Instability and Disorder of the Front of a Tensile Tunnel-Crack Slightly Perturbed within its Plane

Elie Favier; Véronique Lazarus; Jean Baptiste Leblond

doi:10.4028/www.scientific.net/msf.440-441.153

Instability and Disorder of the Front of a Tensile Tunnel-Crack Slightly Perturbed within its Plane

Elie Favier, Véronique Lazarus, Jean Baptiste Leblond

Sorbonne Université

Research output: Contribution to journal › Conference article › peer-review

Abstract

In this paper, we study the time evolution of the shape of the front of a tunnel-crack loaded in mode I in an infinite elastic body and propagating quasistatically according to some Paris-type law. The two parts of the front are assumed to remain symmetrical and differ only slightly from straight lines at each instant, and a first-order perturbation approach is used. It is notably found that the L² norm of the perturbation continuously increases with time, which means, in some sense, that the straight configuration of the front is inherently "unstable". The correlation distance of the perturbation also increases, which mitigates the preceding conclusion since it means, in another sense, that the crack front tends to "straighten back" in time.

Original language	English
Pages (from-to)	153-160
Number of pages	8
Journal	Materials Science Forum
Volume	440-441
DOIs	https://doi.org/10.4028/www.scientific.net/msf.440-441.153
Publication status	Published - 1 Jan 2003
Event	Modern Practice in Stress and Vibration Analysis: Proceedings of the 5th International Conference on Modern Practice in Stress and Vibration Analysis - Glasgow, Scotland, United Kingdom Duration: 9 Sept 2003 → 11 Sept 2003

Keywords

Autocorrelation Function
Correlation Length
Disordering
Fourier Analysis
Linear Perturbation
Mode I
Tunnel-Crack

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Cite this

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title = "Instability and Disorder of the Front of a Tensile Tunnel-Crack Slightly Perturbed within its Plane",

abstract = "In this paper, we study the time evolution of the shape of the front of a tunnel-crack loaded in mode I in an infinite elastic body and propagating quasistatically according to some Paris-type law. The two parts of the front are assumed to remain symmetrical and differ only slightly from straight lines at each instant, and a first-order perturbation approach is used. It is notably found that the L2 norm of the perturbation continuously increases with time, which means, in some sense, that the straight configuration of the front is inherently {"}unstable{"}. The correlation distance of the perturbation also increases, which mitigates the preceding conclusion since it means, in another sense, that the crack front tends to {"}straighten back{"} in time.",

keywords = "Autocorrelation Function, Correlation Length, Disordering, Fourier Analysis, Linear Perturbation, Mode I, Tunnel-Crack",

author = "Elie Favier and V{\'e}ronique Lazarus and Leblond, \{Jean Baptiste\}",

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note = "Modern Practice in Stress and Vibration Analysis: Proceedings of the 5th International Conference on Modern Practice in Stress and Vibration Analysis ; Conference date: 09-09-2003 Through 11-09-2003",

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TY - JOUR

T1 - Instability and Disorder of the Front of a Tensile Tunnel-Crack Slightly Perturbed within its Plane

AU - Favier, Elie

AU - Lazarus, Véronique

AU - Leblond, Jean Baptiste

PY - 2003/1/1

Y1 - 2003/1/1

N2 - In this paper, we study the time evolution of the shape of the front of a tunnel-crack loaded in mode I in an infinite elastic body and propagating quasistatically according to some Paris-type law. The two parts of the front are assumed to remain symmetrical and differ only slightly from straight lines at each instant, and a first-order perturbation approach is used. It is notably found that the L2 norm of the perturbation continuously increases with time, which means, in some sense, that the straight configuration of the front is inherently "unstable". The correlation distance of the perturbation also increases, which mitigates the preceding conclusion since it means, in another sense, that the crack front tends to "straighten back" in time.

AB - In this paper, we study the time evolution of the shape of the front of a tunnel-crack loaded in mode I in an infinite elastic body and propagating quasistatically according to some Paris-type law. The two parts of the front are assumed to remain symmetrical and differ only slightly from straight lines at each instant, and a first-order perturbation approach is used. It is notably found that the L2 norm of the perturbation continuously increases with time, which means, in some sense, that the straight configuration of the front is inherently "unstable". The correlation distance of the perturbation also increases, which mitigates the preceding conclusion since it means, in another sense, that the crack front tends to "straighten back" in time.

KW - Autocorrelation Function

KW - Correlation Length

KW - Disordering

KW - Fourier Analysis

KW - Linear Perturbation

KW - Mode I

KW - Tunnel-Crack

U2 - 10.4028/www.scientific.net/msf.440-441.153

DO - 10.4028/www.scientific.net/msf.440-441.153

M3 - Conference article

AN - SCOPUS:0344064823

SN - 0255-5476

VL - 440-441

SP - 153

EP - 160

JO - Materials Science Forum

JF - Materials Science Forum

T2 - Modern Practice in Stress and Vibration Analysis: Proceedings of the 5th International Conference on Modern Practice in Stress and Vibration Analysis

Y2 - 9 September 2003 through 11 September 2003

ER -

Instability and Disorder of the Front of a Tensile Tunnel-Crack Slightly Perturbed within its Plane

Abstract

Keywords

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