Analysis for a screw dislocation accelerating through the shear-wave speed barrier

Markenscoff, Xanthippi; Huang, Surong

doi:10.1016/j.jmps.2008.01.005

Cited by 28 publications

(35 citation statements)

References 43 publications

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“…To summarize, dynamic extensions of the Peierls-Nabarro equation were derived for screw and edge dislocations (of the glide and climb types) using the Green's function method popularized by Mura, 2 and the Eshelby-type trick of using identity (25). Besides the instantaneous term that shows up in these equations, the origin of which was traced to a missing distributional term in the displacements, an unexpected feature of the dynamic PN equations is a term involving a convolution with the second space derivative of the displacement jump in both edge cases.…”

Section: Discussionmentioning

confidence: 99%

“…(1) of Ref. 25] consists of a sum of two integrals, the second one being extremely singular on the glide plane y = 0, added to a term that compensates for the static field of the dislocation at rest prior to motion. The singularity that develops in her second integral in the limit y → 0 greatly complicates the obtention of the stress on the glide plane.…”

Section: Discussionmentioning

confidence: 99%

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Dynamic Peierls-Nabarro equations for elastically isotropic crystals

Pellegrini

2010

Phys. Rev. B

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The dynamic generalization of the Peierls-Nabarro equation for dislocations cores in an isotropic elastic medium is derived for screw, and edge dislocations of the `glide' and `climb' type, by means of Mura's eigenstrains method. These equations are of the integro-differential type and feature a non-local kernel in space and time. The equation for the screw differs by an instantaneous term from a previous attempt by Eshelby. Those for both types of edges involve in addition an unusual convolution with the second spatial derivative of the displacement jump. As a check, it is shown that these equations correctly reduce, in the stationary limit and for all three types of dislocations, to Weertman's equations that extend the static Peierls-Nabarro model to finite constant velocities.Comment: 14 pages, 1 figure. A few minor typos in published version corrected here (in red

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Dynamic Peierls-Nabarro equations for elastically isotropic crystals

Pellegrini

2010

Phys. Rev. B

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“…Their investigation can be carried out straightforwardly by decomposing the overall rational fraction into partial ones, using the factorization formula (63a). As these field singularities are well known [38,39], the analysis will not be pursued further.…”

Section: Limiting Distribution In the Anti-plane-strain Problem And mentioning

confidence: 99%

On the gradient of the Green tensor in two-dimensional elastodynamic problems, and related integrals: Distributional approach and regularization, with application to nonuniformly moving sources

Pellegrini

Lazar

2015

Wave Motion

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International audienceThe two-dimensional elastodynamic Green tensor is the primary building block of solutions of linear elasticity problems dealing with nonuniformly moving rectilinear line sources, such as dislocations. Elastodynamic solutions for these problems involve derivatives of this Green tensor, which stand as hypersingular kernels. These objects, well defined as distributions, prove cumbersome to handle in practice. This paper, restricted to isotropic media, examines some of their representations in the framework of distribution theory. A particularly convenient regularization of the Green tensor is introduced, that amounts to considering line sources of finite width. Technically, it is implemented by an analytic continuation of the Green tensor to complex times. It is applied to the computation of regularized forms of certain integrals of tensor character that involve the gradient of the Green tensor. These integrals are fundamental to the computation of the elastodynamic fields in the problem of nonuniformly moving dislocations. The obtained expressions indifferently cover cases of subsonic, transonic, or supersonic motion. We observe that for faster-than-wave motion, one of the two branches of the Mach cone(s) displayed by the Cartesian components of these tensor integrals is extinguished for some particular orientations of source velocity vector

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“…For a Volterra dislocation of Burgers vector ∆umoving along the x axis according to x = l(t), in a wave-front asymptotic analysis of the transient (rather than steady-state) radiated fields at the Mach cone, the stress on the Mach cone (x, z, t * )is found to be a delta function, following an analysis as in [19,20]: (a) for screw dislocation:…”

Section: Formation Of the Mach Envelope At The Instant Of The Dislocamentioning

confidence: 99%

Can dislocations accelerate through the shear-wave speed “barrier”?

Markenscoff

Huang

2009

Vietnam J. Mech.

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The question of whether a dislocation can accelerate through the shear-wave speed “barrier” is addressed by analyzing the transient motion of a Volterra dislocation at the instant when the velocity equals the shear-wave speed in the presence of acceleration, which requires an asymptotic analysis at a double root (–at the transition from subsonic to supersonic a pair of complex conjugate roots becomes a double real —). The stresses carried by the forming Mach wave fronts depend on the acceleration at this instant and are found to be O( ln \(r /r^{1/2}\)) singular for a Volterra dislocation both screw and edge. The energy required to push the dislocation through the shear-wave speed “barrier” is determined by means of the “contour-independent” dynamic J integral which defines the self-force on a moving defect, and is obtained as a function of the acceleration as it crosses the “barrier”. While for a Volterra dislocation the energy-rate is singular at this instant, for a more physically realistic ramp-core “smeared” dislocation model, approximating the Volterra dislocation by a delta sequence, this energy rate is obtained by convolution and is finite, with the same result obtained by the theory of distributions. Thus, crossing the “barrier” is theoretically possible as recent experimental evidence in the literature suggests. A “cut-off” constant that remains undetermined will be found in a multiscale analysis by the matching of the self-force based on atomistic calculations modeling the core to the continuum far-field one obtained here. For decelerating motion through the shear-wave speed “barrier” this energy is released as dissipation.

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Analysis for a screw dislocation accelerating through the shear-wave speed barrier

Cited by 28 publications

References 43 publications

Dynamic Peierls-Nabarro equations for elastically isotropic crystals

Dynamic Peierls-Nabarro equations for elastically isotropic crystals

On the gradient of the Green tensor in two-dimensional elastodynamic problems, and related integrals: Distributional approach and regularization, with application to nonuniformly moving sources

Can dislocations accelerate through the shear-wave speed “barrier”?

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