- Email: [email protected]
Characterization of a CAl metal matrix composite precursor
Materials Science and Engineering, A 135(1991) 59-63
59
Characterization of a C-A1 metal matrix composite precursor J. J. Masson and K. Schulte Institute[or Materials Research, I)LR, 1)5000 Kd/n 90 fF.R.(;.)
F. Girot and Y. Le Petitcorps L( "S, University ofBordeaux ( l')ance)
Abstract The quality of metal matrix composites made by hot pressing of prepreg layers mainly depends on the quality of the precursor. Mechanical and chemical characterization of the precursor is therefore an essential task in the development process. This work concentrates on the mechanical characterization of a C-A1 prepreg in order to establish how the strength of fibres is degraded by reaction with aluminium during hot pressing. The prepreg undergoes an annealing treatment, simulating temperature and atmosphere conditions of composite processing. Single fibres are taken and tested in tension. A single Weibull distribution function is used to discuss the strength distributions. Possibilities and limits of this model are reviewed.
1. Introduction
matrix and into the fibre. The roots of the crystals
Metal matrix composite (MMC)manufacturing based on the prepreg route arouses new interest in the aerospace industry because it enables the
act as notches on the fibre surface, which has a weakening effect on fibre strength [2]. Development of A14C ) has been shown to be diffusion controlled and therefore dependent on the time
design of more complicatedly shaped parts having continuous fibres than is possible by liquid infiltration. Structures can be tailored to specific applications via laminate lay-up or filament winding. MMC prepregs are mostly very thin, which offers enough flexibility for tailoring the skin of future aerospace structures, In the development of such composites an important task is the chemical and mechanical characterization of the precursor in order to establish how the strength of fibres is degraded by reaction with the matrix during composite processing, This work deals with the mechanical characterization of a C-A1 prepreg from the TohoBeslon company. The prepreg is composed of high modulus HM35 fibres coated with pure aluminium by an ion plating process [1]. Composite processing is carried out by solid phase diffusion bonding at about 600 °C. Carbon reacts with aluminium to form aluminium carbides (A14C)). Aluminium carbides grow both into the 0921-5093/91/$3.51)
and temperature [3]. Reactivity varies with the type of carbon fibre [2, 4] and composition of the aluminiumalloy[5]. There are two methods for measuring the strength degradation of carbon fibres after reaction with aluminium: ( 1 ) fibres extracted from the composite are tested in tension after dissolution of the matrix (direct method), or (2) aluminium coated fibres undergo an annealing treatment, which simulates hot pressing conditions, followed by a tension test (indirect method). This last method is particularly suitable for MMCs made by the prepreg route. In order to examine the influence of fibre-matrix reaction, tensile tests were carried out on coated and uncoated single fibres.
2. Experimental details The heat treatment was performed in vacuum ( 10 -~ Torr) with a temperature increase rate of © Elsevier Sequoia/Printed in The Netherlands
60
where L is the fibre gauge length, L 0 a reference length, a u the threshold stress below which the failure probability is zero, a0 the scale parameter and m the shape parameter. For brittle materials it is in general recommended to take o u = 0 [8]. Then the distribution function can be expressed as
F(a) = 1 - e x p i
iil
i-i [a0(L~ o1j
(2)
where
(3)
Fig. I. Single fibre test specimen gripped in tensile test machine.
a o ( L ) = ao
300 °C h- ' up to a plateau with a constant ternperature of 550°C, 600°C or 650°C, held for 1 h. Tensile tests were carried out with single fibres using a method similar to ASTM D-3379 [ 6 ] . Fibres were glued on paper tabs (Fig. 1).Thetabs were gripped in the jaws of a movable-cross-head test machine. For better handling the paper tabs were connected by two plastic bridges, which were melted away just before the tensile test was started. Gauge lengths were 5.5, 20 or 40 mm, and the cross-head speed was 0.2 mm min -l. The loads were measured with a precision of + 0.5%. Fibre diameter was determined for each fibre in a scanning electron microscope. In view of the difficulties we met in separating fibres (which bond together) and to isolate a single fibre from the prepreg, we have used dissolution of the aluminium with NaOH. A piece of prepreg material undergoes first the annealing treatment and is then etched with NaOH for 2 h (0.5 N sodium hydroxide solution heated to 60 °C). With this method the fibre weight loss by solvent action on uncoated fibres could be considered not to be significant (less than 0.2%). We conclude that there might not be any influence of etching on the fibre strength.
