Internal Elastic Fields Research Articles

Uniform in‐plane elastic field inside a monoclinic elliptical inhomogeneity with non‐confocal elliptical interphase layer

We employ the Stroh quartic formalism to study the in-plane deformations of a three-phase composite consisting of an elliptical inhomogeneity embedded in an infinite matrix via an intermediate interphase layer itself bounded by two elliptical boundaries. The matrix is subjected to uniform remote in-plane loading. The two corresponding elliptical interfaces (one between the inhomogeneity and the interphase layer and the other between the interphase layer and the surrounding matrix) are non-confocal. The inhomogeneity and the matrix are assumed to be monoclinic materials with the symmetry plane at x3 = 0 whilst the intermediate interphase layer is composed of a mathematically degenerate orthotropic material. The non-confocal character of the two elliptical interfaces is carefully designed according to the orthotropic property of the interphase layer. Two simple conditions are found that ensure that the internal elastic field of stresses and strains inside the elliptical inhomogeneity is uniform. For given material and geometric parameters of the composite, these two conditions give two simple relationships among the three remote in-plane stresses. In addition, the internal uniform elastic field inside the elliptical inhomogeneity and the non-uniform elastic field in the interphase layer are determined in real-form in terms of the two 4 × 4 fundamental elasticity matrices for the inhomogeneity and the matrix and the three 2 × 2 Barnett-Lothe tensors for (only) the matrix.

New Method for Calculation of Radiation Defect Dipole Tensor and Its Application to Di-Interstitials in Copper

The effect of external and internal elastic strain fields on the anisotropic diffusion of radiation defects (RDs) can be taken into account if one knows the dipole tensor of saddle-point configurations of the diffusing RDs. It is usually calculated by molecular statics, since the insufficient accuracy of the available experimental techniques makes determining it experimentally difficult. However, for an RD with multiple crystallographically non-equivalent metastable and saddle-point configurations (as in the case of di-interstitials), the problem becomes practically unsolvable due to its complexity. In this paper, we used a different approach to solving this problem. The molecular dynamics (MD) method was used to calculate the strain dependences of the RD diffusion tensor for various types of strain states. These dependences were used to determine the dipole tensor of the effective RD saddle-point configuration, which takes into account the contributions of all real saddle-point configurations. The proposed approach was used for studying the diffusion characteristics of RDs, such as di-interstitials in FCC copper (used in plasma-facing components of fusion reactors under development). The effect of the external elastic field on the MD-calculated normalized diffusion tensor (ratio of the diffusion tensor to a third of its trace) of di-interstitials was fully consistent with analytical predictions based on the kinetic theory, the parameters of which were the components of the dipole tensors, including the range of non-linear dependence of the diffusion tensor on strains. The results obtained allowed for one to simulate the anisotropic diffusion of di-interstitials in external and internal elastic fields, and to take into account the contribution of di-interstitials to the radiation deformation of crystals. This contribution can be significant, as MD data on the primary radiation damage in copper shows that ~20% of self-interstitial atoms produced by cascades of atomic collisions are combined into di-interstitials.

Вплив механічної обробки поверхні на діелектричні та фотодіелектричні властивості кристалів AIIBVI

The subject matter of the study is the dielectric and photodielectric properties of AIIBVI crystals of composition ZnSe and Cd1-хZnхTe, which are grown from the melt, and the structural defects and internal elastic fields associated with these properties. The goal of the article is to study the patterns of influence of surface machining by grinding, polishing, and local loading on the defective structure in the deformation region, and thus on the dielectric and photodielectric properties of AIIBVI crystals of this composition, which is important given the use of these crystals in aerospace engineering. The tasks to be solved are: to investigate the regularities of the influence of grinding, polishing, and local deformation of the chipped surface of ZnSe and Cd1-хZnхTe samples on their defective structure, dielectric and photodielectric properties, including irreversible changes in properties. The problems were solved by the following methods: dielectric and photodielectric properties of crystals were investigated by the capacitive method; scanning photodielectric spectroscopy was used to measure the photoionization energies of localized states of charge carriers in crystals; the distribution of residual elastic stresses in the samples was studied by the polarization-optical method. The following results were obtained. Grinding and polishing cause the transformation of own and impurity maxima of the spectral dependences of the dielectric parameters of AIIBVI crystals, has a characteristic effect on the coordinate dependences of the dielectric parameters of crystals Cd1-хZnхTe. This is due to the transformation of localized states of carriers, which is confirmed by the study of ZnSe crystals. Concentrated deformation of Cd1-хZnхTe crystals significantly affects their dielectric properties, in particular, causes relaxation of dielectric parameters. Conclusions. Mechanical surface treatment of AIIBVI crystals by grinding and polishing, as well as local mechanical loading of Cd1-хZnхTe samples significantly affect their dielectric and photodielectric properties, which is associated with the formation of a system of defects and internal elastic fields in the deformation regions. An explanation of the observed effects is given.

