Fibre fracture ductile

An understanding of the mechanisms responsible for stress transfer provides the basis for prediction of the stress-strain curve of the composite and its mode of fracture (ductile vs. brittle). Such understanding and quantitative prediction may also serve as a basis for developing composites of improved performance through modification of the fibre-matrix interaction. This might be achieved, for example, through changes in the fibre shape, or treatment of the fibre surface. 

For >> 2 c sufficient embedded length is available to develop a stress equal to the fibre strength, and the failure will be predominantly by fibre fracture. For I ll(, the fibres are so short that they wiii pull out before sufficient stress is developed to cause fibre failure. These strength efficiency factors for a cracked matrix (Eqs 4.11 and 4,12) are smaller than those derived by Kelly (Eqs 4.3 and 4.4) for a composite with a ductile, uncracked matrix. 

Many fibrous composites are made of strong, brittle fibres in a more ductile polymeric matrix. Then the stress-strain curve looks like the heavy line in Fig. 25.2. The figure largely explains itself. The stress-strain curve is linear, with slope E (eqn. 25.1) until the matrix yields. From there on, most of the extra load is carried by the fibres which continue to stretch elastically until they fracture. When they do, the stress drops to the yield strength of the matrix (though not as sharply as the figure shows because the fibres do not all break at once). When the matrix fractures, the composite fails completely. 

The paper is presented in three parts. First, the tests employed to determine the mixed mode fracture envelope of a glass fibre reinforced epoxy composite adhesively bonded with either a brittle or a ductile adhesive are briefly described. These include mode I (DCB), and mixed mode (MMB) with various mixed mode (I/II) ratios. In the second part of the paper different structural joints will be discussed. These include single and double lap shear and L-specimens. In a recent European thematic network lap shear and double lap shear composite joints were tested, and predictions of failure load were made by different academic and industrial partners [9,10]. It was apparent that considerable differences existed between different analytical predictions and FE analyses, and correlation with tests proved complex. In particular, the progressive damage development in assemblies bonded with a ductile adhesive was not treated adequately. A more detailed study of damage mechanisms was therefore undertaken, using image analysis combined with microscopy to examine the crack tip strain fields and measure adherend displacements. This is described below and correlation is made between predicted displacements and failure loads, based on the mixed mode envelope determined previously, and measured values. 

C/SiC composites show a quasi-ductile fracture behaviour, derived from mechanisms like crack deflection and fibre pullout. Figure 14 shows exemplarily these effects within a C/C-SiC composite. The linear-elastic behaviour of C/SiC is less pronounced than for example SiC/SiC composites due to the inherent microcracks in the matrix which occur during cooling-down from processing to room temperature because of the high thermal mismatch between C-fibres and SiC-matrix. 

In every approach one finds a wide range of sophistication. In the continuum approach, the simplest (and most common) models are based on linear elastic fracture mechanics (LEFM), a well developed discipline that requires a linear elastic behaviour and brittle fracture, not always exhibited by fibres. Ductility and the presence of interfaces, not to mention hierarchical structures, make modelling much more involved. The same is true of the atomistic approach fracture models based on bond breaking of perfect crystals, using well established techniques of solid state physics, allow relatively simple predictions of theoretical tensile stresses, but as soon as real crystals, with defects and impurities, are considered, the problem becomes awkward. Nevertheless solutions provided by these simple models — LEFM or ideal crystals — are valuable upper or lower bounds to fibre tensile strength. 

Exceptions to this form of ductile fracture appear in microstructurally clean high-purity metal fibres, which sometimes neck down to a point. On the contrary, in ductile fibres containing large defects, or deep surface notches, necking is absent and a brittle... 

Once the crack is nucleated, crack growth can be modelled using the above-mentioned models, or from a more macroscopic point of view by using the techniques of elasto-plastic fracture mechanics (EPFM) (see, for example, Anderson, 1995, and Broberg, 1999). To the authors knowledge, few results are available of ductile fibre failure based on EPFM, most probably because the small size of fibre diameters invalidates some of the hypotheses on which this theory is based. 

F/g.. . Ductile fractures. (a,b) Thick undrawn nylon monofilament, (c) Polyester fibre, (d) Polyester film, (e.f) Nylon fibre. For further explanation, see Fig. I. 

So far no account has been taken of stress distributions. The experimental evidence, de.scribed in the 3rd paper in this volume (fig. 3), is that there is ductile fracture with a crack which progressively opens into a V-notch until catastrophic failure occurs when the notch covers about half the fibre cross-section. If there is a defect, usually on the surface but sometimes internally (when the V-notch becomes a double cone), the stress concentration will lead to the start of the rupture, although it has a negligible effect on the mean fibre stress at which this occurs. If there is no defect, the evidence is that an initial crack will form by a coalescence of voids that form under high stress. Variation in the degree of orientation across a fibre may well play a part. If the skin of the fibre is more highly oriented, it will reach its limiting extension before the core. 

In the conditions of fibres - representing highly oriented structures - mechanical stretching solicitation, the appearance, evolution and microcracks development, by free radicals mechanism, sequentially occur, by a similar way with the ductile fracture. Figure 3.300 and 301 [878 and 879]. This fact was evidenced using SEM technique [880]. 

In the case of composite materials, the application of mechanical fracture principles, and the approaching manner in this field evolved from the definition of same parameters, which represent criteria of fracture process evaluation, until to the establish of some precise models of deformation and fracture, in function of the matrix nature (ductile or brittle), filler type (particles or fibres), and, for fibres, their geometry and orientation. 

In the case of the composites based on high toughness matrix, e.g. PEEK, the reinforcement with fibres, in the best case will not negatively affect the composite properties. In the case of a weak bond fibre/matrix, for instance PTFE/very short glass fibres, a decrease of fracture toughness is expected. For the rigid matrix (PET at -60 °C), the fibres presence enhances the composite toughness as compared to the ductile matrix. 

Work of fracture is considerably increased when a brittle matrix is reinforced by a system of inclusions in the form of grains or fibres. An internal structure created purposefully transforms a brittle behaviour into a quasi-ductile one, characterized by large deformations and high fracture toughness. This transformation into a composite material is described here on many occasions. 

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