A unified theory of grain boundaries. II. Asymmetric tilt boundaries

Marcinkowski, M. J.; Sadananda, K.

doi:10.1002/pssa.2210180137

Cited by 23 publications

(4 citation statements)

References 5 publications

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“…It has been found in [93] that the model suggested in 1911 agrees well with the experimental data on the angle dependence of boundary energy, when the boundary lies between two special misorientations. Eventually, in [94] the structure of non-symmetrical tilt boundaries is described in the form of a continuous number of steps each of them being adequate to a wedge disclination dipole. The models using the wedge partial disclinations are helpful in studying deformation twinning [9,25, 63 to 65,87,95 to 971 and stresses arising a t the iiiartensitic transformation [87].…”

Section: Modelling Of the Sandgrain And Fragment Structures In Crystalsmentioning

confidence: 99%

Disclinations in solids

Романов

Vladimirov

1983

Phys. Stat. Sol. (a)

118

183

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Section: Modelling Of the Sandgrain And Fragment Structures In Crystalsmentioning

confidence: 99%

Disclinations in solids

Романов

Vladimirov

1983

Phys. Stat. Sol. (a)

118

183

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“…where, again, Bj is determined in terms of fl(x) and f2(x) using (12). Omitting mathematical details, expressions for ~b'l,(zl) and tPh,(z2) are obtained as follows …”

Section: Field Quantities In a Semi-infinite Domainmentioning

confidence: 99%

“…The advent of analytical techniques in materials science proved, beyond doubt, the important role which crystal dislocations play in deformation, micromechanics of fracture, and other materials properties. A detailed work on the use of dislocation theory in modelling materials phenomena such as twining, grain boundaries [11,12], interfacial energy and surface tension [13,14] was conducted by Marcinkowski and Jagannadham. A detailed work on the use of dislocation theory in modelling materials phenomena such as twining, grain boundaries [11,12], interfacial energy and surface tension [13,14] was conducted by Marcinkowski and Jagannadham.…”

Section: Introductionmentioning

confidence: 99%

Green's function for the elastic field of an edge dislocation in a finite orthotropic medium

El–Azab

Ghoniem

1993

Int J Fract

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A fundamental solution of plane elasticity in a finite domain is developed in this paper. A closed-form Green's function for the elastic field of an edge dislocation of arbitrary Burger's vector at an arbitrary point in an orthotropic finite elastic domain, that is free of traction, is presented. The method is based on the classical theory of potential fields, with an additional distribution of surface dislocations to satisfy the free traction boundary condition. A solution is first developed for a dislocation in a semi-infinite half-plane. The resulting field is composed of two parts: a singular contribution from the original dislocation, and a regular component associated with the surface distribution. The Schwarz-Christoffel transformation is then utilized to map the field quantities to a finite, polygonal domain. A closed form solution containing Jacobi elliptic functions is developed for rectangular domains, and applications of the method to problems of fracture and plasticity are emphasized.

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“…dislocation approach than that presented by Bollmann [12]. I n principle, however, both treatments should be similar and have been compared more fully in [2] and [3]. Finally, although no detailed atom description has been presented for an asymmetric twist boundary, it seems reasonable from the results obtained for asymmetric tilt boundaries [3] that these boundaries should also have a well-defined asymmetric coincidence site lattice associated with them.…”

Section: A Generalized Crystallographic Approach To the Analysis Of Tmentioning

confidence: 99%

A unified theory of twist boundaries

Marcinkowski

Dwarakadasa

1973

Phys. Stat. Sol. (a)

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A dislocation approach has been employed to fully describe the structure of a symmetric twist boundary of any degree of misorientation. I n particular, i t is shown that any twist boundary can be described in terms of an array of grain boundary dislocations which can be derived from various combinations of crystal lattice dislocations associated with the two adjacent grains. A well-defined coincidence site lattice is also shown to be associated with each of these given grain boundary dislocation arrays. Various concepts such as the Burgers circuit along with atomic ordering have also been treated with respect t o the symmetric twist boundary.Es wird eine Versetzungsbehandlung zur vollstandigen Beschreibung der Struktur einer symmetrischen Drehgrenze fur jeden Grad der Fehlorientierung angegeben. Speziell wird gezeigt, da13 jede Drehgrenze mit einer Anordnung von Korngrenzenversetzungen beschrieben werden kann, die von verschiedenen Kombinationen von Kristallgitterversetzungen hergeleitet werden konnen, die mit den beiden benachbarten Kornern verbunden sind. Es wird ferner gezeigt, daB ein wohldefiniertes Koinzidenzplatzgitter mit jeder dieser gegebenen Korngrenzenversetzungsanordnungen verknupft ist. Verschiedene Vorstellungen ~ wie die eines Burgerskreises zusammen mit atomarer Ordnungwerden ebenfalls in bezug auf die symmetrische Drehgrenze behandelt.

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A unified theory of grain boundaries. II. Asymmetric tilt boundaries

Cited by 23 publications

References 5 publications

Disclinations in solids

Disclinations in solids

Green's function for the elastic field of an edge dislocation in a finite orthotropic medium

A unified theory of twist boundaries

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