Screw dislocation pileups in a two-phase thin film

The method of continuously distributed dislocations is used to study the distribution of screw dislocations in a linear array piled up near the interface of a two-phase isotropic elastic thin film with equal thickness in each phase. The resulting singular integral equation is solved numerically using the Gauss–Chebyshev integration formula to arrive at the dislocation distribution function and the number of dislocations in the pileup.

Parameter identification of crack-like notches in aluminum plates based on strain gauge data

The identification of crack parameters and stress intensity factors in aluminum plates under tensile loading is in the focus of the presented research. In this regard, data of strain gauges, distributed along the edges of the samples, are interpreted. In the experiments, slit-shaped notches take the role of cracks located in the interior of the specimens. Their positions, inclinations and lengths as well as the magnitudes of external loadings are identified solving the inverse problems of cracked plates and associated strain fields. Exploiting the powerful approach of distributed dislocations, based on Green’s functions provided by the framework of linear elasticity, in conjunction with a genetic algorithm, allows for a very efficient identification of the sought parameters, thus being suitable for in situ monitoring of engineering structures. Tested samples exhibit one or two straight crack-like notches as well as a kinked one.

Influence of Distributed Dislocations on Stability of Hollow Nonlinearly Elastic Sphere

The phenomenon of stability loss of a hollow elastic sphere containing distributed dislocations and loaded with external hydrostatic pressure is studied. The study was carried out in the framework of the nonlinear elasticity theory and the continuum theory of continuously distributed dislocations. An exact statement and solution of the stability problem for a three-dimensional elastic body with distributed dislocations are given. The static problem of nonlinear elasticity theory for a body with distributed dislocations is reduced to a system of equations consisting of equilibrium equations, incompatibility equations with a given dislocation density tensor, and constitutive equations of the material. The unperturbed state is caused by external pressure and a spherically symmet-ric distribution of dislocations. For distributed edge dislocations in the framework of a harmonic (semi-linear) mate-rial model, the unperturbed state is defined as an exact spherically symmetric solution to a nonlinear boundary value problem. This solution is valid for any function that characterizes the density of edge dislocations. The perturbed equilibrium state is described by a boundary value problem linearized in the neighborhood of the equilibrium. The analysis of the axisymmetric buckling of the sphere was performed using the bifurcation method. It consists in determining the equilibrium positions of an elastic body, which differ little from the unperturbed state. By solving the linearized problem, the value of the external pressure at which the sphere first loses stability is found. The effect of dislocations on the buckling of thin and thick spherical shells is analyzed.

The effect of distributed dislocations on bending of a rectangular beam with a preliminarily stressed layer under superposition of large strains

The formulation of problems on the equilibrium of a nonlinearly elastic solid with continuously distributed dislocations is proposed for the case of superposition of large strains. The numerical results showing the effect of distributed dislocations on the stress-strain state of the beam are presented.