Volkersen’s theory

Volkersen s theory predicts that the shear stresses in the adhesive layer reach a maximum at each end of the overlap, when the bonded plates are in pure tension. Photoelastic analyses of these composite structures show that stresses are uniform in the central part of the model adhesive, but high near the edges of the steel plate used in the analysis (Figure 7.2). Stress distributions at the end were found to be independent of the length of the overlap, when its length was at least three times the thickness of the adhesive layer. " ... 

Volkersen s theory is incomplete because it does not account for bending of the adherends from the eccentricity of the loading path. Predictions based on Volkersen s work would seem more valid for double-lap joints where bending is minimized. 

Variation of shear stress with distance along the overlap according to Volkersen s theory... 

Theory of Goland and Reissner. In Volkersen s theory, the so-called tearing or peeling stresses were ignored. Goland and Reissner [16] took the bending deformation of the adherends into account, as well as the transverse... 

Theory ofVolkersen In 1938, Volkersen analyzed the distribution of shearing stresses in the adhesive layers of a lap joint. Volkersen s model is useful only with very stiff adhesives, which do not bend on loading the joint. A dimensioidess stress concentration factor is found to depend on the geometry and the physical parameters of the joint. By introducing further simplifications, certain reasonable geometric conditions, and identical adherends, a simple formula is obtained ... 

Treating the adhesive in the same way as Goland and Reissner, Volkersen (1965) has set up soluble differential equations to describe the tensile stresses (cTsy) and the shear stresses (tsx) in the adhesive layer of a double-lap joint. Volkersen s second theoretical model for the double-lap joint neglects the same adherend stresses as does the second theory of Goland and Reissner, so it has the same bounds of validity. The bending in the double-lap joint does not cause rotations of the overlap region, and so the adhesive stress per unit load is not dependent on the load applied. Thus, the applied load is explicitly factorable from the solution functions for the shear and normal stresses in the adhesive layer. 

A correct stress analysis is necessary to estimate the strength of adhesively bonded joints. Much research on the problem has been carried out since the first theory emerged Volkersen s shear lag model (Volkersen 1938). Since the stress distribution in joints depends on dimensions. 

Adams and Peppiatt [60] have considered the problem of the in-plane transverse stresses and to ascertain the magnitude of such stresses they have used experimental models and analytical and finite-element analyses solutions of the Volkersen theory, but in three dimensions. They demonstrated that Poisson s ratio strains generated in the substrates cause shear stresses, T13, in the adhesive layer and tensile stresses, 0-33, in the substrate acting transverse to the direction of the applied load, but in the plane of the joint. For metal-to-metal joints the transverse shear stress, has a maximum value of about one-third of the maximum longitudinal shear stress, ri2(max), and this occurs at the corners of the overlap. This, therefore, enhances the shear stress concentration which exists at this point due to the effects described above. Bonding substrates of dissimilar stiffness produces greater stress concentration in the adhesive than when similar substrates are employed. 

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