The finite element over-deterministic method to calculate the coefficients of crack tip asymptotic fields in anisotropic planes

Ayatollahi, M.R.; Nejati, Morteza; Ghouli, Saeid

doi:10.1016/j.engfracmech.2020.106982

Cited by 38 publications

(16 citation statements)

References 126 publications

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“…12b). We then applied the finite element over-deterministic (FEOD) method (Ayatollahi and Nejati 2011;Ayatollahi et al 2020). This method makes use of the displacements of a large number of finite element nodal points around the crack tip to form an over-determined system of equations, ( 16)…”

Section: A2 Crack Parameters In An Scb Sample Subjected To Three-point Bendmentioning

confidence: 99%

Introduction of a Scaling Factor for Fracture Toughness Measurement of Rocks Using the Semi-circular Bend Test

et al. 2021

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This article discusses the scale dependence of the mode $$\mathrm {I}$$ I fracture toughness of rocks measured via the semi-circular bend (SCB) test. An extensive set of experiments is conducted to scrutinise the fracture toughness variations with size for three distinct rock types with radii ranging from 25 to 300 mm. The lengths of the fracture process zone (FPZ) for different sample sizes are measured using the digital image correlation (DIC) technique. A theoretical model is also established that relates the value of fracture toughness to the sample size. This theorem is based on the strip-yield model to estimate the length of FPZ, and the energy release rate concept to relate the FPZ length to the fracture toughness. This theoretical model does not rely on any experimental-based curve-fitting parameter, but only on the tensile strength of the rock type as well as the fracture toughness at a specific sample size. The size effects predicted by the theoretical model is in a good agreement with the experimental data on both fracture toughness and the FPZ length. Finally, theoretical correction factors are introduced for various geometrical configurations of the SCB specimen, using which a scale-independent mode $$\mathrm {I}$$ I fracture toughness of the rock material can be estimated from the results of experiments performed on small samples.

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Section: A2 Crack Parameters In An Scb Sample Subjected To Three-point Bendmentioning

confidence: 99%

Introduction of a Scaling Factor for Fracture Toughness Measurement of Rocks Using the Semi-circular Bend Test

et al. 2021

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“…Having obtained the set of points the procedure of the over-deterministic method can be implemented. As it is noted in [17] the basic principle of the over-deterministic method is the use of a large number of numerical data points in order to calculate the crack tip parameters. This is done by forming an algebraic system of equations where the number of equations is more than the number of unknowns.…”

Section: Determination Of Fracture Mechanics Parametersmentioning

confidence: 99%

Determination of Continuum Fracture Mechanics Parameters for Molecular Dynamics Simulations

Степанова¹,

Belova²,

Bronnikov³

2021

14th WCCM-ECCOMAS Congress

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This study is aimed at determination of continuum fracture mechanics parameters such as stress intensity factors, T-stress and higher-order terms, from molecular dynamics simulation performed for copper plate with narrow diamond-like crack. For this purpose, an embedded atom potential (EAM) available in LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) molecular dynamics (MD) software is utilized to accurately describe mixed-mode crack growth. The stresses calculated from MD method using the virial theorem are used for over-deterministic method for extracting stress intensity factors, T-stress and higherorder terms of Williams series expansion. It is shown that the algorithm of the over-deterministic method can be generalized for MD calculations and gives the reasonable value of continuum fracture mechanics parameters. The obtained value of stress intensity factors, T-stresses and higher order terms are compared with the theoretical values for an infinite plate with the central crack under Mode I loading and Mixed Mode loading conditions for several values of the mixity parameter which defines the type of Mixed Mode loading.

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“…Geometrical and material properties used for the calculation of crack parameters. to determine crack parameters from the FEOD method is given in detail in Ayatollahi et al [31]. Table 2 presents the normalised crack parameters A B T A A , , , .…”

Section: Tablementioning

confidence: 99%

“…This paper uses the finite element over-deterministic method (FEOD), recently developed by the authors [31], to determine the coefficients of the first five terms of mode I asymptotic crack tip field for the SCB specimen, for a wide range of geometrical and material factors. We then characterise the K-dominant region in the SCB specimen of an anisotropic rock.…”

Section: Introductionmentioning

confidence: 99%

Crack tip asymptotic field and K-dominant region for anisotropic semi-circular bend specimen

Nejati

Ghouli

Ayatollahi

2020

Theoretical and Applied Fracture Mechanics

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This study reports the coefficients of the crack tip asymptotic field for the semi-circular bend (SCB) specimen made of anisotropic rocks when subjected to pure mode I loading. The finite element over-deterministic method is employed to determine the singular and higher order terms of the crack tip asymptotic field for a wide range of geometry and anisotropy parameters associated with the Mode SCB test. These parameters are helpful when analysing the fracture path and failure mechanism of anisotropic rocks in cases where the process zone is large compared to the crack length. We also apply an energy-based criterion on the crack tip fields to evaluate the size of the K-dominant region as a function of geometry configuration and anisotropy. It is concluded that the ISRMsuggested size requirement for the SCB samples of rock can yield underestimated values of fracture toughness due to the constraints applied to the FPZ development.

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The finite element over-deterministic method to calculate the coefficients of crack tip asymptotic fields in anisotropic planes

Cited by 38 publications

References 126 publications

Introduction of a Scaling Factor for Fracture Toughness Measurement of Rocks Using the Semi-circular Bend Test

Introduction of a Scaling Factor for Fracture Toughness Measurement of Rocks Using the Semi-circular Bend Test

Determination of Continuum Fracture Mechanics Parameters for Molecular Dynamics Simulations

Crack tip asymptotic field and K-dominant region for anisotropic semi-circular bend specimen

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