Shear lag theory

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 ... 

The critical fiber length (L ) of programmed short SMPFs is estimated by the shear-lag theory [41] ... 

Since the fibres are short, we must take account of the variation of tensUe stress along each fibre. This is determined the aspect ratio a = l/d = 400/6 - 66.7, and the dimensionless fiictor n (from eqn 634). In order to evaluate n, we need the ratio 2R/d occurring in the shear lag theory. Assuming, for example, that the fibres are arranged in a square array, the fibre volume fraction is given by... 

The linear elastic stress analysis of a short fibre composite by the shear lag theory is due originally to H. L. Cox. The real composite (see Figure 6.32(a)) is assumed to deform in the vicinity of any particular fibre as if it were the model tem shown in Figure 6.32(b). In the model, the fibre (of diameter d) is surrounded 1 a cylinder of matrix of radius R, embedded in a homogeneous block of material which deforms as the composite as a... 

Fibre stress a, Is evaluated vrith the shear lag theory, (a) The mean fibre separation is labelled 2R. (b) The composite in the vicinity of the fibre is modelled as a cylinder of matrix with radius R surrounding the fibre, embedded in a block which deforms as the composite as a whole, (c) Within the cylinder of matrix, a shear stress r acts at radius r. 

Expression (8) was obtained by a simple balance equation, or from the famous shear lag theory (fully elastic model) of Cox [18], assuming in particular that an ideal... 

Composite strength increases with decrease in L, that is, increase in interfacial adhesion strength x by virtue of the fundamental relationship associated with the well known Kelley-Tyson expression (8) based on a shear-lag theory for metal filaments ... 

Values for 3 obtained in this way are very similar to those calculated as the basis of shear lag theory. Recent work by Wire [14] suggests that the other elastic constants may be calculated better by the methodologies developed by Wilczynski and Tandon and Weng. 

Predicting stress analysis of the fibre-matrix composite under load. A simplified but highly successful solution is known as the shear lag theory (6.N.7). It assumes perfect bonding between fibres and matrix, and results in the following prediction of Of as a function of distance x along the fibre, measured from its centre (recall a = //[Pg.245]

The linear elastic stress analysis of a short fibre composite by the shear lag theory is due originally to H. L. Cox. The real composite (see Fig. 6.32(a)) is assumed to deform in the... 

Several models were all based more or less on the shear lag theory proposed by Cox (1952) who derived that the force P in the fibre at distance x from one end may be represented by the following equation ... 

Values for E obtained in this way are very similar to these calculated on the basis of shear lag theory. A limitation, as pointed out by Hine, Lusti and Gusev [5], relates to the estimates of E and Vf2 using the Halpin-Tsai equation. 

In effect, Hart-Smith equates the yield stress and the failure stress, and says that failure occurs when the adhesive reaches its limiting shear strain. This is illustrated in Fig. 34 which shows the adhesive shear stresses and strains for a double-lap joint as the applied load is progressively increased. It should be noted that the shear strain distribution is not simply a multiple of the low-load case since the assumption of a limiting (plastic) shear stress in the adhesive layer causes a distortion to the elastic shear-lag theory. 

During the early stages of loading, the interaction between the fibre and the matrix is elastic in nature. The first analytical model to describe the stress transfer in the elastic zone was developed by Cox [2], Later models were based on similar concepts they differed only in some of their numerical parameters. These models are usually referred to as shear lag theories. They are based on the analysis... 

The efficiency of fibre reinforcement depends to a large extent on the maximum tensile stress that can be transferred to the fibre. The maximum value would, of course, be the yield strength or tensile strength of the fibre. The shear lag theory (Eqs 3.1-3.3) provides an analytical tool to predict the shear stresses that will develop at the interface in order to achieve this maximum tensile stress. An estimate of the maximum elastic shear stress developed for different levels of... 

Several models (e.g. [7,11,13,14]) have analysed the pull-out of a single fibre from a matrix, based on the shear lag theory up to debonding and frictional slip... 

The stress distribution predicted by Eg. (3.8) is essentially similar to that of the shear lag theory, with a maximum elastic shear stress at the point atwhich the fibre enters the matrix (Figure 3.5(b)). The value of this stress is ... 

The modulus of fibrillar samples can be explained in terms of a fiber-reinforced composite model, in which needlelike nanofibrils are surrounded by a minority matrix of noncrystalline material [15-17], The modulus is highly dependent upon the shear characteristics of the noncrystalline regions separating adjacent nanofibrils, according the the shear lag theory [18], Improved modulus as a function of increasing orientation is attribnted to the increase aspect ratio of the crystalline fibers. 

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