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In this work, the peridynamic corrosion model is used for 3D simulation of pitting corrosion in stainless steel. Models for passivation and salt layer formation are employed to predict detailed characteristics of pit growth kinetic in stainless steels, such as lacy cover formation on top of the pit, and the diffusion-controlled regime at the pit bottom. The model is validated against an experimentally grown pit on 316L stainless steel in NaCl solution. Lacy covers in this model are formed autonomously during the simulation process. They are remarkably similar to the covers observed on top of the real pits.