Weibull analysis of flexural strength of a SiCMoSi2 composite

Scripta METALLURGICA et MATERIALIA

Vol. 29, pp. 677-682, 1993 Printed in the U.S.A.

WEIBULL ANALYSIS OF F L E X U R A L

Pergamon Press Ltd. All rights reserved

STRENGTH OF A siC/MoSi 2 COMPOSITE

J y h - M i n g Ting A p p l i e d Sciences, Inc. Cedarville, Ohio 45314 (Received April 30, 1!)93) (Revised June 8, 1993) Introduction Although m o l y b d e n u m d i s i l i c i d e (MoSi2) exhibits e x c e l l e n t high temperature chemical stability and a m e l t i n g point of 2010 °C, its poor m e c h a n i c a l performance has severely limited its structural applications. As a result, effort has been made recently to strengthen MoSi 2 by adding a second p h a s e r e i n f o r c i n g material. (1,2,3,4,5,6,7,8,9,10,11) The results from these studies show improved mechanical performance due to second phase addition. However, the data of all the studies for the mechanical strength, mostly flexural strength, were not analyzed statistically. It is b e l i e v e d that, due to the b r i t t l e nature of MoSi 2 and the fact that the improvement in fracture toughness of MoSi 2 by second phase addition has been limited, the strength data could be scattered. Therefore, as a part of our investigation on MoSi2-based composites, we have a n a l y z e d the strength data of a 20% (by volume) SiC whiskers r e i n f o r c e d MoSi2 composite using Weibull statistics. A wide range of strength data, indeed, was found. Experimental MoSi 2 powers and SiC w h i s k e r s were obtained from d i f f e r e n t sources. As provided by the manufacturers, the MoSi 2 powders have a purity of 99% and an average particle size of 1 ~m. The SiC whiskers have an average diameter of 0.4 ~m and an average length of 2 ~m. The impurities in both materials were not obtained. SiC/MoSi 2 composite, with 20% (by volume) SiC, was p r e p a r e d by hot pressing. Desired amounts of MoSi 2 powders and SiC whiskers were m e a s u r e d and thoroughly mixed in an aqueous medium. The slurry was then dried o v e r n i g h t to remove all the liquid. After the removal of liquid, the mixture was hot p r e s s e d in three-inch graphite disks by applying 27.6 MPa (4,000 psi) of p r e s s u r e at 1750 °C in argon atmosphere. The a s - p r e s s e d SiC/MoSi~ specimens were then m e a s u r e d for densities by the A r c h i m e d e s method and p r e p a r e d for m i c r o s t r u c t u r a l analysis and bending tests. The m i c r o s t r u c t u r a l analysis was performed using optical microscopy and scanning e l e c t r o n m i c r o s c o p y (SEM) on CClF 3 (Chlorotrifluoromethane) plasma etched specimens. The bending tests were carried out using a four point bending technique d e s c r i b e d in MIL-STD-1942. The p r e p a r a t i o n of bending bars and the testing p r o c e d u r e s can be found in the Standard. In the bending tests, the crosshead speed was m a i n t a i n e d at 0.51 mm/min (0.02 in/min). During the tests, the load and strain r e l a t i o n s h i p was m o n i t o r e d and r e c o r d e d by a computer. The maximum load (breaking load) of each bar was used to calculate the flexural strength a c c o r d i n g to the following equation, where S is the flexural strength, P the b r e a k i n g load, L the outer (support) span, b the specimen width, and d the specimen thickness.

677 0956-716X/93 $6.00 ~ .00 Copyright (c) 1993 Pergamon Press

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678

SiC/MoSi2

S= 3PL 4 bd2

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A total of 45 s p e c i m e n s w e r e tested. The tests w e r e c o n d u c t e d in the following fashion. Five s p e c i m e n s w e r e r a n d o m l y s e l e c t e d at a time, and an average flexural strength was d e t e r m i n e d after each f i v e - s p e c i m e n group was tested. Nine averaged data p o i n t s w e r e then obtained. A f t e r the c o m p l e t i o n of testing, the 45 data points of f l e x u r a l s t r e n g t h w e r e put into a c o m p u t e r program, which allows random s e l e c t i o n of d a t a points. Therefore, d i f f e r e n t numbers of data points were selected as follows: 8 groups of i0 data points, 6 groups of 15 data points, and 4 groups of 30 data points. In each group, the group average was calculated. R e s u l t s and D i s c u s s i o n

