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/EmCarbon-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 pre￾pregs 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 bend￾ing 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 sug￾gests the weakening of the fiber/matrix interface. In the case of T400H carbon-fiber composites, the mechanical behavior is modified for each sintering con￾dition, the ultimate bending strength varying between 300 and 1 lOOMPa and the distance between micro￾cracks from 95 to 550 pm. Composite Tl, hot-pressed when the glass is insufficiently viscous, presents a non￾brittle fracture owing to the easy extraction of non￾impregnated 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 hot￾pressed 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 + M￾gA1204+ 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 deter￾mined from preliminary tests on the Young’s modulus equipment