S.T. Mileiko Current Opinion in Solid State and Materials Science 9(2005)219-229 the interface strength and equal to that of the matrix. Note that Eq (6) was obtained assuming steady state creep fol- lowed the ending of the fibre breakage process on the tran- sitional stage of creep. It occurs that the larger the value of the shorter is the fibre length in the steady-state condition and, hence, the larger is the stress carried by the fibre For regime Cr, creep-rate/stress dependence is obvious: 0=a Ve+o · Alumina- YAG where nf, af, and n are constants in a power low for the fibre Mullite o- Nextel 720 1000110012001300140015001600 Regime br-Cr is a combination of the two regimes just Temperature/C described Note that while evaluating creep characteristics of fibres Fig. 8. Creep polycrystalline mt ICM-fibres in comparison with a Section 2.2.2, Eq. (7)was used. For metal-matrix compos- based commercial fibre presented in Ref [17] ites, either regime E or regime Br-NCr is characteristic, the latter one being of most interest. Hence, normally Eq (6) et the creep law of the matrix will be as given by Eq. used to analyse experimental data (1), just it is convenient to denote the Om, and In 3. 2. TiAl-based-inatrix: strong interface For regime E, the dependence of fibre stress on time at a Hrer=hn+HE∥Em, where Ef and Em are Youngs Hence. the value of parameter a in E4625!多2“分 onstant composite stress, o, will obviously be Titanium wets oxides perfectly; it can be seen on a cr section of the sapphire-fibre/Ti-48Al-matrix compe c()= presented in Fig. 9[20]. During the contact between the ym+m(m-1) "e a fibre and liquid matrix dissolution of the fibre has occurred. Initially sharp corners of the ICM-fibres becom (4) founded. An attempt to measure the interface strength push out was not successful: it occurred to be too st moduli of the fibre and matrix, respectively, Vr and F Creep experiments and their analysis have yielded values are their volume fractions of n and on. Note that at nln=10*- the value of on is the The creep strain of the composite is actually elastic stress to cause 1% of creep strain for 100 h. This character- deformation of the fibre changing with time istic stress is presented in Fig. 10 for temperatures up to 1100C. It can be seen that on a 120 MPa at a temperature Erve at t→∞ as high as 1050C. This means that the effective stress on the fibres is about 500 MPa. This nearly corresponds to For a composite with initially continuous brittle fibres the effective strength of sapphire fibres in a molybdenum creeping in regime Br-NCr, the dependence between creep matrix(Fig. 7) rate and stress is written [16]as It is important to point out two similarities between these two cases. First, in both cases the fibre/matrix inter- (2)+(.= fibre/matrix microstructure of high shear strength for the fibre strength. do is the average strength of a fibre of composites under consideration remain to be revealed. Sec- ond, the effective fibre strength is certainly higher than the length lo and characteristic cross-sectional size d, fibre strength determined by testing separate fibres. healing q=m+B+mB, and fibre surface defects that can be filled with the matrix due to fibre-matrix and matrix-fibre wetting in the alumina- molybdenum and TiAl-sapphire systems, respectively, can be one reason for it. Moreover, in the latter case sharp defects can be rounded as a result of the fibre material dis- An important parameter, a, is a continuity factor describing solution in the molten matrix. the fibre/matrix interface strength, a-0 if there is no Finally, it should be noted that to make a conclusion on bonding at the interface, a= l for an ideal bonding when a possibility to oxide-fibre/Ti-Al composites to becomeLet the creep law of the matrix will be as given by Eq. (1), just it is convenient to denote the constants as gm, rm, and m. For regime E, the dependence of fibre stress on time at a constant composite stress, r, will obviously be rðfÞ ðtÞ ¼ r V f 1 V m V V m þ gmðm 1Þ V fEf rm r rm  m1 t 2 6 4 3 7 5 1 m1 8 >>< >>: 9 >>= >>; ð4Þ Here V = Vm + VfEf/Em, where Ef and Em are Young’s moduli of the fibre and matrix, respectively, Vf and Vm are their volume fractions. The creep strain of the composite is actually elastic deformation of the fibre changing with time eðtÞ ¼ rðfÞ ðtÞ Ef ;e ! r EfV f at t ! 