Weakly nonlinear fracture mechanics: experiments and theory

Bouchbinder, Eran; Livne, Ariel; Fineberg, Jay

doi:10.1007/s10704-009-9427-3

Cited by 30 publications

(12 citation statements)

References 64 publications

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“…Therefore, the moving crack is expected to deflect and propagate along a direction at an angle of 30 • to the original direction of crack propagation. This predicted angle is close to the experimental value of 25 • for PMMA [23], which has been shown to have similar dynamic crack oscillation behavior to polyacrylamide gels [5].…”

Section: ) Crack Branching At High Crack Speedsupporting

confidence: 85%

“…In [4], Ru derived a complete solution for an interface crack in a harmonic elastic bimaterial. For dynamic cracks in hyperelastic materials, more recently, Bouchbinder et al [5] and Livne et al [6] showed that some predictions given by linear elastic fracture mechanics are in direct contradiction with experiment observation of a moving crack tip. These authors stressed the importance of finite-strain analysis for a physically realistic description of moving cracks in hyperelastic materials.…”

Section: Introductionmentioning

confidence: 99%

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Speed-dependent tip fields of a moving crack in a hyperelastic material

2012

Mathematics and Mechanics of Solids

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This paper gives an asymptotic analysis of plane strain deformation and stress fields near the tip of a steady moving crack in a compressible hyperelastic material. The semi-infinite crack is assumed to be in an infinite homogeneous harmonic material under a constant remote mode-I loading. The crack tip deformation and stress fields are derived up to the third order, which ensures the strict positivity of the Jacobian determinant in the vicinity of the moving crack tip. The derived solutions are applied to a specific hyperelastic material for which some recent experimental data are available in the literature. The comparison with the experimental data showed that the crack-face profile and the energy release rate predicted by the present model are in reasonable agreement with experiments and several recent finite-strain elastic models. In addition, the crack branching angle predicted by the present model also agrees well with some known experimental data. All of these results suggest that the harmonic material model has the potential to capture the main features of finite deformation phenomena in the dynamic fracture of hyperelastic materials.

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Section: ) Crack Branching At High Crack Speedsupporting

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Speed-dependent tip fields of a moving crack in a hyperelastic material

2012

Mathematics and Mechanics of Solids

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“…On the other hand, as long as a single crack retains its path stability (42)) as a free parameter (solid lines). Adapted from [184].…”

Section: Cracking a Dynamic Crack Instabilitymentioning

confidence: 99%

The dynamics of rapid fracture: instabilities, nonlinearities and length scales

2014

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Abstract. The failure of materials and interfaces is mediated by cracks, nearly singular dissipative structures that propagate at velocities approaching the speed of sound. Crack initiation and subsequent propagation -the dynamic process of fracture -couples a wide range of time and length scales. Crack dynamics challenge our understanding of the fundamental physics processes that take place in the extreme conditions within the nearly singular region where material failure occurs. Here, we first briefly review the classic approach to dynamic fracture, "Linear Elastic Fracture Mechanics" (LEFM), and discuss its successes and limitations. We show how, on the one hand, recent experiments performed on straight cracks propagating in soft brittle materials have quantitatively confirmed the predictions of this theory to an unprecedented degree. On the other hand, these experiments show how LEFM breaks down as the singular region at the tip of a crack is approached. This breakdown naturally leads to a new theoretical framework coined "Weakly Nonlinear Fracture Mechanics", where weak elastic nonlinearities are incorporated. The stronger singularity predicted by this theory gives rise to a new and intrinsic length scale, nl . These predictions are verified in detail through direct measurements. We then theoretically and experimentally review how the emergence of nl is linked to a new equation for crack motion, which predicts the existence of a high-speed oscillatory crack instability whose wave-length is determined by nl . We conclude by delineating outstanding challenges in the field.

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“…Recently, these issues have been addressed in the framework of the "Weakly nonlinear theory of fracture" [1,[34][35][36][37]. This theory is based on a general expansion of the strain energy functional U in the form…”

Section: Weakly Nonlinear Theory Of Fracture Near-tip Fields and Intr...mentioning

confidence: 99%

Recent developments in dynamic fracture: some perspectives

Fineberg

Bouchbinder

2015

Int J Fract

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We briefly review a number of important recent experimental and theoretical developments in the field of dynamic fracture. Topics include experimental validation of the equations of motion for straight tensile cracks (in both infinite media and strip geometries), validation of a new theoretical description of the near-tip fields of dynamic cracks incorporating weak elastic nonlinearities, a new understanding of dynamic instabilities of tensile cracks in both 2D and 3D, crack front dynamics, and the relation between frictional motion and dynamic shear cracks. Related future research directions are briefly discussed.

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Weakly nonlinear fracture mechanics: experiments and theory

Cited by 30 publications

References 64 publications

Speed-dependent tip fields of a moving crack in a hyperelastic material

Speed-dependent tip fields of a moving crack in a hyperelastic material

The dynamics of rapid fracture: instabilities, nonlinearities and length scales

Recent developments in dynamic fracture: some perspectives

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