PurposeThis paper aims to study the benefits of use of bi-adhesive (combination of two different adhesives) over conventional single adhesive in bonded lap joints. Characterise damage severity due to cohesive and adherent failure as feedback for operating load levels that assist in developing damage tolerance design of the adhesively bonded joints.Design/methodology/approachSingle lap joint where the adherent plate is made up of aluminium alloy joined together with bi-adhesives is analysed. The nature of adhesives ranges from brittle, elastic-plastic, moderately ductile to largely ductile. Numerical analysis is performed considering the material and geometric non-linear behaviour of the joint. The optimum bond ratio of bi-adhesives and the effect of the location of adhesive on the stress distribution are studied. The cohesive zone modelling (CZM) is adopted to account for the cohesive failure of the joint. The adherent plate failure is also addressed by modelling and studying the behaviour of the crack at different locations in the plate using modified virtual crack closure integral (MVCCI).FindingsThe results obtained from the stress analysis show some important characteristic behaviour of the bi-adhesive joint. Although bi-adhesive is expected to result in improved joint strength, the purpose gets defeated if a brittle adhesive is used at the corners and ductile adhesive at the middle. The joint strength based on CZM, evaluated for a single adhesive, is in good comparison with the experimental results from the literature. Also, the location of the crack in the adherent plate plays a significant role in the failure of the joint.Originality/valueEstimating joint strength for the bi-adhesive model using CZM and evaluating damage severity in the presence of de-bond and crack in the bi-adhesive lap joint model assists in developing robust damage tolerance design models of such joints.