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

Research output: Contribution to journal › Article

### Standard

**On the Crack‐Tip Region Stress Field in Molecular Systems: The Case of Ideal Brittle Fracture.** / Gallo, Pasquale.

Research output: Contribution to journal › Article

### Harvard

*Advanced theory and simulations*, vol. 2, no. 10, 1900146. https://doi.org/10.1002/adts.201900146

### APA

*Advanced theory and simulations*,

*2*(10), [1900146]. https://doi.org/10.1002/adts.201900146

### Vancouver

### Author

### Bibtex - Download

}

### RIS - Download

TY - JOUR

T1 - On the Crack‐Tip Region Stress Field in Molecular Systems: The Case of Ideal Brittle Fracture

AU - Gallo, Pasquale

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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/r0.5 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.

AB - 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/r0.5 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.

U2 - 10.1002/adts.201900146

DO - 10.1002/adts.201900146

M3 - Article

VL - 2

JO - Advanced theory and simulations

JF - Advanced theory and simulations

SN - 2513-0390

IS - 10

M1 - 1900146

ER -

ID: 36336677