Shear lag models

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. 

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... 

Gao, X. L. and Li, K. A shear-lag model for carbon nanotube-reinforced polymer composites. International Journal of Solids and Structures 2005 42 1649-67. 

Cox shear-lag model [21] that takes into account the geometrical arrangement of the fibers. 

In instrumented creep tests taken to failure, one learns not only how long specimens last but also how deformation increases throughout the creep process. For lap joints, delay times have been seen in creep tests, probably due to the increasing uniformity of the shear stress state, as predicted by the shear lag model as the creep compliance of the adhesive increases with time. In other situations, no such delay time is seen. A schematic illustration of a creep curve for an adhesive bond consisting of a butt joint bonded with a pressure sensitive foam tape is shown in Fig. 2, exhibiting classical primary, secondary and tertiary regions of creep behaviour. 

The most commonly used theory used to model the stiffness of this type of composite was developed by Cox [1] and further improved by Krenchel [2, 3]. Cox s shear lag model was developed for aligned discontinuous elastic fibers in an elastic matrix. The applied load is transferred from the matrix to the fiber via interfacial shear stresses, with the maximum shear at the fiber ends decreasing to zero at the centre. Thus, the tensile stress in the fiber is zero at the ends and maximum in the middle. Thus, although the efficiency of stress transfer increases with fiber length, it can never reach 100%. In order to accommodate this dependence of reinforcement efficiency on fiber length, Cox introduced a fiber length efficiency factor -rij into the rule-of-mixtures equation for the composite modulus Eg. 

Keywords long glass fiber, glass mat thermoplastic (GMT), shear lag model, rule of mixture, tensile modules, Cox-Krenchel model, aspect ratio, thermal properties, linear thermal expansion coefficient, lofting, tensile strength, Kelly-Tyson model, adhesion, wetting, glass mat, random fiber orientation. 

Siriruk A, Weitsman YJ, Penumadu D (2009a) Polymeric foams and sandwich composites material properties, environmental effects, and shear-lag modeling. Compos Sci Technol 69 (6) 814-820... 

Researchers have performed experiments on CNT/polymer bulk composites at the macroscale and observed the enhancements in mechanical properties (like elastic modulus and tensile strength) and tried to correlate the experimental results and phenomena with continuum theories like micromechanics of composites or Kelly Tyson shear lag model [105,115-120]... 

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