Matrix fracturing

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. 

If structural failure of the fabricated composite occurs by cracks in the matrix, fracture of the particle-matrix interface, or case debonding under any applied load, the extra and exposed surface will cause an enormous rise in the motor pressure during the combustion event with disasterous consequences. 

The descriptions presented in the foregoing sections are concerned mainly with composites containing brittle fibers and brittle matrices. If the composite contains ductile fibers or matrix material, the work of plastic deformation of the composite constituents must also be taken into account in the total fracture toughness equation. If a composite contains a brittle matrix reinforced with ductile libers, such as steel wire-cement matrix systems, the fracture toughness of the composite is derived significantly from the work done in plastically shearing the fiber as it is extracted from the cracked matrix. The work done due to the plastic flow of fiber over a distance on either side of the matrix fracture plane, which is of the order of the fiber diameter d, is given by (Tetelman, 1969)... 

The failure processes in thermoplastics composites with aligned glass fibers of sub-critical transfer length have been characterized (Lauke and Schultrich, 1983, 1986a, b Lauke et al., 1985 Lauke and Pompe, 1988) in terms of matrix fracture mode which is determined mainly by the ductility of the matrix material, loading rate and temperature. The total specific work of fracture, / t, is expressed as the sum... 

In (15.36) rm is the matrix fracture energy, t is the interfacial shear strength, and Ex is the axial modulus of the composite. In (15.37) e refers to the effective properties of the composite, which, for unidirectional fiber reinforcement, can be calculated with good approximation by the rule of mixtures. 

Although the two approaches are very similar, the value of A Tc in Boccaccini s model does not depend on the interfacial shear strength t, as a result of the model chosen for the value of matrix cracking stress. Blissett et al. (1997) suggested that their method was valid for the UD material providing that some key parameters (interfacial shear stress, matrix fracture energy) were determined independently. 

Budiansky, B., Hutchinson, J.W. and Evans, A.G., (1986), Matrix fracture in fibre-reinforced ceramics , J. Mech. Phys. Solids., 34(2), 167-189. 

The matrix fracture behavior can also be described by using stress intensity factors, K. This approach is more convenient than the /-integral in some cases particularly for short cracks and for fatigue.31,84 To apply this approach, it is first necessary to specify the contribution to the crack opening induced by the applied stress, as well as that provided by the bridging fibers. For a plane strain crack of length 2a in an infinite plate, the contribution due to the applied stress is85... 

Fig. 5.7 Macroscopic damage modes that occur during the tensile and flexural creep of fiber-reinforced ceramics. It is assumed that matrix or fiber damage is avoided during initial application of the creep load (see discussion of loading rate effects in the next section). Periodic fiber fracture can occur if the creep rate of the matrix exceeds that of the fibers. Periodic matrix fracture is common when the matrix has a higher creep resistance than the fibers. In this figure, it is assumed that initial microstructural damage is avoided during application of the creep load.

Fig. 5.9 Influence of initial loading rate on fiber and matrix stress and microstructural damage mode in materials where CMR< 1. Under rapid loading, the matrix stress may achieve a level sufficient to initiate matrix fracture.

Considerable energy must be involved in pulling apart the asbestos fibers during the impact energy used in overcoming frictional type forces, forces required to pull individual fibers away and past others. The extent of this mechanism is dependent on the asbestos fiber bundles not being thoroughly wet by the matrix since the better wet open fibers are fractured at the matrix fracture surface. 

Multiple matrix fracture prior to failure of composite... 

CaC03) aj) < aj. The schematic sequence is shown in Fig. 5 stress concentration localised at particle pole (micronic particle), to induce either local matrix fracture (crazing) or interface decohesion (cavitation). 

This sharp variation in toughness has been interpreted as a transition between different fracture mechanisms. Matrix fracture and fibre debonding are the prevailing fracture mechanisms at low values of the fibre orientation factor, while at high values the main fracture mechanism is fibre pull-out. Thus, besides a critical fibre length, also a critical fibre angle should be considered. 

Ti-6.6Al-3.5Zr-1.3Si-l.lB. In as-cast state, as-dendritic structure is practically invisible. Lamellar a -structure of matrix is recognized well. Close to uniformly distributed borides have rod-like morphology and fogged like brushwood. Thickness of rods is between 0.1-1.5 pm. Their length is up to 0.2 mm. Fine (0.1-0.3 pm) silicides are uniformly distributed along matrix. Fracture feature is intensive cleavage microcracking of RT and... 

In composite propellants, a relatively strong bond between binder and filler is important for obtaining high tensile strength. However, the edges and surfaces of the inclusions serve as sites of dangerously high stress concentrations, which could cause internal failure of the softer matrix material. Most studies (I, 2, 6-9) have dealt with the problem of matrix fracture induced by the inclusions. Here, we present the mode of matrix fracture called cavitation,... 

The approach for unsaturated conductivity outlined in previous sections was extended to modeling the unsaturated hydraulic conductivity of rough fracture surfaces (Or Tuller, 2000). Flow on rough fracture surfaces is an essential component required for deriving constitutive relationships for flow in unsaturated fractured porous media (Or Tuller, 2001). The detailed derivations are obtained by consideration of a dual porosity model (matrix - fracture) and the proportional contributions to flow from these different pore spaces. 

Processes being studied in the modeling of the Kamaishi Test included groundwater and heat flow in the rock matrix, fractures, buffer, and their interfaces under varying unsaturated conditions. Before emplacement of buffer and heater, the inflow of water into the test pit was affected, not only by the presence of fractures, but also by the unsaturated condition of the rock near the test pit. Strong variation in the areal distribution of inflow was observed on the walls of the test pit. After the heater and bentonite were emplaced, diffusion of water into the bentonite from the rock occurred simultaneously with drying of the bentonite near the... 

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