Jeffrey W. Kysar

Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene

We measured the elastic properties and intrinsic breaking strength of free-standing monolayer graphene membranes by nanoindentation in an atomic force microscope. The force-displacement behavior is interpreted within a framework of nonlinear elastic stress-strain response, and yields second- and third-order elastic stiffnesses of 340 newtons per meter (N m–1) and –690 Nm–1, respectively. The breaking strength is 42 N m–1 and represents the intrinsic strength of a defect-free sheet. These quantities correspond to a Youngs modulus of E = 1.0 terapascals, third-order elastic stiffness of D = –2.0 terapascals, and intrinsic strength of σint = 130 gigapascals for bulk graphite. These experiments establish graphene as the strongest material ever measured, and show that atomically perfect nanoscale materials can be mechanically tested to deformations well beyond the linear regime.

High-Strength Chemical-Vapor–Deposited Graphene and Grain Boundaries

Graphene Staying Strong Although exfoliated graphene can be extremely strong, it is produced on too small a scale for materials application. Graphene can be produced on a more practical scale by chemical vapor deposition, but the presence of grain boundaries between crystallites apparently weakens the material. Lee et al. (p. 1073) show that postprocessing steps during the removal of the graphene sheets can oxidize the grain boundaries and weaken them. If these steps are avoided, the material is comparable in strength to exfoliated graphene. Unless subjected to chemical attack, the grain boundaries in chemical-vapor–deposited graphene do not weaken the material. Pristine graphene is the strongest material ever measured. However, large-area graphene films produced by means of chemical vapor deposition (CVD) are polycrystalline and thus contain grain boundaries that can potentially weaken the material. We combined structural characterization by means of transmission electron microscopy with nanoindentation in order to study the mechanical properties of CVD-graphene films with different grain sizes. We show that the elastic stiffness of CVD-graphene is identical to that of pristine graphene if postprocessing steps avoid damage or rippling. Its strength is only slightly reduced despite the existence of grain boundaries. Indentation tests directly on grain boundaries confirm that they are almost as strong as pristine. Graphene films consisting entirely of well-stitched grain boundaries can retain ultrahigh strength, which is critical for a large variety of applications, such as flexible electronics and strengthening components.

Strengthening effect of single-atomic-layer graphene in metal–graphene nanolayered composites

Graphene is a single-atomic-layer material with excellent mechanical properties and has the potential to enhance the strength of composites. Its two-dimensional geometry, high intrinsic strength and modulus can effectively constrain dislocation motion, resulting in the significant strengthening of metals. Here we demonstrate a new material design in the form of a nanolayered composite consisting of alternating layers of metal (copper or nickel) and monolayer graphene that has ultra-high strengths of 1.5 and 4.0 GPa for copper-graphene with 70-nm repeat layer spacing and nickel-graphene with 100-nm repeat layer spacing, respectively. The ultra-high strengths of these metal-graphene nanolayered structures indicate the effectiveness of graphene in blocking dislocation propagation across the metal-graphene interface. Ex situ and in situ transmission electron microscopy compression tests and molecular dynamics simulations confirm a build-up of dislocations at the graphene interface.

Crack tip deformation fields in ductile single crystals

Abstract Crack tip deformation fields in ductile single crystal media are studied experimentally. The crack, located between two single crystals of aluminum joined by a thin ductile interlayer of tin, is introduced via selective chemical etching and can be considered “sharp”; the material surrounding the tip is fully annealed. After a Mode I loading is applied, the specimen is sectioned and the in-plane rotation field under plane strain conditions is mapped using Electron Backscatter Diffraction. The observations provide evidence of the main features of the deformation fields predicted by Rice (Mech Mater 6 (1987) 317) using continuum single crystal plasticity, especially the existence of kink shear sector boundaries which had not been unambiguously identified in previous studies. However to explain the measured change in lattice rotation at the kink shear sector boundary, an alternate dislocation structure is deduced which does not require a high concentration of dislocation sources to be distributed along the ray of the putative kink shear sector boundary. Based on this, a lower bound on the dislocation density in the kink shear sector is established experimentally. The results have implications for analytical and numerical simulations of plastic deformation in ductile single crystal media, from the length scale of microns to the macroscopic length scale.

Continuum simulations of directional dependence of crack growth along a copper/sapphire bicrystal interface. Part I : experiments and crystal plasticity background

Abstract Cracks that exhibit relative amounts of ductility along a copper/sapphire bicrystal interface are simulated within the context of continuum mechanics. The specimen in question exhibits a directional dependence of fracture; that is a crack oriented in one direction along the copper/sapphire interface propagates much more during a given load increment than does the crack oriented to propagate in the opposite direction along the interface. This phenomenon had previously been explained on the basis of an energetic competition between dislocation nucleation and cleavage failure at the two crack tips using both the Rice and Thomson (Philos. Mag. 29 (1974) 73) model as well as the more recent type of dislocation nucleation analysis by Rice (J. Mech. Phys. Solids 40 (1992) 239) based on a Peierls-like stress vs. displacement relationship on the slip plane. However, recent experiments by Kysar (Acta Mater. 48 (2000) 3509) have shown that the orientation of the directional dependence of fracture in the copper/sapphire bicrystal is opposite to that predicted on the basis of dislocation nucleation arguments. The goal of the present work is to attempt to explain the directional dependence of fracture solely on the basis of continuum mechanics. In Part I of this pair of papers we review the main results of the experiments and then set the stage for a series of finite element analyses of the bicrystal specimen by reviewing the fundamentals of single crystal plasticity and the general features of crack tip fields in single crystals. We then discuss two different constitutive hardening models for single crystals and predict that, depending on the hardening model, regions of single-slip around the crack tip may degenerate into regions of triple slip. This leads to a discussion of how the near-tip displacement field can change dramatically with constitutive models. Next the constitutive properties used in the simulations are fit to experimental data. Finally we describe the finite element meshes and procedures for simulating the stationary and quasistatically growing cracks. The simulation results are reported in Part II.

