ABSTRACT

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 15.2 Electrochemical kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443 15.3 Problem formulation of 1D pitting corrosion . . . . . . . . . . . . . . . . . . . . . . . . 446 15.4 The peridynamic formulation for 1D pitting corrosion . . . . . . . . . . . . . . . 449 15.5 Results and discussion of 1D pitting corrosion . . . . . . . . . . . . . . . . . . . . . . 453

15.5.1 Pit corrosion depth proportional to √

t . . . . . . . . . . . . . . . . . . . . . . 453 15.5.2 Activation-controlled, diffusion-controlled, and IR-controlled

corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456 15.6 Corrosion damage and the Concentration-Dependent Damage (CDD)

model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459 15.6.1 Damage evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462 15.6.2 Saturated concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464

15.7 Formulation and results of 2D and 3D pitting corrosion . . . . . . . . . . . . . 465 15.7.1 PD formulation of 2D and 3D pitting corrosion . . . . . . . . . . . . . 466 15.7.2 The Concentration-Dependent Damage (CDD) model for

pitting corrosion: example in 2D . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 15.7.3 A coupled corrosion/damage model for pitting corrosion: 2D

example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472 15.7.4 Diffusivity affects the corrosion rate . . . . . . . . . . . . . . . . . . . . . . . . 474 15.7.5 Pitting corrosion with the CDD+DDC model in 3D . . . . . . . . . 475

15.8 Pitting corrosion in heterogeneous materials: examples in 2D . . . . . . . . 476 15.8.1 Pitting corrosion in layer structures . . . . . . . . . . . . . . . . . . . . . . . . 476 15.8.2 Pitting corrosion in a material with inclusions: a 2D example 479

15.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480

of

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 15.10 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481

15.10.1 Convergence study for 1D diffusion-controlled corrosion . . . 481 15.10.2 Convergence study for 2D activation-controlled corrosion

with Concentration-Dependent Damage model . . . . . . . . . . . . . 482 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484

Abstract In this chapter we introduce a peridynamic model for the evolution of damage from pitting corrosion capable of capturing subsurface damage. The model is based on the recent work that has appeared in [12]. Further extension and validation of the model has appeared in [14]. The anodic reaction in corrosion processes (in which electroplating is negligible) is modeled as an effective peridynamic diffusion process in the electrolyte/solid system coupled with a phase-change mechanism that allows for autonomous evolution of the moving interface. In order to simulate creation of subsurface damage, we introduce a corrosion damage model based on a stochastic relationship that connects the concentration in the metal to the damage of peridynamic mechanical-bonds that are superposed onto diffusion-bonds. We study convergence of this formulation for the diffusion-dominated stage. The model leads to formation of a subsurface damage layer, seen in experiments. We validate results against experiments on pit growth rate and polarization data for pitting corrosion. We extend the 1D model to the 2D and 3D, and introduce a new damage-dependent corrosion model to account for broken mechanical bonds that enhance the corrosion rate. This coupled model can predict the pit shape and damage profile in materials with microstructural heterogeneities, such as defects, interfaces, inclusions, and grain boundaries.