In the present work a generally applicable failure model for the assessment of crack onset in adhesive lap joints which is based on finite fracture mechanics is presented. The approach combines a general sandwich-type model with a coupled stress and energy criterion that requires only two fundamental failure parameters: the strength and the toughness of the adhesive. The failure model allows for the analysis of various joint configurations featuring a single overlap as e.g. single lap joints, L-joints, T-joints or DCB specimens. In a comprehensive study, the effects of material parameters on the failure load and the limitations of the present approach regarding the joint configuration are discussed by means of a dimensionless brittleness number. Additionally, the findings are compared to results of a numerical approach using cohesive zone models and to experimental data reported in literature. A good agreement for a wide range of joint configurations is achieved.