Finite Element Analysis of the Double Lap Joint with an Elastic-plastic Adhesive

For an effective adhesively bonded reinforcement of a (typically cracked) plate, sufficient load must be transferred by the adhesive into the reinforcement to prevent the underlying damage from growing. Under severe load, the adhesive may yield (von Mises criterion) plastically. Notwithstanding possible adhesive failure, this may be beneficial to the reinforcement by reducing the peak stress adjacent to the crack. In this paper, characterisation of this stress reduction, compared to the elastic case, was sought by examining the dependence on configurational parameters including plate, adhesive and reinforcement moduli, and adhesive yield stress. Finite element (FE) analyses were conducted for a two-dimensional section through a double-sided (symmetric) lap joint, representative of a typical repair. Stress reductions in the reinforcement of the order of 25% were found. The adhesive yield was shown to be dominated by shear, σ{xy}: and thus behaved essentially one-dimensionally. The linear increase in plastic zone length with applied load, as predicted by the Hart-Smith one-dimensional theory, was in good agreement with the FE results. However the observed load transfer length was 6-18% longer than that predicted by Hart-Smith.