Issue34

P. Hess, Frattura ed Integrità Strutturale, 34 (2015) 341-346; DOI: 10.3221/IGF-ESIS.34.37 341 Focussed on Crack Paths Graphene as a model system for 2D fracture behavior of perfect and defective solids P. Hess Institute of Physical Chemistry, University of Heidelberg, D-69120 Heidelberg, Germany peter.hess@urz.uni-heidelberg.de A BSTRACT . A 2D bond-breaking model is presented that allows the extraction of the intrinsic line or edge energy, fracture toughness, and strain energy release rate of graphene from measured and calculated 2D Young’s moduli and 2D pristine strengths. The ideal fracture stress of perfect graphene is compared with the critical fracture stresses of defective graphene sheets containing different types of imperfections. This includes (multiple) vacancies in the subnanometer range, grain boundaries, slits in the nanometer region, and artificial pre-cracks with sizes of 30 nm to 1 µm. Independent of the type of defect, a common dependence of the critical fracture strength on the square root of half defect size is observed. Furthermore, the results suggest the applicability of the Griffith relation at length scales of several nanometers. This observation is not consistent with simulations pointing to the existence of a flaw tolerance for defects with nanometer size. According to simulations for quasi-static growth of pre-existing cracks, the atomic mechanism may also consist of an alternating sequence of bond-breaking and bond-rotation steps with a straight extension of the crack path. Independent of the exact atomic failure mechanism brittle fracture of graphene is generally assumed at low temperatures. K EYWORDS . Graphene; 2D bond-breaking model; 2D mechanical properties; Fracture mechanism; Fracture toughness; Strain energy release rate. I NTRODUCTION haracterization of the elastic and fracture properties of covalent graphene monolayers is of fundamental scientific interest, because they define the upper limits of mechanical behavior [1]. Since perfect samples with an area sufficient for nanoindentation experiments can be prepared, the intrinsic mechanical properties of the class of two-dimensional (2D) solids can be measured directly by nanoindentation with an atomic force microscope, as first realized for graphene [2]. It is important to note that this opens up the unique possibility of studying fracture mechanics of perfect crystals experimentally, a possibility not available for three-dimensional (3D) solids. Furthermore, many theoretical approaches used in dynamic failure analysis are based on 2D models and thus can be applied directly to 2D solids without simplification. Accordingly, the role played by dimensionality is an important issue in advanced fracture analysis. In addition, graphene sheets are of enormous practical importance owing to promising technological applications of larger samples, which, however, may be more or less defective. Therefore, the influence of structural defects such as vacancies, dislocations, microcracks, grain boundaries, and pre-cracks on crack nucleation and propagation must be C