To interpret the effect of diameter variability on the mechanical strength of polymeric fibres, Wagner proposed a variant of the Weibull model [9]. The new distribution function is expressed as follows: [ (dl~Ia 1"] (4) F(a)=l-exp -~] [o0~J J
3. Analyticalprocedure To discuss the fibre strength distributions, a single Weibull distribution function was used on the basis of the single-risk hypothesis [7]. In this case, the cumulative failure probability function F(a) of strength a is given as F(a)=l-exp
i - ~ kL
o-o, a0 / I
(1)
where d is the fibre diameter, d0 a reference diameter and 6 a third parameter to be estimated. If 6 is taken equal to 1 (or 6 = 2) it is assumed in the Weibull model that surface (or volume) defects are strength limiting. In both cases, the correction factor is proportional to the mean number of critical defects per unit fibre length [10]. After N fibres have been tested under the same conditions, a series of ordered strength values o I ~... ~
F(ai)- i -0.5
(5)
N In order to fit this experimental distribution with the Weibull distribution, two methods are commonly used: the least-squares fitting and the maximum likelihood method. This last method leads to a better fitting, as shown by simulated tests [12[, and is applied in the present work. The likelihood function is
L=[-[f(oi) N i=,
(6)
61 TABLE I Results of single-fibre testing
H M 3 5 : initial M0.Ic HM35;650°(', 1 h H M 3 5 - A I ; initial state H M 3 5 - A l : 550 °C. 1 h H M 3 5 - A l : 600 °C. I h HM35-AI:650°C, 1 h H M 3 5 - A I : 550 °C, I h
N aO H etching
.,\'
d~ liana)
oB (MPa!
m
o. {MPa)
No No No Yes Yes Yes No
33 32 32 27 33 24 31
6.4 _+0.4 (}.5 + 0 . 7 6.4 6.4 +_0.3 6.4 _+0.2 6.5 +{}.7 6.4
4 3 6 0 _+ 1020 4533_+ 1338 4275 _+ 793 3940 _+608 375(} + 592 1762 + 3 5 2 3500 4-_765
5.2 3.6 6.4 8.5 7.5 5.5 --
4745 5019 4597 4184 3990 1905 --
140 l T
ReF...... Ot~meter= 6,4 p2 wiLhout ......Liom
~oo-~ .......................................
(lh, 0~-
o
I
too
in
-T . . . . . .
~
~ • o o
Vacuum) I --
200
aoo
....
I
l--
I
400
soo
600
- -
1
700
Temperature ('C)
Fig. 2. Influence of annealing temperature on the strength of uncoated and aluminium-coated H M 3 5 fibres.
,,.5
s£~ s £ s
~
/
l
Ht135, I
I
65e
C,
Ih
G£5 7:~ ?£s 8£~ a . s
O~rneter ~n pm Fig. 3. Influence of diameter on the fibre strength.
TABLE 2
where j'(o) is the probability density function. T h e parameters m, o{} and d maximizing L are the maximum likelihood estimators.
