PSI - Issue 37

Larisa Stepanova et al. / Procedia Structural Integrity 37 (2022) 900–907 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

901

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the nanoscale due to discreteness od molecular and atoms. To provide physical insight in failure phenomena at nanoscale and investigate the atomistic nature of fracture one can use atomistic modelling. Up to now with this purpose many researchers basing on atomistic modelling have made successful attempts to calculate stress intensity factors (SIF) and other fracture mechanics parameters (Cheng and Sun (2011), Wilson et al. (2019), Roy and Roy (2019), Buehler et al. (2004), Tsai et al. (2010), Gallo (2020), Mai and Choi (2018), Tsai et al. (2010), Singh et al. (2019), Stepanova and Bronnikov (2019), Stepanova and Bronnikov (2020), Stepanova and Belova (2021)). Thus, in the earliest, in our opinion, work of Buehler et al. (2004) large-scale atomistic simulations of a Mode I crack propagating in a harmonic lattice are presented. The main objective of the paper (Buehler et al. (2004)) is to study the stress and strain fields near a rapidly propagating mode I crack. The atomistic stress intensity factors are obtained and compared with the asymptotic continuum mechanics solutions of the dynamical elastic fields for different crack velocities. The authors show that both atomistic stress and strain can be successively related to the corresponding continuum quantities. The study reveals that atomistic simulation results agree well with the continuum theory predictions. It implies that the continuum theory can be applied for nanoscale problems. In (Wilson et al. (2019)) it is notes that stress intensity factors 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. Th у authors accentuate that at atomic scales fracture occurs as a series of atomic bonds breaking, differing from the continuum description. As a consequence, a formal analogue of the continuum SIFs 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. The authors (Wilson et al. (2019)) present a novel numerical method to determine SIFs from molecular dynamics (MD) simulations. 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. The overarching objective of the paper (Roy and Roy (2019)) is to investigate the validity of application of continuum based linear fracture mechanics methodology. The authors compare predictions obtained by the atomistic simulations for J-integral with the results of the continuum theory. The results show significant deviation from linear elastic fracture mechanics for crack lengths below a certain threshold. In view of some discrepancies between continuum and atomistic approaches it is still debated whether a continuum - based concept should be applied to a discrete system and whether continuum fracture mechanics parameters could be computed from MD simulations. Thus, one can conclude that MD simulations need to be performed to confirm the conclusions. This must be done with the most severe scrutiny lest errors at comparing the results of continuum and atomistic approaches. The approach based on wide and thorough computer experiments with the model material is realized in the present paper. The overwhelming goal of the study is to determine stress intensity factors from atomistic simulations for mixed mode loadings in full range of the mixity parameter describing mixed mode loadings.

Nomenclature ij 

stress tensor components around the crack tip

i u

displacement field

, r 

polar coordinates of the system with its origin at the crack tip coefficients of the terms of the Williams series expansion

m

k a

, I II K K , ( ) k m ij f  , ( ) k m i g  ( ) ( )

mode-I stress intensity factors

angular functions included in stress distribution related to the geometric configuration, load and mode angular functions included in displacement distribution related to the geometric configuration, load and mode

m

index associated to the fracture mode

shear modulus

G