By Pocius A.V., Dillard D.A.
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Additional info for Adhesion science and engineering
When non-dimensionalized by the average shear stress, as shown in Fig. 13a, the shear lag model predicts that the maximum stress becomes larger for longer joints sustaining the same average shear stress. Fig. 13b shows the same data, but non-dimensionalized by Pw, effectively comparing different length joints supporting the same applied load. Beyond a point, increasing the joint length does not reduce the maximum shear stress predicted by the shear lag model. These figures also provide convincing evidence about the dangers of reporting average shear stress at break when testing lap joints, especially if the properties of the adherends or adhesives are changing, or if the geometry of the joint is not the same.
Because of the difficulty in machining feather-edges on complex adherends, there is a tendency to use the discrete version of a bevel joint, the step lap joint. This geometry is easy to machine, and especially well suited to manufacture laminated composite joints. The key feature to note is that there will be shear stresses anywhere there is a relative change in adherend stiffness. For tapered adherends, there is a distributed change along the entire length of the joint, resulting in a uniform shear stress distribution over this region.
A beam on an elastic foundation represented as a series of discrete, independent springs. At the right is a differential element of the beam showing moment, shear, and distributed loading. "(A coshx + B sinhx) +ehx(Ccoshx + D sinhx). (19) The coefficients are determined by the relevant boundary conditions. To cast this solution in terms of adhesive bonds, the adhesive, of thickness h, is assumed to be linearly elastic with a modulus of Ea, unaffected by deformations in the surrounding material, and acting over a bond width w on the beam.