Results
of diameter size correction
HM35
4. Results and discussion Results are summarized in Table 1. In the case of no etching the diameter of each fibre could not be determined. That is why a mean value of 6.4 y m was taken as the constant fibre diameter. For the coated H M 3 5 fibre annealed at 55{}°C, two series of tests were carried out before and after removal of the aluminium coating by NaOH. In the last case the mean strength is 1 1% smaller because of testing difficulties (coated fibres are mostly crooked), In Fig. 2 are plotted the mean strengths vs. annealing temperatures. T h e uncoated H M 3 5 fibre keeps its strength after an annealing treatment at 650 °C. On the contrary, the strength of the coated fibre decreases dramatically after an annealing treatment at temperatures higher than 600°C. For the 6{}0°C temperature the fibre keeps 87% of its initial strength,
H M 3 5 ; 650 °C, I h H M 3 5 - A l : 55{} °C, 1 h
HM35-Al: 600 °C, 1 h HM35 AI;650°C, 1 h
(~
rh
6. (MPa)
0 {$= 6 0
5.2 5.6 3.6
4745 4695 5019
~= 10 8= 5 0
5.3 8.5 8.5 7.5
4942 4184 4183 3990
c~= I 1
8.0
3996
0
0 8= 16
5.5 7.3
1905 1900
In L - 274 272 -276
-
-266 - 209 - 209 - 2 5 6 -
-
254
175
- 1 6 9
T h e general trend is that fibres with large diameters have a lower strength than those with a smaller diameter (Fig. 3). This has been taken into account and the parameters of the Wagner model have been estimated. Results are listed in Table 2. {$ is the estimated size exponent (maximizing the likelihood function). T h e size exponent takes values much greater than 1 or 2 and has a tremendous scatter. It seems to be more a random parameter depending on statistical and experimental scatter than a parameter related to a
62
2
HM35,^L
2,5
~,-z / y 7.8
7.2
7.4
7,8
(ram)
l.o
80 600o
sooo o
° . o,.,,7,,h,
/,s, 7.6
I~augeo Length
"8.c
~*
-,.o . . . .
5
8.0
8.2
8.4
" 8.6
.8
Ln Strength
HM35/A[
"7,: ,
Fig. 4. Weibull plots in the linearized form.
:ooo
~
~
Ln L ----Fig. 5. Scale parameter vs. gauge length on a logarithmic scale.
TABLE 3 Confidence intervals for the shape parameter
HM35-AI Initial state 550 °C, 1 h 600 °c, 1 h 650 °c, 1 h
N
m
Imp,m2],90%
32 27 33 24
6.4 8.5 7.7 5.9
4.9-7.8 6.2-10.0 5.9-9.3 4.3-7.3
TABLE 4 Confidence intervals for the scale p a r a m e t e r HM35-AI
N
o0
lnitial state
32 27 33
4597 4184 3990
550°C, l h
600 °c, I h
650 °C, 1 h
24
1905
[O[)l,
002], 90% 4371-4837 4010-4369 3826-4163
1786-2033
physical model. It is interesting to note that, while the estimated shape parameter dz can vary widely in proportion to ~, the scale parameter d 0 remains almost constant, This leads to the following conclusions, (1) 6 o is the only parameter in which we can have at last some confidence. (2) If a diameter size correction is made we would recommend that a constant value be taken for the size exponent (d = 1 or 2 [10]). In the following, no further diameter size correction has been considered, In Fig. 4 the cumulative distribution curves are shown in the linearized form. The experimental data fit relatively well using the single Weibull distribution function, Table 1 shows that the scatter in the scale parameter is large and no influence of the annealing treatment can be observed. In order to
obtain an idea of the statistical scatter of the parameters in the maximum likelihood estimation, confidence intervals for rn and a0 have been calculated [13] (Tables 3 and 4). Estimated values are in the confidence intervals with 90% probability. The scatter in m is about _+25%, while the scatter in ao is only _+7%. A better way to estimate the shape parameter m seems to be the linear logarithmic dependence of strength on gauge length (eqn. (3)). Indeed, this parameter is used to extrapolate fibre strength at different lengths [14]. Tests were carried out with untreated coated fibres at three different gauge lengths. In Fig. 5 the scale parameters o0 are plotted vs. gauge length on a logarithmic scale. By linear regression analysis we determined m = 3.4. Moreover, assuming a confidence interval of _+7% for a0, we estimated a confidence interval for m of + 25% also by using this method, but theoretically it could be arbitrarily improved by considering results at more extreme gauge lengths. 5. Conclusions (1) After an annealing treatment at 600 °C for 1 h aluminium-coated HM35 fibres keep about 87% of their initial strength. Treatments at higher temperatures lead to a dramatic drop in strength. (2) Results of single-fibre were well fitted by a single Weibull distribution function. (3) A better correlation can be achieved by considering diameter size effects. However, O0 is the only parameter in which we can have enough confidence. (4) The shape parameter m has a high scatter.
