Stress interface shear

Critical interface shear stress t, (Pa). This is a shear stress that causes a relative slide on the phase interface of the two components,... 

The interface shear stress can be derived from the observed fragment length if one assumes that its absolute value is constant over the whole fragment length. Based on simple equilibrium of length, one can derive that in each point along the fiber... 

The average shear strength at the interface, t., whether bonded, debonded or if the surrounding matrix material is yielded, whichever occurs first, can be approximately estimated from a simple force balance equation for a constant interface shear stress (Kelly and Tyson, 1965) ... 

In the second approach shown in Fig 3.12(b), a force is applied continuously using a Vickers microhardness indenter to compress the fiber into the specimen surface (Marshall, 1984). For ceramic matrix composites where the bonding at the interface is typically mechanical in nature, the interface shear stress, Tf, against the constant frictional sliding is calculated based on simple force balance (Marshall, 1984) ... 

Fig. 4.2. Variations of fiber axial stress, of, and interface shear stress, Tj, according to Eqs. (4.1) and (4.2),...

Fig. 4.7. Distributions of (a) fiber axial stress, a, (b) matrix axial stress, Om., and (c) interface shear stress. T along half the embedded fiber length, L, in the fiber fragmentation test.

Fig. 4.10. Distribution of (a) normalized fiber axial stress, a)/a, and (b) normalized interface shear stress, along the fiber axis, r/a, for elastic moduli E = 1,5. 3.0 and 6.0 GPa with a constant f = 230 GPa.

Fig. 4.31. Distributions of (a) fiber axial stress and (b) interface shear stress along the axial direction obtained from micromechanics analysis for different fiber volume fractions, Vf = 0.03, 0.3 and 0.6 (—) single fiber composite (--------) three cylinder composite model. After Kim et al. (1994b).

Fig. 4.34. Maximum interface shear stresses obtained at loaded and embedded fiber ends from FEM...

Fig. 4,40. Distributions of interface shear stress, r, along the fiber length at a constant applied stress o = 4.0GPa for carbon fiber-epoxy matrix composites in fiber pull-out and fiber push-out. After...

Fig. 7.11. Normalized interface shear stress distributions along the fiber length for composites with and without PVAL coating coating thickness t = 5 pm and Young s modulus ratio of coating to matrix...

Fig. 7.12. Maximum interface shear stresses plotted (a) as a function of Young s modulus ratio of coating to matrix, Ej/Em for coating thickness t = 50 /tm, and (b) as a function of coating thickness t for Young s modulus ratio of coating to matrix, Ei/Em = 0.5. After Kim et al. (1994c)...

By averaging the out-of-plane constitutive equations, the interface shear stresses Tj in Eqs. (8) are expressed in terms of the in-plane displacements u and, averaged across the thickness of respectively the damaged (-0 ) layer and the outer sublaminate (0, /9 ), so that... 

The 0(k) term from the interface shear-stress condition (7-299) is, in general,... 

Assumptions must be made about the matrix and interface behaviour before Eq. (4.27) is integrated. If the matrix remains elastic and the interface does not fail, the shear stress rises to a maximum at the fibre ends, where the tensile strains in the fibre Cf and the matrix differ the most. Flowever, a ductile polypropylene matrix is assumed to yield in shear at a stress Ty = 20 MPa. This will occur near the fibre ends, so the interface shear stress is... 

In the presence of weak fiber/coating bonds, the matrix cracks generate a single long debond at the surface of fibers (adhesive failure type, figure 10). The associated interface shear stresses are low, and load transfers through the debonded interfaces are poor. The matrix... 

From Equations (8.19) and (8.20), it is seen that once the crack tip opening wq, crack tip slip 5q, loading force P, and the rotation of the two adherends are simultaneously recorded, the interface shear stress t(5q) and interface normal stress ff(wo) can be determined experimentally. 

Table 4 reports the interface shear stresses that have been extracted from the hysteresis loops, as well as pull out lengths and matrix crack spacing distances. These latter data provide also a measure of interface strength. Both sets of data indicated the same trends, and they support the above statements. The interface shear stresses (t) obtained for the minicomposites reinforced with Hi-Nicalon S fibers are quite low (Table 4). Weak interfaces could be logically expected for this Hber/interphase system, fhe current values of x fall within the range of data detennined on SiC/SiC minicomposites reinforced with Nicalon or Hi-Nicalon fibers [7, 12, 14]. Furthermore, it...

After debonding, the bond stress is gradually replaced by friction and there are different models proposed by several authors. One of the first was by Greszczuk (1969) who derived and solved an equation relating external load to the interface shear stress. Certain qualitative verification of this solution... 

Several methods have been proposed for predicting the stress state at the interface, which can then be used to estimate the bond strength. The shear lag method has received extensive treatment by several investigators. This method determines the interface shear stress concentration at the end of the fiber as well as shear stress variation along the fiber. Additional methods include the Lame solution for a shrink fit, classical elasticity boundary value problems, and finite-element analysis. 

The interface shear stresses can be expressed in terms of the in-plane displacements = 1,2 as... 

The deformation or ploughing modes can also be well described for plastic and possibly even brittle fracture systems using modem numerical techniques. As with the elastomeric systems the models basically include geometric terms, such as 6, some load and various parameters such as an interface shear stress but more importantly a relatively accessible bulk deformation or dissipation property of the material. For the case of elastomers, an appropriate viscoelastic loss tangent is sufficient and for a ductile polymer some pressure dependent yield stress. There are many examples in the literature where good correlations have been obtained between a bulk mechanical test and a frictional response. Properly, it has been seen as the domain of others, perhaps polymer scientists, to seek to provide interrelationships between molecular structure and deformation dynamics and the consequent bulk material responses. 

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