Refined Mathematical Model of the Stress State of Adhesive Lap Joint: Experimental Determination of the Adhesive Layer S
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REFINED MATHEMATICAL MODEL OF THE STRESS STATE OF ADHESIVE LAP JOINT: EXPERIMENTAL DETERMINATION OF THE ADHESIVE LAYER STRENGTH CRITERION S. S. Kurennov
UDC 624.078.4
A new mathematical model of adhesive joint was developed and experimentally validated, in which the Vlasov–Pasternak two-parameter elastic bed model was used to simulate the stress state of the bonding layer. According to this elastic model, the adhesive layer was regarded as a membrane located in the middle of the adhesive layer thickness, between which and the bearing layers there were elastic elements. The outer bearing layers were regarded as beams in the Timoshenko approximation. The tangential stresses were considered to be constant across the thickness of the adhesive layer, and the normal (cleavage) stresses to be variable. This approach allows one to describe different types of boundary conditions for tangential stresses in the adhesive layer at the ends of the adhesive line, viz.: there are no tangential stresses at the edge of the adhesive joint if there are no adhesive spews, or the tangential stresses reach a maximum at the edge of the adhesive line if these spews exist. The problem was reduced to a system of ordinary differential equations in displacements and rotation angles of bearing layers. The system was solved by the matrix method. It was found that the sagging of the adhesive greatly reduced the maximum cleavage stresses in the adhesive layer. Tensile tests of adhesive lap-jointed metal rods were carried out. The proposed model was used to evaluate the strength criterion of the adhesive layer. It was shown that the best approximation of calculated and experimental data was provided by the maximum principal stress criterion. The proposed approach can be used to solve joint design problems. Keywords: stress-strain state, three-layer rod, bonding layer, adhesive, Vlasov–Pasternak foundation. Introduction. There are several mathematical models of adhesive lap joint, which allow one to describe the stress-strain state (SSS) of an adhesive-bonded structure in an analytical form [1–3]. In the classical Volkersen, Goland, and Reissner lap joint models, the tangential stresses in the adhesive reach a maximum at the joint edges, which is often physically impossible since the outer edge of the bonding layer can have a free boundary. To avoid this contradiction, authors [4] proposed to consider the normal stresses in the adhesive to be linearly variable across the thickness of the adhesive layer, but not constant as in the previous models. In work [5], a two-parameter elastic foundation (bed) model was used to describe the stress state of the bonding layer. The multiparameter elastic foundation theory was extended in the works of Vlasov, Pasternak [6], and Filonenko-Borodych. The above-mentioned adhesive joint model was further extended in [7–9]. Besides the above approach for modeling the adhesive layer’s SSS, a more complex model was created [10], in which the adhesive is regarded as a two-dimensional continuum. Earlier [11], a model with
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