Refined Mathematical Model of the Stress State of Adhesive Lap Joint: Experimental Determination of the Adhesive Layer Strength Criterion

Abstract

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.