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... 

A third mechanism operating at the crack tip is the energy required to pull the broken fiber out of the matrix (Fig. 18). The work required is the product of the shear strength times the pull-out length (lp). The total work of fracture can now be estimated as the sum of each of the contributions of the above mechanisms resulting in the relationship... 

Sliding stress, r(MPa) Push-out force Pull-out length, h Saturation crack spacing, /s Hysteresis loop, Se Unloading modulus, EL 1-200... 

Characteristic strength, Sc (GPa) Fracture mirrors Pull-out length, h 1.2-3.0... 

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. 

Shaw and Faber30 reported that the toughness of mullite/20 vol. % SiC whisker composites with either ARCO/ACMC or Tateho whiskers remained relatively constant up to temperatures of 1100°C. At temperatures >900°C they also observed considerable whisker pull-out lengths up to 100 /urn. However, the number of pull-outs was always <0.01% of the total whisker volume and only observed with whiskers that were perpendicular to the crack plane. 

Furthermore, for a given concentration of fibres, the toughness values associated to type fibres are always lower. This trend is related to the microscopic features observed on tl e surfaces of rupture and correlated to acoustic emission analysis. SEM micrographs of il e surfaces of rupture (Fig. 16a and 16b) clearly show long pull-out lengths of the type A fibres with very smooth surfaces whereas type B fibres are covered with matrix. The cohesive ruptui e of the matrix reinforced with type B fibres is consistent with the occurrence of a unique population of acoustic emission events (Fig. 16a) whereas two populations are observed wiih type A fibres (Fig. 16b) associated to fibre decohesion and sliding mechanisms. 

Estimate the increase in fracture toughness that is expected from each mechanism. Indicate any assumptions in your analysis (try to be realistic). For part c), estimate the pull-out length required for the pull-out contribution to be equivalent to that of bridging. 

Table 4 reports the interface shear stresses that have been extracted from the hysteresis loops, as well as pull out lengths and matrix crack spacing distances. These latter data provide also a measure of interface strength. Both sets of data indicated the same trends, and they support the above statements. The interface shear stresses (t) obtained for the minicomposites reinforced with Hi-Nicalon S fibers are quite low (Table 4). Weak interfaces could be logically expected for this Hber/interphase system, fhe current values of x fall within the range of data detennined on SiC/SiC minicomposites reinforced with Nicalon or Hi-Nicalon fibers [7, 12, 14]. Furthermore, it...

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,).

Obviously the strength of the interfacial bonding between the CNTs and the polymer matrix will have a major impact upon their ability to reinforce the composite. Wagner et al. [114] studied this issue by conducting experiments in which a MWNT, attached to an AFM tip, was embedded in a polymer and pulled out. The force versus pull-out length was recorded for a poly(ethylene-butene) matrix resulting in an interfacial shear strength of 47 MPa. This value is consistent with other measurements where estimates of 50 MPa for various nanotube types were recorded [12]. 

Hartness [100], working with XAS and HMS fibers in a PEEK matrix showed similar behavior. The similarities between PEEK and PP are probably greater than the differences in their crystalline structure. Beaumont [101] has shown that with HMS (treated) fiber, there is almost no pull-out, whereas with HMU (untreated) fiber, extensive debonding and pull-out take place. The pull-out lengths can be measured and using an analytical technique outlined by Phillips [102], values can be obtained for the nylon/fiber interfacial bond strength and fracture energies. 

In a simple approximation, we can assume that the pull-out length varies between 0 and half of the critical length Iq. The mean energy dissipation per fibre is thus... 

The fracture surface of an as-received sample is shown in Figure 2. The fracture surface exhibits the characteristic fiber pull-out typical of quasi-ductile glass matrix composite materials [13,15]. However, inspection of the fracture surfaces reveals that the average pull-out lengths are not uniform across the composite section but depend on the relative orientation of the fibre bundles and the fracture propagation plane. Areas exhibiting fewer fibres are observed when these were oriented parallel to the fracture surface. This behaviour explains qualitatively the lower Kic values determined in this material in comparison to unidirectional fibre reinforced composites, as mentioned above, where all fibres contribute equally to toughening by the pull-out mechanism [13,15]. 

SEM micrographs taken from the fracture surfaces evidence that the dominating failure mode of short fiber hybrid composites is fiber pull-out. Recall that fiber pull-out strongly depends on the quality of the Interfacial adhesion. The remaining voids after the fibers were pulled out Indicate for poor interfacial adhesion the maximum pull-out length of the fibers was ca. 100 pm. 

The load N can be calculated assuming fibre-matrix frictional bond r, and taking a pull-out length of /yv, which is only the right term in Eq. 3.36, O,5/acos0 (the other term in Eq. 3.36, is reiated to the part of the fibre which separates from the matrix on bending, Eigure 3.27) ... 

On examination of the samples with 5% flax fiber content, it can be noted that samples with higher glycerol content show shorter pull-out lengths and more breakage. Therefore it can be argued that an increase in glycerol content does not... 

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