Structural bonding of composite materials is being used in shipbuilding and civil industries. Due to manufacturing and in-service constraints, the bonded regions are characterized by adhesive layers with a thickness of up to 10 mm. With such thicknesses, a weakness to be recognized, from both scientific and applied points of view, is the stress gradient at bi-material edges and corners, exacerbated by differences in materials properties. This study aims to investigate the fracture onset and crack deflection in adhesive joints with thick bond-lines (≈ 10 mm) under global mode I loading. More specifically, the role of adherend-adhesive modulus-mismatch and the role of pre-crack length, Δ𝑎, are scrutinized. The parameters controlling the crack path directional stability are also discussed. Single-material (i.e. steel-steel and GFRP-GFRP) and bi-material (i.e. steel-GFRP) double-cantilever beam joints bonded with a structural epoxy adhesive are tested. The tests are aided by a 3D image acquisition system. Moreover, the different joints are modelled analytically, considering a beam on elastic-plastic foundation, to indicate and include characteristic length scales of the problem (e.g. adhesive thickness, yield plastic zone, elastic zone). To link the experimental findings to existing theoretical models, the behaviour of the different joints is also assessed numerically. An empirical relation, in terms of geometrical and material properties of the joints, that defines the transition between non-cohesive and cohesive fracture onset is found - for a given material mismatch (Δ𝑎crit./ℎadher)4 ∼ (𝑡a/ℎadher). In general, for Δ𝑎 < Δ𝑎crit.: the stress singularity near the bi-material corner rules over the stress singularity at the pre-crack tip. The bi-material corner with the highest modulus-mismatch dictates the region of fracture initiation; for Δ𝑎 ⩾ Δ𝑎crit.: the stress singularity at the pre-crack tip is dominant, resulting in cohesive fracture onset. However, the cracking direction rapidly deflects out from the adhesive layer centre-line. Positive 𝑇-stress along the crack tip is found considering 10 mm thick bond-line, being one of the factors for unstable crack path.