Stress Transfer Across the Interface

Apart from the elastic stress transfer at the perfectly bonded interface, another important phenomenon that must be taken into account is the stress transfer by friction, which is governed by the Coulomb friction law after the interface bond fails. Furthermore, matrix yielding often takes place at the interface region in preference to interfacial debonding if the matrix shear yield strength, Xm is significantly smaller than the apparent interface bond strength, tb. It follows thus 

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The significance of Rosen s work lies in the attempt of quantifying the efficiency of stress transfer across the interface with respect to the fiber length, by introducing the concept of ineffective length . The ineffective fiber length, (2L), was defined by specifying some fraction, (f>, of the undisturbed stress value below which the fiber shall be considered ineffective. (2i) normalized with fiber diameter, 2a, is derived as... 

There are situations where polymer blends may exhibit unique characteristics for utility in composite systems. One of these examples involves the segregation of conductive carbon black at the interface of phase separated polymer blends to yield a much lower concentration to reach the percolation threshold [ 1098,1099 ]. Another area of interest involves the addition of a polymer offering excellent adhesion to the filler as well as mechanical compatibility (or miscibility) with the matrix polymer. The polymeric interfacial agent can offer improved dispersion of this filler in addition to improved stress transfer across the interface between matrix and filler. The preferential concentration of filler particles in one phase is a situation... 

There are two well-accepted models for stress transfer. In the Cox model [94] the composite is considered as a pair of concentric cylinders (Fig. 19). The central cylinder represents the fiber and the outer region as the matrix. The ratio of diameters r/R) is adjusted to the required Vf. Both fiber and matrix are assumed to be elastic and the cylindrical bond between them is considered to be perfect. It is also assumed that there is no stress transfer across the ends of the fiber. If the fiber is much stiffer than the matrix, an axial load applied to the system will tend to induce more strain in the matrix than in the fiber and leads to the development of shear stresses along the cylindrical interface. Cox used the following expression for the tensile stress in the fiber (cT/ ) and shear stress at the interface (t) ... 

In the macrocomposite model it is assumed that the load transfer between the rod and the matrix is brought about by shear stresses in the matrix-fibre interface [35]. When the interfacial shear stress exceeds a critical value r0, the rod debonds from the matrix and the composite fails under tension. The important parameters in this model are the aspect ratio of the rod, the ratio between the shear modulus of the matrix and the tensile modulus of the rod, the volume fraction of rods, and the critical shear stress. As the chains are assumed to have an infinite tensile strength, the tensile fracture of the fibres is not caused by the breaking of the chains, but only by exceeding a critical shear stress. Furthermore, it should be realised that the theory is approximate, because the stress transfer across the chain ends and the stress concentrations are neglected. These effects will be unimportant for an aspect ratio of the rod Lld> 10 [35]. 

The surface characteristics of these species are determined by the particulates and stress transfer across the membrane will tend to be low, reducing internal circulation within the drop. The structure of the interface surrounding the drop plays a significant role in determining the characteristics of the droplet behaviour. We can begin our consideration of emulsion systems by looking at the role of this layer in determining linear viscoelastic properties. This was undertaken by... 

Kim, J.K. and Mai, Y.W, (1996b). Modelling of stress transfer across the fiber-matrix interface. In Numerical Analysis and Modelling of Composite Materials. (J. Bull ed.). Blackie Academic Professional, Glasgow, Ch. 10, pp. 287-326. 

Griffin32 demonstrated that the decline in properties of starch-filled composites could be mitigated somewhat by treating the surface of the starch granules to make them more hydrophobic. This treatment improved the adhesion and stress transfer across the particle/matrix interface and resulted in improved properties relative to no treatment, although properties were still generally reduced compared to the unfilled polymer. 

Adhesion commonly refers to the potential for stress transfer across an interface between two materials [81]. In a fiber-reinforced composite, adhesion will result in stress transfer between fiber and matrix. The matrix thus acts to transfer stress between adjacent fibers. The adhesion between fiber and matrix will affect shear stress transfer in a composite. In addition, stress will be transferred from the ends of broken fibers to adjacent fibers through the interface and the matrix. 

The role of the interface in such a thermal feedback process, in a two-phase system, is to provide a mechanism by which the local deformation process can proceed in a band that includes the transition region between the phases, (e.g. an interfacial craze ) or cross from one phase to the other. Suppose, for one extreme set of circumstances, that the intermolecular forces between the phases are of comparable strength to the forces within either phase. This means chemisorption, or pol3mier grafting, with about the same number of strong bonds per unit area as in the bulk. Then it is obvious how the local stress and deformation are transferred across the interface. 

We now turn attention to conditions at the electrodes. These play vital roles in establishing the pre-breakdown conditions in the liquid under high electric stress and in triggering the breakdown itself. It has been natural to invoke electron injection at the cathode as an important component since high fields will lower the potential barrier to electron transfer across the interface whether it occurs by a thermally activated or tunnelling process. However, employment of the Schottky formula for field-assisted thermionic emission or the Fowler-Nordheim one for tunnel emission which are appropriately applicable only for electron transfer to a vacuum is a much too simplified solution to the problem. 

A discontinuous fiber composite is one that contains a relatively short length of fibers dispersed within the matrix. When an external load is applied to the composite, the fibers are loaded as a result of stress transfer from the matrix to the fiber across the fiber-matrix interface. The degree of reinforcement that may be attained is a function of fiber fraction (V/), the fiber orientation distribution, the fiber length distribution, and efficiency of... 

These parameters refer separately to the filler and the matrix. However, besides these parameters, there is another factor, which is of cardinal importance for the characterization of a composite system, which is the effectiveness of the bond between matrix and filler in transferring stresses across the interface. 

The entire picture described above strongly suggests that we make a marine layer model with a prescribed internal flow field. The top of the layer is nearly as wall-like as the bottom because vertical disturbances are strongly resisted by buoyant forces. Therefore, little Reynolds stress momentum transfer occurs across the interface just as there is almost no normal transport of species (a property with which Angelenos are familiar). 

There is a great deal of theoretical and experimental information from micrometeorological research on the transfer of momentum, heat, and mass at solid and liquid surfaces and across their associated air boundary layers (hence the term boundary layer models for relationships arising from this approach). Based on the analogy between transfer of momentum and mass, it has been shown that k is proportional to the friction velocity in air (u ) and that k is also proportional to Sc. Apart from an assumption that the surface was smooth and rigid, it was also necessary to assume continuity of stress across the interface in order to convert the velocity profile in air to the equivalent profile in the water (Deacon, 1977). The relationship developed by Deacon is as follows ... 

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