13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Edge dislocation emission from nanovoid with the effect of neighboring nanovoids and surface stress Yingxin Zhao1, Qihong Fang1,2*, Youwen Liu1, Chunzhi Jiang1,3 1 College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082 Hunan Province, PR China 2 School of Mechanical and Manufacturing Engineering, The University of New South Wales, NSW 2052, Australia 3 Department of Physics and Electronic Information Engineering, Xiangnan University, Chenzhou 423000, PR China * Corresponding author: email address Fangqh1327@tom.com Abstract Experimental evidence, molecular dynamics simulations and theoretical analyses of nanovoid growth and coalescence in ductile materials indicate that nanovoid growth, coalescence, and stain localization depend strongly on distribution and volume fraction of the nanovoids in ductile porous materials. In the light of this mechanism, a generalized self-consistent theoretical model to describe the dislocation emitted from nanovoid accounting for the effect of neighboring nanovoids is suggested. The explicit solution to the critical stress is derived by means of the complex variable method. The influence of the nanovoid size, the surface effect, nanovoid content and uniform distribution density of neighboring nanovoids in the effective medium on the critical condition required for dislocation emission from nanovoid surface is discussed. Keywords dislocation emission; neighboring nanovoid interactions; nanovoid volume fractions; surface stress 1. Introduction The effect of preexisting volume defects, such as voids and cracks, is generally to lead to an increase in ductility and a reduction in the load carrying capacity of the porous material. A critical mechanism of ductile damage usually involves the nucleation, growth and coalescence of nanovoids, as a result of the applied loading conditions, in a plastically deforming porous materials. According to what we know, there is lacking study about nanovoid growth by dislocation mechanisms, which depends on the size and distribution of the nanovoids in nanoporous materials. In order to quantitatively estimate the interaction of multiple nanovoids in the particular case of porous solids, a generalized self-consistent analytical approach is utilized to study the effects of neighboring defect interactions, and void distribution and volume fractions on the dislocation emission from nanovoid surface, in which a large number nanovoids are statistically homogeneously distributed. It is also a feasible choice for two-dimensional situations in which the voids are roughly cylindrical and near uniformly distributed. The size-effect modeled here pertains to the surface elasticity theory of Gurtin-Murdoch on the nanometer scale. The explicit solution to the critical stress is derived by means of the complex variable method. The influence of the nanovoid size, the surface effect, nanovoid content and uniform distribution density of neighboring nanovoids in the effective medium on the critical condition required for dislocation emission from nanovoid surface is discussed. 2. Modeling and solution In this section, we present a framework for a generalized self-consistent theory accounting for the effect of neighboring nanovoids in ductile nanoporous materials, based on the dynamics of void nucleation and growth. For a two-dimensional case, the constitutive model for the material is divided into three regions: the inner circular region representing the nanovoid phase, the intermediate annular region representing the matrix phase, and the infinitely extended outer region representing composite phase or effective medium. Elastic deformation under plane strain conditions is assumed and the nanovoids are assumed to be and remain cylindrical, and are statistically homogeneously distributed so that their shape is characterized by a single parameter.
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