Energy release or absorption due to simultaneous expansion of many interacting nano-holes in elastic materials

The energy release or absorption due to simultaneous expansion of many interacting nano-holes in elastic materials under plane strain deformation is studied as influenced by the surface effect along rims of nano-holes. The M-integral classically used in macro mechanics with defects is extended to treat the problem with many interacting nano-holes. After some manipulations, the energy change due to the simultaneous expansion of many nano-holes represented by the M-integral is evaluated. Four different arrays of many nano-holes under a monotonically increasing tensile loading are considered. Attention is focused on the influence induced from the surface tension, the surface Lame constants, and the interaction among many nano-holes on the M-integral. It is concluded that the surface tension yields significant influence on the M-integral, whereas the surface Lame 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 nano-voids under consideration. It is also found that the interaction among multiple nano-holes 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.