Energy release or absorption due to simultaneous expansion of many interacting nanoholes in elastic materials

Abstract

The energy release or absorption due to simultaneous expansion of many interacting nanoholes in elastic materials under plane strain deformation is studied as influenced by the surface effect along rims of nanoholes. The M-integral classically used in macro mechanics with defects is extended to treat the problem with many interacting nanoholes. After some manipulations, the energy change due to the simultaneous expansion of many nanoholes represented by the M-integral is evaluated. Four different arrays of many nanoholes under a monotonically increasing tensile loading are considered. Attention is focused on the influence induced from the surface tension, the surface Lamé constants, and the interaction among many nanoholes on the M-integral. It is concluded that the surface tension yields significant influence on the M-integral, whereas the surface Lamé constants offer much smaller influence, which could be neglected with some relative errors less than 2%. It is found that, unlike those in macro mechanics with defects, the simultaneous expansion could either release energy (the positive value of the M-integral) or absorb energy (the negative value of the M-integral), depending on the loading levels. There is a neutral loading point, at which the M-integral transforms from a negative value to a positive value in all arrays of nanovoids under consideration. It is also found that the interaction among multiple nanoholes influences the value of the neutral loading point significantly because the mutual influence induced from both the interacting effect and the surface effect yields a quite different feature from those induced from the interacting effect only. That is, the surface effect always inhibits the influence of the interacting effect on the M-integral.

Large chip production mechanism under the extreme load cutting conditions

“…At any deforming moment (when large chip has a certain curvature), an interface-stress neutral plane will occur between the stretched and compressed zones. By using of the plane cross-section assumption [20] , it assumes the current curvature is in linear changes, as the stress neutral plane moves away from the tool-chip contact direction, the deformation amount will gradually increase. The neutral plane for large chip is a geometric plane, which moves along the chip material layer during the crimping process.…”