Origin of crack tip instabilities

Marder, Michael; Gross, Steve

doi:10.1016/0022-5096(94)00060-i

Cited by 280 publications

(260 citation statements)

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“…In addition, it is necessary to prescribe that the displacement of nodes ahead of the transition front remain below this critical displacement [Marder & Gross (1995)]. This admissibility criterion is violated when the feeding wave amplitude (at a given frequency) is high enough.…”

Section: Discussionmentioning

confidence: 99%

“…The radiation creates the speed-dependent wave resistance, which cannot be detected in a homogeneous material model, [Slepyan (2002), Slepyan (2010a)]. This phenomena accounts for instabilities in the crack path propagation in a homogeneous material, which is attributed to the composition of its microstructure, [Marder & Gross (1995)], that can yield complex crack behaviour such as micro-branching and oscillation of the crack paths [Bouchbinder et al (2010)]. …”

Section: Introductionmentioning

confidence: 99%

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Analysis of dynamic damage propagation in discrete beam structures

Movchan

Mishuris

Slepyan

2016

International Journal of Solids and Structures

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In the last decade, significant theoretical advances were obtained for steady-state fracture propagation in spring-mass lattice structures, that also revealed surprising fracture regimes. Very few articles exist, however, on the dynamic fracture processes in lattices composed of beams. In this paper we analyse a failure (feeding) wave propagating in a beam-made lattice strip with periodically placed point masses. The fracture occurs when the strain of the supporting beam reaches the critical value. The problem reduces to a Wiener-Hopf equation, from which the complete solution is obtained. Two cases are considered when the feeding wave transmits into the intact structure as a sinusoidal wave(s) or only as an evanescent wave. For both cases, a complete analysis of the strain inside the structure is presented. We determine the critical level of the feeding wave, below which the steady-state regime does not exist, and its connections to the feeding wave parameters and the failure wave speed. The accompanied dynamic effects are also discussed. Amongst much else, we show that the switch between the two considered regimes introduces a rapid change in the minimum energy required for the failure wave to propagate steadily. The failure wave developing under an incident sinusoidal wave is remarkable due to the fact that there is an upper bound of the domain where the steady-state regime exists. In the present paper, only the latter is examined; the alternative regimes are considered separately.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of dynamic damage propagation in discrete beam structures

Movchan

Mishuris

Slepyan

2016

International Journal of Solids and Structures

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“…The effective sharpness of the blade depends upon the power with which it presses through material; press too hard, and it blunts, presenting enormous resistance to speeding up further. Both idealized calculations [3,4], as well as more realistic simulations [5,6] showed how this process could occur, as indicated on the right hand side of Fig. . Last fall, Sharon, Fineberg, and Gross [7] showed that cracks in Plexiglas develop branching structures, as shown on the right hand side of Fig. .…”

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confidence: 99%

Energetic developments in fracture

Marder

1996

Nature

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What drives physicists to study cracks? There is certainly some attraction in being able to tell the children one is getting paid to break things. There is also a perverse pleasure in learning the physical laws underlying irreversible change, decay, and destruction. A paper of Eran Sharon, Steven Gross, and Jay Fineberg, "Energy Dissipation in Dynamic Fracture" which appeared on 18 March in Physical Review Letters contains an answer to an old and deceptively simple question, "How fast do things break, and why?"The first scientific attempts to answer this question go back to research of Hubert Schardin and Wolfgang Struth in 1937[1], who used sparks to take photographs of cracks in less than one ten-millionth of a second. They concluded that "the maximum velocity of propagation of glass fractures is to be considered a physical constant," and they measured crack speeds that were approximately one quarter the speed of sound in many different glasses.Some time after these experiments came theories of crack motion, which firmly insisted that cracks should move at about twice the speed observed. The classic theory[2], developed by B. V. Kostrov, J. D. Eshelby, and L. B. Freund, left little room for uncertainty. Cracks leave two new surfaces behind them. The speed at which vibrations travel across a free surface is the Rayleigh wave speed, a speed governing the motion of sound when one raps one's knuckles on the top of a table, or the speed at which earthquakes travel on the surface of the earth. Cracks, said the theory, should move at this Rayleigh wave speed too -but it does not happen. In Plexiglas, for example, the Rayleigh wave speed is around 1000 metres per second, but cracks never exceed 600 metres per second. This descrepancy was widely acknowledged to 1

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“…Thus, a better understanding of fracture mechanisms in solids is obviously of crucial importance for a safer design of civil engineering structures. A large number of studies-both experimental and theoretical-have been devoted to the simplest model case of a single crack, growing in either brittle or viscoplastic materials [1][2][3][4][5][6][7][8]. Those works have shown that dynamical instabilities and/or heterogeneities may destabilize the crack dynamics, leading to strong deviations and roughness in the crack paths [6][7][8][9][10][11][12].…”

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confidence: 99%