PSI - Issue 32

L.V. Stepanova et al. / Procedia Structural Integrity 32 (2021) 261–272 Author name / StructuralIntegrity Procedia 00 (2019) 000–000

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1. Introduction Computational modeling of fracture has significant engineering relevance as a predictive capability to quantify material failure under load, an essential consideration during design (Wilson et al. (2019), Singh (2019), Stepanova and Bronnikov (2020)). For the last few decades, advances in modeling have continually demonstrated this predictive capability. As it is noted in (Wilson et al. (2019))while linear elastic fracture mechanics provides a continuum representation of fracture, there are a number of significant phenomena related to atomic scale that can’t be described by continuum theory. Nowadays there are some attempts to determine stress intensity factors from molecular dynamics modelling. Thus, in (Wilson et al. (2019)) a novel numerical method for determination of SIFs from atomistic simulations is presented. The authors Wilson et al. (2019)) of Using atomiccoordinates to describe the displacement field about a crack tip, the authors Wilson et al. (2019)) projected observed displacements onto theset of continuous displacement fields defined by the Williams expansion, with the expansion coefficients determiningthe stress intensity factors. The authors found agreement with experimental data of fracture toughness in silica glass. A computational scheme to analyze the mixed-mode fracture of grain boundaries in polycrystalline solids was developed in (Mai et al. (2018)). The authors extract the atomic -level J-based integral to estimate stress intensity factors for Mode I and mode II loadings. The individual SIFs were obtained from the atomic-level J integral and J based mutual integral, respectively. The singular K-field near an interfacial crack in anisotropic bi-materials as an auxiliary field was incorporated with discrete atomic information obtained from MD simulations of crack propagation along grain boundaries in polycrystalline solids. As the authors notice this technique is advantageous for studying the inter-granular fracture of brittle polycrystalline solids at an atomic scale, as crack propagation along grain boundaries can generally be considered as a mixed-mode fracture.

Nomenclature ij σ

stress tensor components around the crack tip

, r θ

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 θ , ( ) k m i g θ ( ) ( )

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 G

index associated to the fracture mode

shear modulus mixity parameter

e M

In (Dehaghani et al. (2020)) fracture toughness and crack propagation behavior of nanoscale beryllium oxide graphene-like structures is analyzed and the critical value of stress intensity factor according to the linear fracture mechanics under Mode I is calculated. Thus, the values stress intensity factors are determined by the conventional macroscopic linear fracture mechanics and the possibilities of atomic scale simulation are not used. In (Tsai et al (2010)) the fracture behavior of a graphene sheet with a center crackwas characterized using atomistic simulation and linear elasticfracture mechanics (LEFM). In the atomistic simulation, the graphene was regarded as an atomistic structure, containing discretecarbon atoms; nevertheless, in the LEFM, it was modeled as an isotropic homogeneous media. Results from atomistic simulationindicated that because of the discrete attribute, there is no stresssingularity near the crack tip. Therefore, the concept of stressintensity factor, which is generally employed in the continuummechanics, may not be suitable for modeling the crack behaviorin the atomistic graphene sheet. In order to validate the strain energy release rate concept, the energy variation before and after thecrack extension were evaluated in both continuum and atomisticmodel. For the discrete atomistic model, two methods, i.e., the global energy method and the crack closure method, were employedto compute the energy variation as well as the strain