Amongst the available methods to model fracture processes, the phase field approach has proved to be efficient and has received extensive attention. However, the approach is computationally demanding as it requires a very high resolution, both in space and time to resolve the fracture characteristics. In this paper, a novel adaptive phase field method is proposed for modelling quasi-static crack propagation in brittle materials. The adaptive refinement is based on the stability analysis which is combined with the quadtree decomposition. The stability analysis is based on a linear perturbation method that is used herein to determine the onset of fracture initiation on the fly. Three standard benchmark problems are solved to show the efficiency and the robustness of the proposed method. It is shown that the proposed framework does not require any post processing technique for adaptive refinement and yet is effective. © 2021 Elsevier B.V.