ДИФФУЗИОННОЕ ЗАРОЖДЕНИЕ ПОР В СТЫКАХ ЗЕРЕН СУБМИКРОКРИСТАЛЛИЧЕСКИХ МАТЕРИАЛОВ

The conditions of diffusional cavity nucleation in submicrocrystalline materials processed by the methods of intensive plastic deformation (equal-channel angular pressing, multiaxial forging, high pressure torsion, etc.) are analyzed. To date, the question of the mechanism of nucleation of cavities in such materials remains debatable due to the fact that the processing of materials by the methods of intensive plastic deformation is carried out at high hydrostatic pressures that prevent the appearance of pores. The possibility of diffusive nucleation of nanopores in the region of triple junctions of grains containing negative strain-induced wedge disclinations, generating high tensile stresses in the vicinity of triple junctions, comparable in magnitude to external hydrostatic pressure, is shown. Such junction disclinations inevitably occur at the grain junctions due to the heterogeneity of the plastic deformation through the ensemble of polycrystal grains. It is shown that an important condition for the nucleation of cavities is not only the presence of high internal tensile stresses from junction disclinations, but also an extremely high concentration of nonequilibrium strain-induced vacancies characteristic of submicrocrystalline metals, comparable in values to the vacancy concentration, at temperatures close to solidus. The influence of the strength of junction disclinations, the value of external hydrostatic pressure and the degree of supersaturation of the material by nonequilibriumstrain-induced vacancies on the rate of diffusional nucleation and the volume of critical pore nuclei is analyzed. It is established that in order to effectively suppress the process of pore formation in the grain boundary triple junctions, it is necessary to apply an external hydrostatic pressure that compensates for internal elastic fields from junction disclinations.

Boundary Element Calculation of Near-Boundary Solutions in 3D Generally Anisotropic Solids by the Self-Regularization Scheme

AbstractThis research targets investigation of the internal elastic field near the boundaries of 3D anisotropic bodies by the boundary element method (BEM). This analysis appears to be most important, especially for the interest in the internal solutions near corners or crack tips, where structural failure is most likely to occur. Although the BEM is very efficient for analyzing the problem, nearly singular integration will arise when the internal point of interest stays near the boundary. The present work is to show how the self-regularized boundary integral equation (BIE) can be applied to the interior analysis for 3D generally anisotropic bodies. So far, to the authors' best knowledge, no implementation work has been reported in the literature for successfully treating the near boundary solutions in 3D generally anisotropic solids. In the end, a few benchmark examples are presented to demonstrate the veracity of the present approach for the interior BEM analysis of 3D anisotropic elasticity.

Influence of the twin microstructure on the mechanical properties in magnetic shape memory alloys

The microstructure evolution, i.e. reorientation of martensite variants, is an important deformation mechanism in shape-memory alloys. This microstructure evolution occurs by the motion of twin boundaries and the nucleation and annihilation of twins in the hierarchical microstructure. An appropriate discrete disclination model for the description of the internal elastic fields and microstructure evolution is introduced for representative volume elements. The model is applied to an experimentally characterized microstructure, i.e. conjugation boundary, and the predicted mechanical response is verified by comparison to experimental measurements. The influence of the twin microstructure on the homogenized stress-strain curve is studied. It is found that regular twinned microstructures have a low strain energy and a high resistance against deformation. These simulations also reason the origin of the microstructural stability of conjugation boundaries.

An arbitrarily shaped inclusion with uniform eigencurvatures in an infinite plate, semi-infinite plate, two bonded semi-infinite plates or a circular plate

Within the framework of the Kirchhoff–Love isotropic and homogeneous plate theory, we obtain, in a unified manner, the analytic solutions to the Eshelby’s problem of an inclusion of arbitrary shape with uniform eigencurvatures in an infinite plate, a semi-infinite plate, one of two bonded semi-infinite plates or a circular plate by means of conformal mapping and analytical continuation. The edge of the semi-infinite plate can be rigidly clamped, free or simply supported, while that of the circular plate can be rigidly clamped, free or perfectly bonded to the surrounding infinite plate. Several examples of practical and theoretical interests are presented to demonstrate the general method. In particular, the elementary expressions of the internal elastic fields of bending moments and deflections within an (n + 1)-fold rotational symmetric inclusion described by a five-term mapping function, a symmetric airfoil cusp inclusion, a symmetric lip cusp inclusion and an inclusion described by a rational mapping function in an infinite plate are derived.

AN INCLUSION OF ARBITRARY SHAPE IN AN INFINITE OR SEMI-INFINITE ISOTROPIC MULTILAYERED PLATE

This paper proposes a simple method based on analytical continuation and conformal mapping to obtain an analytic solution for a two-dimensional arbitrarily shaped Eshelby inclusion with uniform main plane eigenstrains and eigencurvatures in an infinite or semi-infinite isotropic laminated plate. The main plane of the plate is chosen in such a way that the in-plane displacements and out-of-plane deflection on the main plane are decoupled in the equilibrium equations. Consequently, the complex potential formalism for the isotropic laminate can be readily and elegantly established. One remarkable feature of the present method is that simple elementary expressions can be obtained for the internal elastic field within the inclusion of any shape in an infinite laminated plate. Several examples are presented to illustrate the general method.