1: ð5Þ For a composite with initially continuous brittle fibres creeping in regime Br–NCr, the dependence between creep rate and stress is written [16] as r ¼ krm rðfÞ 0 krm !b l0 d 2 4 3 5 mþ1 q e_ gm 1 q V f þ rm e_ gm 1 m V m ð6Þ where b is the exponent in the Weibull distribution for the fibre strength, rðfÞ 0 is the average strength of a fibre of length l0 and characteristic cross-sectional size d, q = m + b + mb, and k ¼ a 2 3 1 m m 2m þ 1 2 ffiffiffi 3 p p !1 2 1 2 4 3 5 1 m : An important parameter, a, is a continuity factor describing the fibre/matrix interface strength, a ! 0 if there is no bonding at the interface, a = 1 for an ideal bonding when the interface strength and equal to that of the matrix. Note that Eq. (6) was obtained assuming steady state creep fol￾lowed the ending of the fibre breakage process on the tran￾sitional stage of creep. It occurs that the larger the value of a the shorter is the fibre length in the steady-state condition and, hence, the larger is the stress carried by the fibre. For regime Cr, creep-rate/stress dependence is obvious: r ¼ rf e_ gf 1 n V f þ rm e_ gm 1 m V m ð7Þ where gf, rf, and n are constants in a power low for the fibre similar to Eq. (1). Regime Br–Cr is a combination of the two regimes just described. Note that while evaluating creep characteristics of fibres, Section 2.2.2, Eq. (7) was used. For metal–matrix compos￾ites, either regime E or regime Br–NCr is characteristic, the latter one being of most interest. Hence, normally Eq. (6) is used to analyse experimental data. 3.2. TiAl-based-matrix: strong interface Titanium wets oxides perfectly; it can be seen on a cross￾section of the sapphire–fibre/Ti–48Al–matrix composite presented in Fig. 9 [20]. During the contact between the fibre and liquid matrix dissolution of the fibre has occurred. Initially sharp corners of the ICM-fibres become rounded. An attempt to measure the interface strength by push out was not successful: it occurred to be too strong. Hence, the value of parameter a in Eq. (6) is equal 1. Creep experiments and their analysis have yielded values of n and rn. Note that at gn = 104 h1 the value of rn is the stress to cause 1% of creep strain for 100 h. This character￾istic stress is presented in Fig. 10 for temperatures up to 1100 C. It can be seen that rn 120 MPa at a temperature as high as 1050 C. This means that the effective stress on the fibres is about 500 MPa. This nearly corresponds to the effective strength of sapphire fibres in a molybdenum matrix (Fig. 7). It is important to point out two similarities between these two cases. First, in both cases the fibre/matrix inter￾face strength is extremely high. For the molybdenum matrix, which is wetted with molten alumina well, the situ￾ation is clear. Particular mechanisms of formation of the fibre/matrix microstructure of high shear strength for the composites under consideration remain to be revealed. Sec￾ond, the effective fibre strength is certainly higher than the fibre strength determined by testing separate fibres. Healing fibre surface defects that can be filled with the matrix due to fibre–matrix and matrix–fibre wetting in the alumina– molybdenum and TiAl–sapphire systems, respectively, can be one reason for it. Moreover, in the latter case sharp defects can be rounded as a result of the fibre material dis￾solution in the molten matrix. Finally, it should be noted that to make a conclusion on a possibility to oxide–fibre/Ti–Al composites to become Fig. 8. Creep resistance of some ICM-fibres in comparison with a polycrystalline mullite-based commercial fibre presented in Ref. [17]. 224 S.T. Mileiko / Current Opinion in Solid State and Materials Science 9 (2005) 219–229