Graphite Layer ¦Ò Bond And Crack Propagation Of The Relationship Between Research And Prediction

Since the discovery of the first carbon nanotube(lijima,1991),it has been extensively applied in the field of physics,chemistry,material,electron,photics etc, duing to its excellent mechanical,electromagnetic and chemical properties.Lately, the researches of carbon nanotubes have focused on their mechanical behaviors. There have done many researches on their mechanical properties,such as;elastic module,stretch,flections,except its microcosmic mechanism of rupture.This paper study microcosmic fracture mechanism of graphite sheet and make preparations for the research of carbon nanotubes.The carbon nanotubes crimped from graphite sheet,have the similar bond structure with graphite,in which the bondσplays a major role in one plane and decides the rigidity and intensity of carbon nanotubes,but the bondπfunctions between two adjacent graphite layers,the force field of which is weaker than that of bondσ.In addition,there have force of van der Waals and electromagnetics in carbon nanotubes.This paper shows the relationship between the bondσof a one atom thick graphite sheet and the crack extension in the linear elastic fracture theory under the consideration of edge-to-edge coupling.The area around a crack tip is described by the molecular model with the modified Morse potential,and the remaining area is modeled by the linear elastic fracture theory.The condition of edge-to-edge coupling means that the displacements of the atoms along borderline are equal to those given by the linear elastic fracture theory.The plane-strain is only considered in order to avoid interferes from the bondπand van der Waals force.Firstly,by solving the linearized equations from the molecular model,the displacements of atoms and the relations between the bond stretching strain and the stress intensity factor are obtained.The fracture toughnesses of graphite for modeⅠandⅡare evaluated under the consideration that the bond stretching strain from the atoms at the tip of a crack reaches the peak value of the atom force field.It should be mentioned that for modeⅡof fracture,the atom force field of the bond which forms an angle with the straight crack at a crack tip reaches the peak value before those of other bond around the crack tip.This result is consistent with maximum stress theory and is qualitative correct.Also,the atoms' displacements and bond stretching strain indicate that the scale effect and the material damage exist around the tip of a crack before crack extension.Secondly, we adopt nonlinear analysis and normal perturbation solution for the research of fracture extension of graphite,the conclusion of which is the same with linear analysis in quality.On the other hand,the result that the graphic fracture toughness of modeⅠand modeⅡof nonlinear equation is more closed to experiment.The paper through linear and nonlinear analysis on the fracture extension of graphite,explore the applicability of coupling method of molecular mechanics and continuum theory,and lay foundation for the research of rupture behavior of carbon nanotubes.