A geometrically nonlinear analysis of coplanar crack propagation in some heterogeneous medium

Vasoya, Manish; Leblond, Jean-Baptiste; Ponson, Laurent

doi:10.1016/j.ijsolstr.2012.10.001

Cited by 22 publications

(20 citation statements)

References 21 publications

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“…More precisely, modeling the simplified 3D problem [64][65][66][67][68][69] may be combined with the out-of-theplane fluctuations (namely the current work) to yield a full 3D theory. Various elements needed in that direction can be found in the literature [50,[70][71][72][73] but such a theory is still far from being formulated.…”

Section: Discussionmentioning

confidence: 99%

Stability and roughness of tensile cracks in disordered materials

Katzav

Adda-Bedia

2013

Phys. Rev. E

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We study the stability and roughness of propagating cracks in heterogeneous brittle two-dimensional elastic materials. We begin by deriving an equation of motion describing the dynamics of such a crack in the framework of linear elastic fracture mechanics, based on the Griffith criterion and the principle of local symmetry. This result allows us to extend the stability analysis of Cotterell and Rice [B. Cotterell and J. R. Rice, Int. J. Fract. 16, 155 (1980)] to disordered materials. In the stable regime we find stochastic crack paths. Using tools of statistical physics, we obtain the power spectrum of these paths and their probability distribution function and conclude that they do not exhibit self-affinity. We show that a real-space fractal analysis of these paths can lead to the wrong conclusion that the paths are self-affine. To complete the picture, we unravel a systematic bias in such real-space methods and thus contribute to the general discussion of reliability of self-affine measurements.

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Section: Discussionmentioning

confidence: 99%

Stability and roughness of tensile cracks in disordered materials

Katzav

Adda-Bedia

2013

Phys. Rev. E

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“…where G eff C is the average adhesion energy of the interface (see Vasoya et al, 2013 for the analogous result in fracture). We observe good agreement between the experiments and the theoretical model.…”

Section: Stripesmentioning

confidence: 99%

Adhesion of heterogeneous thin films II: Adhesive heterogeneity

Xia

Ponson

Ravichandran

et al. 2015

Journal of the Mechanics and Physics of Solids

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“…To explore the non-linear response of cracks pinned by defects of larger contrasts, Leblond et al (2012) extended Rice (1985)'s first-order formula for a semi-infinite crack in an infinite body to second order, under the assumption of independence of the unperturbed stress intensity factor imposed by the loading with respect to the average crack front location. Then, Vasoya et al (2013) released this hypothesis, thus extending the range of application of Leblond et al (2012)'s formula to general loading conditions. Recently, Willis (2013) and Willis and Movchan (2014) investigated the dynamic perturbation of a crack up to second order.…”

Section: Introductionmentioning

confidence: 99%

“…Still, since both Leblond et al (2012)'s and Vasoya et al (2013)'s works considered only infinite bodies, the combined effect of the finite size of the specimens and the geometrical nonlinearities induced by strong defects remains unexplored, and it is the aim of this work to address this question. The results of our calculations apply to several experimental situations involving strong heterogeneities, and for which the crack front perturbation wavelength compares with the thickness of the specimen (Santucci et al, 2010;Chopin et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Finite size and geometrical non-linear effects during crack pinning by heterogeneities: An analytical and experimental study

Vasoya

Unni

Leblond

et al. 2016

Journal of the Mechanics and Physics of Solids

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Crack pinning by heterogeneities is a central toughening mechanism in the failure of brittle materials. So far, most analytical explorations of the crack front deformation arising from spatial variations of fracture properties have been restricted to weak toughness contrasts using first order approximation and to defects of small dimensions with respect to the sample size. In this work, we investigate the non-linear effects arising from larger toughness contrasts by extending the approximation to the second order, while taking into account the finite sample thickness. Our calculations predict the evolution of a planar crack lying on the mid-plane of a plate as a function of the material parameters and the loading conditions, especially in the case of a single infinitely elongated obstacle. Peeling experiments are presented which validate the approach and evidence that the second order term broadens its range of validity in terms of toughness contrast values. The work highlights the non-linear response of the crack front to strong defects and the central role played by the thickness of the specimen on the pinning process.

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A geometrically nonlinear analysis of coplanar crack propagation in some heterogeneous medium

Cited by 22 publications

References 21 publications

Stability and roughness of tensile cracks in disordered materials

Stability and roughness of tensile cracks in disordered materials

Adhesion of heterogeneous thin films II: Adhesive heterogeneity

Finite size and geometrical non-linear effects during crack pinning by heterogeneities: An analytical and experimental study

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