We present a new theoretical and computational framework for modelling electro-chemo-mechanical fracture. The model combines a phase field description of fracture with a fully coupled characterisation of electrolyte behaviour, surface chemical reactions and stress-assisted diffusion. Importantly, a new physics-based formulation is presented to describe electrolyte-containing phase field cracks, appropriately capturing the sensitivity of electrochemical transport and reaction kinetics to the crack opening height. Unlike other existing methods, this approach is shown to accurately capture the results obtained with discrete fracture simulations. The potential of the electro-chemo-mechanical model presented is demonstrated by particularising it to the analysis of hydrogen embrittlement in metallic samples exposed to aqueous electrolytes. The finite element implementation takes as nodal degrees-of-freedom the electrolyte potential, the concentrations of relevant ionic species, the surface coverage, the concentration of diluted species, the displacement field and the phase field order parameter. Particular attention is devoted to improve stability and efficiency, resulting in the development of strategies for avoiding ill-constrained degrees of freedom and lumped integration schemes that eliminate numerical oscillations. The numerical experiments conducted showcase the ability of the model to deliver assumptions-free predictions for systems involving both free-flowing and crack-contained electrolytes. The results obtained highlight the role of electrolyte behaviour in driving the cracking process, evidencing the limitations of existing models.

翻译：我们提出了一种新的理论和计算框架，用于模拟电化学-力学断裂行为。该模型将断裂的相场描述与电解质行为、表面化学反应及应力辅助扩散的完全耦合表征相结合。重要的是，提出了一种新的基于物理的公式来描述含电解质相场裂纹，恰当捕捉电化学传输和反应动力学对裂纹张开高度的敏感性。与现有其他方法不同，该方法能准确重现离散断裂模拟结果。通过将所提出的电化学-力学模型特化应用于暴露于水溶液电解质中的金属样品氢脆分析，展示了其潜力。有限元实现以电解质电势、相关离子浓度、表面覆盖率、稀释物质浓度、位移场和相场序参量为节点自由度。重点致力于提升稳定性和效率，由此发展了避免约束不当自由度的策略以及消除数值振荡的集成积分方案。所进行的数值实验表明，该模型能够对涉及自由流动电解质和裂纹内含电解质的系统进行无假设预测。所得结果凸显了电解质行为在驱动裂纹扩展过程中的作用，并证明了现有模型的局限性。