The average density of the c o m p o s i t e was d e t e r m i n e d by m e a s u r i n g the densities of I0 specimens to be 5.54 ± 0.01 g/cc. This is e q u i v a l e n t to 97.4% of the theoretical density (5.69 g/cc) of fully dense composite. Microstructural analysis on as p o l i s h e d and e t c h e d s p e c i m e n s indicates little porosity. The distribution of SiC in MoSi 2 was found to be fairly uniform. The m i c r o s t r u c t u r e of an etched specimen is shown in Fig. IA. The grain sizes of MoSi 2 ranged from 2 ~m to 8 ~ and the a v e r a g e was e s t i m a t e d to be a p p r o x i m a t e l y 4 ~m. Figure IA also shows that a g g l o m e r a t i o n of SiC w h i s k e r s o c c u r r e d d u r i n g the p r e p a r a t i o n of the composite. As shown in Fig. IB, the w h i s k e r shape of SiC is m o r e perceivable when the etched s p e c i m e n was e x a m i n e d by SEM. Figure IB also shows that CClF 3 has selectively etched away Mosi2, l e a v i n g sic e x t r u d i n g from the matrix. The flexural strength of S i C / M o S i 2 was c a l c u l a t e d by Eq. (i). The average of all 45 data was c a l c u l a t e d to be 457 MPa. For comparison, the average flexural strength of MoSi 2 p r o c e s s e d p r e v i o u s l y by the same way was d e t e r m i n e d to be 273.7 MPa. (12) The average values of f l e x u r a l s t r e n g t h c a l c u l a t e d from each data group are listed in Table I. A l s o listed in Table I are the p e r c e n t a g e differences between each group a v e r a g e and the average of 45 specimens. A percentage difference was o b t a i n e d by s u b t r a c t i n g the average of 45 s p e c i m e n s from a group average and then d i v i d e d by the a v e r a g e of 45 specimens. P r o v i d e d that the average of all 45 s p e c i m e n s r e p r e s e n t s a "final" average, then the percentage differences w o u l d be the "errors" w h e n an inefficient n u m b e r of data points is collected. W i t h i n c r e a s i n g n u m b e r s of specimens, the "error" decreases, indicating a s t a t i s t i c a l a n a l y s i s is required. The s t a t i s t i c a l analysis used in this study was the W e i b u l l analysis. W e i b u l l s t a t i s t i c s w e r e s e l e c t e d b e c a u s e of their a c c u r a c y and simpleness. The m i n i m u m n u m b e r of data points n e e d e d for such an a n a l y s i s has been suggested to be 30. (13) In this study, 45 data points were used. W e i b u l l analysis was carried out u s i n g the f o l l o w i n g 2 - p a r a m e t e r equation:

Ln(Ln( (ll--_p)) ) =Ln(S m) +constant where p is the p r o b a b i l i t y and m the W e i b u l l modulus, w h i c h defines the width of data distribution. U s i n g this equation, the flexural s t r e n g t h data w e r e analyzed and w e r e p l o t t e d in Fig. 2. The W e i b u l l m o d u l u s was d e t e r m i n e d to be 5.0, which

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SiC/MoSi 2

indicates a wide range of t e s t i n g data. Weibull m o d u l u s of about 7 to 12. (14)

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It is clear that w i t h t h e b r i t t l e n a t u r e of S i C / M o S i 2 composite, a s t a t i s t i c a l analysis is necessary in o r d e r to e x p l a i n the s t r e n g t h data. As i n d i c a t e d in Table I, when i0 data p o i n t s are used, w h i c h c o m m o n l y h a p p e n s , the d i f f e r e n c e between the average of i0 d a t a p o i n t s and the a v e r a g e of a g r o u p of data points sufficient for s t a t i s t i c a l analysis, e.g. 45 points for W e i b u l l analysis, can be as high as 17.6%. For 15 d a t a points, it can be n e a r l y 15%. Conclusions SiC/MoSi 2 composite has r e c e i v e d i n c r e a s i n g a t t e n t i o n in the past few years. Effort involved in the d e v e l o p m e n t of this m a t e r i a l has y i e l d e d good flexural str e n g t h but limited i m p r o v e m e n t in f r a c t u r e toughness. This implies that the c o m p o s i t e s y s t e m d e v e l o p e d so far e x h i b i t s a brittle nature. It was found in this study that the Weibull m o d u l u s of a Si C / M o S i 2 is only 5, w h i c h is e x p e r i m e n t a l evidence of the b r i t t l e n e s s of S i C /M o S i 2. This r e s u l t clearly suggests a sta t i s t i c a l analysis is n e e d e d to e v a l u a t e the s t r e n g t h of this r e l a t i v e l y new c o m p o s i t e system. Acknowledqement The authors w o u l d like to a c k n o w l e d g e the support for the study from Defense A d v a n c e d R e s e a r c h P r o j e c t s A g e n c y under C o n t r a c t No. D A A H 0 1 - 9 1 - C - R I 5 6 .

