Adhesively bonded joints are known to suffer from creep and relaxation phenomena due to the viscous nature of the adhesive. These effects are detrimental to the durability of structural joints as they can lead to progressive and slow crack propagation rate phenomena and possible delayed failure. Master curve approaches are often used to assess the durability of structural assemblies, but the physical justification for such approaches requires additional investigation to more accurately assess the coupling between structural effects and the possible complex long-term rheological behaviour of the adhesive layer. Following similar approaches developed to study the steady-state crack propagation regime in bulk materials, an Eulerian description of crack propagation along a viscous adhesive layer during a double cantilever beam test is implemented. Taking into account viscoelastic-viscoplastic and various hardening rules, some master curves can be obtained describing the evolution of the crack propagation rate as a function of the stationary loading conditions. With such a model, the role of adhesive layer behaviour and joint geometry on crack propagation conditions can be discussed, as well as the applicability of such a master curve approach.