63
No influence of the annealing treatment has been observed. (5) The scale parameter oo(L ) can be estimated with relatively good confidence ( ± 7%). (6) Finally, the shape parameter rn should n o t be determined from only one test series, but by linear regression of the data in the In oo(L ) t,s. In L plot. With this estimation method a better confidence for the shape parameter can be achieved. Acknowledgments The authors are grateful to Mr. J. G6ring for helpful discussions and to the EC for funding this work under Contract MA 1E/0063-C. References I M. Yoshida, S. lkegami, T. Ohsaki and T. Ohkita, Soc. Adv. Mater. Process Eng., 24 1211197911417-1426.
2 S. Kohara and N. Nuto, Proc. 1st Euro. Conf. Compos. Mater., 1985, Euro. Ass. Compos. Mater., 1985, pp.
738-743.
3 A. Okura and K. Motoki, Compos. Sci. Technol., 24 (1985) 243 252, 4 H.S. Yoon, A. Okura and H. lchinose, I'roc. Int. ('op(ll on lnterfiwial l'hemmwna in Cornposiw Materials, Butterworths, kondon, 1989, pp. 258-263. 5 Y. Kimura, J. Mater. Sci., 19 (1984) 3107-3114. 6 B. Kanka, Ger, I'alent, ()~l~'nlegtmgv~'chr!l?. l)k 3,~¢15425 A1, 1989. 7 W. Weibull, d. Appl. Mech., I,S' ( 1951 ) 293. 8 K. Trustrum and A. De S. Jayatilaka, Y. Mater. Sci., 14 (197911118(1 10S4. 9 H. D. Wagner, J. l'olym. Sci. B, f'olym. Phys., 27 (1989) ll5. 10 J. G6ring, F. Flucht and G. Ziegler, f'roc. 4th Euro. Conf. (ompos. Mater., Stuttgart. 1990, Elsevier, 1990, pp. 543-548. 11 B. Bergman, ,1. Mater. Sci. Lett., 3 {1984) 689-692. 12 A. Khalili, Statistik und f'estigkeit, I)KG Semin., Stuttgart, t:ebruary 22-23, 1989. 13 1). R. Thoman, L. J. Bain and J. C. E. Antic, "Fechnometrics, II 1.31(1969) 445-460. 14 El. M. Asloun, J. B. Donnet, G. Guilpain, M. Nardin and J. Schultz, J. Mater. Sci., 24 (1989) 3504 3510.
59
Characterization of a C-A1 metal matrix composite precursor J. J. Masson and K. Schulte Institute[or Materials Research, I)LR, 1)5000 Kd/n 90 fF.R.(;.)
F. Girot and Y. Le Petitcorps L( "S, University ofBordeaux ( l')ance)
Abstract The quality of metal matrix composites made by hot pressing of prepreg layers mainly depends on the quality of the precursor. Mechanical and chemical characterization of the precursor is therefore an essential task in the development process. This work concentrates on the mechanical characterization of a C-A1 prepreg in order to establish how the strength of fibres is degraded by reaction with aluminium during hot pressing. The prepreg undergoes an annealing treatment, simulating temperature and atmosphere conditions of composite processing. Single fibres are taken and tested in tension. A single Weibull distribution function is used to discuss the strength distributions. Possibilities and limits of this model are reviewed.
1. Introduction
matrix and into the fibre. The roots of the crystals
Metal matrix composite (MMC)manufacturing based on the prepreg route arouses new interest in the aerospace industry because it enables the
act as notches on the fibre surface, which has a weakening effect on fibre strength [2]. Development of A14C ) has been shown to be diffusion controlled and therefore dependent on the time
design of more complicatedly shaped parts having continuous fibres than is possible by liquid infiltration. Structures can be tailored to specific applications via laminate lay-up or filament winding. MMC prepregs are mostly very thin, which offers enough flexibility for tailoring the skin of future aerospace structures, In the development of such composites an important task is the chemical and mechanical characterization of the precursor in order to establish how the strength of fibres is degraded by reaction with the matrix during composite processing, This work deals with the mechanical characterization of a C-A1 prepreg from the TohoBeslon company. The prepreg is composed of high modulus HM35 fibres coated with pure aluminium by an ion plating process [1]. Composite processing is carried out by solid phase diffusion bonding at about 600 °C. Carbon reacts with aluminium to form aluminium carbides (A14C)). Aluminium carbides grow both into the 0921-5093/91/$3.51)
and temperature [3]. Reactivity varies with the type of carbon fibre [2, 4] and composition of the aluminiumalloy[5]. There are two methods for measuring the strength degradation of carbon fibres after reaction with aluminium: ( 1 ) fibres extracted from the composite are tested in tension after dissolution of the matrix (direct method), or (2) aluminium coated fibres undergo an annealing treatment, which simulates hot pressing conditions, followed by a tension test (indirect method). This last method is particularly suitable for MMCs made by the prepreg route. In order to examine the influence of fibre-matrix reaction, tensile tests were carried out on coated and uncoated single fibres.
