Equation of motion for dislocations with inertial effects

Pillon, Laurianne; Denoual, Christophe; Pellegrini, Yves-Patrick

doi:10.1103/physrevb.76.224105

Cited by 35 publications

(46 citation statements)

References 24 publications

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“…The mobility law of dislocations is adjusted to account for the likely presence of high speed dislocations [1,18,21,[23][24][25][26][27][28]; data about the mobility of dislocations is extracted from MD simulations of aluminum [22] (see Supplementary Materials).…”

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confidence: 99%

Attenuation of the Dynamic Yield Point of Shocked Aluminum Using Elastodynamic Simulations of Dislocation Dynamics

et al. 2015

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When a metal is subjected to extremely rapid compression, a shock wave is launched that generates dislocations as it propagates. The shock wave evolves into a characteristic two-wave structure, with an elastic wave preceding a plastic front. It has been known for more than six decades that the amplitude of the elastic wave decays the further it travels into the metal: this is known as "the decay of the elastic precursor". The amplitude of the elastic precursor is a dynamic yield point because it marks the transition from elastic to plastic behaviour. In this letter we provide a full explanation of this attenuation using the first method of dislocation dynamics to treat the time dependence of the elastic fields of dislocations explicitly. We show that the decay of the elastic precursor is a result of the interference of the elastic shock wave with elastic waves emanating from dislocations nucleated in the shock front. Our simulations reproduce quantitatively recent experiments on the decay of the elastic precursor in aluminum, and its dependence on strain rate.The dynamic behaviour of crystalline solids subjected to shock compression plays a central role in diverse applications, including bird strikes in aerospace [1], crashworthiness in the automobile industry [2], and manufacturing processes such as laser shock peening [3], amongst many others. Upon being shocked within a range of strain rates and pressures of typically 10 6 − 10 10 s −1 and 5 − 50GPa [1], the shock front in crystalline materials often displays a characteristic two-wave structure near the loading surface: the plastic wave front leading to the Hugoniot shocked state is preceded by an elastic precursor wave [1]. The amplitude of the elastic precursor wave decays as the wave front advances[1, 4]-a phenomenon known as the 'decay of the elastic precursor'. The amplitude of the elastic wave marks the onset of plasticity, i.e. it is the dynamic yield point. The subsequent plastic wave is commonly ascribed to the generation and motion of dislocations, the agents of plasticity in crystalline solids [9].The cause of its attenuation remains unclear after six decades [4][5][6][7][8]. Clifton and Markenscoff [4] calculated analytically the amplitude attenuation of a planar elastic shock wave caused by the destructive interference of elastic wavelets emanating from pre-existing dislocations set into motion by the passage of a shock wave of infinite strain rate; dislocation generation by the shock was neglected. Consequently, the elastic precursor decay was attributed to the density and initial velocity of pre-existing dislocations. Armstrong et al.[10] studied the dislocation relaxation mechanisms during high strain rate shock loading, concluding that dislocation generation dominates plastic relaxation under shock loading. This is because the number of pre-existing dislocations is about two to three orders of magnitude less than that generated during the shock [1,4,7].In this letter we show that we can account for the experimentally observed residual disloca...

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confidence: 99%

Attenuation of the Dynamic Yield Point of Shocked Aluminum Using Elastodynamic Simulations of Dislocation Dynamics

et al. 2015

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“…16 The self-force has been extensively discussed by Markenscoff and co-workers under an assumptions of rigid dislocation core. 25 Based on Eshelby's seminal work (valid at small velocities), the issue of radiative-damping losses has been addressed by Al'shits et al, 26 and a phenomenological EoM aimed at velocities less than the shear wave-speed has been proposed by Pillon et al 21 More recently, these questions were re-examined by the present author, resulting in an extended EoM that, in principle, allows for arbitrary core variations with time. 24 However, the theory still lacks an independent governing equation for the core, and must be completed by an ad-hoc approximation to be of use, which considerably restricts its domain of validity.…”

