In this talk, I present an existence result for a variational model of quasi-static crack growth with cohesive fracture energies featuring an activation threshold. The evolution is characterized by an irreversibility condition formulated in terms of a maximal opening variable, a global stability condition, and an energy balance. A key challenge in the proof is establishing a suitable version of the jump-transfer lemma for cohesive fracture evolution, where the formation or absence of microscale cracks plays a crucial role. This is based on joint work with Vito Crismale.