Shear lag

Net-tension failures can be avoided or delayed by increased joint flexibility to spread the load transfer over several lines of bolts. Composite materials are generally more brittle than conventional metals, so loads are not easily redistributed around a stress concentration such as a bolt hole. Simultaneously, shear-lag effects caused by discontinuous fibers lead to difficult design problems around bolt holes. A possible solution is to put a relatively ductile composite material such as S-glass-epoxy in a strip of several times the bolt diameter in line with the bolt rows. This approach is called the softening-strip concept, and was addressed in Section 6.4. 

In the push out test [93], the fiber is pushed into the matrix rather than being pulled out. The test allows the measurement of two quantities, Fdcb (the force at which debonding occurs) and F/., (the force needed to push the fiber through the matrix sample if it is thin enough). The bond shear strength Tdeb is calculated using the shear lag theory ... 

Cox (1952) first considered a shear-lag model where an elastic fiber is embedded in an elastic matrix which is subjected to uniaxial tension. Perfect bonding is assumed... 

A modified shear-lag model has been proposed by Rosen (1964, 1965) based on a multiple fiber composite. Fig. 4.4 shows the composite model Rosen considered wherein a fiber is embedded in a matrix which in turn is surrounded by an average composite material. The FAS and IFSS are given in the same form as those of Eqs. (4.1) and (4.2) given earlier by Cox (1952) ... 

For the cylindrical coordinates of the shear-lag model shown in Fig. 4.6, the governing conditions adopted in this analysis are essentially the same as those described in Section 4.2.3, There is one exception in that the mechanical equilibrium condition between the external stress, internal stress components given by Eq. (4.11) is replaced by... 

The results presented in Section 4.3.6 suggest that the shear lag models based on a single fiber composite is inadequate for modelling a composite with a high fiber f). From the experimental viewpoint, to measure the relevant fiber-matrix interface properties, the fiber volume fraction in single fiber pull-out tests is always very low (i.e. Ff <0.01). This effectively means that testing with these specimens has the... 

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. 

Shetty, D.K. (1988). Shear-lag analysis of fiber push-out (indentation) tests for estimating interfacial friction stress in ceramic-matrix composites. J. Am. Ceram. Soc. 71, C.107-109,... 

The foregoing summary of applications of composites theory to polymers does not claim to be complete. There are many instances in the literature of the use of bounds, either the Voigt and Reuss or the Hashin-Shtrikman, of simplified schemes such as the Halpin-Tsai formulation84, of simple models such as the shear lag or the two phase block and of the well-known Takayanagi models. The points we wish to emphasize are as follows. 

In most simple applications of models all that is really being achieved is curve fitting. This applies to the Takayanagi models (which are one dimensional and assume uniformity of stress and strain within each element) as well as to simple fibre models such as the shear lag. 

In the case of the y relaxation, it was concluded that there are two mechanisms for the change in modulus and hence for tan 5. The first is an increase in the efficiency of stress transfer (i.e. the shear lag factor) with falling temperature due to the quenching of molecular motions. These are predominantly if not entirely in the non-crystalline regions. Secondly, the quenching of these molecular motions also gives rise to an... 

The brittle film cracking with plastic deformation of the ductile substrate at the interface has been described by using the shear lag model. " This model, which was proposed in the analysis of the fragmentation of fiber composites," " develops a relation for the critical stress producing the steady-state cracking of the film. It assumes that the interfacial shear stress, on the one hand, is activated at each crack tip along the characteristic slip length r, and, on the... 

Fig. 16 Modeling of the stress distribution in a cracked film with plasticity at the interface using the shear lag approximation, (a) linear evolution of the normal stress along the characteristic slip length r/2 and (b) sharp evolution of the interfacial shear stress x. along the characteristic slip length r/2.

Here CT is the applied stress, while N/, k = 1,2 and Aj are constants depending on the inplane stiffness properties of the intact material shear lag parameters K,K2i and... 

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