On the Crack‐Tip Region Stress Field in Molecular Systems: The Case of Ideal Brittle Fracture

Abstract

Continuum-based fracture mechanics breaks down at the nanoscale where the discrete nature of atoms cannot be neglected. Intriguingly, this work shows that the concept of stress intensity factor is still valid if the atoms are modeled. Molecular statistics simulations are conducted on single-edge cracked samples of ideal brittle silicon, varying the size until few nanometers. The local virial stress, derived as the functional derivative of the free energy of a molecular system with respect to the deformation tensor, is used as a measure of the mechanical stress at the atomic level. Then, stress intensity factor at failure is evaluated. The results show that regardless of the size, the atomistic stress field varies according to the classical 1/r 0.5 relation, and discrete stress intensity factors can be derived for all the geometries. Continuum values, in contrast, fail to describe the fracture when the length of the singular stress field is smaller than 4-5 times the fracture process zone. Thus, this work shows that the stress intensity factor from atomic stress may be useful to describe the fracture criterion at extremely small dimensions, provided that virial stress is accepted as a representation of mechanical stress at the atomic level.

Brittle Failure of Nanoscale Notched Silicon Cantilevers: A Finite Fracture Mechanics Approach

“…The FFM, as introduced earlier, is a coupled criterion, i.e., it requires two conditions to be full-filled, one based on stress and the other on energy considerations. The stress criterion could be developed by considering the virial stress, provided that it is accepted as a representation of the mechanical stress at the atomic scale as recently showed in [20], or by employing a traction vector-based stress recently proposed in [54]. The energy criterion, instead, could be defined based on interatomic potential energy as provided in some recent examples based on the energy release rate [22,23] and on the averaged strain energy density [17].…”

“…Several studies have recently quantified the small scale breakdown of continuum-based linear elastic fracture mechanics (LEFM) and have demonstrated that continuum-based methods are still valid at small scale if that limit is not reached [15][16][17][18]. The breakdown was expressed in terms of the ratio between the crack singular stress field length, which surprisingly is still characterizing the crack at a very small scale [19][20][21], and the fracture process zone. When this ratio is in the order of 4-5, continuum-based LEFM breaks down and the discrete nature of atoms cannot be ignored.…”

Some Considerations on Stress Intensity Factor at Atomic Scale

“…Recently, fracture tests by means of MS simulations were conducted by using opensource code LAMMPS [24]. While details can be found in [23], important aspects are presented hereafter. The modified Stillinger-Weber (SW) interatomic potential [25] was employed.…”

“…Setting aside the debate on the validity of the virial stress as a representation of mechanical stress at atomic scale, in the present work the focus is on the applicability of classic continuum concepts in the presence of defects, such as the stress intensity factor (SIF). By reviewing recent molecular statistics (MS) analyses on single-edged cracked samples loaded under mode I [23], and representative of ideal brittle fracture, it is demonstrated that the virial stress shows the trend of inverse square root singularity and that computation of the SIF according to Irwin's concept is possible. Furthermore, the breakdown of continuum linear elastic fracture mechanics, recently defined by means of energy concepts [11][12][13], is here quantified by using merely the stress fields.…”

Micromechanical Modeling of Fatigue Crack Nucleation around Non-Metallic Inclusions in Martensitic High-Strength Steels

“…In the past, different types of materials have been the focus of micromechanical investigations on fatigue crack initiation in the absence of NMI. Selected works are for example: On polycrystalline ferritic and ferritic-pearlitic steels [24][25][26], on martensitic steels [27][28][29], on aluminum alloys [30], on nickel-base alloys [18,23,31,32] and finally on ideal brittle materials [33,34]. The listed works are exemplary and there is no claim to completeness.…”