Carbonation induced corrosion represents a significant challenge in the durability and structural integrity of reinforced concrete elements. This process occurs when carbon dioxide from the atmosphere penetrates the concrete cover and reacts with the alkaline components of the cement paste, resulting in a decrease in pH and the depassivation of steel reinforcement. Eventually, corrosion residues are formed over the metal surface leading to cracking and spalling of the concrete cover. Concrete carbonation is modelled via a system of coupled transport-diffusion-reaction equations that describe the environmental carbon dioxide diffusion-reaction, pore water saturation and rebar corrosion. Changes in concrete composition and mechanical properties are also considered. As rust deposits increase in volume, cracking and spalling of concrete cover is observed and modelled using the phase field approach for fracture.