PSI - Issue 32

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

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energy re-lease rate. On the other hand, the finite element analysis was per-formed in the continuum graphene sheet for the estimation of thestrain energy release rate. It was denoted that the strain energy re-lease rate calculated based on the global energy method and crackclosure method are almost the same. Furthermore, it was demonstrated that the global energy method is a simple manner in theatomistic simulation for the calculation of the strain energy releaserate. A comparison of atomistic simulation with finite element results illustrated that the strain energy release rates obtained fromcontinuum model coincided with that in the discrete model associated with the same loading condition. As a result, the conceptof strain energy release rate is regarded as a physical quantity thatcan establish connections between the atomistic simulation andcontinuum modeling for modeling the fracture of covalentlybonded graphene sheet. The overarching objective of (Roy and Roy (2019)) was to investigate the validity of application of continuum based linear elastic fracture mechanics methodology at the nanoscale, and to extend the concept of the continuum J integral to the atomistic domain, by addressing the following key issues: (a) computation of continuous variables, such as displacement and their derivatives, from discrete atomistic quantities, (b) including nonlocality in J that is inherent in atomistic computations due to long range inter-atomic forces, and (c) incorporating entropic effects due to thermal motion in a atomistic system which is not present in a conventional continuum description. an atomistic J-integral is implemented as a nano-scale fracture metric to investigate flaw-tolerance at the nanoscale. Predictions obtained using the atomistic J are compared with linear elastic fracture mechanics predictions for the case of a single (zig-zag) graphene sheet with a center-crack under tensile loading at room temperature, and show significant deviation from LEFM for crack lengths below a certain threshold. However, the authors conclude that thecritical J integral value obtained from the methodology discussed in this paper were found to be in good agreement with the valueavailable in literature. In (Cheng and Sun (2011)) it is noted that stress intensity factor is one of the most significant fracture parameters in linear elastic fracture mechanics (LEFM). Due to its simplicity, many researchers directly employed this concept to explain their results from molecular simulation. However, stress intensity factor defines the amplitude of the singular stress, which is the product of continuum elasticity. Under atomistic systems without the stress singularity, the concept of stress intensity factor must be examined. In addition, the difficulty of studying the stress intensity factor in atomistic systems may be traced back to the ambiguous definition of the local atomistic stress. In this study, the definition of the local virial stress is adopted. Subsequently, through the consideration of K-dominance, the approximated stress intensity factor based on the atomistic stress can be projected within a reasonable region. Moreover, the influence of cutting interatomic bonds to create traction free crack surfaces and the critical stress intensity factor is also discussed. The paper (Gallo (2020)) reviews recent molecular statistics numerical experiments of cracked samples and discusses the crack-tip region stress in ideal brittle materials. Continuum-based linear elastic fracture mechanics breaks down at extremely small scales where the discrete nature of materials has to be considered. However, as it is noted in (Gallo (2020)) recent results have shown that the concept of stress intensity factor is still valid. In (Gallo (2020)) by means of molecular statistics simulations on single-edge cracked samples of ideal brittle silicon it is shown that the stress intensity factor derived from the virial stress may be useful to describe the fracture at extremely small dimensions and to quantify the breakdown of continuum-based linear elastic fracture mechanics. Thus, one can notice that conclusions are very different and versatile. This is due to 1) differences in basic concepts of continuum fracture mechanics and discrete atomistic approach and 2) lack of right understanding and approaches for correct comparison of results of simulation obtained by two different schemes. Therefore, the goal of this study is to obtain the fracture mechanics parameters (stress intensity factor, T-stress and coefficients of higher order terms in the Williams series expansion of the crack-tip stress and displacement fields) from atomistic simulations and to compare continuum fracture mechanics parameters and the same parameters obtained from molecular dynamics modelling. 1.1. Details of molecular dynamics simulations All atomistic simulations are based on molecular dynamics method with a classical molecular dynamics code Large-scale Atomic/Molecular Massively Parallel Simulator(LAMMPS) using an embedded atom model EAM potential a copper crystal (Cu_u3.eam). FCC copper is considered.The plate with a central crack under tensile loading and mixed mode loading has been modeled. For the full MD model simulations start with the static