PSI - Issue 40

L.V. Stepanova et al. / Procedia Structural Integrity 40 (2022) 392–405 Stepanova L.V., Belova O.N. / Structural Integrity Procedia 00 (2022) 000 – 000

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Keywords: Stress intensity factors; T-stress; atomistic modelling; molecular dynamics method; continuum fracture mechanics, overdeterministic method.

1. Introduction The main motivation of this study is the desire to compare the fundamental results of classical fracture mechanics with the results of computer modelling of the stress-strain state in cracked specimens by the molecular dynamics method on the example of a copper plate with a central crack under mixed mode loading. In the conventional mechanics of brittle fracture, the main parameter reflecting the stress-strain state of a body with a defect under loads is the stress intensity factors for Mode I and Mode II loadings. A number of questions arise related to the determination of the parameters of classical fracture mechanics based on molecular dynamics modelling of fracture processes. Will the stress intensity factors calculated on the basis of stress fields at the crack tip in a sample with a central crack, studied using the molecular dynamics simulations, with dimensions of orders of several hundred angstroms, be quantitatively the same as in the classical fracture mechanics for the sample with the same dimensions? Will the value of the invariant J-integral calculated using the molecular dynamics method coincide with the results of classical fracture mechanics for a sample of the same configuration? What exactly are the limitations that appear when the parameters of classical fracture mechanics are computed using the results of molecular dynamics modelling? Whether these restrictions, for example, on the distance from the crack tip, or on the number of atoms in the model, are universal, general, or will depend on the configuration of the sample, on the crystal structure under consideration. What is the meaning of the stress intensity factor in the case of molecular dynamics modelling? It is well known that the stresses in a plate with a central crack are limited in the case of molecular dynamics modelling, but, nevertheless, this stress intensity factor is calculated in many studies and correlations between the fracture processes at the nano and macro levels are found. Based on the results of visualization of fracture processes at the nanoscale, it is possible to see the stress distribution at the crack tip. A reasonable question arises: is it possible to compare the angular stress distributions in the vicinity of the crack tip in the case of a Mode I crack, Mode II crack and mixed mode loading? These questions are not new-for the community of specialists in the field of fracture mechanics (Cheng and Sun (2011), Dehaghani et al. (2020), Gallo (2020), Mai and Choi (2018), Singh et al. (2019), Shimada et al. (2015), Roy and Roy (2019), Machova et al. (2017), Wilson et al (2017), Stepanova and Bronnikov (2020), Stepanova and Belova (2021), Tsai et al. (2010)). Currently, there is a large number of papers devoted to this issue. Academic interest has primarily focused on the determination of stress intensity factors. Thus, Shimada and co-authors (Shimada et al. (2015)) note that materials fail by the nucleation and propagation of a crack, the critical condition of which is quantitatively described by fracture mechanics that uses an intensity of singular stress field characteristically formed near the crack-tip. However, the continuum assumption basing fracture mechanics obscures the prediction of failure of materials at the nanoscale due to discreteness of atoms. Then the authors demonstrated the ultimate dimensional limit of fracture mechanics at the nanoscale, where only a small number of atoms are included in a singular field of continuum stress formed near a crack tip. Surprisingly, a singular stress field of only several nano-meters still governs fracture as successfully as that at the macroscale, whereas both the stress intensity factor and the energy release rate fail to describe fracture below a critically confined singular field of 2 – 3 nm. It implies breakdown of fracture mechanics within the framework of the continuum theory. Wilson and his co-authors (Wilson et al. (2017)) note that stress intensity factors (SIFs) are used in continuum fracture mechanics to quantify the stress fields surrounding a crack in a homogeneous material in the linear elastic regime. Critical values of the SIFs define an intrinsic measure of the resistance of a material to propagate a crack. At atomic scales, however, fracture occurs as a series of atomic bonds breaking, differing from the continuum description. As a consequence, a formal analogue of the continuum stress intensity factors calculated from atomistic simulations can have spatially localized, microstructural contributions that originate from varying bond configurations. The ability to characterize fracture at the atomic scale in terms of the SIFs offers both an opportunity to probe the effects of chemistry, as well as how the addition of a microstructural component affects the accuracy. A novel numerical method to determine SIFs from molecular dynamics (MD) simulations is presented by Wilson and his colleagues. The accuracy of this approach is first examined for a simple model, and then applied to atomistic simulations of fracture in amorphous silica. MD simulations provide time and spatially dependent SIFs, with results that are shown to be in good agreement with experimental values for fracture toughness in silica glass. Thus, a novel