitch-based fibers, even though their textures are different.18-*’ In the same way, the value for the T400H fiber was also chosen to equal 0.2, on the basis of manufacturer’s data and results obtained for T300 fiber, which has a texture similar to that of the T400H.’ The results of the calculations [eqns (1) and and (3)] using the assumption that of = of are shown in Fig. 5 and Table 3. A great difference is seen between the longitudinal and transverse CTEs of the carbon fibers, as could be foreseen from their textures.’ No comparison between our results and those of other authors can 0.3 0.25 0.2 Ip 0.15 s^ o-1 fk 0.05 0 -0.05 -0.1 Temperature (“C) (a) 03 - 0.25 -- (b) be made owing to the lack of studies on these fibers. It can only be noted that the orders of magnitude and the shape of the relative expansion curves are close to the results obtained for other fibers, sometimes obtained with other techniques. *i-*3 Nevertheless, if our calculations had been carried out without considering that of = c$, the results would have been different but still credible, except at low temperature.24*25 3.4 Calculation of the thermal residual stresses The thermal residual stresses have been calculated for a fiber volume fraction of 0.35 in three cases: 1. on cooling from 800 to 20°C for a vitreous matrix [composites equivalent to the composites P3 and Tl; Figs 6(a) and Fig. 71(a)] since, above 800°C the dilatometric curve has shown that the stresses can still be relaxed;24 Table 2. Elastic data for the matrix, and the P25 and T4OOH carbon fibers Young’s modulus Poisson’s ratio YMAS matrix E,= 157GPa u,=O.29 P25 fiber T400H fiber 2: ;$$$ $::;;2: &=0.2 vf, = 0.2n uf, = 0.4 4, = 0.4