Employing of the discrete Fourier transform for evaluation of crack-tip field in periodic materials

Ryvkin, Michael; Hadar, Or

doi:10.1016/j.ijengsci.2014.10.001

Cited by 14 publications

(9 citation statements)

References 15 publications

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“…The estimated average values are plotted in Figure 7a. Previous research on the fracture properties of porous materials has mainly focused on infinite media, assuming that any specimens cut from the same brittle material, characterized by the same porosity and microstructural features, will in fact exhibit the same fracture behaviour [34][35][36]. However, this study suggests that, for constant porosity, smaller specimens will appear tougher than their larger counterparts since they exhibit lower stress intensities for the same loading.…”

Section: Macroscale: Homogenized Materialsmentioning

confidence: 85%

K-dominance and size effect in mode I fracture of brittle materials with low to medium porosity

Touliatou

Wheel

2018

Engineering Fracture Mechanics

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Linear Elastic Fracture Mechanics usually only considers the singular stresses when describing the conditions under which fracture would occur in a brittle material. However, it is becoming more widely recognised that non-singular stresses can become significant depending on the geometry and configuration of the specimen. This study investigates the impact of non-singular stresses on the stress intensity of low to medium porosity brittle materials. To address this, discrete finite element models of Double Cantilever Beam (DCB) samples were created and the full near-tip stress field in mode I loading was numerically evaluated. A parametric study was conducted, examining the influence of overall specimen size, material porosity and crack tip location relative to the nearest void. Results indicate a prominent size effect on the stress intensity at the crack tip of porous materials, with smaller specimen exhibiting tougher behaviour than their respective larger counterparts. This size effect, which is amplified with increasing porosity, is closely correlated with the variation of non-singular stresses, both parallel and normal to the crack plane. A model to predict the behaviour of porous specimen for different sizes is suggested based on the findings.

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Section: Macroscale: Homogenized Materialsmentioning

confidence: 85%

K-dominance and size effect in mode I fracture of brittle materials with low to medium porosity

Touliatou

Wheel

2018

Engineering Fracture Mechanics

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“…Following References [12,15], the jumps of the field variables at the opposite sides of the considered rectangular region form the requested boundary conditions that should be imposed in solving the problem of the composite half-plane with internal defects. These jumps are defined as follows:…”

Section: The Boundary Conditionsmentioning

confidence: 99%

“…Next, the finite discrete double Fourier transform is applied, which reduces the formulated problem of a rectangular region that consists of numerous cells to a single cell in the transform domain. It should be noted that the idea of employing a nontrivial analytical solution of an auxiliary homogenized medium as boundary conditions in conjunction with the discrete Fourier transform has been first presented by Reference [15]. The solution of the resulting governing equations in conjunction with the imposed boundary and interfacial continuity conditions, formulated in the transform domain, is obtained by employing the higher-order theory [14].…”

Section: Introductionmentioning

confidence: 99%

The Effect of Defects in Piezoelectric Composite Half-Planes with Surface Electrodes

Aboudi

2020

J. Compos. Sci.

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An analysis for the prediction of the electromechanical field in composite piezoelectric half-planes with attached surface electrode is presented. The composite half-planes are composed of distinct constituents and may include internal defects in various locations. The solution is carried out in a sufficiently large rectangular region, the boundary conditions of which are obtained from the corresponding solution of a homogeneous piezoelectric half-plane. This is followed by the application of the discrete Fourier transform at the domain of which a boundary-value problem is formulated. The solution of this boundary-value problem, followed by the inversion of the Fourier transform, provides, in conjunction with an iterative procedure, the electromechanical field at any point of the rectangular region. Applications are given for a piezoelectric half-plane with defects in the form of a cavity and of short and semi-infinite cracks as well as of a periodically bilayered composite with a crack in one of its layers.

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“…As mentioned, the analysis presented in Aboudi ( 2012) is limited to the analysis of composites with one or several internal short cracks (finite crack length), and its generalization to long (semi-infinite) cracks is not possible. In a recent investigation, Ryvkin and Hadar (2015) presented a new approach according to which the knowledge of the K-field (the crack tip field) in a homogenized material enables the analysis of a material with periodic microstructure in which an embedded semi-infinite crack and other localized effects exist. To that end, the jumps of this K-field of the homogenized material, are applied at the boundaries of a rectangular region which must be sufficiently far away from localized effects.…”

Section: Introductionmentioning

confidence: 99%

“…In the present article, the approach of Ryvkin and Hadar (2015) is utilized to generalize the analysis in Aboudi (2012) for short cracks, albeit by an a different approach. As a result of this generalization, the electromechanical field distribution in piezoelectric composites of periodic microstructure in which a semi-infinite crack exists can be determined.…”

Section: Introductionmentioning

confidence: 99%

Field distributions in piezoelectric composites with semi-infinite cracks

Aboudi

2016

Journal of Intelligent Material Systems and Structures

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A method is offered for the prediction of the electromechanical field in periodic piezoelectric composites with embedded semi-infinite cracks. It is based on the knowledge of the K-field in piezoelectric materials in which the material constants are replaced by the effective moduli of the piezoelectric composite. In addition to the existing semi-infinite crack, the proposed method can analyze localized inhomogeneities near the crack tip. The established effective K-field is applied at the boundaries of a rectangular domain that should be sufficiently far away from the crack tip and the other inhomogeneities. The proposed approach is based on the combined utilization of a micromechanical analysis, the representative cell method and the higher-order theory. The micromechanical analysis establishes the effective electromechanical constants of the piezoelectric composite, and the representative cell method reduces the periodic composite that is discretized into numerous identical cells to a single cell problem in the Fourier transform domain. The governing equations and constitutive relations that are formulated in this single cell are solved by employing the higher-order theory where discretization into subcells is employed. The inverse of the Fourier transform provides the electromechanical field at any point in the composite. The proposed approach is verified for crack fronts that are parallel and perpendicular to the poling direction (axis of symmetry). Applications are given for a cracked porous piezoelectric material, cracks that have been arrested by cavities and for a periodically bilayered composite with a semi-infinite crack.

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Employing of the discrete Fourier transform for evaluation of crack-tip field in periodic materials

Cited by 14 publications

References 15 publications

K-dominance and size effect in mode I fracture of brittle materials with low to medium porosity

K-dominance and size effect in mode I fracture of brittle materials with low to medium porosity

The Effect of Defects in Piezoelectric Composite Half-Planes with Surface Electrodes

Field distributions in piezoelectric composites with semi-infinite cracks

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