Section: Introductionmentioning

confidence: 91%

“…18,19 However, such phenomenological approaches (including relativistic ones 20 ) have been ruled out by phase-field calculations when acceleration is fast, and when the velocity becomes a sizable fraction of the shear wave speed. 21 As has long been recognized, 22 the key to dislocation inertia resides in the phenomenon of radiation reaction. At nonsupersonic velocities, inertia arises from the finite-width dislocation moving within its own wavefield emitted at every past instant, which results in retarded self-interaction and makes motion history-dependent.…”

Section: Introductionmentioning

confidence: 99%

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Equation of motion and subsonic-transonic transitions of rectilinear edge dislocations: A collective-variable approach

Pellegrini

2014

Phys. Rev. B

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A theoretical framework is proposed to derive a dynamic equation motion for rectilinear dislocations within isotropic continuum elastodynamics. The theory relies on a recent dynamic extension of the Peierls-Nabarro equation, so as to account for core-width generalized stacking-fault energy effects. The degrees of freedom of the solution of the latter equation are reduced by means of the collective-variable method, well-known in soliton theory, which we reformulate in a way suitable to the problem at hand. Through these means, two coupled governing equations for the dislocation position and core width are obtained, which are combined into one single complex-valued equation of motion, of compact form. The latter equation embodies the history dependence of dislocation inertia. It is employed to investigate the motion of an edge dislocation under uniform time-dependent loading, with focus on the subsonic/transonic transition. Except in the steady-state supersonic range of velocities-which the equation does not address-our results are in good agreement with atomistic simulations on tungsten. In particular, we provide an explanation for the transition, showing that it is governed by a loading-dependent dynamic critical stress. The transition has the character of a delayed bifurcation. Moreover, various quantitative predictions are made, that could be tested in atomistic simulations. Overall, this work demonstrates the crucial role played by core-width variations in dynamic dislocation motion.

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“…The latter is a function of the γ-surface energies from which the linear elastic part has been subtracted. As described in [22][23][24], a PNG calculation involves a nodal mesh, homothetic to the crystal structure, which incorporates γ-surfaces energies. Once a discrete Volterra dislocation is introduced into the volume, the equilibrium of displacement jump fields is determined through a viscous relaxation scheme.…”

Section: The Png Modelmentioning

confidence: 99%

Dislocation modelling in Ti₂AlN MAX phase based on the Peierls–Nabarro model

Gouriet

Carrez

Cordier

et al. 2015

Philosophical Magazine

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In this study, we determined the core structure and the Peierls stress of 1 3 h2 1 1 0i dislocations in Ti 2 AlN MAX phase. We use a generalized PeierlsNabarro model, called Peierls-Nabarro-Galerkin (PNG), coupled with first principles calculations of generalized stacking fault (GSF). The GSF calculations show that dislocation glide in the basal plane will occur preferentially between M (here Ti) and A (here Al) planes. Additionally, the results of PNG calculations demonstrate that whatever the dislocation character, 1 3 h2 1 1 0i dislocations are dissociated in the basal plane, with a dissociation distance below the experimental resolution of transmission electron microscopy observations. Finally, the Peierls stress calculations show that the edge and screw characters are the easiest characters to glide in the basal plane.

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Equation of motion for dislocations with inertial effects

Cited by 35 publications

References 24 publications

Attenuation of the Dynamic Yield Point of Shocked Aluminum Using Elastodynamic Simulations of Dislocation Dynamics

Attenuation of the Dynamic Yield Point of Shocked Aluminum Using Elastodynamic Simulations of Dislocation Dynamics

Equation of motion and subsonic-transonic transitions of rectilinear edge dislocations: A collective-variable approach

Dislocation modelling in Ti₂AlN MAX phase based on the Peierls–Nabarro model

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Equation of motion for dislocations with inertial effects

Cited by 35 publications

References 24 publications

Attenuation of the Dynamic Yield Point of Shocked Aluminum Using Elastodynamic Simulations of Dislocation Dynamics

Attenuation of the Dynamic Yield Point of Shocked Aluminum Using Elastodynamic Simulations of Dislocation Dynamics

Equation of motion and subsonic-transonic transitions of rectilinear edge dislocations: A collective-variable approach

Dislocation modelling in Ti2AlN MAX phase based on the Peierls–Nabarro model

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Dislocation modelling in Ti₂AlN MAX phase based on the Peierls–Nabarro model