Interfacial radial stress

There are many features in the analysis of the fiber push-out test which are similar to fiber pull-out. Typically, the conditions for interfacial debonding are formulated based on the two distinct approaches, i.e., the shear strength criterion and the fracture mechanics approach. The fiber push-out test can be analyzed in exactly the same way as the fiber pull-out test using the shear lag model with some modifications. These include the change in the sign of the IFSS and the increase in the interfacial radial stress, (o,z), which is positive in fiber push-out due to expansion of the fiber. These modifications are required as a result of the change in the direction of the external stress from tension in fiber pull-out to compression in fiber push-out. 

For the cylindrical coordinates of the fiber push-out model shown in Fig. 4.36 where the external (compressive) stress is conveniently regarded as positive, the basic governing equations and the equilibrium equations are essentially the same as the fiber pull-out test. The only exceptions are the equilibrium condition of Eq. (4.15) and the relation between the IFSS and the resultant interfacial radial stress given by Eq. (4.29), which are now replaced by ... 

Takaku, A. and Arridge, R.G.C. (1973). The effect of interfacial radial and shear stress on fiber pull-out in composite materials. J. Phys. D Appl. Phys. 6, 2038-2047. 

Thermal residual strains are generated in composite materials on the microscale and macroscale. The former arise from a mismatch in the coefficients of thermal expansion of the fibre and the matrix. This effect is magnified by the presence of fibre bundles, where the radial stresses can change from compressive to tensile and influence interfacial failure under... 

A close look at the stress state indueed within this joint indicates clearly a complex interaction of strain, and there are many useful commentaries on the limitations of this test(4, 5. 25, 31). If the adherend and adhesive moduli are very different (e.g. the ratio of epoxy to steel moduli, E E = 40), the axial strains in the adhesive will be about 40 times greater than those in the adherend with a similar ratio for the lateral (Poisson s) strains. Where the two materials join, this conflict is resolved by generating large interfacial radial shear stresses (Fig. 4.11(c)). Joint strength inereases with a decrease in adhesive thickness, and in a thin bondline affected completely by adherend restraint a eomplex stress arises. The ratio of the applied stress to the strain across the adhesive is then defined as the apparent or constrained Young s modulus, a(5)-... 

E ( denotes the axial elastic modulus of the fiber, where as V)2f is the longitudinal Poisson s ratio of the fiber, determined by measuring the radial contraction under an axial tensile load in the fiber axis direction and Gm denotes the matrix shear modulus. It should be noted that the negative sign in the expression for the shear stress is introduced to be consistent with the definition of an interfacial shear stress in classical theory of elasticity. The radial stress at the interface is given by ... 

Fig. 21 shows interfacial shear stresses for a carbon fiber-epoxy system. The low modulus of the epoxy matrix produces a similar effect on the stress distribution, as in the case of isotropic fibers. Calculations of interfacial shear strength assume either a maximum interfacial shear stress criterion or a maximum radial tensile stress criterion, ignoring other stress components and residual stresses in both cases. The interfacial shear strength (T ) is calculated from ... 

The interfacial stress distributions along the interface in the axial direction near the fiber ends for a model with Vf = 0.36 are shown in Fig. 24. It is noticed that the interfacial axial (shear stress (r, ) stress distributions for models with different fiber-volume fractions are of similar shapes but the shear stress is higher for higher-volume fractions. The radial stress is... 

This means that the cylinder will contract axially at a rate that is directly proportional to the interfacial energy and inversely proportional to the viscosity and the radius. The same result could have been obtained from a conventional stress analysis, using Laplace s equation for the radial stress (<7r = -y v o) and recognizing that there is an axial membrane stress of... 

The maximum retardation of polarized light occurs at the particle-matrix interface and this value is given in Table 2 as a function of crosslink density for the natural rubber-benzene system. The effects of crosslink density on the interfacial swelling, radial stress, and radial extension ratio are given in detail elsewhere [7],... 

The reduced oxidation near sample corners is related to these stress effects, either by retarded diffusion or modified interfacial reactionsManning described these stresses in terms of the conformational strain and distinguished between anion and cation diffusion, and concave and convex surfaces. He defined a radial vector M, describing the direction and extent of displacement of the oxide layer in order to remain in contact with the retreating metal surface, where ... 

With a strong interfacial bond, when a fiber fractures, the high stresses in the matrix near the broken ends are relieved by the formation of a short radial crack in the resin. There is no interfacial debonding and corresponding friction at a sheared interface, but rather, the load is transferred to the fiber by elastic deformation of the resin. The lack of adhesive failure in this case is responsible for the relatively low emission observed. 

When fiber composites are fabricated, they are often densified at a high temperature. At these temperatures the materials tend to flow and stresses can relax. As the material is cooled, however, if there is a difference between the contraction behavior of the fiber and its surrounding matrix, a state of residual stress is obtained. For example, if the thermal expansion of the fiber is less than the matrix, the matrix contracts more in cooling than the fiber, placing the fiber in compression. For the opposite case, the fiber is under radial and circumferential tension. For this latter case, a perfect interfacial bond must be assumed. 

Figure 8.38 Possible microcracking configurations for an inclusion under residual stress a) interfacial failure b) inclusion failure and c) radial cracking.

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