Scaling of brittle failure: strength versus toughness

Proceedings of the 10th International Conference on Fracture Mechanics of Concrete and Concrete Structures, 2019

In this work, we investigate the elementary processes of brittle failure initiation with molecular simulation techniques. Failure initiation theories aim at bridging the gap between energy-driven failure at high stress concentrations and stress-driven failure in absence of stress concentration, and thus capturing the transition at moderate stress concentrations and associated scale effects. We study graphene, which is one of the few materials with a sufficiently small characteristic length (ratio between toughness and strength) to be addressed by molecular simulations. We also consider a toy model that proves helpful for physical interpretations. Performing molecular simulations of precracked graphene, we found that its failure behavior can overcome both strength and toughness in situations of very high or low stress concentrations, respectively; which is consistent with one particular theory, namely Finite Fracture Mechanics (FFM), which considers failure initiation as the nucleation of a crack over a finite length. Details of the atomic mechanisms of failure are investigated in the athermal limit (0K). In this limit, failure initiates as an instability (negative eigenvalue of the Hessian matrix), irrespective of the stress concentration. However, the atomic mechanisms of failure and their degeneracy (eigenvector of the negative eigenvalue) strongly depend on stress concentration and points to the nucleation of a deformation band whose length decreases with stress concentration. This atomic description is quite similar to FFM theory. At finite temperature, failure is no more deterministic because of thermal agitation. An extensive study to characterize the effects of temperature, loading rate and system size leads to the formulation of a universal scaling law of strength and toughness which extends existing theory (Zhurkov) to size effects. Interestingly, the scalings of stress-driven failure (strength) and of energy-driven failure (toughness) differ only regarding the scaling in size, which relates to the effect of stress concentration on degeneracy identified in the athermal limit.

International Journal of Fracture, 2020

A major challenge in the macroscopic modeling of brittle failure initiation is to reconcile stressdriven failure in absence of stress concentration and energy-driven failure under high stress concentration (crack). In this paper, we perform athermal molecular simulations to investigate the underlying physics behind stress-to energy-driven failures. In the athermal limit, the evolution of an atomic system is deterministic and is obtained by energy minimization. Failure is expected when the system suddenly bifurcates to a broken configuration which can be formally evaluated as an atomic instability characterized by a negative eigenvalue of the Hessian matrix. We applied this methodology to a 2D toy model and to pristine graphene. Both stress-and energy-driven failures are triggered by an instability at the atomic scale, but the two types of failure differ widely regarding the mechanisms of instability (eigenvectors) and their multiplicity (degeneracy). With respect to existing macroscopic theories of failure initiation, these results raise some issues. In particular,

13th International Conference on Fracture (2013)

"A molecular dynamics (MD) simulation to assess the effect of crack length on the ultimate tensile strength of infinitely large armchair and zigzag graphene sheets is presented. The strength of graphene is inversely proportional to the square-root of crack length as in continuum fracture theories. Further comparison of the strength given by MD simulations with Griffith’s energy balance criterion demonstrates a reasonable agreement. Armchair and zigzag graphene sheets with 2.5 nm long crack exhibit around 55% of the strength of pristine sheets. Investigation of the influence of temperature on the strength of graphene indicates that sheets at higher temperatures fail at lower strengths, due to high kinetic energy of atoms. We also observe out-of-plane deformations of the crack tip at equilibrium configuration of both types of sheets due to compressive forces acting on the crack surface. This deformation propagates with applied strain in the direction normal to the crack and eventually generates ripples in the entire sheet."

Journal of Materials Research, 2009

Decreasing scales effectively increase nearly all important mechanical properties of at least some “brittle” materials below 100 nm. With an emphasis on silicon nanopillars, nanowires, and nanospheres, it is shown that strength, ductility, and toughness all increase roughly with the inverse radius of the appropriate dimension. This is shown experimentally as well as on a mechanistic basis using a proposed dislocation shielding model. Theoretically, this collects a reasonable array of semiconductors and ceramics onto the same field using fundamental physical parameters. This gives proportionality between fracture toughness and the other mechanical properties. Additionally, this leads to a fundamental concept of work per unit fracture area, which predicts the critical event for brittle fracture. In semibrittle materials such as silicon, this can occur at room temperature when the scale is sufficiently small. When the local stress associated with dislocation nucleation increases to tha...

Journal of the Mechanics and Physics of Solids, 2018

This paper presents the implication of crystallographic orientation on toughness and ideal strength in graphene under lattice symmetry-preserving and symmetry-breaking deformations. In symmetrypreserving deformation, both toughness and strength are isotropic, regardless of the chirality of the lattice; whereas, in symmetry-breaking deformation they are strongly anisotropic even in the presence of vacancy defects. The maximum and minimum of toughness or strength occur along the zigzag direction and the armchair direction, respectively. The anisotropic behavior is governed by a complex interplay among bond-stretching deformation, bond-bending deformation, and the chirality of the lattice. Nevertheless, the condition for crack-nucleation is dictated by the maximum force required for bond rupture, and it is independent of the chiral angle of the lattice or loading direction. At the onset of crack-nucleation a localized nucleation zone is formed, wherein the bonds rupture locally satisfying the maximum bond-force criterion. The nucleation zone acts as the physical origin in triggering the fracture nucleation process, but its presence is undetectable in the macroscopic stress-strain data.

