Capturing material toughness by molecular simulation: accounting for large yielding effects and limits

Abstract

The inherent computational cost of molecular simulations limits their use to the study of nanometric systems with potentially strong size effects. In the case of fracture mechanics, size effects due to yielding at the crack tip can affect strongly the mechanical response of small systems. In this paper we consider two examples: a silica crystal for which yielding is limited to a few atoms at the crack tip, and a nanoporous polymer for which the process zone is about one order of magnitude larger. We perform molecular simulations of fracture of those materials and investigate in particular the system and crack size effects. The simulated systems are periodic with an initial crack. Quasi-static loading is achieved by increasing the system size in the direction orthogonal to the crack while maintaining a constant temperature. As expected, the behaviors of the two materials are significantly different. We show that the behavior of the silica crystal is reasonably well described by the classical framework of linear elastic fracture mechanics (LEFM). Therefore, one can easily upscale engineering fracture properties from molecular simulation results. In contrast, LEFM fails capturing the behavior of the polymer and we propose an alternative analysis based on cohesive crack zone models. We show that with a linear decreasing cohesive law, this alternative approach captures well the behavior of the polymer. Using this cohesive law, one can anticipate the mechanical behavior at larger scale and assess engineering fracture properties. Thus, despite the large yielding of the polymer at the scale of the molecular simulation, the cohesive zone analysis offers a proper upscaling methodology.

Irradiation‐induced brittle‐to‐ductile transition in α‐quartz

“…Note that, while crack length can have significant effect on maximum stress achieved for the system, fracture energy is found to be independent of the crack length or system size using the present methodology. A detailed analysis of system size and crack length effects has been done by Brochard et al for materials with and without plastic deformations. Overall, we observe that both silica glass and crystalline quartz exhibit brittle failure with little plastic behavior.…”

Scaling of brittle failure: strength versus toughness

“…In practice, r pl is often much larger than the size of an atom, and using Equation (7) at the atomic scale is questionable. We investigated this issue in previous work (Brochard et al, 2015(Brochard et al, , 2016. Regarding the present study, the toy model has a very low process zone: using the toughness estimation (Eq.…”

“…So we expect Equation (7) to be reproduced precisely at the atomic scale. In contrast, the characteristic length r pl is about 1.5 nm for graphene and capturing the toughness with Equation (7) is possible for system at least 10 nm large which starts to be computationally expensive (see Brochard et al (2016)). So, we limit ourselves to the study of tensile failure for graphene.…”

“…Yet, the modeling of failure initiation remains quite debated. Many initiation criteria have been proposed in the literature but no consensus exists (Brochard et al, 2016). The various theories aim at reconciling two well understood limit cases, namely tensile strength and fracture toughness.…”

A potential-of-mean-force approach for fracture mechanics of heterogeneous materials using the lattice element method

“…Hossain et al, 2014;Nguyen et al, 2015 ). A persistent question yet remains as to the application of fracture mechanics methods to discrete material systems, despite the growing number of applications ranging from molecular scale (for an overview on the topic see Brochard et al, 2015 and references cited herein) to meso-scale of heterogeneous materials (for a recent review, see Bonamy and Bouchaud, 2011 ).…”