Shear lag analysis

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,... 

Volkersen presented his shear lag analysis in 1938. It is based on the following assumptions ... 

Groth, H., Shear lag analysis and testing of adhesive Joints with viscoelastic and viscoplastic adhesives, Proceedings of Nordic Composites and Sandwich Meeting, Royal Institute of Technology Stockholm, Nov. 19-20 1991, Organised by Nordic Industrial Fund and KTH,... 

The shear lag analysis proposed by Greszczuk [6] shows that the shear strength Tj is varied along the embedded length as described in Rgure 3. This stress is given by ... 

Micromechanical models such as Cox shear-lag and Halpin-Tsai are often used to predict the stiffness and strength of discontinuously short-fiber reinforced composites. Experimental results of tensile measurements are then compared or correlated with such theoretical models. The shear-lag analysis originally proposed by Cox considered a discontinuous fiber embedded in an elastic matrix with a perfectly bonded interface and loaded in tension along the fiber direction [25]. The analysis tabes into account the difference in strain displacements of the fiber and matrix along the interface. The stress transfer depends on the interfacial shear stress between the fiber and the matrix. The stress transfer from fiber ends is neglected in the analysis. The Cox model incorporates the aspect ratio (a = l/d where I is the fiber length and d the diameter) of the fiber into... 

In spite of the assumptions, the shear lag analysis does provide a great deal of useful insight. Perhaps the most questionable assumption involves the failure to consider the couple, thus the analysis is conducted on an object that is not... 

Trantina [55] applied fracture mechanics to adhesive joints with some success and applied the failure criteria to a finite element model to find adhesive fracture energies. The influence of the glueline thickness was not accounted for. Hu [56] used a shear lag analysis and applied failure criteria in terms of Jc and it was shown that this gave good predictions of failure and was also able to account for the adhesive thickness. It was noted that this is consequently a good method of predicting failure for adhesive materials loaded in shear. 

The microbond technique was analyzed by Naim [56] and more recently by Scheer and Naim [57]. In the first paper, a variational mechanics analysis of the stresses in the microbond specimen was completed. In the second paper, a new, more complete shear-lag analysis was presented. The proposed shear-lag result for analyzing the microbond test results is given by the equation in terms of the force of debonding ... 

Bascom and Jensen [67], used an approach similar to that of Drzal and coworkers. Wimolkiatisak et al. [70] found that the fragmentation length data fitted both the Gaussian and Weibull distributions equally well. Fraser et al. [71 ] developed a computer model to simulate the stochastic fracture process and, together with the shear-lag analysis, described the shear transmission across the interface. Netravali et al. [72], used a Monte Carlo simulation of a Poisson-Weibull model for the fiber strength and flaw occurrence to calculate an effective interfacial shear strength X using the relationship ... 

Verpoest et al. [81] presented a micromechanical analysis to show that for increasing applied strains, the fiber aspect ratio can reach values which are lower than those predicted by Kelly s shear-lag analysis. They also proposed that the single-fiber fragmentation test could be used to estimate the different components of the interface shear strength, that is, the bond strength, the friction strength and the matrix yield strength. 

Naim, J. A., Generalized shear-lag analysis including imperfect interfaces, Adv. Comp. Letters,... 

In Volkersen s shear lag analysis it is assumed that the adhesive deforms only in shear, while the adherend deforms only in tension, as illustrated in Fig. 8. Consider the relative displacements of the upper... 

Therefore, based on classic shear lag analysis (also based on definition of shear strain), it can be shown that for a fixed strain rate (function) the effect of increased cross-head rate can be induced by increasing the interphase thickness (i.e., application of fiber sizing). Indeed, the experimental results reveal shorter fragment lengths for increased cross-head rate and/or presence of fiber sizing. Based on this premise, the following superposition relations can be written for the interfacial strength, Tc ... 

The shear-lag analysis of fiber-reinforced composites considers that below a certain length, a fiber is no longer effective in supporting the transfer of load from the matrix. There is thus a minimum effective fiber length that can... 

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