Strain Shielding from Mechanically Activated Covalent Bond Formation during Nanoindentation of Graphene Delays the Onset of Failure

Abstract

Mechanical failure of an ideal crystal is dictated either by an elastic instability or a soft-mode instability. Previous interpretations of nano-indentation experiments on suspended graphene sheets [1,2], however, indicate an anomaly: the inferred strain in the graphene sheet directly beneath the diamond indenter at the measured failure load is anomalously large compared to the fracture strains predicted by both soft-mode and acoustic analyses. Through multi-scale modeling combining the results of continuum, atomistic, and quantum calculations; and analysis of experiments, we identify a strain-shielding effect initiated by mechanochemical interactions at the graphene-indenter interface as the operative mechanism responsible for this anomaly. Transmission electron micrographs (TEM) and a molecular model of the diamond indenter's tip suggest that the tip surface contains facets comprising crystallographic {111} and {100} planes. Ab initio and molecular dynamics (MD) simulations confirm that a covalent bond (weld) formation between graphene and the crystallographic {111} and {100} facets on the indenter's surface can be induced by compressive contact stresses of the order achieved in nano-indentation tests. Finite element analysis (FEA) and MD simulations of nano-indentation reveal that the shear stiction provided by the induced covalent bonding restricts relative slip of the graphene sheet at its contact with the indenter, thus initiating a local strain-shielding effect. As a result, subsequent to stress-induced bonding at the graphene-indenter interface, the spatial variation of continuing incremental strain is substantially redistributed, locally shielding the region directly beneath the indenter by limiting the buildup of strain while imparting deformation to the surrounding regions. The extent of strain shielding is governed by strength of the shear stiction, which depends upon the level of hydrogen saturation at the indenter's surface. We show that, at intermediate levels of hydrogen saturation, the strain-shielding effect can enable the graphene to support experimentally-determined fracture loads and displacements without prematurely reaching locally limiting states of stress and deformation.Keywords: Graphene, ideal strength, lattice stability, nano-indentation, mechanochemistry, strain-shielding. Lee, et al. [1] measured the fracture strength of graphene using nano-indentation experiments and reported an unprecedentedly high intrinsic strength, measuring orders of magnitude greater than those of conventional materials. The nano-indentation involves instrumented indentation of a suspended graphene sheet by a nanoscale diamond indenter up to the point of failure. However, the local stress and strain beneath the indenter are not directly measurable in such nano-indentation experiments; instead, the indentation load (F ) as a function of indentation depth (u z | r=0 ) during the course of indentation is recorded. Finite Elements Analysis (FEA) based on an appropriate constitutive description of graphe...

Fracture of graphene: a review

“…As shown in Fig. 21, both large and small hydrogen (Kumar and Parks 2015). a Illustration of the indenter surface with varying hydrogen saturations.…”

“…With multi-scale analysis combing quantum, MD and FEM simulations, Kumar and Parks (2015) investigated the failure of graphene under nano-indentation, focusing on mechanochemical interactions at the graphene-indenter interface. Based on ab initio and MD simulations, they showed that covalent bonding between graphene and certain crystallographic facets on a diamond indenter can form under the compressive contact stresses during indentation.…”

Property control by elastic strain engineering: Application to graphene

“…This method relies on the fact that the physical and mechanical properties of materials are functions of elastic strain [Gilman, 2003] and they also depend on the symmetry of crystal lattice, that can be altered by elastic strain. Nanomaterials such as thin films, nanowires, nanopillars and atomic sheets can withstand ultra-high stresses without plasticity or fracture [Zhu and Li, 2010;Kumar and Parks, 2015]. Consequently, the elastic strain level achievable in nanomaterials can be 100 times larger than in the macroscopic materials.…”

“…It consists of sp 2 -hybridized carbon atoms and demonstrates outstanding stretchability, up to about 20-30%, without being damaged [Kumar and Parks, 2015;Dmitriev et al, 2012;Liu et al, 2007;Lee et al, 2008;Baimova et al, 2012a]. This makes graphene perfect for ESE.…”

“…Commonly, strain in graphene is obtained due to the presence of a substrate. The other way is to apply strain to freestanding graphene, e.g., by means of nanoindentation [Kumar and Parks, 2015].…”