TABLE

I.

The average v a l u e s of f l e x u r a l s t r e n g t h c a l c u l a t e d from v a r i o u s data groups. The p e r c e n t a g e d i f f e r e n c e ("error") b e t w e e n each g r o u p a v e r a g e and the total average are also given.

Group

Average

5 data p o i n t s

i0 data p o i n t s

15 data p o i n t s

30 data p o i n t s

Avg. MPa

"Error" %

Avg. MPa

"Error" %

Avg. MPa

"Error" %

Avg. MPa

"Error" %

435 386 506 518 399 557 494 388 429

- 4.7 -15.5 10.7 13.3 -12.7 21.9 8.1 -15.0 - 6.0

531 411 392 512 387 478 441 537

16.3 -i0.I -14.1 12.0 -15.2 4.6 - 3.5 17.6

479 442 391 471 491 437

4.8 - 3.2 -14.4 3.0 7.5 - 4.3

467 476 438 464

2.2 4.3 - 4.1 1.6

of 45 s p e c i m e n s :

457 MPa.

680

SiC/M°Si2

Vol.

(A)

(S)

Fig. i. M i c r o g r a p h s of an etched SiC/MoSi 2 specimen. Photos were taken by (A) an optical microscope and (B) by an scanning electron microscope. In (A), the dark phase is SiC.

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References i. T.C. LU, A.G. Evans, R.J. Hecht, and R. Mehrabian, "Toughening of MoSi 2 with A Ductile (Niobium) Reinforcement," Acta Metall. Mater, Vol. 39, No. 8, pp. 1853-62, 1991. 2. D.H. Carter, J.J. Petrovic, R.E. Honnell, and W.S. Gibbs, Composites," Ceram. Eng. sci. Proc., i0 [9-10], pp. 1121-9, 1989.

"SiC/MoSi 2

3. C.B. Lim, T. ¥ano, and T. Iseki, "Microstructure and Mechanical Properties of RB-SiC/MoSi 2 Composite," J. Mater. Sci., Vol. 24, pp. 4144-51, 1989. 4. J.-M. Young and S.M. Jeng, "Interface and Mechanical Composites," J. Mater. Res., Vol. 6, No. 3, 1991.

Behavior

of MoSi2-based

5. D.H. Carter and P.L. Martin, "Tantalum and Niobium Reinforced MoSi2," Mater. Res. Soc. Symp. Proc., Voi.194, pp.131-8 (1990). 6. L. Xaio, Y.S. Kim, and R. Abbaschian, "Ductile Phase Toughening of MoSi 2 Chemical Compatibility and Fracture Toughness," Mater. Res. Soc. Symp. Proc., Voi.194, pp.399-404 (1990). 7. J.M. Young and S.M. Jeng, "Development of MoSi~-based Composites," Meter. Res. Soc. Symp. Proc., Voi.194, pp.139-46 (1990). 8. J.J. Petrovic, R.E. Honnel, and A.K. Vasudevan, "SIC Reinforced MoSi 2 Alloy Matrix Composites," Mater. Res. Soc. Symp. Proc., Voi.194, pp.123-30 (1990). 9. W.S. Gibbs, J.J. Petrovic, and R.E. Honnel, "SIC Whisker-MoSi 2 Matrix Composites," Ceram. Eng. sci. Proc., 8 [7-8] pp. 645-48 (1987). 10. F.D. Gac and J.J. Petrovic, :Feasibility of a Composite of siC Whiskers an MoSi 2 Matrix," J. Am. Ceram. Soc., 68 [8] C200-I (1985). ii. A.K. Vasudevan and J.J. Petrovic, High Temperature Elsevier Science Publishers, B.V. Amsterdam (1992). 12. J. Ting, " Molybdenum Disilicide Matrix Composite Report, Contract No. DAAH01-91-C-RI56, February, 1992.

structural

in

Silicides,

by Slip Casting",

Final

13. G.D. Quinn, "Fractographic Analysis and the Army Flexure Test Method," Advance in Ceram. Vol. 22, 1988. 14. J.-M. Ting, Y. Ko, and R.Y. Lin, "The effects of raw material characteristics on the microstructure and strength of sintered alumina", Bull. Am. Ceram. Soc., p. 1167, July, 1991.