Energy release or absorption due to simultaneous rotation of two nano voids in plane elastic materials as influenced by both surface effect and interacting effect

Abstract

In this paper, the L-integral analysis for two nano-sized voids in plane elasticity under uniaxial loading is present. Three surface parameters are considered including the surface tension and two surface Lame constants. Attention is focused on the mutual influence on the L-integral from both the surface effect at voids’ rims and the interacting effect between voids. A close-form expression of L-integral for multiple nano voids is obtained. Comparing with those in macro fracture mechanics, the L-integral shows some different features when the surface effect is taken into account. It is concluded that under tensile loading and due to the mutual influence, the L-integral might be either positive or negative, depending on the loading level. The numerical results show that the surface tension is the dominant one in surface parameters on impacting the L-integral. It is also concluded that the surface effect shields the energy release (positive L-integral value) while enhances the energy absorption (negative L-integral value). The two-state L-integral analysis is performed to clarify the way that the surface effect impacts the L-integral. It is concluded that the contribution to L-integral from the voids’ configuration could either be negative or positive, while that from the surface effect is always negative. Besides, the size dependence in the present problem is studied in detail.