Periodic displacement and stress fields near a phase boundary in the isotropic elasticity theory

Bonnet, R.

doi:10.1080/01418618108236150

Cited by 51 publications

(42 citation statements)

References 14 publications

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“…The elastic constants are given by (5) and are (in GPa): -For Al 2 The results obtained in this case are appreciably superposable with the results of Bonnet (4) obtained in isotropic elasticity.…”

Section: Applicationsupporting

confidence: 68%

“…The problem becomes more difficult when the bicristal is constituted of two plates of different nature (heterostructure) (1). R. Bonnet (2) proposed a method to solve this problem analytically and got the field of displacements and stresses in the case of isotropic elasticity.…”

Section: Introductionmentioning

confidence: 99%

“…The thin bicristal Al/Al 2 Cu, that made the object of several investigations (2)(3)(4)(5), is treated like example.. a cartesian frame Ox 1 x 2 x 3 with a period 1/g in the plan of an interface separating two different anisotropy media. For the limiting case corresponding to 1/g>>h + and h -, the problem reduces to a single straight interfacial defect interacting with the free surfaces.…”

Section: Introductionmentioning

confidence: 99%

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Lámina delgada bifásica deformada por dislocación interfacial en elasticidad elástica

Madani¹,

Brioua²,

Outtas³

et al. 2005

Bol. Soc. Esp. Ceram. Vidr.

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The purpose of this work is the numerical resolution, in the case of anisotropic elasticity, of the problem of a dislocation parallel and near to the two free surfaces of a thin bicrystal. This case is obtained while making the period of a network of misfit dislocations much greater than the thickness of the two foils. As a result, in the vicinity of the dislocation, the limiting bondary conditions will be close to that of Volterra translation dislocation. The elastic fields of displacement and stress are calculated for various orientations of the burgers vector. Before this calculation, we tested the precision of the results of the program by comparing the interfacial relative displacement obtained from this one to the results of the analytical expression describing this same displacement. The thin bicristal Al/Al 2 Cu, that made the object of several investigations, is treated like example. The results obtained are compared to those obtained in isotropic elasticity. Keywords: dislocation, misfit, interface, networks Lámina delgada bifásica deformada por dislocación interfacial en elasticidad elásticaEste trabajo aborda la resolución numérica en anisotropía elástica, del problema de una dislocación paralela cercana a las superficies libres de un bi-cristal delgado. Este problema se genera cuando el periodo de la red de dislocaciones desplazadas es mucho mayor que el espesor de la bi-lámina. Como resultados, en la vecindad de la dislocación, las condiciones de contorno estarán cercanas a la dislocación de traslación de Volterra. Los campos elásticos de desplazamiento y las tensiones se calcularon para distintas orientaciones del vector de burgers. Como paso previo a los cálculos, se comprobó la precisión de los resultados del programa comparando le desplazamiento relativo interracial obtenido con los resultados de la expresión analítica que describen dicho desplazamiento. Se emplearon como ejemplo bi-cristales de Al/Al 2 Cu, debido a su empleo en varias investigaciones. Los resultados fueron comparados con los obtenidos en elasticidad isótropa.

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Section: Applicationsupporting

confidence: 68%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Lámina delgada bifásica deformada por dislocación interfacial en elasticidad elástica

Madani¹,

Brioua²,

Outtas³

et al. 2005

Bol. Soc. Esp. Ceram. Vidr.

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“…1) are generated in the whole bicrystal to produce homogeneous biaxial distortions parallel to the interface of interest. This operation leads to a mechanical force equilibrium in the coherent bicrystal that is not explicitly taken into account in the Olson-Cohen-Bonnet approaches [19,25,26], for which the coherency strains are concentrated in the vicinity of the interfaces. The complete elastic distortion field D tot may be written as the superposition of the uniform coherency and the Volterra dislocation distortions, denoted by D dis .…”

Section: Theory Of Interface Dislocationsmentioning

confidence: 99%

“…The complete elastic distortion field D tot may be written as the superposition of the uniform coherency and the Volterra dislocation distortions, denoted by D dis . Due to the periodicity of the interface dislocation structures, described by the two O-lattice vectors p o 1 = p o 2 in a Cartesian coordinate system with basis vectors (x 1 , x 2 n, x 3 ) and with the interface located at x 2 = 0, the complete distortion field may be expressed, outside of dislocation cores, as the biperiodic Fourier series at any position x [16,25,26], i.e.…”

Section: Theory Of Interface Dislocationsmentioning

confidence: 99%

Effect of interface dislocation Burgers vectors on elastic fields in anisotropic bicrystals

Vattré

Demkowicz

2014

Computational Materials Science

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A recent anisotropic elasticity formalism for quantifying interface dislocation arrays is used to compute the variations in long-range elastic fields and short-range strain energies of misfit dislocations due to changes in the Burgers vectors of the interface dislocations. The importance of selecting proper reference states for tilt and twist grain boundaries as well as a heterophase interface formed by tetragonal crystals is discussed in terms of partitioning of strain and rotation fields. For constrained interfaces consistent with the FrankBilby equation, the present work shows that examining the strain energies of different admissible dislocation configurations may be used as a criterion for predicting the most favorable structures.

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Tests by TEM contrast simulations of the elastic field of a buried (001) low angle twist boundary in silicon

Boussaid¹,

Fournel

Bonnet³

2005

Physica Status Solidi (b)

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A buried (001) low angle twist boundary (misorientation angle 0.48°) in silicon is investigated by the technique of two-beam transmission electron microscopy using bright-field images obtained from diffracting vectors g{400}, g{311} and g{220}, and g{nnn} with n = 3 and 4. To analyse its elastic field, the concept of interfacial "relaxation centres" is assumed, for which the relative displacement field of the two crystals is zero. These centres are located in the middle of each square formed by a dislocation unit cell. This assumption is tested positively for the first time for a double periodic network of screw dislocations. For the image contrast calculations, the elastic field of the network is that of two perpendicular families of screw misfit dislocations in the sense of Bonnet (1981). Since the two-beam bright-field approximation is weak to explain the experimental images taken with g{nnn} and n = 3 and 4, extra N beam image calculations involving N < 7 systematic reflections along g{nnn} have been carried out with a devoted programme. All the computed images prove to be in good agreement with the experimental images, still validating the adopted elastic field.

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Periodic displacement and stress fields near a phase boundary in the isotropic elasticity theory

Cited by 51 publications

References 14 publications

Lámina delgada bifásica deformada por dislocación interfacial en elasticidad elástica

Lámina delgada bifásica deformada por dislocación interfacial en elasticidad elástica

Effect of interface dislocation Burgers vectors on elastic fields in anisotropic bicrystals

Tests by TEM contrast simulations of the elastic field of a buried (001) low angle twist boundary in silicon

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