Stress intensity factors, T-stresses and higher order coefficients of the Williams series expansion and their evaluation through molecular dynamics simulations

Stepanova, L. V.; Belova, O. N.

doi:10.1080/15376494.2022.2084800

Cited by 10 publications

(3 citation statements)

References 62 publications

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“…The influence of higher order terms (n ≤ −1 or n ≥ 2) on the stress field of a cracked plate under in-plane loading can be important in some engineering applications [3,4,5,6,7]. The further modified maximum tangential stress (FIMTS) criterion takes into account several stress terms and can assess the mode I fracture toughness (PIc) of rocks better than the traditional maximum tangential stress (MTS) criterion [8].…”

Section: Introductionmentioning

confidence: 99%

Advanced crack tip field characterization using conjugate work integrals

Melching,

Breitbarth

2023

Preprint

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The quantitative characterisation of crack tip loads is fundamental in fracture mechanics. Although the potential influence of higher order terms on crack growth and stability is known, classical studies solely rely on first order stress intensity factors. We calculate higher order Williams coefficients using an integral technique based on conjugate work integrals and study the convergence with increasing crack tip distance. We compare the integral method to the state-of-the-art fitting method and provide results for higher-order terms with several crack lengths, external forces, and sizes for widely used middle tension, single-edge cracked tension, and compact tension specimen under mode-I loading.

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Section: Introductionmentioning

confidence: 99%

Advanced crack tip field characterization using conjugate work integrals

Melching,

Breitbarth

2023

Preprint

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“…В настоящее время метод молекулярной динамики (МД), будучи наиболее адаптируемым вычислительным методом для моделирования материалов на атомном/ молекулярном уровнях, нашел свое широкое применение для моделирования многих физических, механических, биологических, химических явлений и процессов на атомарном уровне [1][2][3][4][5][6][7]. Среди методов атомистического моделирования моделирование, основанное на методе МД, является наиболее подходящим методом для исследования процессов разрушения, поскольку динамика атомов теоретически отслеживается путем решения ньютоновского уравнения движения.…”

Section: Introductionunclassified

“…Среди методов атомистического моделирования моделирование, основанное на методе МД, является наиболее подходящим методом для исследования процессов разрушения, поскольку динамика атомов теоретически отслеживается путем решения ньютоновского уравнения движения. В частности, классическое моделирование МД является мощным инструментом для моделирования материалов в наноразмерном масштабе благодаря его относительно низкой вычислительной стоимости за счет использования эмпирических силовых полей (моделей межатомного взаимодействия) [1][2][3][4][5][6][7]. Особенно большой интерес вызывает моделирование нанотрубок, изготовленных из различных материалов, находящихся под воздействием сложных термомеханических нагрузок [2][3][4].…”

Section: Introductionunclassified

Modelling the Crack Propagation and Analysis of the Inclined Crack Path in the Pipe With the Extended Finite Element Method and Molecular Dynamics Method

Belova,

Stepanova

2023

PSP

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The article is devoted to a comparative analysis of the results of computational simulation experiments aimed at determining the inclined crack propagation paths a linearly elastic medium, performed using two fundamentally different approaches, namely discrete atomistic approach and continuum mechanics approach. The aim of the study is to construct paths of an inclined crack in a pipe under the uniaxial tensile loading by means of an extended finite element method (continuum approach) and using the molecular dynamics method (discrete, molecular atomistic approach). Computer simulations of uniaxial tension of a pipe with a through-the-thickness inclined crack were performed using the extended finite element method of the multi-functional computational software SIMULIA Abaqus. In parallel with the finite element analysis, a molecular dynamic simulation of the uniaxial tension of a nanoscopic tube with a through-the-thickness inclined crack in the LAMMPS software package for several materials (monocrystalline copper and monocrystalline aluminum with a face-centered crystal lattice) with the embedded atom potentials available in the LAMMPS open code was carried out. The sizes of macroscopic and nanoscopic pipes and crack lengths are selected taking into account the geometric similarity of the samples. Hereupon, the paths of the propagation of an inclined crack in a pipe under axial stretching conditions are obtained. Computations were carried out for several characteristic values of the crack inclination angles: 30, 45, 60 and 75° to the pipe axis. It is found that the crack propagation paths obtained within the framework of the continuum mechanics approach and atomistic simulations are similar to each other. It is established that for different angles of the crack location, the similarity of the crack growth trajectories in the pipe is preserved at various scale length levels: macroscopic and nanoscopic scales.

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