Supershear bursts in the propagation of a tensile crack in linear elastic material

Barras, Fabian; Carpaij, René; Geubelle, Philippe H.; Molinari, Jean‐François

doi:10.1103/physreve.98.063002

Cited by 8 publications

(5 citation statements)

References 48 publications

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“…The paper has found novel local solutions to mode I and mode II fracture in isotropic linear elasticity that describe supersonic and intersonic crack propagation showing remarkable similarities to experimental and computational models previously reported in the literature (Gao et al 2001;Rosakis 2002;Abraham et al 2002;Guo et al 2003;Buehler et al 2003;Hao et al 2004;Petersan et al 2004;Willmott and Field 2006;Radi and Loret 2008;Bizzarri et al 2010;Schubnel et al 2011;Barras et al 2018;Yue et al 2019;Mai et al 2020). Despite these results, no theoretical predictions describing Mach cone solutions had been reported in the literature before.…”

Section: Discussionsupporting

confidence: 73%

“…However, recent results both experimental and computational have shown crack propagation at significantly higher speeds both in the intersonic range and even beyond the speed of sound (Rosakis et al 1999;Needleman 1999;Abraham and Gao 2000;Huang and Gao 2001;Gao et al 2001;Rosakis 2002;Abraham et al 2002;Guo et al 2003;Buehler et al 2003;Hao et al 2004). Moreover, some of the published results exhibit features akin to shock waves of supersonic flow where solution discontinuities are seen to emerge from the crack tip as it travels along the material (Petersan et al 2004;Willmott and Field 2006;Radi and Loret 2008;Bizzarri et al 2010;Schubnel et al 2011;Barras et al 2018;Yue et al 2019;Mai et al 2020). No analytical models have been reported that predict such behaviour in linear elasticity.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

Bonet

Gil

2021

Int J Fract

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This paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous solutions of the equations of motion for isotropic linear elasticity in two dimensions. Instead of the classical second order elastodynamics equations in terms of the displacement field, equivalent first order equations in terms of the evolution of velocity and displacement gradient fields are used together with their associated jump conditions across solution discontinuities. The paper postulates supersonic and intersonic steady-state crack propagation solutions consisting of regions of constant deformation and velocity separated by pressure and shear shock waves converging at the crack tip and obtains the necessary requirements for their existence. It shows that such mathematical solutions exist for significant ranges of material properties both in plane stress and plane strain. Both mode I and mode II fracture configurations are considered. In line with the linear elasticity theory used, the solutions obtained satisfy exact energy conservation, which implies that strain energy in the unfractured material is converted in its entirety into kinetic energy as the crack propagates. This neglects dissipation phenomena both in the material and in the creation of the new crack surface. This leads to the conclusion that fast crack propagation beyond the classical limit of the Rayleigh wave speed is a phenomenon dominated by the transfer of strain energy into kinetic energy rather than by the transfer into surface energy, which is the basis of Griffiths theory.

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Section: Discussionsupporting

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

Bonet

Gil

2021

Int J Fract

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“…Nevertheless there are applications where an interfacial crack study is required along a predefined path, for example, in geosciences when a weak interface is to be studied, [48][49][50][51] when rough cracks may, under mixed-mode loading, produce interlocking stresses increasing the shear strength [52][53][54][55][56][57][58][59][60] or in the study of adhesive bonds in laminar structures.…”

Section: Isotropic Body Weak Interfacementioning

confidence: 99%

Coupling between cohesive element method and node‐to‐segment contact algorithm: Implementation and application

Pundir

Anciaux

2021

Numerical Meth Engineering

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In materials, the evolution of crack surfaces is intimately linked with the self-contact occurring between them. The developed contact forces not only mitigate the effect of stress concentration at crack tip but also contribute significantly to the transfer of shear and normal stresses. In this article, we present a numerical framework to study the simultaneous process of fracture and self-contact between fracturing surfaces. The widely used approach, where contact constraints are enforced with the cohesive element traction separation law, is demonstrated to fail for relative displacements greater than the characteristic mesh length. A hybrid approach is proposed, which couples a node-to-segment contact algorithm with extrinsic cohesive elements. Thus, the fracture process is modeled with cohesive elements, whereas the contact and the friction constraints are enforced through a penalty-based method. This hybrid cohesive-contact approach is shown to alleviate any mesh topology limitations, making it a reliable and physically based numerical model for studying crack propagation along rough surfaces.

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“…Numerical modeling of frictional sliding has been under increased scrutiny. The Boundary Integral Method (BIM) [27] has been widely used to simulate rupture propagation on frictional interfaces [28,29,12,13]. Although computationally efficient, BIM is mostly limited to planar interfaces in infinite domains.…”

Section: Introductionmentioning

confidence: 99%

Finite element modeling of dynamic frictional rupture with rate and state friction

Rezakhani

Barras

Brun

et al. 2020

Journal of the Mechanics and Physics of Solids

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Numerous laboratory experiments have demonstrated the dependence of the friction coefficient on the interfacial slip rate and the contact history, a behavior generically called rate and state friction. Although numerical models have been widely used for analyzing rate and state friction, in general they consider infinite elastic domains surrounding the sliding interface and rely on boundary integral formulations. Much less work has been dedicated to modeling finite size systems to account for interactions with boundaries. This paper investigates rate and state frictional interfaces in the context of finite size systems with the finite element method in explicit dynamics. It is shown that due to the highly non-linear nature of rate and state friction and its sensitivity to numerical noise, the time integration step to achieve an accurate steady state solution is orders of magnitude smaller compared to the stable time step required in boundary integral formulations. We provide evidence that the noise, which is source of instability in the finite element solution, originates from internal discretization nodes. We then investigate the long term behavior of the sliding interface for two different friction laws: a velocity weakening law, for which the friction monotonously decreases with increasing sliding velocity, and a velocity weakening-strengthening law, for which the friction coefficient first decreases but then increases above a critical velocity. We show that for both friction laws at finite times, that is before wave reflections from the boundaries come back to the sliding interface, a temporary steady state sliding is reached, with a well-defined stress drop at the interface. This stress drop gives rise to a stress concentration and leads to an analogy between friction and fracture. However, at longer times, that is after multiple wave reflections, the stress drop is essentially zero, resulting in losing the analogy with fracture mechanics. Finally, the simulations reveal that velocity weakening is unstable at long time scales, as it results in an acceleration of the sliding blocks. On the other hand, velocity weakening-strengthening reaches a steady state sliding configuration.

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Supershear bursts in the propagation of a tensile crack in linear elastic material

Cited by 8 publications

References 48 publications

Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

Coupling between cohesive element method and node‐to‐segment contact algorithm: Implementation and application

Finite element modeling of dynamic frictional rupture with rate and state friction

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