Fiber pull-out length

Since fiber pull-out length, p , is difficult to measure with any accuracy from the fracture surface of composite specimens containing high V(, Rpo is often expressed in terms of the inherent properties of the composite constituents. There are three cases considered here depending on the fiber length relative to the critical transfer length. 

Fig. 7.5. (a) Transverse impact fracture toughness and (b) fiber pull-out length versus testing temperature for carbon fiber-epoxy matrix composites with and without PVAL coatings on fibers. After Kim and... 

Fig. 1.18 Bounds on the relationship between the non-dimensional fiber pull-out length and the Weibull modulus.

The only alternative approaches for evaluating Sc, known to the authors, are based on pull-out and fragment length measurements.46 Both quantities depend on Sc and m, as well as r. Consequently, if r is known, Sc can be determined. For example, m can be evaluated by fitting the distribution of fiber pull-out lengths to the calculated function. Then, Sc can be obtained for the mean value, h, using Eqn. (12). This approach has not been extensively used and checked. 

Table 4 Main features of the tensile behaviour of minicomposites determined from the force-deformation curves (Fj is proportional limit) and from SEM fractography (fiber pull out length Ip, crack spacing distance at saturation d,).

Theoretical analyses of interfacial debonding and frictional pull-out in the fiber pull-out test were initially modeled for ductile matrices (e.g. tungsten wire-copper matrix (Kelly and Tyson, 1965, Kelly, 1966)) assuming a uniform IFSS. Based on the matrix yielding over the entire embedded fiber length, as a predominant failure mechanism at the interface region, a simple force balance shown in Fig. 4.19 gives the fiber pull-out stress, which varies directly proportionally to the cylindrical surface area of the fiber... 

Fig. 4.19. Fiber pull-out stress as a function of embedded fiber length, /./2a, for a tungsten wire embedded copper matrix composite system. Open symbols for pulled-out specimens solid symbols for fractured specimens. After Kelly and Tyson (1965).

Fig. 4.22. Distributions of (a) fiber axial stress, a, (b) matrix axial stress, and (c) interface shear stress, Zi, along the embedded fiber length in fiber pull-out. After Zhou et al. (1992a, b, c).

Fig. 4.38. Comparisons of partial debond stress, (rj, between fiber pull-out and fiber push-out as a function of debond length, f, for (a) release agent coated steel fiber-epoxy matrix composites and (b) untreated SiC fiber-glass matrix composites. After Kim ct al. (1994c).

Fig. 4,40. Distributions of interface shear stress, r, along the fiber length at a constant applied stress o = 4.0GPa for carbon fiber-epoxy matrix composites in fiber pull-out and fiber push-out. After...

Fig. 4.43. Growth of debond length, (, with increasing number of cycles, N, for (a) fiber pull-out and (b) fiber push-out. Initial debond length t = lOmm. After Zhou el al. (1993).

Figs. 4.44 and 4.45 show the increase in the debond length, f, and displacement, as a result of the reduction of p (from Po = 0.22 to p = 0.07) under cyclic loading. It is interesting to note that both I and 5 remain constant until the coefficient of friction, p, is reduced to a critical value p. (= 0.144 and 0.166, respectively for fiber pull-out and fiber push-out). The implication is that the debond crack does not grow... 

Fig. 6.2. Variation of fiber pull-out toughness, f po, as a function of discontinuous fibers of length, f. After...

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