Effects of surface residual stress and surface elasticity on the overall yield surfaces of nanoporous materials with cylindrical nanovoids

Abstract Mechanical properties of a material near the surfaces and interfaces are different from those of the same material far from the surfaces/interfaces. The effect of this difference on the effective mechanical properties of heterogeneous materials becomes significant when the size of inhomogeneities is at the scale of nanometers. In this article, within a micromechanical framework, the effects of surface residual stress and surface elasticity are taken into account to obtain a macroscopic size-dependent yield function for nanoporous materials containing aligned cylindrical nanovoids. Based on the modified Hill’s condition, the strains are decomposed into two parts, a part due to the external loadings and another part due to the surface residual stress. Then, using the size-dependent effective elastic moduli of the material, an overall yield function is derived. The yield function then is simplified for different practical loading conditions. In addition, considering some numerical examples of metal matrices with nanoporosity, it is shown that the surface stress, including the surface residual stress, has a significant influence on the yielding of these materials with voids of radii smaller than 50 nm. The results show that the effect of the surface residual stress is much more important than the surface elasticity effect, and it should be considered in estimating the yield strength of nano-heterogeneous materials.

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