Stress transfer

The steel belt, which provides strength and protection for the ply or pHes, is encased ia a compouad that must possess adhesioa to the steel which provides stress transfer from the very rigid steel to the many times more flexible tread, sidewall, and textile carcass components. The wedge compound is formulated to reduce belt-edge sheer stresses while tying the belt to the carcass and reduciag hysteresis. 

The mechanism of chemical adhesion is probably best studied and demonstrated by the use of silanes as adhesion promoters. However, it must be emphasized that the formation of chemical bonds may not be the sole mechanism leading to adhesion. Details of the chemical bonding theory along with other more complex theories that particularly apply to silanes have been reviewed [48,63]. These are the Deformable Layer Hypothesis where the interfacial region allows stress relaxation to occur, the Restrained Layer Hypothesis in which an interphase of intermediate modulus is required for stress transfer, the Reversible Hydrolytic Bonding mechanism which combines the chemical bonding concept with stress relaxation through reversible hydrolysis and condensation reactions. 

Naturally, fibers and whiskers are of little use unless they are bonded together to take the form of a structural element that can carry loads. The binder material is usually called a matrix (not to be confused with the mathematical concept of a matrix). The purpose of the matrix is manifold support of the fibers or whiskers, protection of the fibers or whiskers, stress transfer between broken fibers or whiskers, etc. Typically, the matrix is of considerably lower density, stiffness, and strength than the fibers or whiskers. However, the combination of fibers or whiskers and a matrix can have very high strength and stiffness, yet still have low density. Matrix materials can be polymers, metals, ceramics, or carbon. The cost of each matrix escalates in that order as does the temperature resistance. 

Polymeric binder can be added to the network either as an aqueous latex dispersion or as a solution that should be dried prior to lamination in this process. In either case, the polymer should form a film and join adjacent fibers together and thus improve the stress transfer characteristics of the fibrous network. Provided that the proper film forming conditions are available, the property profile of the bonded network is determined to a significant degree by the properties of the polymeric binder at the temperature of use [20,22]. For example, if a softer type of product is desired, a binder with a relatively low glass transition temperature Tg) is often chosen. 

PBAs are designed explicitly to meet the needs of specific applications on the basis of their property-processing-cost performances. One polymer is incorporated into the matrix of other polymers to impart specific characteristics as per the requirement along with the appropriate compatibilizer to ensure stress transfer in between phases. The polymer blend constituents and composition must, therefore, be selected on the basis of the compensation of properties, considering the advantages and disadvantages associated with each phase. Table 12 indicates some of the components used as modifiers. 

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... 

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) ... 

When a fiber breaks, the normal stress at each of its broken ends become zero. Over a distance of 1 /2 from each end, stress builds back up to the average value by shear stress transfer at the fiber-matrix interface. Also, the stress state in a region close to the broken ends contain the following ... 

Since most polymers, including elastomers, are immiscible with each other, their blends undergo phase separation with poor adhesion between the matrix and dispersed phase. The properties of such blends are often poorer than the individual components. At the same time, it is often desired to combine the process and performance characteristics of two or more polymers, to develop industrially useful products. This is accomplished by compatibilizing the blend, either by adding a third component, called compatibilizer, or by chemically or mechanically enhancing the interaction of the two-component polymers. The ultimate objective is to develop a morphology that will allow smooth stress transfer from one phase to the other and allow the product to resist failure under multiple stresses. In case of elastomer blends, compatibilization is especially useful to aid uniform distribution of fillers, curatives, and plasticizers to obtain a morphologically and mechanically sound product. Compatibilization of elastomeric blends is accomplished in two ways, mechanically and chemically. 

The behavior of the composites under tension can be explained based on the stress-transfer theory of Cox et al. [176]. The analysis of mechanics of short fiber-mbber composites is difficult than that for continuous fiber-mbber composites. This is because of the fact that fiber end effects are important in short fiber reinforcement which are absent in the case of continuous fiber... 

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]. 

All computations so far have been performed with the full width of the chain length distributions, i.e. chains with aspect ratios Lld< 10 have also been included. However, the effects of stress transfer across chain ends and the stress concentrations may become important below this aspect ratio. In the theory by Yoon these effects are neglected. In particular, for the Flory distribution containing a relatively large proportion of very short chains, the effects may be considerable. Therefore, calculations are performed in which the negative effect of the very short rods is approximated by assuming that for an aspect ratio L/d<4 the contribution of these rods to the strength is set to zero. 

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... 

CNT can markedly reinforce polystyrene rod and epoxy thin film by forming CNT/polystyrene (PS) and CNT/epoxy composites (Wong et al., 2003). Molecular mechanics simulations and elasticity calculations clearly showed that, in the absence of chemical bonding between CNT and the matrix, the non-covalent bond interactions including electrostatic and van der Waals forces result in CNT-polymer interfacial shear stress (at OK) of about 138 and 186MPa, respectively, for CNT/ epoxy and CNT/PS, which are about an order of magnitude higher than microfiber-reinforced composites, the reason should attribute to intimate contact between the two solid phases at the molecular scale. Local non-uniformity of CNTs and mismatch of the coefficients of thermal expansions between CNT and polymer matrix may also promote the stress transfer between CNTs and polymer matrix. 

D. Cai, M. Song, A simple route to enhance the interface between graphite oxide nanoplatelets and a semi-crystalline polymer for stress transfer, Nanotechnology, 20 (2009) 315708. 

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