2022

Micro and nanoscale materials have remarkable mechanical properties, such as enhanced strength and toughness, but usually display sample-to-sample fluctuations and non-trivial size effects, a nuisance for engineering applications and an intriguing problem for science. Our understanding of size-effects in small-scale materials has progressed considerably in the past few years thanks to a growing number of experimental measurements on carbon based nanomaterials, such as graphene carbon nanotubes, and on crystalline and amorphous micro/nanopillars and micro/nanowires. At the same time, increased computational power allowed atomistic simulations to reach experimentally relevant sample sizes. From the theoretical point of view, the standard analysis and interpretation of experimental and computational data relies on traditional extreme value theories developed decades ago for macroscopic samples, with recent work extending some of the limiting assumptions of the original theories. In this review, we discuss the recent experimental and numerical literature on micro and nanoscale fracture size effects, illustrate existing theories pointing out their advantages and limitations and finally provide a tutorial for analyzing fracture data from micro and nanoscale samples. We discuss a broad spectrum of materials but provide at the same time a unifying theoretical framework that should be helpful for materials scientists working on micro and nanoscale mechanics.

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.

Chemical Physics Letters, 2010

Fracture of a monolayer graphene is governed by the competition between bond breaking and bond rotation at a crack tip. Using atomistic reaction pathway calculations, we identify a kinetically favorable fracture path that features an alternating sequence of bond rotation and bond breaking. Our results suggest that the mechanical cracking can create fracture edges with nanoscale morphologies due to the non-uniform bond deformation and rupture induced by the localized high stresses near the crack tip. Such fractured edges may provide a structural basis of tailoring the electronic properties of graphene either intrinsically or by further edge functionalization.

Nature Reviews Materials, 2018

Micro and nanoscale materials have remarkable mechanical properties, such as enhanced strength and toughness, but usually display sample-to-sample fluctuations and non-trivial size effects, a nuisance for engineering applications and an intriguing problem for science. Our understanding of size-effects in small-scale materials has progressed considerably in the past few years thanks to a growing number of experimental measurements on carbon based nanomaterials, such as graphene carbon nanotubes, and on crystalline and amorphous micro/nanopillars and micro/nanowires. At the same time, increased computational power allowed atomistic simulations to reach experimentally relevant sample sizes. From the theoretical point of view, the standard analysis and interpretation of experimental and computational data relies on traditional extreme value theories developed decades ago for macroscopic samples, with recent work extending some of the limiting assumptions of the original theories. In this review, we discuss the recent experimental and numerical literature on micro and nanoscale fracture size effects, illustrate existing theories pointing out their advantages and limitations and finally provide a tutorial for analyzing fracture data from micro and nanoscale samples. We discuss a broad spectrum of materials but provide at the same time a unifying theoretical framework that should be helpful for materials scientists working on micro and nanoscale mechanics.

International Journal of Applied Mechanics, 2023

The thermo-mechanical coupling mechanism of graphene fracture under thermal gradients possesses rich applications whereas hard to study due to its coupled non-equilibrium nature. We employ non-equilibrium molecular dynamics to study the fracture of graphene by applying a fixed strain rate under different thermal gradients by employing different potential fields. It is found that for AIREBO and AIREBO-M the fracture stresses do not strictly follow the positive correlations with the initial crack length. Strain-hardening effects are observed for "REBO-based" potential models of small initial defects, which is interpreted as blunting effect observed for porous graphene. The temperature gradients are observed to not show clear relations with the fracture stresses and crack propagation dynamics. Quantized fracture mechanics verifies our molecular dynamics calculations. We provide a unique perspective that the transverse bond forces share the loading to account for the nonlinear increase of fracture stress with shorter crack length. Anomalous kinetic energy transportation along crack tips is observed for "REBO-based" potential models, which we attribute to the high interatomic attractions in the potential models. The fractures are honored to be more "brittle-liked" carried out using machine learning interatomic potential (MLIP), yet incapable of simulating post fracture dynamical behaviors. The mechanical responses using MLIP are observed to be not related to temperature gradients. The temperature configuration of equilibration simulation employing the dropout uncertainty neural network potential with a dropout rate of 0.2 is reported to be the most accurate compared with the rest. This work is expected to inspire further investigation of non-equilibrium dynamics in graphene with practical applications in various engineering fields. Novelty Statement • Using non-equilibrium molecular dynamics, graphene fracture is studied under temperature gradients with fixed strain rates to examine the effects of initial defect sizes, temperature differences, and interatomic forcefields.