Crack propagation in brittle materials can be described in terms of trade-off between a bulk and surface energies, characterized by a material's fracture toughness. Crack nucleation, however, is a much more complex process involving fracture toughness, material strength, i.e. the range of stresses a material can sustain while deforming elastically, and complex scale effects. Phase-field models of fracture have become ubiquitous due to their ability to account for complex fracture patterns in a wide range of materials and multi-physics settings. When seen as gradient damage models, they properly account for tensile crack nucleation. A case can be made that crack nucleation cannot be fully accounted for in variational models based on Griffith-like surface energy, and it has been suggested that one needs to renounce to the variational nature of the models. Instead, I will introduce a new approach using a cohesive energy depending on the crack opening, focussing on the anti-plane case. Unlike existing models, this approach is capable of handling arbitrary convex strength surfaces and behaves in a Griffith-like manner for ``large'' crack openings.