Experimental studies have shown that the active particles of electrodes undergo phase transformations during ion-insertion, which are accompanied by diffusion induced stresses that result in fracture at the particle surface. Only a few studies have considered the effect that the surface stress has on the diffusion-induced stress that occurs in electrode materials that undergo elastic deformations during ion-insertion, while no studies have accounted for the effect of surface stresses in the case when plastic deformation is also present. In addition, there are only few comprehensive studies on the competing effect between the surface stress and the strain gradient during ion diffusion. The present work sheds light on the effect that the particle size has on the stresses generated due to the phase transformations that take place during ion-insertion by accounting for the surface residual stress with strain gradient elasticity or strain gradient plasticity. Due to the presence of surface stresses, the stress on the particle outer surface can be significantly reduced. In particular, when the residual surface stress and the surface elastic modulus are both positive, the hoop stress at the outer surface remains compressive, whereas tensile stresses are required for crack formation. This work, therefore, indicates that surface modification could be an effective approach for improving the structural integrity of electrodes during the lithiation process. The additional consideration of strain gradients further reduces the value of the equivalent plastic strain for elasto-plastic electrode particles. These findings render prospective insights for designing next-generation mechanically stable phase transforming electrode materials.

实验研究表明，电极的活性粒子在离子插入过程中发生相变，伴随着扩散引起的应力，导致粒子表面破裂。只有少数研究考虑了表面应力对离子插入过程中发生弹性变形的电极材料中发生的扩散诱导应力的影响，而没有研究考虑在塑性变形情况下表面应力的影响也存在。此外，关于离子扩散过程中表面应力与应变梯度之间的竞争效应的综合研究也很少。目前的工作通过考虑具有应变梯度弹性或应变梯度塑性的表面残余应力，阐明了粒子尺寸对由于离子插入过程中发生的相变而产生的应力的影响。由于表面应力的存在，颗粒外表面的应力可以显着降低。特别是，当残余表面应力和表面弹性模量都为正时，外表面的环向应力保持压缩，而裂纹形成需要拉伸应力。因此，这项工作表明，表面改性可能是改善锂化过程中电极结构完整性的有效方法。对应变梯度的额外考虑进一步降低了弹塑性电极颗粒的等效塑性应变值。这些发现为设计下一代机械稳定相变电极材料提供了前瞻性见解。