Predicting Pit-to-Crack Transition by Using Peridynamics

Environmentally assisted cracking (EAC) is considered as the primary cause of failure of metallic structures and components with environmental and, occasionally, catastrophic consequences. Stress-corrosion cracking (SCC) is one of the main types of EAC mechanisms. It can be defined as the progressive failure of the material due to the presence of non-cyclic tensile stress and the exposure to a corrosive environment. In some cases, the tensile stress necessary to trigger the phenomenon can be as low as 5% of the yield stress. Due to the substantial number of SCC critical environment-material combinations, a wide range of systems related to different industries are affected by this phenomenon such as pipelines, nuclear power systems, aerospace and marine vehicles, boilers, cooling water systems, and oil and gas drilling and production systems. When inspection and maintenance of structures is inherently challenging, the damage tolerance approach is not feasible. This means that a deterministic model is necessary to improve the safety and reduce the cost of over-conservative designs. Pitting corrosion is often the precursor of SCC. Despite the availability of advanced computing resources and software, predicting SCC and pitting corrosion propagation poses many challenges. The formation of corrosion pits occurs preferentially in areas where the tensile residual stresses are highest. Also, residual stresses exist at different length scales. Moreover, it is widely recognized that SCC damage is affected by metallurgical (e.g. chemical composition, material micro-structure, micro-chemistry) and environmental variables (e.g. temperature, electrode potential, PH, dissolved chemical species) which play a role at different length scales. Simulation of pitting corrosion involves a moving electrode-electrolyte boundary (interface) across which the concentrations of ions and their gradients are discontinuous (sharp-interface assumption). The construction of solutions to non-linear second-order partial differential equations associated with electro-diffusive transport in the electrolyte domain and with propagating interfaces present formidable challenges for both sharp interface approaches and diffuse interface approaches. One of the major computational challenges with sharp-interface models is that the standard finite element method cannot capture the interfacial discontinuities within a finite element and would necessitate remeshing when the interface morphology changes, which is unavoidable. Methods such as arbitrary Eulerian-Lagrangian, meshfree/meshless, or moving mesh for evolving sharp interfaces can be tedious and/or computationally expensive, especially, when Neumann and Dirichlet boundary conditions are prescribed on the interface. Due to the aforementioned reasons, a new multi-scale and multi-physics numerical methodology will be developed by using peridynamics for modeling of pit nucleation, pit growth, transition from pit to crack, short SCC crack growth and long SCC crack growth. Peridynamic framework will enable the coupling of electrochemical-mass transport problem with corrosion front movement while introducing a characteristic length-scale. Furthermore, it will consider not only the diffusion of ions due to concentration gradients but also electro-migration of dissolved ionic species in the aqueous solution environment within the pit and the rate of depletion or production of ions due to chemical reactions for investigating corrosion. The electro-diffusion of ions will be modeled based on dilute solution theory using the Nernst-Planck equations along with the assumption of local electro-neutrality. The proposed approach will enable simultaneous analyses at different length scales within the same numerical framework. Completion of the proposed project will lead to computational and analytical tools that will help in designing against SCC and pitting corrosion in marine structures.