13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- The Characterization of Dominating Region of Fracture (process region) around a Crack tip Based on the Concept of Mechanical Similarity and Atomic Mechanics A. Toshimitsu Yokobori, Jr. 1,*, Yoshiko Nagumo 1, Takahiro Yajima 1 Toshihito Ohmi 1 1 Department of Nanomechanics, Tohoku University, Sendai, 980-8579, Japan * Corresponding author: yokobori@md.mech.tohoku.ac.jp Abstract Brittle fracture at a crack tip is considered to be caused within a specified local region, that is, process region. However, the determination of this scale has not yet been theoretically clarified. The difficulty of this determination will be due to the wide range scale analysis from the range of nano scale (atomic scale) to macro scale (crack size scale). In this paper, on the basis of the atomic mechanics using super atom and hybrid method of the fractal concept which concerns self-similarity with the proposed analysis of scale projection from macro to nano scales, the disturbed region of atom arrangements around a crack tip were clarified under the local stress field by crack and dislocation. This disturbed region was related to fracture dominating region (process region) which is in good agreement with the scale obtained from experimental consideration by R. Ritchie. Keywords Process region, Mechanical similarity, Atomic mechanics, Brittle fracture 1. Introduction The fracture criterion of materials is considered to be a condition that fracture occurs when a specified mechanical condition is satisfied in the local damage region around a crack. As the criterion, the energy and the local stress conditions [1-3] in this region or the hybrid theory which is taken into account for both conditions [4] have been proposed. There are corresponding local damage regions in brittle fracture, fatigue fracture and creep fracture, respectively. Each scale of these local damage regions is different respectively. For example, each local damage region is considered to correspond with the plastic region [5] for fatigue fracture and creep damage region [6] for creep fracture. For brittle fracture, the end region or process region are considered to be the dominating region of fracture [7]. However, its physical meaning has not yet been clarified. Under this condition, determination of this local region using the experimental fracture toughness has been conducted and the scale of this region is considered to be that of several grains [8]. The process region is considered to be a disordered region of atomic arrangement [3] which concerns fracture of atomic bond. This analysis requires the effects of crack, dislocations and atoms of which scales are order of mm, μm and nm on local stress field around a crack or dislocation groups. Since it is necessary to construct two dimensional atomic arrangements to realize a modeled crack or dislocations, conduction of this analysis by atomic mechanics alone requires large scale and high accuracy numerical analyses. Under this background, authors aim to show the possibility of conducting the analysis of determination of local dominating region of brittle fracture by convenient scale of numerical analysis such as PC level analysis to conduct various calculations conveniently. The concept of this analysis is as follows. (1) The macro and micro local stress fields such as a crack and a dislocation are introduced as mechanical boundary conditions of the region of analysis. It causes the elimination of the necessity of the establishment of two dimensional atomic models, which gives the validity of conducting one dimensional analysis. (2) By utilizing property of potential system of atomic force, instead of using actual atoms array, super atoms array is considered since the mechanical similarity is valid between them. Super atom
RkJQdWJsaXNoZXIy MjM0NDE=