Development of fracture facets from a crack loaded in mode I+III: Solution and application of a model 2D problem

Leblond, Jean-Baptiste; Frelat, Joël

doi:10.1016/j.jmps.2013.11.001

Cited by 13 publications

(27 citation statements)

References 32 publications

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“…The increase is very quick when c/d goes to unity, because in this limit the unbroken ligaments preventing the release of elastic energy shrink rapidly. But the use of Leblond and Frelat (2014)'s approximate solution certainly leads here to some overestimation of the effect, since as just noted, these ligaments in fact never completely disappear.…”

Section: Examplesmentioning

confidence: 87%

“…The expression of g here will itself be deduced, via Irwin's classical formula, from the expressions of the 2D stress SIF k I , k I I . In Leblond and Frelat (2014)'s work, these SIF were written in the form…”

Section: Problem Considered and Outline Of The Methods Of Solutionmentioning

confidence: 99%

“…This is because in the case of tilted facets the release of elastic energy is hindered by the permanence of unbroken ligaments between them. Note that although this conclusion is based on results obtained using Leblond and Frelat (2014)'s approximate solution, applicable to the sole case where c < d, it is by no means limited to this case. Indeed it is intuitively obvious, and confirmed by Fleck (1991)'s numerical calculations (see his Fig.…”

Section: Examplesmentioning

confidence: 98%

“…The approximate expressions of the functions F p i j (c/d , α) proposed by Leblond and Frelat (2014) (in the sole case c < d) are as follows:…”

Section: Appendix 1: Approximate Expressions Of the Functions F P I Jmentioning

confidence: 99%

“…Use will be made, for this inner problem, of a very recent solution of Leblond and Frelat (2014); this solution, obtained by combining an analytical approach based on Muskhelishvili (1953)'s method and a numerical, finite-element-based one, applies only to values of the ratio c/d of the facet width to the facet spacing smaller than unity and is approximate (although generally accurate). It must be stressed, however, that the model developed is not, in principle, constrained to refer to this specific solution; other, analytical or even purely numerical solutions could be used, if available.…”

Section: Introductionmentioning

confidence: 99%

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Multiscale cohesive zone model for propagation of segmented crack fronts in mode I+III fracture

2015

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International audienceQuasistatic crack propagation in mixed-mode I+III fracture is widely observed to be unstable, the instability being characterized by the segmentation of the parent crack into a periodic array of daughter cracks shaped as flat facets rotated towards the principal stress axis. While there has been recent progress to characterize this instability, no global theory is presently available to describe all aspects of the propagation of the segmented front, including both " local " features like the angle of rotation of the facets and the ratio of their width to their spacing, and " global " ones like the effective energy-release-rate of the segmented crack front and the tendency of the facets to coarsen. This paper embarks on the development of such a theory, based on the assumption that the spacing of the facets is much smaller than their length, and asymptotic matching of outer and inner solutions for the mechanical fields on scales comparable to the facet length and spacing, respectively. The inner problem is shown to reduce to a 2D linear elastic fracture mechanics problem in the plane perpendicular to the crack propagation axis. The solution of this problem is used to develop an effective cohesive zone description of the crack front on a scale much larger than the facet spacing. Such a description leads to a system of 1D integral equations for the outer mechanical fields on the cohesive zone, which may be solved numerically. Numerical examples are given that notably illustrate the prediction of the effective energy-release-rate of the segmented crack front in terms of the various geometrical parameters; this energy-release-rate is predicted to be smaller for a segmented front than for the parent planar front, with the conclusion that segmentation acts as a toughening mechanism. Implications upon the phenomenon of facet coarsening are also briefly discussed

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Section: Examplesmentioning

confidence: 87%

Section: Problem Considered and Outline Of The Methods Of Solutionmentioning

confidence: 99%

Section: Examplesmentioning

confidence: 98%

“…The approximate expressions of the functions F p i j (c/d , α) proposed by Leblond and Frelat (2014) (in the sole case c < d) are as follows:…”

Section: Appendix 1: Approximate Expressions Of the Functions F P I Jmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multiscale cohesive zone model for propagation of segmented crack fronts in mode I+III fracture

2015

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Validation of a 3-D adaptive stable generalized/eXtended finite element method for mixed-mode brittle fracture propagation

2020

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Mode I+III multiscale cohesive zone model with facet coarsening and overlap: Solutions and applications to facet orientation and toughening

Lazarus

Prabel

Cambonie

et al. 2020

Journal of the Mechanics and Physics of Solids

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When subjected to some anti-plane shear mode III loading, segmentation of the crack front frequently occurs during propagation: even if the crack is initially planar, propagation produces facets/segments rotated toward the shear free direction. These facets induce some modifications in the local loading of the crack tips that can be captured through the multi-scale cohesive zone model proposed by Leblond et al., 2015. Assuming that the width of the facets is small in comparison to their length, the facets can be considered at the microscale, as a bidimensional periodic array of tilted cracks perpendicularly to the direction of propagation, and at the macroscale, as a growing Cohesive Zone. The model was developed initially supposing a constant period, small tilt angles and non-overlapping facets. The first aim of this paper is to relax these assumptions to deal with more realistic cases. For this, the microscale problem is solved using XFEM and the outputs are further incorporated into the model to get some results on the macroscale, in particular the effective fracture energy. The second objective is to introduce some experiments to show the relevance of the assumptions made and to demonstrate the ability of the approach (i) to determine the inclination of the facets and (ii) to quantify, in both fatigue and brittle fracture, the toughening due to the decrease of the crack opening driven by the unbroken ligaments between the facets.

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Development of fracture facets from a crack loaded in mode I+III: Solution and application of a model 2D problem

Cited by 13 publications

References 32 publications

Multiscale cohesive zone model for propagation of segmented crack fronts in mode I+III fracture

Multiscale cohesive zone model for propagation of segmented crack fronts in mode I+III fracture

Validation of a 3-D adaptive stable generalized/eXtended finite element method for mixed-mode brittle fracture propagation

Mode I+III multiscale cohesive zone model with facet coarsening and overlap: Solutions and applications to facet orientation and toughening

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