J O U R N A L O F M A T E R I A L S S C I E N C E L E T T E R S ? ( 1 9 8 8 ) 1042

C o m m e n t o n " C a r b o n f i b r e - t h e r m o p l a s t i c m a t r i x , a d h e s i o n "

G. D IAZ Departamento de Ciencia e Ingenieria de Materiales, /DIEM, Facultad de Ciencias Fisicas y Mathem~ticas, Universidad de Chile, Casilla 1420, Santiago, Chile

In the very interesting work ofDi Landro and Pegoraro [1], in which Weibull statistics are used, we have observed a misunderstanding about the meaning of Weibull's parameters. According to Di Landro and Pegoraro's notation, the Weibull function is

f( O- - - o.p O, ~ o.p

qb(a) = ~ \ o.o / (1)

(0 O. "~ o.p

where o.p and a 0 are Weibull's parameters, ~(o.) is the specific-risk-of-fracture function, and a is the ten- sile strength, ap is the minimum value of o., i.e. the threshold strength below which the failure probability is zero. The Weibull modulus, m, is a measure of the dispersion of fracture strength. It is an important material parameter characterizing the scattering of material strength; large values of m indicate uni- formity while small values represent a large scattering. a 0 has been termed the Weibullian characteristic strength, and it is a normalizing factor that does not correspond directly to any readily determined physical quantity. The controversial parameter is a0, because Di Landro and Pegoraro believe that a0 is the maxi- mum value of the tensile strength. However, it is easy to see that o,0 can take any value between 0 and infinity, i.e.

0 < a0 < oo (2)

and it is a fabrication parameter. In order to obtain a maximum value of tensile strength it is necessary to radically modify the Weibull function, q~(a), as carried out by Kies and used, for instance, by Kalish et al. [2] in their Equation 3. The Kies function is as follows

K \ \ / % ~ o. ~< o.~

4~(o.) = o. < % (3)

O. ~ O" s

where K is a constant that is derived in a natural way when establishing the agreement between the experi- mental data and the functions theoretically obtained, o-s is the maximum strength above which the proba- bility of failure is equal to 1. Hence study of the maximum strength should be made using not the Weibull function but the Kies function.

On the other hand, Di Landro and Pegoraro claim that the expression for the average strength, 5,r, of a monofilament consisting of n ideal links and given by

6rr = o.---d--~-da = o.p + n - ~ F 1 + p

(4)

where Pn(a) is the probability of failure of a chain of n links, has not been presented before in the literature. However, this equation (Equation 13 in [1]) is indeed well-known from Weibull's early works [3, 4], in which it appears together with its detailed derivation and also with the moments of different order about zero and about the mean, and Pearson's constants.

References 1. L. DI L A N D R O and M. P E G O R A R O , J, Mater. Sei. 22

(1987) 1980. 2. D. K A L I S H , B. K. T A R I Y A L and R. O. P I C K W I C K ,

Amer. Ceram. Soe. Bull. 56 (1977) 491. 3. W. WEIBULI., lngeniiJrs Vetenskaps Akad. Handl. 151

(1938) I. 4. Idem, ibid. 153 (1939) l.

Received 2 October 1987

and accepted 27 June 1988

1 042 0261-8028/88 $03.00 + .12 © 1988 Chapman and Hall Ltd