Instability in dynamic fracture

Fineberg, Jay; Marder, Michael

doi:10.1016/s0370-1573(98)00085-4

Cited by 422 publications

(553 citation statements)

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“…However, experiments (Ravi-Chandar and Knauss 1984a,b;Knauss and Ravi-Chandar 1985;Fineberg 1996, 1999) and analytical investigations (Yoffe 1951;Eshelby 1970;Gao 1993Gao , 1996 predict that after exceeding a certain critical ratio v crit /c R <1, the crack tends to branch rather than continuing its motion in a straight path, reducing its speed. Interestingly, the analytical studies tend to overestimate this critical ratio when compared with the experimental observations (Ravi-Chandar and Knauss 1984b; Knauss and Ravi-Chandar 1985;Gao 1993Gao , 1996Fineberg and Marder 1999).…”

Section: Crack Tip Velocity As Branching Criterionmentioning

confidence: 94%

“…We use critical ratios of v crit /c R =0.7-0.8 in the numerical simulations reported below in our goal to compare the current formulation with the published numerical results of Xu and Needleman (1994) and Falk et al (2001). These values are relatively high for the experimental observations of branching in PMMA Fineberg 1996, 1999;Fineberg and Marder 1999) for the considered problem. We refer to Linder and Armero (2009) for a study of the influence of the critical ratio v crit /c R in the numerical simulations.…”

Section: Crack Tip Velocity As Branching Criterionmentioning

confidence: 99%

“…This challenging problem has become a benchmark for the computational modeling Zhou et al (1996a) of dynamic fracture. We refer among others to Dally (1979), Ravi-Chandar and Knauss (1984a,b), Knauss and Ravi-Chandar (1985), Ramulu and Kobayashi (1985), Fineberg et al (1991), Satoh (1996), Fineberg (1996, 1999), Fineberg and Marder (1999), and references therein, for a discussion of some experimental observations. Numerical simulations of the problem have been reported in Falk et al (2001), Klein et al (2001), Belytschko et al (2003), Zhou and Molinari (2004), Zhou et al (2005), Huespe et al (2006), Song et al (2006), Duarte et al (2007), Karedla and Reddy (2007), Remmers et al (2008), Zhang et al (2007), Zi et al (2007), to mention just a few references employing a variety of different numerical approaches.…”

Section: Crack Branching In Brittle Materialsmentioning

confidence: 99%

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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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Section: Crack Tip Velocity As Branching Criterionmentioning

confidence: 94%

Section: Crack Tip Velocity As Branching Criterionmentioning

confidence: 99%

Section: Crack Branching In Brittle Materialsmentioning

confidence: 99%

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Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

2009

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“…Many material ruptures occur by a "one crack" mechanism and a lot of effort is being devoted to the understanding, detection and prevention of the nucleation of cracks [3,4]. Exceptions to the "one crack" rupture mechanism are heterogeneous materials such as fiber composites, rocks, concrete under compression and materials with large distributed residual stresses.…”

Section: Introductionmentioning

confidence: 99%

“…What we need are models that incorporate the underlying physics to identify and use relevant precursory patterns. Here, we propose innovative steps in this direction that are based on two key concepts : the role of heterogeneity and the possible existence of a hierarchy of characteristic scales.Many material ruptures occur by a "one crack" mechanism and a lot of effort is being devoted to the understanding, detection and prevention of the nucleation of cracks [3,4]. Exceptions to the "one crack" rupture mechanism are heterogeneous materials such as fiber composites, rocks, concrete under compression and materials with large distributed residual stresses.…”

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confidence: 99%

Critical ruptures

2000

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The fracture of materials is a catastrophic phenomenon of considerable technological and scientific importance. Here, we analysed experiments designed for industrial applications in order to test the concept that, in heterogeneous materials such as fiber composites, rocks, concrete under compression and materials with large distributed residual stresses, rupture is a genuine critical point, i.e., the culmination of a self-organization of damage and cracking characterized by power law signatures. Specifically, we analyse the acoustic emissions recorded during the pressurisation of spherical tanks of kevlar or carbon fibers pre-impregnated in a resin matrix wrapped up around a thin metallic liner (steel or titanium) fabricated and instrumented by Aérospatiale-Matra Inc. These experiments are performed as part of a routine industrial procedure which tests the quality of the tanks prior to shipment and varies in nature. We find that the seven acoustic emission recordings of seven pressure tanks which was brought to rupture exhibit clear acceleration in agreement with a power law "divergence" expected from the critical point theory. In addition, we find strong evidence of log-periodic corrections that quantify the intermittent succession of accelerating bursts and quiescent phases of the acoustic emissions on the approach to rupture. An improved model accounting for the cross-over from the non-critical to the critical region close to the rupture point exhibits interesting predictive potential. * Corresponding author: D. Sornette, University of California, Los Angeles, 3845 Slichter Hall, Box 951567 Los Angeles, CA 90095-1567. Tel.: +1 (310) 825 28 63 Fax.: +1 (310) 206 3051-e-mail: sornette@moho.ess.ucla.edu. Plan of the studyIn this paper, we first present in section 2 a brief review of the "critical rupture" concept with an emphasis on the role of heterogeneity. Section 3 describes the experimental systems and the properties of the acoustic emission time series that we analyse with three theoretical formulas derived from the critical rupture concept. We present a brief justification for these three power laws. Section 4 gives the results obtained on the acoustic emission energy release rate on seven systems. Section 5 analyses the cumulative energy releases of these seven systems. Section 6 describes the relative merits of the three power law formulas for the prediction of the critical pressure of rupture and section 7 concludes.2 Review of the "critical rupture" concept BackgroundThe damage and fracture of materials is of enormous technological interest due to their economic and human cost. They cover a wide range of phenomena like, e.g., cracking of glass, aging of concrete, the failure of fiber networks in the formation of paper and the breaking of a metal bar subject to an external load. Failure of composite systems are of utmost importance in naval, aeronautics and space industry [1]. By the term composite, we refer to materials with heterogeneous microscopic structures and also to assemblages of macro...

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Cracks and Atoms

Holland¹,

Marder

1999

Adv. Mater.

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Atomic features are essential for understanding some materials properties. The example of brittle fracture is reviewed here, concentrating on molecular dynamics simulations of silicon. The Figure shows a visualization of an unstable crack at 8.97 % strain along (111). The choice of the potential, the implementation of non‐zero temperature, and comparison of the results with experiment are particularly emphasized.

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Instability in dynamic fracture

Cited by 422 publications

References 125 publications

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

Critical ruptures

Cracks and Atoms

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