Stress interfacial shear

The analysis depends on whether the interfacial failure occurs by yielding or by crack propagation. The simplest analysis is based on interfacial yielding where the shear stress is assumed to be distributed uniformly over the interface from top to bottom. According to this analysis, the interfacial shear stress increases uniformly until every location in the interface gives way simultaneously. 

The purpose of these experiments was to characterize different flow details under conditions when the superficial gas velocity is constant and the superficial liquid velocity increases. The upward flow regimes are presented in Fig. 5.33. Figure 5.33a shows the stratified flow pattern at [/gs = 20 m/s and J/ls = 0.005 m/s. In the region of pure stratified flow the liquid layer is drawn upward by the gas via the interfacial shear stress. No droplets could be observed at the interface. Such a regime was also observed by Taitel and Dukler (1976), and Spedding et al. (1998). 

Melcher, JR Taylor, GI, Electrohydrodynamics A Review of the Role of Interfacial Shear Stresses, Annual Review of Fluid Mechanics 1, 111, 1969. 

Cheremisinoff and Davis (1979) relaxed these two assumptions by using a correlation developed by Cohen and Hanratty (1968) for the interfacial shear stress, using von Karman s and Deissler s eddy viscosity expressions for solving the liquid-phase momentum equations while still using the hydraulic diameter concept for the gas phase. They assumed, however, that the velocity profile is a function only of the radius, r, or the normal distance from the wall, y, and that the shear stress is constant, t = tw. ... 

For the interfacial shear stress with roll waves, the following expression was used ... 

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]. 

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. 

Fig. 2,10. Fiber strain and interfacial shear stress (IFSS) profiles along the fiber length for a heat-treated Kevlar 49 fiber-epoxy resin composite. At applied strains of (a) 0.60% (b) 1.90% and (c) 2,5%. After...

Barsoum, M. and Tung, F.C. (1991). Effect of oxidation on single fiber interfacial shear stresses in a SiC--borosilicate glass system. J. Am. Ceram. Soc. 74, 2693-2696. 

Brun, M.K. and Singh, R.N. (1988). Effeet of thermal expansion mismatch and fiber coating on the fiber/ matrix interfacial shear stress in ceramic matrix composites. Adv. Ceram. Mater. 3, 506-509. 

Goettler, R.W. and Faber, K.T. (1989). Interfacial shear stress in fiber-reinforced glasses. Composites Sci. Technol. 37, 129-147. 

Singh, R.N. (1988). Role of fiber-matrix interfacial shear stress on the toughness of reinforced oxide matrix composites. In High Temperature High Performance Composites. Mat. Res. Soc. Symp. Proc.. Vol, 120 (F.D, Lemkey, S.G. Fishman, A.G. Evans and J.R. Strife, eds.), MRS, Pittsburgh, PA, pp. 259-264,... 

Figure 5.93 Distribution of tensile stress (top) and interfacial shear stress (bottom) along a short fiber. Reprinted, by permission, from N. G. McCrum, C. P. Buckley, and C. B. Bucknall, Principles of Polymer Engineering, 2nd ed., p. 276. Copyright 1997 by Oxford University Press.

Gersappe [250] used an MD simulation to probe the molecular mechanisms by which nanofillers reinforce the polymer matrix. Liao and Li [251] used Molecular Modeling to quantify CNT-polymer interfacial shear stress and found it to be about one order of magnitude higher than that of microfiber-reinforced composites. 

Imposing a shear stress parallel to the fiber axis of a unidirectional composite creates an interfacial shear stress. Because of the disparity in material properties between fiber and matrix, a stress concentration factor can develop at the fiber-matrix interface. Linder longitudinal shear stress as shown by the diagram in Fig. 13, the stress concentration factor is interfacial. The analysis shows that the stress concentration factor can be increased with the constituent shear modulus ratio and volume fraction of fibers in the composite. Under shear loading conditions at the interface, the stress concentration factor can range up to 11. This is a value that is much greater than any of the other loadings have produced at the fiber-matrix interface. 

From the brief discussion above, it can be seen that our knowledge of the pressure drop and the interfacial shear stress in the gas stream of a wetted-wall column is very unsatisfactory at present. Since the pressure drop is an important quantity in more complicated two-phase flows, of which gas/film flow is the simplest case, this is particularly unfortunate, and a great deal of detailed experimental work is necessary on this topic. 

The fiber modulus and matrix shear modulus are also required for the analysis. The fiber s coordinates are recorded directly from the stage controllers to the computer. The operator begins the test from the keyboard. The x and y stages move the fiber end to a position directly under the debonder tip the z stage then moves the sample surface to within 4 yum of the tip. The z-stage approach is slowed down to 0.04 jan/step at a rate of 6 steps/s. The balance readout is monitored, at a load of 2 g the loading is stopped, and the fiber end returned to the field of view of the camera. The location of the indent is noted and corrections are made, if necessary, to center the point of contact. Loading is then continued from 4 g in approximately 1 g increments. Debond is determined to have occurred when an interfacial crack is visible for 90-120° on the fiber perimeter. The load at which this occurs is used to calculate the interfacial shear stress at debond. 

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. 

By electromagnetic means, surface charges can be induced and accumulated on the boundary of a dielectric material [94], Liquid samples can be treated the same way. For a non-uniform external electric field, interfacial shear stress in liquids is generated, inducing flow motion which tends to eliminate this stress. In this way, new interfaces are formed and mixing can be achieved. 

Schrenk et al. (66) were among the first to report and study this interfacial instability, which they attributed to exceeding a critical value of interfacial shear stress. This criterion... 

Fig. 12.38 Predicted interfacial shear stress at the polyester/EVA interface. [Reprinted by permission from H. Mavridis and R. N. Shroff, Multilayer Extrusion Experiments and Computer Simulation, Polym. Eng. Sci., 34, 559 (1994).]...

The basic Nusselt analysis ignores inertial effects in the condensed film and subcooling effects. Approximate methods of accounting for subcooling were discussed above. A method of accounting for both effects is discussed in this section. To illustrate the method, condensation on an isothermal vertical plate is again considered [52] to [54]. Interfacial shear stress effects will be neglected. 

The test method consists of uniaxially straining a sample of the film-substrate couple as shown schematically in Figure 1. The film thickness is t, and the specimen width is w. Under tensile strain, an interfacial shear stress, x(x), is produced. While the film is bonded to the substrate, the shear stress, x(x), at the interface causes a tensile stress, metal film. When the strain is sufficient, the tensile stress will reach the ultimate tensile strength of the film, tr. Then, if the film fails by brittle... 

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