Pull-out of fibers

If the fiber-matrix interfacial adhesion is poor, debonding at the fiber-matrix interface occurs, followed by pulling out of fibers from the matrix see case (a) in Fig. 7.2. If partial interfacial adhesion is present, fiber gliding occurs (case (b) in Fig. 7.2), and if interfacial adhesion is strong enough, fiber breakdown results see case (c) in Fig. 7.2 [1]. 

The second step is slipping along the fiber interface and partial or total pulling out of fibers from the matrix polymer with energy absorption parts and Wp. 

In the single fiber pull out test (SFPO), a small portion of the fiber is embedded in the bulky matrix and the interfacial strength is calculated from the peak load when the fiber is pulled out of the composite. 

As fibers are crushed in the composite, their strength increases. So long as the fibers interact with each other they can stand a load. When, however, the fiber length becomes so small that the shear stresses between the fiber and the matrix become about as low as the shear strength at the interphase the crushing process will stop and fiber fragments will be pulled out of the matrix. 

To evaluate the stability of the debond process, the instability parameter, z,nax, is compared, z ax values calculated based on Eqs. (4.104) and (4.139) respectively for fiber pull-out and fiber push-out give z ax = 6-5, 6.2 mm for coated steel wire-epoxy matrix and z ax = 0.5, 0.49 mm for the untreated SiC-fiber-glass matrix composite... 

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).

The analytical solutions derived in Sections 4.3 and 4.4 for the stress distributions in the monotonic fiber pull-out and fiber push-out loadings are further extended to cyclic loading (Zhou et al., 1993) and the progressive damage processes of the interface are characterized. It is assumed that the cyclic fatigue of uniform stress amplitude causes the frictional properties at the debonded interface to degrade... 

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...

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... 

Zhou, L.M., Kim, J.K. and Mai, Y.W. (1992b). A comparison of instability during interfacial debonding in fiber pull-out and fiber push-out. In Proc. Second Intern. Symp. on Composite Materials and Structures (ISCMS-2) (C.T. Sun and T.T. Loo, eds.), Peking University press, Beijing, pp. 284-289. 

Patrikis. A.K., Andrews, M.C. and Young, R.J. (1994). Analysis of the single fiber pull-out test by the use of Raman spectroscopy part I Pull-out of aramid fibers from an epoxy resin. Composites Sci. Technol. 52, 387 396. 

Despite the emphasis on favorable interactions between the matrix and reinforcement and compound formation between them, it may be beneficial in certain circumstances for the interaction between the two primary constituents to be relatively weak. This is especially true in ceramic-ceramic composites, where both constituents are brittle, and the only way to impart some ductility on the composite is for the interphase to fail gracefully —that is, for the fibers to actually pull out of the matrix in a controlled manner. Optimization of the interphase properties in advanced composites is currently the focus of much research. 

The axial strength of the composite can be calculated by applying Eq. (5.107). In the most common case, the matrix is more ductile than the fibers, such that the matrix critical strain exceeds the fiber critical strain, > / 1 low volume fraction of fibers, the fibers located with their ends within a distance 5 of the failure plane do not fracture, but rather simply pull out of the matrix. This movement is resisted by the friction stress, r7. The proportion of fibers for which this occurs is IJl, and the mean stress resisting pull-ont is cryi. The fibers therefore contribute a mean stress of CT/ = el ll and from Eq. (5.107) the strength becomes... 

Only handmade single sheets of paper were fabricated until, in 1798, a machine that could make continuous rolls of paper was invented in France. This machine consisted of a conveyor belt submerged at one end in a vat of suspended cellulose fibers. The conveyor belt was a screen so that water would drain from it as fibers were pulled out of the suspension. The entangled fibers were then squeezed through a series of rollers to create a long continuous sheet of paper. Within a few years, an improved version of this machine that used heated rollers was produced in England. The improved machine was called the Fourdrinier, after a wealthy industrialist who financed its creation. Automated Fourdrinier machines, such as the one shown in Figure 18.2, are still used today. 

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