Mechanical properties of thin glassy polymer films filled with spherical polymer-grafted nanoparticles

It is commonly accepted that the addition of spherical nanoparticles (NPs) cannot simultaneously improve the elastic modulus, the yield stress, and the ductility of an amorphous glassy polymer matrix. In contrast to this conventional wisdom, we show that ductility can be substantially increased, while maintaining gains in the elastic modulus and yield stress, in glassy nanocomposite films composed of spherical silica NPs grafted with polystyrene (PS) chains in a PS matrix. The key to these improvements are (i) uniform NP spatial dispersion and (ii) strong interfacial binding between NPs and the matrix, by making the grafted chains sufficiently long relative to the matrix. Strikingly, the optimal conditions for the mechanical reinforcement of the same nanocomposite material in the melt state is completely different, requiring the presence of spatially extended NP clusters. Evidently, NP spatial dispersions that optimize material properties are crucially sensitive to the state (melt versus glass) of the polymeric material.

Characterization of Plastic Deformation Induced by Microscale Laser Shock Peening

Electron backscatter diffraction (EBSD) is used to investigate crystal lattice rotation caused by plastic deformation during high-strain rate laser shock peening in single crystal aluminum and copper sample on (I 10) and (001) surfaces. New experimental methodologies are employed which enable measurement of the in-plane lattice rotation under approximate plane-strain conditions. Crystal lattice rotation on and below the microscale laser shock peened sample surface was measured and compared with the simulation result obtained from FEM analysis, which account for single crystal plasticity. The lattice rotation measurements directly complement measurements of residual strain/stress with X-ray micro-diffraction using synchrotron light source and it also gives an indication of the extent of the plastic deformation induced by the microscale laser shock peening.

Directional dependence of fracture in copper/sapphire bicrystal

Abstract Two cracks that propagate along the interface of a copper/sapphire bicrystal in opposing directions exhibit a directionally dependent fracture behavior. Rice, Suo and Wang, using the Rice–Thomson model, suggested that the phenomenon could be explained on the basis of crack tip dislocation nucleation concepts. We show that the experimentally observed orientation of directional dependence is opposite that of the prediction. Further, it is shown that Beltz and Wang, who had previously reported the experimentally observed orientation to be in accord with predictions, incorrectly measured the orientation. The crack opening displacement profile of the two cracks, as measured interferometrically and via AFM, is shown to exhibit a directional dependence. The results of finite element simulations of the specimen offer an explanation for the directional dependence of fracture on the basis of the continuum crack tip fields.

Energy dissipation mechanisms in ductile fracture

Abstract The objective is to investigate energy dissipation mechanisms that operate at different length scales during fracture in ductile materials. A dimensional analysis is performed to identify the sets of dimensionless parameters which contribute to energy dissipation via dislocation-mediated plastic deformation at a crack tip. However, rather than using phenomenological variables such as yield stress and hardening modulus in the analysis, physical variables such as dislocation density, Burgers vector and Peierls stress are used. It is then shown via elementary arguments that the resulting dimensionless parameters can be interpreted in terms of competitions between various energy dissipation mechanisms at different length scales from the crack tip; the energy dissipations mechanisms are cleavage, crack tip dislocation nucleation and also dislocation nucleation from a Frank–Read source. Therefore, the material behavior is classified into three groups. The first two groups are the well-known intrinsic brittle and intrinsic ductile behavior. The third group is designated to be extrinsic ductile behavior for which Frank–Read dislocation nucleation is the initial energy dissipation mechanism. It is shown that a material is predicted to exhibit extrinsic ductility if the dimensionless parameter bρdisl1/2 (b is Burgers vector, ρdisl is dislocation density) is within a certain range defined by other dimensionless parameters, irrespective of the competition between cleavage and crack tip dislocation nucleation. The predictions compare favorably to the documented behavior of a number of different classes of materials.

Continuum simulations of directional dependence of crack growth along a copper/sapphire bicrystal interface. Part II : crack tip stress/deformation analysis

Abstract The goal of this work is to explain the directional dependence of fracture of interfacial cracks in a copper/sapphire bicrystal in terms of continuum stress and deformation fields. In Part I of this pair of papers, we briefly review the main results of experiments by Kysar (Acta Mater. 48 (2000) 3509) and discuss how the orientation of the directional dependence of fracture is contrary to predictions made on the basis of crack tip dislocation nucleation concepts. We then set the stage for a series of finite element analyses of the bicrystal specimen. In Part II the simulation results are presented. We first conclude that the assumptions which enter into the crack tip dislocation nucleation analyses are valid. Therefore, the orientation of the directional dependence is opposite that of the dislocation nucleation analyses, in spite of the fact that crack tip dislocation nucleation may occur as predicted. We then show that the directional dependence of fracture, at least for the copper/sapphire bicrystal specimen, can be explained by the fact that the quasistatically growing brittle crack has the propensity to generate a significantly higher normal opening stress along its prolongation than does the ductile crack. This conclusion is valid for a wide range of crack growth criteria as well as material constitutive models and parameters. We also present results of the simulated crack opening displacement profiles of the two crack and compare them to experimental measurements. The results do not satisfactorily explain the qualitative features of the normal crack opening displacement profile; however we discuss some possible reasons why the finite element method may not be able to accurately model the crack opening displacement profile.