Conservative Integrals of Dislocations and Characteristics of Crack Propagation in Nanomaterials

Abstract

This study reveals the unique features of defects in nanomaterials that cannot be described by a conventional approach. It is reported that the nanostructure exhibits different properties/behaviors that cannot be observed in the macro-sized structure. Therefore, sometime the conventional theory (which is based on the continuum medium) cannot estimates the nanostructures. Numerous studies have revealed the uniqueness of nanostructures and tried to extend the conventional theory to nanoscale. This study also verifies and broaden the application of conventional theory in nanoscale. However, our study focuses on the defects in nanostructure. The defects cause the significant impact of a structure failure and thus the effect of uniqueness in nanoscale on the defects must be revealed precisely. Here, we show the numerical and theoretical evidence to show the unique behaviors of the defects in nanostructure. Specifically, we investigated a conservative integral of dislocation and a characteristic of a crack in nanostructure. For a dislocation, we derive a stress field of steadily moving dislocation and reveal that the path-independence of J-integral breaks. For a crack, we observed the fracture mode change with the size change of the nanostructure. Molecular Dynamic (MD) simulation is employed for the study to observe and analyze the mechanical behavior of nanostructures and the defects inside. The result of MD simulation is then compared to the theories. In the study of dislocation, we show the stress field and J-integral of steadily moving dislocation. Oppose to common believe (conventional theory), the stress field of steadily moving dislocation is asymmetric and thus the J-integral loses the path-independence. The magnitude of stress decrease/increase in ahead/behind the steadily moving dislocation. J-integral of steadily moving dislocation loses path-independence and become inversely proportional to the radius of the contour. The discrete nature causes a lattice wave emission from the steadily moving dislocation and lead the asymmetric stress field and eventually the breakdown of J-integral path-independence. We modify the conventional theory and successfully estimate the stress field as well as the J-integral of steadily moving dislocation. For the study of fracture behavior of a nano-crack embedded in nanostructure, we mainly focused on influence of the size-dependent properties of nanostructure on crack. We construct a center crack embedded in a (100) metal nanoplate and apply strain until the material failure. In Linear Elastic Fracture Mechanics (LEFM), the Griffith stress is known as the criterion for the brittle crack propagation. By the expectation of Griffith stress, extremely short crack remarkably enlarges the Griffith stress, and it may exceed the ideal stress of the material. However, when it comes to nanostructure, the strength of a material is size-dependent. Hence, the fracture condition as well as the strength of the structure must be considered simultaneously in nanoscale. Owing to the size dependent strength of nanostructure, the fracture mode exhibit Brittle-to-Ductile (BTD) transition with the size change of the nanostructure.