A computer simulation on tensile strength of surface-Damaged fibers
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I.
INTRODUCTION
D U R I N G preparation and/or service, fibers in composites are often degraded by abrasion, chemical reaction at fibermatrix interface, and so on. The reduction in fiber strength in such cases can be attributed to the introduction of the flaws such as surface irregularities, [1'2] pits, and brittle reaction layers which introduce notches on fiber surfaces due to premature fracture, c3-9] as schematically shown in Figure 1. All of these flaws can be regarded as surface notches (cracks). However, the effects of the existence of such surface flaws on strength of fibers and composites have not been studied in detail up to date, and therefore the influences of the factors such as average flaw size, coefficient of variation of flaw size, density of flaws, and gage length on the strength of surface-damaged fibers have been unknown, probably due to the difficulty in measuring these factors other than gage length in practical composites. However, without such a difficulty in measurement, the influences of these factors can be inferred if one employs a computer simulation technique based on the Monte-Carlo method. The aim of the present paper is to show the results of the computer simulation experiment on tensile strength of surface-damaged fibers using a simple model.
II.
EXPERIMENTAL PROCEDURE
A. Model In the present study, a simple model was considered, which assumed that the strength distribution of fibers without surface flaws obeys the Weibull distribution function, [~~ the flaw size obeys the normal- or exponential distribution function, and surface flaws act as notches of mode I. If the strength of fibers without surface flaws and flaw size obey other distribution functions, the present procedure can be applied in a similar manner. SHOJIRO OCHIAI, Associate Professor, and KOZO OSAMURA, Professor, are with the Department of Metallurgy, Kyoto University, Sakyo-ku, Kyoto 606, Japan. Manuscript submitted August 3, 1987. METALLURGICALTRANSACTIONS A
(a)
(b)
(c)
Fig. 1 - Schematic representation of fibers whose surfaces are damaged with irregularities (a), pits (b), and coated layer made by chemical reaction between fiber and matrix (c).
In the present study, the fibers with a length l were regarded to be composed of the elements with a length 10. The number of the elements in one fiber M~ was given by M1 = l/lo. First the strengths of the elements were determined in the following procedure and then the strength of fibers with Ml elements was determined by the lowest value among the strength values of Ml elements. This procedure is based on the weakest link reasoning.
B. Determination of Strength 1. Strength of fibers without surface damages According to the Weibull distribution, t~~ the probability of failure P at a stress tr is given by P = 1 - exp{-l[(o- - o-,)/O-o]m}
[1]
where m is the Weibull modulus, I is the length, and tro is the normalizing parameter, and the o-, is the stress below which there is no probability of failure. The o', is in general very low and it is often treated as zero
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