最后，应用新的弹性理论和扩散理论，研究了锂离子电池纳米电极在充放电过程中的力学行为，预测了纳米球颗粒电极和纳米线电极内部化学场扩散诱导的应力和位移分布。研究发现：表面效应能够有效抑制纳米电极在充放电过程中的体积膨胀，使纳米电极中正应力及平均应力降低；此外，纳米线电极中von Mises应力降低，但纳米球颗粒电极中von Mises应力保持不变。上述研究结果能够为锂离子电池的电极优化设计提供理论指导，通过合理选择纳米电极的特征尺寸和几何形状，能够避免电极内部应力集中或膨胀变形引发的失效现象，从而有效延长锂离子电池的使用寿命。
The mechanical properties of nanostructured materials exhibit size effect due to their large ratio of surface area to volume which is also called surface effect. Such phenomenon cannot be predicted within the framework of the classical continuum mechanics since no internal length scale is involved. As for this issue, the surface elastic theory (Gurtin-Murdoch theory) is widely used to study the mechanical properties in nanomaterials. The linear surface constitutive relation related to surface energy density or surface stress is established, in which surface elastic constants are involved to characterize the surface effect. Such parameters can only be determined by molecular dynamics and require a significant amount of computing resources. Furthermore, a negative value of the surface elastic constant is often found which brings out some difficulties for the theoretical applications. In this paper, a novel elastic theory based on the surface energy density is adopted to characterize the surface effect. The surface elastic constants are no longer involved in the theory. Only the bulk surface energy density and surface relaxation are introduced to characterize the surface properties of nanomaterials. Both the two parameters are easy to determine with clearly physical meanings. Based on the novel elastic theory, the mechanical properties in several typical nanostructured materials are investigated, including the static bending and vibration of Timoshenko nanobeam, plain-strain and axisymmetric nanocontact problems, adhesive nanocontact problem and the stress and displacement distributions of nanoelectrodes in lithium-ion battery. The influential mechanisms of surface effect on the mechanical properties of nanostructured materials are further revealed. The main contents and contributions of this paper are as follows:
Firstly, a fixed-fixed and cantilevered Timoshenko nanobeam model are established to predict the size-dependent effective elastic modulus and resonant frequency of nanobeam, in which both the surface effect and the shear deformation are considered. It can be found that when the length of a nanobeam is fixed, with the increase of the cross-section size, both the effective elastic modulus and resonant frequency experience a transition from the dominant of the surface effect to the coupling influences of the surface effect and shear deformantion, and further to the dominant of the shear deformation. The surface effect stiffens a fixed–fixed nanobeam while softens a cantilevered one. The shear deformation always makes a nanobeam soft. The above results agree well with the existing experiment data and could give a theoretical guidance of the design of nano-electro-mechanical systems.
The plain-strain and axisymmetric nanocontact problems are systematically investigated. Boussinesq contact models with considering surface effect are established and general solutions are obtained. Three two-dimensional nanocontact models (an elastic half-space under an uniform pressure, an elastic half-space punched by a flat-ended indenter or a cylindrical one) and three axisymmetric ones (an elastic half-space under an axisymmetrically uniform pressure, an elastic half-space punched by a rigid flat-ended cylindrical indenter or a spherical one) are analyzed respectively. It can be found that surface effect on the nanocontact behaviors cannot be neglected when the contact width or contact radius is on the same magnitude with the intrinsic length scale, i.e., the ratio of the bulk surface energy density to the bulk shear modulus of the indented material. Compared with the classical contact solutions, surface effect could not only make the normal stresses smoother and more uniform, but also lead to smaller and more uniform displacements as well as a non-zero shear stress at the contact surface. Furthermore, the size effect of nanoindentation hardness is predicted for the case of rigid spherical indenter. It can be found that nanoindentation hardness increases with the reduction of the indenter radius or the external load.
The adhesive contact behaviors at nanoscale are investigated by combining the new elastic theory and classical adhesive contact model based on Lennard-Jones force law. An axisymmetric adhesive contact model between a rigid spherical indenter and an elastic half-space with surface effect is established. The surface energy density of the indented bulk substrate, as only one additional parameter, serves as an important factor to characterize the surface property. It is found that the surface effect can be enhanced by decreasing the shear modulus of the indented material or the radius of the spherical indenter. As compared with the classical adhesive contact solutions based on Lennard-Jones force law, surface effect could not only lead to a smaller maximum pull-off force and flatter deformation of the substrate, but also increase the corresponding approaches at turning points in hysteretic phenomenon which occurs more easily for the case of soft substrate or large indenter. When neglecting the external load, the corresponding approaches become smaller than classical predictions, which demonstrates the substrate becomes hardened when surface effect is considered. The results agree qualitatively with the existing experimental data.
Lastly, combining the new elastic theory and diffusion theory, the diffusion-induced stresses and displacements of nanostructured electrodes in lithium-ion batteries are analyzed, including spherical nanoparticle and nanowire electrode. It is found that when the characteristic size of the electrode is at nanoscale, the surface effect could not only restrain the volume expansion of the nanoelectrodes, but also reduce the normal stresses and average one. The von Mises stress in nanowire electrodes decreases as compared with the classical solutions while the von Mises stress in spherical nanoparticle could not be influenced by surface effect. The results provide a theoretical guidance on the design of the electrodes. The tendency for mechanical degradation of electrodes caused by stress concentration and huge volume expansion could be avoided by choosing nanoeletrodes with reasonable size and geometry, which could prolong the service life of lithium-ion batteries.
|贾宁. 表面效应对典型纳米结构材料力学行为的影响[D]. 北京. 中国科学院大学,2018.|