Study of size effects in the Dugdale model through the case of a crack in a semi-infinite plane under anti-plane shear loading

Ferdjani, Hicheme; Abdelmoula, Radhi; Marigo, Jean‐Jacques; Borgi, S. El

doi:10.1007/s00161-009-0098-0

Cited by 8 publications

(9 citation statements)

References 10 publications

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“…So, many studies to grasp and describe the fracture behavior of piezoelectric materials under electro-mechanical loading have been done. In most studies, the research orientation carried in general is on the mode of cracking; mode I as in [19,21,38], mode II as in [12] (for a composite laminates material), mode III as in [3][4][5]17,30,36], mixed mode as in [29], or on the model; Griffith model as in [14,21,42], Dugdale-Barenblatt model as in [8,15], or in the position of the crack in the structure; infinite plane as in [19,25], semi-infinite plane as in [8] (for a non-piezoelectric material) or still on the composition of the structure; only one material as in [25], bi-material as in [22,39].…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Griffith crack at the interface of two piezoelectric materials under anti-plane loading

Gherrous

Ferdjani

2016

Continuum Mech. Thermodyn.

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The main objective of this work is the contribution to the study of the piezoelectric structures which contain preexisting defect (crack). For that, we consider a Griffith crack located at the interface of two piezoelectric materials in a semi-infinite plane structure. The structure is subjected to an anti-plane shearing combined with an in-plane electric displacement. Using integral Fourier transforms, the equations of piezoelectricity are converted analytically to a system of singular integral equations. The singular integral equations are further reduced to a system of algebraic equations and solved numerically by using Chebyshev polynomials. The stress intensity factor and the electric displacement intensity factor are calculated and used for the determination of the energy release rate which will be taken as fracture criterion. At the end, numerical results are presented for various parameters of the problem; they are also presented for an infinite plane structure.

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Section: Introductionmentioning

confidence: 99%

Analysis of a Griffith crack at the interface of two piezoelectric materials under anti-plane loading

Gherrous

Ferdjani

2016

Continuum Mech. Thermodyn.

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“…2). Different criteria of the initiation and propagation of these zones were deduced by Ferdjani et al (2009) from an energy minimization principle. They are presented in the following Sections without demonstration.…”

Section: Crack Growthmentioning

confidence: 99%

“…For mode I case, Ferdjani et al (2007) studied a crack in an infinite isotropic medium under uniform traction. For mode III case, Ferdjani (2008Ferdjani ( , 2013 and Ferdjani et al (2009) considered a crack in a semi-infinite isotropic medium in an infinite isotropic strip, and at the interface of a strip and a half-plane constituted of different isotropic materials under uniform anti-plane shearing, respectively. For the mixed mode case, Ferdjani and Marigo (2015) studied a crack at the interface of a strip and a half-plane constituted of the same isotropic material under uniform traction.…”

Section: Introductionmentioning

confidence: 99%

Study of the anti-plane problem of a Dugdale-Barenblatt crack in a welded strip using the integral equation method

Chaouche

Ferdjani

Tala‐Ighil

2019

Journal of Theoretical and Applied Mechanics

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The elasto-static anti-plane problem of a Dugdale-Barenblatt crack in a welded infinite strip is formulated in terms of a singular integral equation (SIE). The weld joint is modeled as a tri-material structure: the weld metal (WM), the base metal (BM) and the heat-affected zone (HAZ). The HAZ is modeled with an exponentially variable shear modulus. The SIE is solved using Tchebychev polynomials. The influence of the elastic mismatching (the ratio between the shear modulus of WM and BM) and width of the HAZ on the fracture load and on the crack propagation is investigated.

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“…This problem is a particular case of a family of plane elastic problems which can be solved with the method of complex potentials developed by [15]. Without detailing the calculation steps, we can directly use the results by identifying the normal stress distribution with…”

Section: Determination Of the Fully Cohesive Branchmentioning

confidence: 99%

“…In this context of cohesive force models, some partial results have already been obtained. For instance, [15,16] study the size and shape effects of preexisting defects in the case of Dugdale's model. It is in particular shown that the value of the loading at which the first cohesive crack occurs strongly depends on the shape of the preexisting defect.…”

Section: Introductionmentioning

confidence: 99%

A generalisation to cohesive cracks evolution under effects of non-uniform stress field

Pham

Laverne²,

Marigo

2018

Vietnam J. Mech.

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The aim of the present work is to study the stabilizing effect of the non-uniformity of the stress field on the cohesive cracks evolution in two-dimensional elastic structures. The crack evolution is governed by Dugdale's or Barenblatt's cohesive force models. We distinguish two stages in the crack evolution: the first one where all the crack is submitted to cohesive forces, followed by a second one where a non cohesive part appears. Assuming that the material characteristic length dc associated with the cohesive model is small by comparison to the dimension L of the body, we develop a two-scale approach, and using the complex analysis method, we obtain the entire crack evolution with the loading in a closed form for the Dugdale's case and in semi-analytical form for the Barenblatt's case. In particular, we show that the propagation is stable during the first stage, but becomes unstable with a brutal jump of the crack length as soon as the non cohesive crack part appears. We discuss also the influence of all the parameters of the problem, in particular the non-uniform stress and cohesive model formulations, and study the sensitivity to imperfections.

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Study of size effects in the Dugdale model through the case of a crack in a semi-infinite plane under anti-plane shear loading

Cited by 8 publications

References 10 publications

Analysis of a Griffith crack at the interface of two piezoelectric materials under anti-plane loading

Analysis of a Griffith crack at the interface of two piezoelectric materials under anti-plane loading

Study of the anti-plane problem of a Dugdale-Barenblatt crack in a welded strip using the integral equation method

A generalisation to cohesive cracks evolution under effects of non-uniform stress field

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