2. Experimental details The heat treatment was performed in vacuum ( 10 -~ Torr) with a temperature increase rate of © Elsevier Sequoia/Printed in The Netherlands
60
where L is the fibre gauge length, L 0 a reference length, a u the threshold stress below which the failure probability is zero, a0 the scale parameter and m the shape parameter. For brittle materials it is in general recommended to take o u = 0 [8]. Then the distribution function can be expressed as
F(a) = 1 - e x p i
iil
i-i [a0(L~ o1j
(2)
where
(3)
Fig. I. Single fibre test specimen gripped in tensile test machine.
a o ( L ) = ao
300 °C h- ' up to a plateau with a constant ternperature of 550°C, 600°C or 650°C, held for 1 h. Tensile tests were carried out with single fibres using a method similar to ASTM D-3379 [ 6 ] . Fibres were glued on paper tabs (Fig. 1).Thetabs were gripped in the jaws of a movable-cross-head test machine. For better handling the paper tabs were connected by two plastic bridges, which were melted away just before the tensile test was started. Gauge lengths were 5.5, 20 or 40 mm, and the cross-head speed was 0.2 mm min -l. The loads were measured with a precision of + 0.5%. Fibre diameter was determined for each fibre in a scanning electron microscope. In view of the difficulties we met in separating fibres (which bond together) and to isolate a single fibre from the prepreg, we have used dissolution of the aluminium with NaOH. A piece of prepreg material undergoes first the annealing treatment and is then etched with NaOH for 2 h (0.5 N sodium hydroxide solution heated to 60 °C). With this method the fibre weight loss by solvent action on uncoated fibres could be considered not to be significant (less than 0.2%). We conclude that there might not be any influence of etching on the fibre strength.
To interpret the effect of diameter variability on the mechanical strength of polymeric fibres, Wagner proposed a variant of the Weibull model [9]. The new distribution function is expressed as follows: [ (dl~Ia 1"] (4) F(a)=l-exp -~] [o0~J J
3. Analyticalprocedure To discuss the fibre strength distributions, a single Weibull distribution function was used on the basis of the single-risk hypothesis [7]. In this case, the cumulative failure probability function F(a) of strength a is given as F(a)=l-exp
i - ~ kL
o-o, a0 / I
(1)
where d is the fibre diameter, d0 a reference diameter and 6 a third parameter to be estimated. If 6 is taken equal to 1 (or 6 = 2) it is assumed in the Weibull model that surface (or volume) defects are strength limiting. In both cases, the correction factor is proportional to the mean number of critical defects per unit fibre length [10]. After N fibres have been tested under the same conditions, a series of ordered strength values o I ~... ~
F(ai)- i -0.5
(5)
N In order to fit this experimental distribution with the Weibull distribution, two methods are commonly used: the least-squares fitting and the maximum likelihood method. This last method leads to a better fitting, as shown by simulated tests [12[, and is applied in the present work. The likelihood function is
L=[-[f(oi) N i=,
(6)
61 TABLE I Results of single-fibre testing
H M 3 5 : initial M0.Ic HM35;650°(', 1 h H M 3 5 - A I ; initial state H M 3 5 - A l : 550 °C. 1 h H M 3 5 - A l : 600 °C. I h HM35-AI:650°C, 1 h H M 3 5 - A I : 550 °C, I h
N aO H etching
.,\'
d~ liana)
oB (MPa!
m
o. {MPa)
No No No Yes Yes Yes No
33 32 32 27 33 24 31
6.4 _+0.4 (}.5 + 0 . 7 6.4 6.4 +_0.3 6.4 _+0.2 6.5 +{}.7 6.4
4 3 6 0 _+ 1020 4533_+ 1338 4275 _+ 793 3940 _+608 375(} + 592 1762 + 3 5 2 3500 4-_765
5.2 3.6 6.4 8.5 7.5 5.5 --
4745 5019 4597 4184 3990 1905 --
140 l T
ReF...... Ot~meter= 6,4 p2 wiLhout ......Liom
~oo-~ .......................................
