Analytical models of adhesively bonded joints—Part I: Literature survey

THE appearance of a treatise in English upon the mathematical theory of elasticity is an event the potential importance of which may be judged by the that the author, in his frequent suggestions for collateral reading, refers to only three such, those of Southwell, Timoshenko, and Love. In spirit and content Sokolnikoff}s book differs greatly from each and all of these. It may be described by a possible sub-title: “A pure mathematician surveys topics related to certain problems in the mathematical theory of elasticity”. It is symptomatic of the change in outlook of American mathematics over the past few decades. Mathematical Theory Of Elasticity Prof. I. S. Sokolnikoff with the collaboration of Asst. Prof. R. D. Speche. Pp. xi + 373. (New York and London: McGraw-Hill Book Co., Inc., 1946.) 22s. 6d.

Mathematical Theory Of Elasticity

A critique of bond strength measurements

Stresses in a standard metal-to-metal adhesive-bonded lap joint are analysed by a two-dimensional finite-element method and comparisons are made with previous analyses. Particular attention is paid to the stresses at the ends of the adhesive layer. Unlike previous work, which assumes the adhesive to have a square edge, the adhesive spew is treated as a triangular fillet. The highest stresses exist at the adherend corner within the spew. Linear elastic behaviour is assumed throughout.A rubber model is reported which confirms these results physically.Good agreement was also obtained between some practical results and the finite-element predictions.

Stress analysis of adhesive-bonded lap joints

Strengthening of steel structures with fiber-reinforced polymer composites

Poisson's ratio strains in the adherends of a simple adhesive lap joint induce transverse stresses both in the adhesive and in the adherends.Two simultaneous second-order partial-differential equations were set up to describe the normal stresses along and across an adherend and were solved both by an approximate analytical method and a finite-difference technique: the two solutions agreed closely. The adhesive shear stresses can then be obtained by differentiating these solutions. The transverse shear stress has a maximum value for metals of about one-third of the maximum longitudinal shear stress, and this occurs at the corners of the lap, thus making the corners the most highly stressed parts of the adhesive.Bonding adherends of dissimilar stiffness was shown to produce greater stress concentrations in the adhesive than when similar adherends are used.

Effect of poisson's ratio strains in adherends on stresses of an idealized lap joint

Axisymmetric butt joints are widely used as specimens for testing the response of adhesives to shear and tensile stresses. When analysing the results from these tests, the stress distributions must be accurately known. A finite-element analysis has been used to examine the effect of non-rigid adherends and a spew fillet in solid and annular butt joints for a range of geometries and adhesive properties. It has been shown that stress concentrations occur in butt joints loaded in tension; in the latter case, the stress concentration is directly due to the presence of the spew fillet.

Stress analysis of axisymmetric butt joints loaded in torsion and tension

Models of adhesive joints have been constructed in which hard rubber has been used as the adherends and relatively soft foam rubber as the adhesive. The models were scaled to represent various types of lap joint. Very good agreement was obtained when the experimental results were compared with available theory, showing that the model accurately represented the shear-stress distribution in the adhesive.Two joints are shown in which the adhesive thickness was profiled (one optimally, the other linearly) to reduce or eliminate the shear-stress concentration at the ends.

N A Peppiatt

Papers

Stress analysis of adhesive-bonded lap joints

Effect of poisson's ratio strains in adherends on stresses of an idealized lap joint

Stress analysis of axisymmetric butt joints loaded in torsion and tension

Rubber model for adhesive lap joints