The use of quantitative metallography in determining properties of composites
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Beck for encouragement as well as for making availa b l e f i l m s of e a r l i e r i n v e s t i g a t i o n s . 6 T h a n k s a r e d u e to M r . A. J . K l e i n f o r c o m p e t e n t h e l p i n p r e p a r i n g samples. This work was supported by grants from the Army Research Office, Durham, and the National Science Foundation. I. W. Jeitschko, A. G. Jordan, and Paul A. Beck: Trans. TMS-AIME, 1969, vol. 245, pp. 335-39. 2. B. Deyris, J. Roy-Montreuil,R. Fruchart, and A. Michel:Bull. Soc. Chim. France, 1968,vol. 1968, pp. 1303-04. 3. J. Roy-Montreuil,B. Deyris, R. Fruchart, and A. Michel: Compt. Rend., 1968, vol. C266, pp. 615-17. 4. W. Jeitschko: Acta Cryst., 1970, vol. B26, pp. 815-22. 5. K. Yvon, W. Jeitschko and E. Parth& Report of the Laboratory for Research on the Structure of Matter, Universityof Pennsylvania,Philadelphia,Pa., 1969. 6. D. I. Bardos, R. E. Malik, F. X. Spiegel, and Paul A. Beck: Trans. TMS-AIME, 1966, vol. 236, pp. 40-48.
composites and has been discussed by Crossman, Yue, and Vidoz. 4 In this theory the reinforcing phase (fibers or lamellae) is characterized by a distribution i n s t r e n g t h s . T h e l o a d c a r r i e d by a f a i l e d r e i n f o r c i n g fiber or lamellae is redistributed equally among the r e m a i n i n g f i b e r s o r l a m e l l a e in t h a t p a r t i c u l a r c r o s s section. The fractured reinforcement is not ineffective over its entire length, however. Above and below the fractured surface, shear stresses in the matrix gradually transfer a tensile load to the fiber. At a distance 5/2 above and below the fracture, the rei n f o r c i n g p h a s e a g a i n c a r r i e s t h e f r a c t i o n of l o a d p r e d i c t e d by t h e " r u l e of m i x t u r e s . , ' C o m p o s i t e failure then occurs when-in any given cross section of v e r t i c a l e x t e n t i 6 / 2 - f a i l u r e of o n e a d d i t i o n a l f i b e r o r l a m e l l a e i n c r e a s e s t h e l o a d on t h e r e m a i n i n g to the extent that they all fail. In order to predict composite strengths in this model, the ineffective length, 5, m u s t b e k n o w n a s w e l l a s t h e d i s t r i b u t i o n o f r e inforcing phase strengths, f(a),* for fibers or lamellae ~f(o) do is the fraction of fibers of length 6 that fail between a stress of o and a+do.
of l e n g t h 6. R o s e n a n d F r i e d m a n h a v e s h o w n t h a t if t h e d i s t r i b u t i o n i n s t r e n g t h s , g(5), o f f i b e r s of l e n g t h l i s k n o w n , t h i s c a n b e d i r e c t l y c o n v e r t e d t o f (a) p r o v i d e d 5 i s a l s o k n o w n . T
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