Dynamic Fracture In Graphene Of Finite Element Model

Graphene has attracted great interests of scholars from many fields such as mechanics for itsnovel two-dimensional material dimensions and properties of hexagonal crystal structure. With thegradual application of graphene in composite toughening, artificial muscles and other smart materials,mechanical properties such as fracture under dynamic loads are drawing researchers’ attentionincreasingly. Meanwhile, industrially manufactured graphene is always prepared with structuraldefects, so graphene easily breaks in research and practical applications. Thus, it is very important toinvestigate the fracture characteristics of graphene particularly under dynamic fracture characteristicsas well as to prevent and control crack propagation problem in the application process of graphenematerials.Currently, the theories of dynamic fracture of brittle materials have been proposed by manyscholars, but they are seldom used to describe a ‘real two-dimensional material’. Hence, twodimensional atomic crystal graphene is adopted to examine the above theory. On the other hand, thesize of the model is limited for the mechanical behaviors simulation of large-scale nano materials byatomistic molecular mechanics (MM). Instead, the finite element (FE) approximate model based oncontinuum mechanics can overcome the disadvantage.Based on Li and Chou’s molecular structural mechanics, a FE model considering largedeformation and nonlinear geometric effects is developed to predict the dynamic fracture in grapheneand the brittle crack along zigzag direction in a graphene strip under pure opening loads ofdisplacements at different strain rates is investigated.Firstly, the C-C bonds are represented by Timoshenko beams considering shear deformation. Thenonlinear constitutive relation is derived from the Tersoff-Brenner potential and is customized by thesubroutine VUMAT. The fracture criterion of equivalent beams is also determined. A FE model ofgraphene is then constructed using Timoshenko C-C beam by Abaqus software. The calculatedYoung’s modulus and Poisson’s ratio by the model graphene showed good agreements with previousresults in literatures.Secondly, a graphene strip model with initial crack is established. The dynamic fracture ofzigzag-type crack at different loading strain rates is then realized by applying uniform normal loadingof edge displacements and quasi-static analysis.Finally, the characteristics of crack growth under different strain rates, such as instantaneous/average velocity, critical stress intensity factor as well as critical energy release rate, arecalculated and analyzed to be compared with the ones by MD simulation. At last, related existingtheoretical prediction of dynamic fracture of brittle materials is verified and the dynamic fracturecharacteristics of zigzag-type crack in graphene are summarized.