Fibre fracture bending

Some modes may dominate for example, for large bending strains in a flexible structure, fibre fracture in tension and fibre kinking in compression wdl dominate near both surfaces. Matrix cracks can cause delamination when they reach a ply interface. If the structure is stiff enough to resist with a significant force, then local indentation damage, and shear-driven delamination in the interior, wdl occur. Figure 9.2 shows schematically the different modes of fadure in three zones of a laminate. The peanut shape deformations (3) have this shape because the compression under the impact force suppresses the delaminations. 

Figure 7. / / Distribution of resistance factor (fibre content/bending moment ratio) along the length of a beam. Note that fracture occurred at the point of minimum fibre content [28].

Another aspect to be considered is the difficulty in producing curved structures with the same fibre content as flat laboratory panels. This effect is shown in Figure 16, at the comer the laminate thickness is larger than at the flat section and fibre content is rather lower. This will affect the bending stiffness of the arm and the predicted failure load. This figure also shows the fillet, which is critical to initiation in the specimens without implanted defects. It is well known that fillets can significantly alter the load path in lap shear joints and increase the failure loads (see [1] and Figure 3 for example). If a fracture mechanics approach is to be applied this effect must be considered. Some recent studies on stress intensity factors for such cases may allow this to be addressed [22]. 

For example, on the side face of a bending bar the tensile stress decreases with distance from the specimen edge. With increasing curvature of the bending bar, the cracks are driven inward to the neutral fibre. The position of the crack tip,yljp, at maximum bending deformation has to be inserted into (7) in order to calculate the tensile stress at the crack tip olip = oxx(ylip) (Fig. 11).The fracture toughness follows then from the equation Kk = K,([Pg.153]

Fibre Textile Fracture Fatigue Tensile Bending Twisting Abrasion... 

Fi. 10. (a.b) Polye.sler fibres after a single bend, (c-e) Flex fatigue in polyester kink-band fracture, (f) Flex fatigue shear splitting in nylon, (g) Flex fatigue shear splitting in polyester. For further explanation. 

The transverse tensile strength (TTS) was measured with the 3-point bending fixture at l/h=5, but now with the fibres parallel to the rollers. Fracture initiates at the point of maximum tensile stress in the bottom face of the beam below the central roller. Samples with a length of 10 mm (this is the width in the test) were cut between perspex plates with a diamond saw in order to obtain smooth cuts. The transverse tensile strength was calculated as TTS = 3/2 F/(w h) (1/h). 

Usually aramid composites yield somewhat in compression in a bending test before they finally fracture in shear. This also has a more pronounced negative effect on the SBS values of composites with treated than on those with untreated fibres. Application of the compression correction as mentioned in [7] reduces the intercept of eq. (5) further and leads to an even closer agreement with eqs. (1) and (3). Compressive yielding, and hence the correction for this effect is less for beams with... 

The mechanical properties of asbestos fibre cements may be calculated from the law of mixtures or by using the fracture mechanics formulae from which can be seen the specific work of fracture and R-curve. Mai, et al. (1980) observed also that crack initiation was close to the bending strength, which was related to a quasi elastic and brittle behaviour. For specimens with a depth greater than 50 mm the size effect on mechanical behaviour was negligible. For smaller specimens the pull-out fibres across cracks could not be developed before quick crack propagation took place followed by the failure of the specimen. 

Figure 5.7 Variation of specific work of fracture with cellulose fibre mass fraction in composite elements subjected to bending, after Andonian et al. (1979).

The approach developed by Brandt (1985) was illustrated by examples of optimal solutions for an element subjected to tension and another to bending. As an objective function the fracture energy accumulated up to a specified limit state was selected. The results calculated were obtained after derivation of proposed simplified expressions with respect to the only variable - the angle 6 of fibre system orientation. Later, the tests of specimens with various fibre orientation were executed and analyzed. All details of calculation and testing may be found in papers by Brandt (1986, 1991) and final results are summarized in Figures 8.20a and 8.20b. From these curves certain confirmation of theoretical results may be concluded, at least in the general shape of the curves and characteristic numerical values. However, there were no tests of elements with small values of angle 0 <6 <30° and the existence of an extremum for 0 0° was neither confirmed nor excluded because of techni-... 

An attempt to calculate the work of fracture in FRC elements at cracking was published by Brandt (1982,1985) for elements under axial tension, and later extended to bending (Brandt 1986). The formulae were derived for calculation of the work in the fracture process in which fibres are pulled out of the matrix across a crack. For that purpose the following assumptions were accepted ... 

Brandt, A. M., Stroeven, R, Dalhuisen, D., Donkei L. (1989) Fracture mechanics tests of fibre reinforced concrete beams in pure bending, Report 25.1-89-7/C4, Faculty of Civil Eng., Delft University of Technology. 

Brittle fractures of fibres in the lower layers of the laminate structure can be also observed as the results of further flexure and bending. This is the same principle to breaching the strength of the whole laminate. Breaking the continuity fibres is unacceptable from the point of view of the further exploitation of the laminate, as a construction material. 

Herein are contained the experimental results of an investigation into the influence of short steel fibres on the bearing capacity and deformability of concrete and reinforced concrete elements subject to bending. The fibres are either dispersed at random along the entire cross-section or in a part of the tensile zone. The beams were loaded until fracture using two concentrated forces. The following parameters were measured and observed ultimate flexural strength, deflections in... 

Methods of testing and evaluating SFRC (Steel Fibre Reinforced Concrete) made using different types of fibres (hooked-end, enlarged ends, indented and metallic glass), have been investigated in experiments on thin beams loaded in bending. The tests were aimed at evaluation of fracture behaviour of various kinds of thin layer SFRC, used e.g. in shotcrete. 

The bundled structure may also provide a reinforcing unit which is flexible and can be engaged in some local bending as it bridges a crack. Such local bending in a brittle matrix composite may produce premature fracture when the fibre is brittle but with a bundled reinforcement, even with brittle filaments, local bending capacity can be provided by the inner filament that are only loosely bonded to the matrix and can slide one relative to the other [91,92]. These special characteristics play an important role in the case of glass fibre reinforced cements and will be further discussed in Chapters 5 and 8. 

Figure 10.19 Effect of the content of fibrillated polypropylene fibres on the maximum bending load and fracture energy of concretes in impact, expressed as a percentage of the values for beams with no fibres (after Mindess and Vondran [8]).

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