The knowledge of aging processes in polymers is of great interest for many applications in engineering, as the usually very complex mechanisms can reduce the lifetime of machine components drastically. Often those single mechanisms are coupled strongly, which makes the modeling even more complicated. One damaging interaction might occur when dealing with cracking in polymers: The crack may enable oxidation deep inside the material rather than being restricted to original surface regions. The oxidation state of the polymer, in turn, can support the crack propagation by embrittling the material and by lowering the crack resistance. This supported propagation of the crack, again, causes progression of the oxidation deeper inside the material and the whole procedure might repeat and carry the crack tip even deeper into the material. In the present work, a new approach to capture some of those mechanisms is presented. Here, the phase field method, which has evolved into a strong and versatile tool for modeling material processes, is used to describe the oxidation process. An energy, including a gradient-based term to describe interfaces and another term corresponding to the reaction, drives the evolution. This is underlain by a separate approach for diffusion of oxygen which is able to trigger the change from a virgin material to a fully oxidized material. In this work, cracks are able to carry the oxidation under the surface and thus might accelerate the whole process. Different numerical experiments based on the finite element method have been performed and are presented to introduce the developed model.