Disordering of a dynamic planar crack front in a model elastic medium of randomly variable toughness
type: Item
instance of: scholarly article
title: Disordering of a dynamic planar crack front in a model elastic medium of randomly variable toughness
zbMATH Open document ID: 0814.73046
DOI: 10.1016/0022-5096(94)90083-3
author: Gilles Perrin
author: James R. Rice
published in: Journal of the Mechanics and Physics of Solids
publication date: 1994-08-14T00:00:00Z
review text: This paper is the development of the work of \textit{J. R. Rice, Y. Ben- Zion} and \textit{K.-S. Kim} [J. Mech. Phys. Solids 42, No. 5, 813-843 (1994; Zbl 0806.73056)] concerning strictly linearized analysis of the propagation of a planar crack with a nominally straight front in a model elastic solid with a single displacement component. The aim of this paper is to consider a crack propagating in a region of randomly variable toughness and ask how much the crack front deviates, statistically, from straightness. It is supposed that the material rupture is ruled by the local energy release rate criterion. Using the above cited results, the corresponding first-order expression is given for the deviation of a crack front from straightness as a direct integral expression for the deviation of the material toughness from uniformity in the crack plane. Then this expression is used to analyse the autocorrelation of the crack front position when the toughness deviations are random. The authors introduce two autocorrelation functions, namely one is defined by statistical properties of the random toughness, \(\tau(z,t)\), and other is the deviation from straightness of the crack front, \(A(z,t)\), (\(z\) is the coordinate along the crack front, \(t\) is the time). Applying time and space Fourier transform, the power spectra of \(\tau\) and \(A\) are related. From hypothesis that \(A(z,t)\) is a stationary random variable, \(A\) is expressed as a linear functional of \(\tau(z,t)\), and then a statistical analysis of the deviation from straightness \(A\) is performed. It is shown that while the straight shape is indeed recovered for propagation through a zone of precise uniform value of the critical local energy release rate, \(G_{\text{crit}}\), the straight crack front becomes increasingly more disordered as it propagates through a region of arbitrary small but sustained random variation in \(G_{\text{crit}}\). Then the authors conclude that the straight crack front is configur…
Mathematics Subject Classification ID: 74R99
Mathematics Subject Classification ID: 74A40
zbMATH DE Number: 618142
zbMATH Keywords: energy release rate criterion
zbMATH Keywords: autocorrelation
zbMATH Keywords: random toughness
zbMATH Keywords: Fourier transform
zbMATH Keywords: linearized perturbation analysis
Wikidata QID: Q56997454
reviewed by: Ivan A. Parinov
MaRDI profile type: Publication
full work available at URL: 0022-5096(94)90083-3
OpenAlex ID: W2029563487
cites work: Dynamic Fracture Mechanics
cites work: Q4275389
cites work: Q3993473
cites work: Three-dimensional perturbation solution for a dynamic planar crack moving unsteadily in a model elastic solid
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description: scientific article; zbMATH DE number 618142