Theoretical prediction of tensile strength of fibers as a function of thickness of brittle zones on fiber surfaces
- PDF / 624,464 Bytes
- 7 Pages / 594 x 774 pts Page_size
- 65 Downloads / 195 Views
1. I N T R O D U C T I O N
IN artificial composites, interfacial chemical reaction between fiber and matrix often takes place during preparation a n d / o r service. The reaction has been known as one of the causes in reducing the strength of composites. In most reported cases of interfacial reaction, the formed reaction zone is brittle and fails at a small strain, thus often forming a circumferential notch. The formed notch hastens a fracture of the fiber in the case where the interface is strong enough to permit the formed notch to extend into the fiber) -4 On the other hand, in the case where the interfacial bonding is weak and the exerted shear stress on the interface exceeds the interfacial shear strength, debonding occurs and leads to no loss in fiber strength, because debonding will cause blunting of the notch tip? In general, the fiber strength is determined by i) when brittle zone fails; namely when a notch is formed, ii) when notch extends into the fiber and iii) when interracial debonding arises. In order to describe the fracture mode of the fiber coated with brittle zone, quantitative estimation of i), ii) and iii) is indispensable. In this work, to derive i), ii) and iii) in a quantitative manner, we employ a model of two-component composite cylinder of inner core of fiber and outer case of brittle zone, shown in Fig. 1 where the radii of the fiber and composite are shown by a and b, respectively, the thickness of the brittle zone by c ( = b - a), and the distance from the broken end of the zone by z. The basic concept of the present method to analyze the fracture mode of the coated fiber is as follows; For a formation of a notch i), for the notch extension ii), and for the interfacial debonding iii), we calculate the fiber strains at z = 0 as unifying parameters; namely we derive the fiber strain at z = 0, at whose strain level a SHOJIRO OCHIAI is Associate Researcher and YOTARO MURAKAMI is Professor, Department of Metallurgy, Kyoto University, Sakyo-ku, Kyoto 606, Japan. Manuscript submitted May 12, 1980.
notch is formed, ~3, the strain at z = 0 at whose level the notch extends, c~, and the strain at z = 0 at whose level debonding arises, c~. We derive c3, c~ and e~ by applying Weibull theory, 6 the fracture mechanics and the shear lag analysis proposed by Dow, 7 respectively. Denoting the failure strain of the bare fiber by e3,, we can know which of notch formation, notch extension, and interfacial debonding occurs, by comparison e3, c~, c~ and e), with each other, since the sequence of them, in principle, corresponds to the sequence of occurrence. However, the values of c'r, c~ and e~ are calculated only mathematically so that we should give physical meaning when we interpret the calculated sequence as similarly as in our previous work? For instance, when the calculated sequence is c~ ~ c~ ~ c~ ~ c~, the mathematical meaning of this sequence is that, notch is formed at first, then debonding occurs and then notch extension occurs, but in actual behavior of the model composite, each event does not
Data Loading...