(lh, 0~-
o
I
too
in
-T . . . . . .
~
~ • o o
Vacuum) I --
200
aoo
....
I
l--
I
400
soo
600
- -
1
700
Temperature ('C)
Fig. 2. Influence of annealing temperature on the strength of uncoated and aluminium-coated H M 3 5 fibres.
,,.5
s£~ s £ s
~
/
l
Ht135, I
I
65e
C,
Ih
G£5 7:~ ?£s 8£~ a . s
O~rneter ~n pm Fig. 3. Influence of diameter on the fibre strength.
TABLE 2
where j'(o) is the probability density function. T h e parameters m, o{} and d maximizing L are the maximum likelihood estimators.
Results
of diameter size correction
HM35
4. Results and discussion Results are summarized in Table 1. In the case of no etching the diameter of each fibre could not be determined. That is why a mean value of 6.4 y m was taken as the constant fibre diameter. For the coated H M 3 5 fibre annealed at 55{}°C, two series of tests were carried out before and after removal of the aluminium coating by NaOH. In the last case the mean strength is 1 1% smaller because of testing difficulties (coated fibres are mostly crooked), In Fig. 2 are plotted the mean strengths vs. annealing temperatures. T h e uncoated H M 3 5 fibre keeps its strength after an annealing treatment at 650 °C. On the contrary, the strength of the coated fibre decreases dramatically after an annealing treatment at temperatures higher than 600°C. For the 6{}0°C temperature the fibre keeps 87% of its initial strength,
H M 3 5 ; 650 °C, I h H M 3 5 - A l : 55{} °C, 1 h
HM35-Al: 600 °C, 1 h HM35 AI;650°C, 1 h
(~
rh
6. (MPa)
0 {$= 6 0
5.2 5.6 3.6
4745 4695 5019
~= 10 8= 5 0
5.3 8.5 8.5 7.5
4942 4184 4183 3990
c~= I 1
8.0
3996
0
0 8= 16
5.5 7.3
1905 1900
In L - 274 272 -276
-
-266 - 209 - 209 - 2 5 6 -
-
254
175
- 1 6 9
T h e general trend is that fibres with large diameters have a lower strength than those with a smaller diameter (Fig. 3). This has been taken into account and the parameters of the Wagner model have been estimated. Results are listed in Table 2. {$ is the estimated size exponent (maximizing the likelihood function). T h e size exponent takes values much greater than 1 or 2 and has a tremendous scatter. It seems to be more a random parameter depending on statistical and experimental scatter than a parameter related to a
62
2
HM35,^L
2,5
~,-z / y 7.8
7.2
7.4
7,8
(ram)
l.o
80 600o
sooo o
° . o,.,,7,,h,
/,s, 7.6
I~augeo Length
"8.c
~*
-,.o . . . .
5
8.0
8.2
8.4
" 8.6
.8
Ln Strength
HM35/A[
"7,: ,
Fig. 4. Weibull plots in the linearized form.
:ooo
~
~
Ln L ----Fig. 5. Scale parameter vs. gauge length on a logarithmic scale.
