PSI - Issue 39

Larisa Stepanova et al. / Procedia Structural Integrity 39 (2022) 748–760 Author name / Structural Integrity Procedia 00 (2019) 000–000

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continuum mechanics quantities (Moller et al. (2018)). Thus, stress intensity factors (SIF) are used in classical continuum linear elastic fracture mechanics to describe the stress, strain and displacement fields in the vicinity of the crack in a homogeneous material in linear elastic regime (Wilson et al. (2019)). The criteria of classical linear elastic fracture mechanics use a severe intensity of singular stress and strain fields in the neighborhood of the crack tip (Shimada et al. (2015), Hello (2018), Karihaloo and Xiao (2001), Hello et al. (2012)). It is well-known that fracture is successively described by the singular field of continuum stress. In the framework of continuum representation, nowadays the multi-parameter description of the crack-tip fields is employed. It has been shown that the multi-point approach for the approximation of the crack-tip fields can significantly clarify and refine the stress-strain state. Many researchers showed the significance of higher-order terms of the Williams series expansion (Malikova and Vesely (2014), Hello (2018), Zhabbarov and Stepanova (2020)). They show that the higher-order (non-singular) terms in the Williams power series play an important role in describing fracture processes in linear elastic media. The coefficients of higher-order terms can be obtained analytically (Hello et al. (2012), Hello (2018), Nejati et al. (2020), Stepanova and Roslyakov (2016)), numerically via finite element analysis (Zhabbarov and Stepanova (2020), Li and Zheng (2021)) and experimentally by interference-optic methods of solid mechanics (Ayatollahi and Moazzami (2017), Stepanova (2020)). Thus, it can be concluded that the higher-order terms of the Williams’ series are substantial and the procedure of determination of the coefficients in the Williams power series, albeit with many questions, is, generally, well designed and tested. Meanwhile, it’s worth noting that the continuum assumption-based linear elastic fracture mechanics obscures the prediction of failure of materials at the nanoscale due to discreteness of molecular and atoms. While linear elastic fracture mechanics provides a continuum description of fracture there are a number of essential phenomena related to atomic scale properties that can’t be explained by continuum presentation. To ensure physical understanding in failure phenomena and fracture processes at nanoscale and analyse 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 compute 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 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 for the dynamical elastic fields for different crack velocities. The authors demonstrate 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 means that the continuum theory can be applied for nanoscale problems. In (Wilson et al. (2019)) it is noted 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. The authors emphasize 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)) propose 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. Moller and co-authors propose a force based scaling law for atomistically informed continuum models and confirm the applicability of linear elastic fracture mechanics in the nanometer range close to crack tips in brittle materials (Moller et al. (2018)). They show that atomistically determined stresses ahead of the crack tip agree wel with the prediction of linear elastic fracture mechanics. 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