Confirming the continuum theory of dynamic brittle fracture for fast cracks

Sharon, Eran; Fineberg, Jay

doi:10.1038/16891

Cited by 243 publications

(243 citation statements)

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“…the tip behaves as a massless "particle" where the accelerationv plays no role (of course material inertia is essential for this equation to hold), and that the limiting propagation velocity is c R . The equation has been shown to beautifully describe crack's motion when its underlying assumptions are met [8,[16][17][18][19]. In particular, this description was shown to be valid in experiments in the brittle acrylic, PMMA, for v < 0.4c R (when cracks are indeed simple) [17].…”

Section: The Equation Of Motion For Simple Cracksmentioning

confidence: 97%

“…The equation has been shown to beautifully describe crack's motion when its underlying assumptions are met [8,[16][17][18][19]. In particular, this description was shown to be valid in experiments in the brittle acrylic, PMMA, for v < 0.4c R (when cracks are indeed simple) [17]. More recent experiments showed the equation of motion to be in excellent quantitative agreement with measurements of dynamic cracks in brittle gels for an unprecedented range of velocities, 0 < v < 0.96c R , approaching the limiting velocity [14].…”

Section: The Equation Of Motion For Simple Cracksmentioning

confidence: 99%

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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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Section: The Equation Of Motion For Simple Cracksmentioning

confidence: 97%

Section: The Equation Of Motion For Simple Cracksmentioning

confidence: 99%

Recent developments in dynamic fracture: some perspectives

Fineberg

Bouchbinder

2015

Int J Fract

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“…5), while if T > 0 the branches will diverge away from this direction. Figure 5: Path followed by the branch when a < 0, and a comparison with the functional form Y (X) ∼ X 2/3 proposed in (Sharon and Fineberg, 1999).…”

Section: The Shape Of the Branched Cracksmentioning

confidence: 99%

“…In order to estimate the T -stress for the real experimental setups of (Fineberg et al, 1992;Sharon and Fineberg, 1999;Livne et al, 2005), we solved the elastostatic problem of a semiinfinite straight crack in an infinite strip of half-width W , whose top and bottom edges are fixed at positions ±δ above their initial positions (see Fig. 13).…”

Section: The Shape Of the Branched Cracksmentioning

confidence: 99%

Theory of dynamic crack branching in brittle materials

2007

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The problem of dynamic symmetric branching of a tensile crack propagating in a brittle material is studied within Linear Elastic Fracture Mechanics theory. The Griffith energy criterion and the principle of local symmetry provide necessary conditions for the onset of dynamic branching instability and for the subsequent paths of the branches. The theory predicts a critical velocity for branching and a well defined shape parameterized by a branching angle and a curvature of the side branches. The model rests on a scenario of crack branching based on reasonable assumptions and on exact dynamic results for the anti-plane branching problem. Our results reproduce within a simplified 2D continuum mechanics approach the main experimental features of the branching instability of fast cracks in brittle materials.

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“…For the localized cohesive laws, we consider the values σ max = τ max = E/25 = 129.6 MPa and a linear softening modulus of S n = S m = −24 GPa/ mm. These values correspond to a fracture energy of G f = 0.35 kJ/m 2 , as it is characteristic of PMMA (Sharon and Fineberg 1999). We consider a finite element discretization consisting of 40 × 41 standard displacement-based bilinear quadrilaterals for the half specimen x ≥ 0 due to the symmetry in the geometry and the loading.…”

Section: Problem Setupmentioning

confidence: 99%

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

2009

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This paper presents the extension of some finite elements with embedded strong discontinuities to the fully transient range with the focus on dynamic fracture. Cracks and shear bands are modeled in this setting as discontinuities of the displacement field, the so-called strong discontinuities, propagating through the continuum. These discontinuities are embedded into the finite elements through the proper enhancement of the discrete strain field of the element. General elements, like displacement or assumed strain based elements, can be considered in this framework, capturing sharply the kinematics of the discontinuity for all these cases. The local character of the enhancement (local in the sense of defined at the element level, independently for each element) allows the static condensation of the different local parameters considered in the definition of the displacement jumps. All these features lead to an efficient formulation for the modeling of fracture in solids, very easily incorporated in an existing general finite element code due to its modularity. We investigate in this paper the use of this finite element formulation for the special challenges that the dynamic range leads to. Specifically, we consider the modeling of failure mode transitions in ductile materials and crack branching in brittle solids. To illustrate the performance of the proposed formulation, we present a series of numerical simulations of these cases with detailed comparisons with experimental and other numerical results reported in the literature. We conclude that these finite element methods handle well these dynamic problems, still maintaining the aforementioned features of computational efficiency and modularity.

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Confirming the continuum theory of dynamic brittle fracture for fast cracks

Cited by 243 publications

References 20 publications

Recent developments in dynamic fracture: some perspectives

Recent developments in dynamic fracture: some perspectives

Theory of dynamic crack branching in brittle materials

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

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