Micromechanics of defects in solids

Mura, T.; Barnett, D.M.

doi:10.1007/978-94-009-3489-4

Cited by 3,030 publications

(1,498 citation statements)

References 399 publications

(494 reference statements)

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“…Each grain, characterized by the viscoplastic compliance M c(tg) and a backextrapolated strain rate g0 is in turn regarded as an inhomogeneous inclusion embedded in such an HEM. The problem of a viscoplastic inhomogeneity embedded in a homogeneous viscoplastic matrix being acted upon by a uniform stress N' at infinity can be solved using the inclusion problem formalism [10,13]. Define the deviations of stress and strain rate in the inclusion with respect to the polycrystal averages as ga = gk -/~k (6) 61'=: ol'-ZI '…”

Section: Vpsc Formulationmentioning

confidence: 99%

A self-consistent viscoplastic model: prediction of rolling textures of anisotropic polycrystals

Lebensohn

Tomé

1994

Materials Science and Engineering: A

280

114

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The plastic properties of anisotropic polycrystalline aggregates and polyphase materials are in general non-homogeneous and, as a consequence, so is the local plastic deformation. We present in this work a model that describes the plastic behaviour of non-homogeneous materials composed of anisotropic regions (grains or phases). Our model is based on describing each region as a viscoplastic inclusion embedded in the effective medium represented by the other grains, and incorporates explicitly the grain interaction with its surroundings and the plastic anisotropy of grain and matrix. Within the model the grain response is coupled to the overall response of the polycrystal and the grain deformation may differ from the polycrystars. A characteristic of our approach is that those deformation systems with lower critical resolved shear stress tend to be more active, and less than five systems per grain are sufficient to accommodate the imposed overall deformation.In this work we explore the consequences and the limits of the model, and its dependence on the assumed rate sensitivity as well. We combine the self-consistent formulation with a volume fraction transfer scheme for treating the reorientation due to twinning, and simulate rolling textures of brass (f.c.c.), Zircaloy (h.c.p.), calcite (trigonal) and uranium (orthorhombic). We compare the results with experimental measurements and Taylor-type predictions, infer information concerning the microscopic deformation mechanisms and discuss the limits of applicability of the approach.

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Section: Vpsc Formulationmentioning

confidence: 99%

A self-consistent viscoplastic model: prediction of rolling textures of anisotropic polycrystals

Lebensohn

Tomé

1994

Materials Science and Engineering: A

280

114

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“…The elastic distortion tensor β ji is in the following relationship [40] with the tensor of elastic stresses σ i j :…”

Section: Discussionmentioning

confidence: 99%

“…The plastic distortion β * l i j of the dislocation-disclination (semi)loop under consideration is given as [40] …”

Section: Discussionmentioning

confidence: 99%

“…With the above expressions for the plastic distortion β * i j of the ensemble of continuously distributed dislocation-disclination semiloops, let us calculate the stress field created by this ensemble. Following the general approach [40], the plastic distortion β * i j induces the displacement field given in its general form as…”

Section: Appendixmentioning

confidence: 99%

“…In the case of an isotropic medium, we have [40] C jlmn = λδ jl δ mn + µ(δ jm δ ln + δ jn δ lm ), (A.14)…”

Section: Appendixmentioning

confidence: 99%

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Nanoscale defect structures at crystal–glass interfaces

Bobylev

Ovid’ko

Романов

et al. 2005

J. Phys.: Condens. Matter

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A theoretical model of two-phase crystal-glass composite materials is suggested which is based on the disclination description of glassy structures. In the framework of the model, the crystal-glass composite is described as a solid that contains nanoscale configurations of disclination-dislocation loops in the glassy phase. Specific defects at the crystal-glass interface are defined and theoretically described which are misfit disclinations generated as extensions of parent wedge disclinations present in the glassy phase. In doing so, the defect ensemble in the crystal-glass composite is characterized by nanoscale inhomogeneities in both the defect density and stress in the vicinity of the crystal-glass interface. The formulae for the stress fields created by ensembles of the disclination-dislocation loops in crystal-glass composites are derived. With these formulae, the energy of the crystal-glass interface is estimated.

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Dislocation and point-force-based approach to the special Green's Function BEM for elliptic hole and crack problems in two dimensions

Denda

Kosaka

1997

Int. J. Numer. Meth. Engng.

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SUMMARYIn this paper we give the theoretical foundation for a dislocation and point-force-based approach to the special Green's function boundary element method and formulate, as an example, the special Green's function boundary element method for elliptic hole and crack problems. The crack is treated as a particular case of the elliptic hole. We adopt a physical interpretation of Somigliana's identity and formulate the boundary element method in terms of distributions of point forces and dislocation dipoles in the infinite domain with an elliptic hole. There is no need to model the hole by the boundary elements since the traction free boundary condition there for the point force and the dislocation dipole is automatically satisfied. The Green's functions are derived following the Muskhelishvili complex variable formalism and the boundary element method is formulated using complex variables. All the boundary integrals, including the formula for the stress intensity factor for the crack, are evaluated analytically to give a simple yet accurate special Green's function boundary element method. The numerical results obtained for the stress concentration and intensity factors are extremely accurate.1997 by John Wiley & Sons, Ltd.

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Micromechanics of defects in solids

Cited by 3,030 publications

References 399 publications

A self-consistent viscoplastic model: prediction of rolling textures of anisotropic polycrystals

A self-consistent viscoplastic model: prediction of rolling textures of anisotropic polycrystals

Nanoscale defect structures at crystal–glass interfaces

Dislocation and point-force-based approach to the special Green's Function BEM for elliptic hole and crack problems in two dimensions

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