PSI - Issue 50

L.V. Stepanova et al. / Procedia Structural Integrity 50 (2023) 275–283 Author name / Structural Integrity Procedia 00 (2023) 000 – 000

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1. Introduction Traditional formalism of contemporary fracture mechanics of brittle materials relied on the ideas of continuum solid mechanics and does not take into consideration the crystal structure of the material. Theoretical and computational approaches to introduce the crystal structures in the fracture analysis have been developed recently (Gao et al. (2001), Buehler et al. (2004), Machova et al. (2017), Chakraborty and Ghost (2021), Birang and Steinmann (2021), Stepanova et al. (2021)). Attempts to account for effects of the crystalline structure of the materials in solid mechanics are continuing to invent nowadays (Peng et al. (2022), Diaz et al. (2022), Stepanova and Belova (2022)). Thus, in (Birang and Steinmann (2021)) the basics of the discrete configurational mechanics of crystalline lattice are established. In (Birang and Steinmann (2021)) deformational and configurational formulations for a crystalline system with the Lennard – Jones potential were gained. Modern computational methods and approaches, such as molecular dynamics metods, provide much greater numerical opportunities and a much larger set of interatomic interaction potentials (Birang and Steinmann (2021)). Studies conducted using the molecular dynamics method and aimed at computing stress tensor elements in the proximity of the notch and crack tips have already begun to be carried out about twenty years ago. To the author's knowledge, the first attempts to compare the continuum fracture mechanics and atomistic calculations date back to 2001 and 2004 (Gao et al. (2001), Buehler et al. (2004)), where the Lennard – Jones potential was utilised. The study (Buehler et al. (2004)) reveals that nanoscale modelling results agree well with the continuum mechanics prognosis. However, modified interaction potentials have now appeared, which make it conceivable to perceive the crystalline structures of a broad range of materials with high accuracy. Modeling of nonlinear deformations and fracture processes using molecular dynamics methods is becoming a common reality and a common tool for modeling stress fields and displacements near a stress concentrator (Chakraborty and Ghost (2021), Peng et al. (2022), Machova et al. (2017), Stepanova and Belova (2022), Stepanova et al. (2021)). Moreover, parallel algorithms underlying the concurrent atomistic-continuum methodology are developing (Diaz et al. (2022)). Thus, in (Diaz et al. (2022)) the new parallel algorithm for concurrent atomistic continuum (CAC) formulation is presented. It is pertinent to note that the algorithm can be integrated into exiting molecular dynamics codes. In (Diaz et al. (2022)) the CAC methodology is described and its parallel implementation in LAMMPS is realized. Despite the results obtained and the regularities of the failure processes revealed using the methods of atomistic modeling (Gao et al. (2001), Buehler et al. (2004), Chakraborty and Ghost (2021), Peng et al. (2022), Machova et al. (2017), Stepanova and Belova (2022), Stepanova et al. (2021), Diaz et al. (2022)), many questions remain unlit and open. For instance, is it possible to directly compare the stress components at the notch and crack tips obtained by continuous and discrete approaches? The present work is devoted to the atomistic modeling of stress fields engulfing the crack tip under mode I and mixed mode loadings. Determination of stress, strain and displacement fields is an urgent problem of modern continuum mechanics of a deformable solid. However, it is understandable that the failure processes and nonlinear deformations observed at the macroscopic level and currently described using the mathematical apparatus of continuum mechanics are due to the crystalline structure of the material under consideration. Since continuum mechanics proceeds from the concept of continuity, it can’t describe the crystalline structure of the material. Currently, the molecular dynamics approach has been applied to calculate the parameters of fracture mechanics (Gao et al. (2001), Buehler et al. (2004), Peng et al. (2022), Machova et al. (2017), Stepanova and Belova (2022), Stepanova et al. (2021), Diaz et al. (2022), Chakraborty and Ghost (2021)). The primary aim of this work is to establish the stress-strain state at the atomistic scale using molecular dynamics modeling of the crystalline structure of the material. The monocrystalline fcc copper and aluminum were chosen. The objectives of the study are to determine the elastic properties of monocrystalline copper and aluminum by the method of molecular dynamics and to compare the elastic properties obtained by this method with known values from macroscopic experiments. Further, the intent of the study is to determine the components of the stress tensor near the crack tip under normal separation conditions and mixed mode loading.