The Continuum Theory of Stationary Dislocations

Wit, R. de

doi:10.1016/s0081-1947(08)60703-1

Cited by 207 publications

(61 citation statements)

References 8 publications

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“…The tractions are required to be equal and opposite at corresponding points of (g+ and ¢g_ and on the external boundaries it is assumed that homogeneous boundary conditions hold. Then the resulting displacement field in the body is given by the Somigliana formula [12] Urn(f ) ------feCijkl Aui(r)Gzm" k(r', r)nj dS (2.1) where dui(r ) = uS(r)-uT(r ) is the displacement discontinuity across the crack and (n j) is the unit normal to ~ in the sense of pointing from c~+ to c~_. The comma notation is used to denote partial differentiation with respect to the indicated component of r.…”

Section: Application Of the Somigliana Formulamentioning

confidence: 99%

Penny-shaped cracks

Guidera

Lardner

1975

J Elasticity

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AB S TRACTThe Somigliana formula is used to reduce an arbitrary elastic crack problem to a system of three integral equations for the components of displacement discontinuity. For the case of a penny shaped crack situated in an infinite isotropic medium with the crack faces subjected to arbitrary tractions, the integral equations are solved explicitly. In particular integral formulae are obtained for the stresses on the plane of the crack beyond the crack-tip, and hence for the stress intensity factors. The special case of uni-directional shear traction on the crack is examined.

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Section: Application Of the Somigliana Formulamentioning

confidence: 99%

Penny-shaped cracks

Guidera

Lardner

1975

J Elasticity

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“…4 and eqs. (17) and (19). If the dislocation loops are longer than L c , the saddle point configuration is the conventional double-kink type; this thermal activation is regarded as a typical dislocation-like reaction.…”

Section: Discussionmentioning

confidence: 99%

“…This model is, of course, a drastic simplification of the actual prismatic dislocation loops in metals. For example, in the present model we ignore contributions such as the vertices of the prismatic dislocation loops and self-interactions of the dislocation segments, 17,18) etc. Nevertheless, we can systematically investigate and analytically express the properties of the dislocation loops.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Thermal Activation of High-Mobility Dislocation Loops

Ohsawa

Kuramoto

2005

Mater. Trans.

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We report thermally activated transport of highly mobile dislocation loops in terms of a line tension model where the dislocation loops are assumed to be a flexible string. The activation energy and transition rate are calculated on the basis of a classical rate theory. The activation energy merely increases with the length of the dislocation loops. However, the activation process and temperature dependence of the transition rate qualitatively change at a critical length L c . If the dislocation loops are longer than the critical length, the thermal activation occurs through the conventional double-kink formation process on the dislocation lines. On the other hand, if the dislocation loops are shorter than that, the saddle point configuration is not the double-kink type but non-deformation one. Therefore, the critical length L c is a plausible criterion for the dislocation loops to distinguish dislocation like from point-defect like in size.

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“…Here the dislocation loop is on the z = 0 plane, with the normal stress component σ zz being presented. The stress distribution of a square loop can be evaluated using a dislocation mechanics simulation based on the vector formula of Devincre (17) , and a circular loop calculated with the analytic solution by de Wit (11) . Fig 4 (a) and (b) confirm that the distribution of a circular loop differs from that of a square loop.…”

Section: Interaction Energy Of Dislocationsmentioning

confidence: 99%

Theoretical Investigation of the Displacement Burst Observed in Nanoindentation by Collective Dislocation Loops Nucleation Model

Tsuru

Shibutani²

2008

JCST

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Abrupt growth of displacement observed in the relationship between indent load and indent depth in nanoindentation of crystalline materials, so-called displacement burst, has been recognized as one of the representative examples of nanoscale plastic behavior (nanoplasticity). This phenomenon corresponds to the early stage of plastic deformation and is greatly influenced by the collective dislocation emission. In the present paper a simplified model is constructed for the first displacement burst with use of the elastic theory based on both the Hertzian contact theory and the classical dislocation theory to evaluate the displacement burst in nanoindentation. The result of the analytical model for the energy equilibrium revealed that there is a strong correlation between burst width and critical indent depth that corresponds to the dislocation emission. Finally, it is shown that more than one hundred high-density dislocations are generated simultaneously and surface step corresponding to the Burgers vector of dislocation dipole of each emitted dislocation causes significant displacement burst.

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The Continuum Theory of Stationary Dislocations

Cited by 207 publications

References 8 publications

Penny-shaped cracks

Penny-shaped cracks

Analysis of the Thermal Activation of High-Mobility Dislocation Loops

Theoretical Investigation of the Displacement Burst Observed in Nanoindentation by Collective Dislocation Loops Nucleation Model

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