TABLE 3 Confidence intervals for the shape parameter
HM35-AI Initial state 550 °C, 1 h 600 °c, 1 h 650 °c, 1 h
N
m
Imp,m2],90%
32 27 33 24
6.4 8.5 7.7 5.9
4.9-7.8 6.2-10.0 5.9-9.3 4.3-7.3
TABLE 4 Confidence intervals for the scale p a r a m e t e r HM35-AI
N
o0
lnitial state
32 27 33
4597 4184 3990
550°C, l h
600 °c, I h
650 °C, 1 h
24
1905
[O[)l,
002], 90% 4371-4837 4010-4369 3826-4163
1786-2033
physical model. It is interesting to note that, while the estimated shape parameter dz can vary widely in proportion to ~, the scale parameter d 0 remains almost constant, This leads to the following conclusions, (1) 6 o is the only parameter in which we can have at last some confidence. (2) If a diameter size correction is made we would recommend that a constant value be taken for the size exponent (d = 1 or 2 [10]). In the following, no further diameter size correction has been considered, In Fig. 4 the cumulative distribution curves are shown in the linearized form. The experimental data fit relatively well using the single Weibull distribution function, Table 1 shows that the scatter in the scale parameter is large and no influence of the annealing treatment can be observed. In order to
obtain an idea of the statistical scatter of the parameters in the maximum likelihood estimation, confidence intervals for rn and a0 have been calculated [13] (Tables 3 and 4). Estimated values are in the confidence intervals with 90% probability. The scatter in m is about _+25%, while the scatter in ao is only _+7%. A better way to estimate the shape parameter m seems to be the linear logarithmic dependence of strength on gauge length (eqn. (3)). Indeed, this parameter is used to extrapolate fibre strength at different lengths [14]. Tests were carried out with untreated coated fibres at three different gauge lengths. In Fig. 5 the scale parameters o0 are plotted vs. gauge length on a logarithmic scale. By linear regression analysis we determined m = 3.4. Moreover, assuming a confidence interval of _+7% for a0, we estimated a confidence interval for m of + 25% also by using this method, but theoretically it could be arbitrarily improved by considering results at more extreme gauge lengths. 5. Conclusions (1) After an annealing treatment at 600 °C for 1 h aluminium-coated HM35 fibres keep about 87% of their initial strength. Treatments at higher temperatures lead to a dramatic drop in strength. (2) Results of single-fibre were well fitted by a single Weibull distribution function. (3) A better correlation can be achieved by considering diameter size effects. However, O0 is the only parameter in which we can have enough confidence. (4) The shape parameter m has a high scatter.
63
No influence of the annealing treatment has been observed. (5) The scale parameter oo(L ) can be estimated with relatively good confidence ( ± 7%). (6) Finally, the shape parameter rn should n o t be determined from only one test series, but by linear regression of the data in the In oo(L ) t,s. In L plot. With this estimation method a better confidence for the shape parameter can be achieved. Acknowledgments The authors are grateful to Mr. J. G6ring for helpful discussions and to the EC for funding this work under Contract MA 1E/0063-C. References I M. Yoshida, S. lkegami, T. Ohsaki and T. Ohkita, Soc. Adv. Mater. Process Eng., 24 1211197911417-1426.
2 S. Kohara and N. Nuto, Proc. 1st Euro. Conf. Compos. Mater., 1985, Euro. Ass. Compos. Mater., 1985, pp.
738-743.
3 A. Okura and K. Motoki, Compos. Sci. Technol., 24 (1985) 243 252, 4 H.S. Yoon, A. Okura and H. lchinose, I'roc. Int. ('op(ll on lnterfiwial l'hemmwna in Cornposiw Materials, Butterworths, kondon, 1989, pp. 258-263. 5 Y. Kimura, J. Mater. Sci., 19 (1984) 3107-3114. 6 B. Kanka, Ger, I'alent, ()~l~'nlegtmgv~'chr!l?. l)k 3,~¢15425 A1, 1989. 7 W. Weibull, d. Appl. Mech., I,S' ( 1951 ) 293. 8 K. Trustrum and A. De S. Jayatilaka, Y. Mater. Sci., 14 (197911118(1 10S4. 9 H. D. Wagner, J. l'olym. Sci. B, f'olym. Phys., 27 (1989) ll5. 10 J. G6ring, F. Flucht and G. Ziegler, f'roc. 4th Euro. Conf. (ompos. Mater., Stuttgart. 1990, Elsevier, 1990, pp. 543-548. 11 B. Bergman, ,1. Mater. Sci. Lett., 3 {1984) 689-692. 12 A. Khalili, Statistik und f'estigkeit, I)KG Semin., Stuttgart, t:ebruary 22-23, 1989. 13 1). R. Thoman, L. J. Bain and J. C. E. Antic, "Fechnometrics, II 1.31(1969) 445-460. 14 El. M. Asloun, J. B. Donnet, G. Guilpain, M. Nardin and J. Schultz, J. Mater. Sci., 24 (1989) 3504 3510.