Generalized Kanzaki force field of extended defects in crystals with applications to the modeling of edge dislocations

Gurrutxaga-Lerma, B.; Verschueren, J.

doi:10.1103/physrevmaterials.3.113801

Cited by 5 publications

(3 citation statements)

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“…As Equation (22) is linear, its solution may be expressed in terms of the lattice Green's function as follows [310]:where is any source term expressed as a Kanzaki force distribution [309,313,322]. By source term, we mean any boundary condition; because Equation (22) is a force balance, we require the boundary condition to be expressed as a distribution of forces acting on the atoms of the perfect lattice.…”

Section: Atomistic Models Of Gliding Dislocationmentioning

confidence: 99%

“…In this case, these forces would have to be those that when acting on the atoms of the perfect lattice generate the displacement field of a dislocation. This makes the forces be Kanzaki forces [25,309,313,322]. In the case of a uniformly gliding screw dislocation, the Kanzaki force distribution that acts as a source term is given by [25,313]where if the particle i is above (below) the glide plane and j below (above), and 0 otherwise.…”

Section: Atomistic Models Of Gliding Dislocationmentioning

confidence: 99%

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The mechanics and physics of high-speed dislocations: a critical review

Gurrutxaga-Lerma

Verschueren

Dini

2020

International Materials Reviews

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High speed dislocations have long been identified as the dominant feature governing the plastic response of crystalline materials subjected to high strain rates. They allegedly control deformation and failure response of industrial processes in a large range of applications, including machining, laser shock peening, punching, drilling, crashworthiness, foreign object damage,etc. Despite decades of study, achieving a consensus on the role and influence high speed dislocations have on the materials response observed at the macro-scale by the means of rigorous mechanistic grounding remains elusive. This article reviews both experimental and theoretical efforts made to address this issue in a systematic way. The lack of experimental evidence and direct observation of high speed dislocations means that most work on the matter is rooted on theory and simulations. This article offers a critical review of the competing theoretical accounts of high speed mechanisms, their underlying hypothesis, insights, and shortcomings. It explores the role that the speed of sound plays in the modelling of high speed dislocations, the way dislocations are modelled in the elastic continuum and how this approach can be used to study plasticity at high strain rates. The role atomistic models of dislocations have played in clarifying high speed motion mechanisms, and how they have led to the development of dislocation velocity-stress relations describing dislocation mobility is then also discussed. The article also reviews modelling efforts aimed at describing high speed dislocation mobility, and how different proposed physical mechanisms believed influence the motion. The article closes with an overview of the current state of the art and suggestions for key developments needed to improve our fundamental understanding in future research.

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Section: Atomistic Models Of Gliding Dislocationmentioning

confidence: 99%

Section: Atomistic Models Of Gliding Dislocationmentioning

confidence: 99%

The mechanics and physics of high-speed dislocations: a critical review

Gurrutxaga-Lerma

Verschueren

Dini

2020

International Materials Reviews

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“…In other words, the remaining singularities (including at the core) must be removed by regularizing the core in an appropriate fashion [50]. Recent work on modeling dislocation cores (from theory) in a realistic way can be found in [31,[51][52][53][54] and references therein. Furthermore, we saw that when simulating dislocations in larger codes, the computationally less expensive steady state solution (2.31) can be expected to be a fairly good approximation for subsonic screw dislocations with low to moderate acceleration compared to its more general counterpart (and our main result) Eq.…”

Section: Discussionmentioning

confidence: 99%

A general solution for accelerating screw dislocations in arbitrary slip systems with reflection symmetry

Blaschke

2020

Preprint

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Solutions to the differential equations of linear elasticity in the continuum limit in arbitrary crystal symmetry are known only for steady-state dislocations, i.e. line defects moving at constant velocity. Troubled by singularities at certain 'critical' velocities (typically close to certain sound speeds), these dislocation fields are thought to be too idealized, and divergences are usually attributed to neglecting the finite size of the core and to the restriction to constant velocity. In the isotropic limit, accelerating pure screw and edge dislocations were studied some time ago, but a generalization to anisotropic crystals has not been attempted before. This is the gap this work aims to fill, albeit restricted for now to pure screw dislocations and hence to slip systems featuring a reflection symmetry, a prerequisite to studying pure screw dislocations without mixing with edge dislocations. Further generalizations to include edge and mixed dislocations as well as regularizations of the dislocation core are beyond the scope of this paper and are left for future work.

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