A phase field formulation for dissolution-driven stress corrosion cracking

We present a new theoretical and numerical framework for modelling mechanically-assisted corrosion in elastic-plastic solids. Both pitting and stress corrosion cracking (SCC) can be captured, as well as the pit-to-crack transition. Localised corrosion is assumed to be dissolution-driven and a formulation grounded upon the film rupture-dissolution-repassivation mechanism is presented to incorporate the influence of film passivation. The model incorporates, for the first time, the role of mechanical straining as the electrochemical driving force, accelerating corrosion kinetics. The computational complexities associated with tracking the evolving metal-electrolyte interface are resolved by making use of a phase field paradigm, enabling an accurate approximation of complex SCC morphologies. The coupled electro-chemo-mechanical formulation is numerically implemented using the finite element method and an implicit time integration scheme; displacements, phase field order parameter and concentration are the primary variables. Five case studies of particular interest are addressed to showcase the predictive capabilities of the model, revealing an excellent agreement with analytical solutions and experimental measurements. By modelling these paradigmatic 2D and 3D boundary value problems we show that our formulation can capture: (i) the transition from activation-controlled corrosion to diffusion-controlled corrosion, (ii) the sensitivity of interface kinetics to mechanical stresses and strains, (iii) the role of film passivation in reducing corrosion rates, and (iv) the dependence of the stability of the passive film to local strain rates. The influence of these factors in driving the shape change of SCC defects, including the pit-to-crack transition, is a natural outcome of the model, laying the foundations for a mechanistic assessment of engineering materials and structures.

我们提出了一个新的理论和数值框架，用于对弹塑性固体中的力学辅助腐蚀进行建模。该框架能够捕捉点蚀和应力腐蚀开裂（SCC）以及从点蚀到开裂的转变。假定局部腐蚀是由溶解驱动的，并提出了一种基于膜破裂 - 溶解 - 再钝化机制的公式，以纳入膜钝化的影响。该模型首次纳入了机械应变作为电化学驱动力的作用，加速了腐蚀动力学。通过利用相场范式解决了与追踪不断演变的金属 - 电解质界面相关的计算复杂性，从而能够精确近似复杂的SCC形态。耦合的电化学 - 力学公式使用有限元方法和隐式时间积分方案进行数值实现；位移、相场序参量和浓度是主要变量。我们研究了五个特别令人感兴趣的案例，以展示该模型的预测能力，结果显示其与解析解和实验测量结果高度吻合。通过对这些典型的二维和三维边值问题进行建模，我们表明我们的公式能够捕捉：（i）从活化控制腐蚀到扩散控制腐蚀的转变，（ii）界面动力学对机械应力和应变的敏感性，（iii）膜钝化在降低腐蚀速率方面的作用，以及（iv）钝化膜稳定性对局部应变率的依赖性。这些因素在驱动SCC缺陷形状变化（包括从点蚀到开裂的转变）方面的影响是该模型的自然结果，为工程材料和结构的力学评估奠定了基础。