Elastic Distortion of Dislocations in Deforming FCC Crystals

ABSTRACTA computational technique is developed to predict the statistics of internal elastic fields of three-dimensional dislocation systems in deforming crystals. The internal elastic fields are computed based on 3D dislocation realizations generated by the method of dislocation dynamics simulation. Preliminary results are presented for the statistical characteristics of the elastic strain, lattice rotation and dislocation density tensor fields. The importance of the current analysis is discussed in the context of direct comparison of simulations with spatially resolved 3D X-ray microscopy measurements of lattice rotation and the dislocation density tensor.

Kinetics of self-interstitial cluster aggregation near dislocations and their influence on hardening

Kinetic Monte Carlo (KMC) computer simulations are performed to determine the kinetics of SIA cluster ‘clouds’ in the vicinity of edge dislocations. The simulations include elastic interactions amongst SIA clusters, and between clusters and dislocations. Results of KMC simulations that describe the formation of ‘SIA clouds’ during neutron irradiation of bcc Fe and the corresponding evolution kinetics are presented, and the size and spatial distribution of SIA clusters in the cloud region are studied for a variety of neutron displacement damage dose levels. We then investigate the collective spatio-temporal dynamics of SIA clusters in the presence of internal elastic fields generated by static and mobile dislocations. The main features of the investigations are: (1) determination of the kinetics and spatial extent of defect clouds near static dislocations; (2) assessment of the influence of localized patches of SIA clouds on the pinning–depinning motion of dislocations in irradiated materials; and (3) estimation of the radiation hardening effects of SIA clusters. The critical stress to unlock dislocations from self-interstitial atom (SIA) cluster atmospheres and the reduced dislocation mobility associated with cluster drag by gliding dislocations are determined.

On the elastic boundary value problem of dislocations in bounded crystals

A new formulation of the elastic boundary value problem of dislocations in bounded crystals is developed. This formulation is based on the ansatz that the stress field of dislocations in bounded domains can be constructed as the sum of a contribution corresponding to the classical infinite-domain solution plus a correction that is determined here from a mathematically well posed problem. The formulation of the elastic boundary value problem given here ensures that the equilibrium of the overall stress field is rigorously satisfied, specifically when dislocations intersect the boundary. The implications of this new formalism for dislocation dynamics simulation are discussed for the cases of bounded crystals and crystal volumes representative of uniformly loaded infinite crystals. An approximate computational solution of the elastic boundary value problem is presented based on the concept of virtual dislocations and the use of a non-singular form of the infinite-domain solution of the dislocation stress field. This computational solution addresses the issues of singularity and global equilibrium of the boundary traction associated with the corrective field. Sample results are presented for the internal stress in bounded crystals containing 3D dislocation configurations produced using the dislocation dynamics simulation method. The results illustrate the statistical character of the internal elastic field.

Elastic instability condition of the raft structure during creep deformation in nickel-base superalloys

A condition for destabilizing the raft structure has been deduced from elastic energy calculations with the concept of “effective eigenstrain”, where the effect of creep deformation is included in addition to the lattice mismatch. The calculations indicate that the 0 0 1 raft structure is stabilized by a small amount of creep deformation but becomes unstable when the creep strain in the γ phase exceeds the magnitude required to fully relax the lattice mismatch. The excess creep strain is required to produce an internal elastic field that suppresses further creep deformation, and has to be introduced in the primary creep stage. Via the instability of the 0 0 1 raft structure, the raft structure gradually turns into a wavy one in the second creep stage before its collapse.

Statistics of Internal Elastic Fields and Dislocation Density Tensor in Deformed FCC Crystals

ABSTRACTThe statistics of internal elastic fields and dislocation density tensor associated with arbitrary 3D dislocation distributions have been modeled using probability density function and pair correlations. Numerical results for these quantities have been obtained for dislocation structures generated by the method of dislocation dynamics simulation.

Internal fields and other contributions to flow stress

In this paper the generalization of the results on the experimentally measured elastic dislocation resistance contribution to flow stress of a number of f.c.c. alloys at formation in defect subsystems of different substructures was carried out. The method of study was the transmission electron diffraction microscopy on thin foils. The validity of a familiar theoretical relation for the internal elastic field was confirmed: τ e = α e μbϱ 1/2. The α e coefficient values of elastic field of dislocation ensemble calculated theoretically and obtained experimentally were compared. The experiment showed that dislocation structures in Cu, Ni and Fe based alloys are characterized by the well correlated dislocation arrangement resulted in screening of the internal elastic field.