Effect of surface residual stress and surface layer stiffness on mechanical properties of nanowires

The mechanical properties of nanowires are significantly affected by surface effects. In this work, we investigate the potential mechanisms of surface residual stress and surface layer stiffness on the bending behavior of nanowires. The deflection equation of nanowires under pure bending is first derived from the Young–Laplace equation and the Euler–Bernoulli beam theory. Subsequently, a new finite element model based on Galerkin’s weighted residual method is developed to verify the accuracy of the theoretical solution. The theoretical and numerical solutions present the significant effects of surface residual stress and surface layer stiffness on the elastic properties of nanowires depending on the feature size, boundary conditions, and sectional geometry of the nanowires. Specifically, the surface residual stress makes the simply-supported and fixed–fixed nanobeams stiffer; however, it makes the cantilever nanobeam softer. Besides, the sectional geometry of the nanowires has a noticeable impact on their transverse deflection. If the size of circumscribed circle of the cross section remains constant, the nanowires become harder as the numbers of sectional sides increase for the specific feature size and boundary conditions. If the cross-sectional area remains unchanged, the deflection of the nanowires fluctuates as the number of cross-sectional side increases. We realize that the overall Young’s modulus of nanowires is closely related to the feature size. As the cross-sectional feature size is below a critical value, the surface residual stress dominates the bending behavior of the nanowire. As the sectional feature size exceeds the critical feature size that is correlated to the nanowire boundary conditions, the factor dominating the bending behavior gradually transforms from the surface residual stress to the surface layer stiffness. This study provides a theoretical framework for developing a design strategy that incorporates surface effects in the engineering of nano/microscale architected advanced materials.