Anisotropic continuum theory of lattice defects

Polysynthetically twinned crystals of TiAl with a nearly stoichiometric composition have been grown and deformed in compression at room temperature. The yield stress and deformation behaviour depend strongly on the angle between the twin boundaries and the compression axis rather than on the crystallographic orientation of the compression axis. The yield stress is high when compression is perpendicular or parallel to the twin boundaries, and is generally very low for specimens where the twin boundaries are at an intermediate angle to the compression axis. The ratio of the highest to the lowest values of yield stress is almost 8:1. This large difference in yield stress has been found to be related to the difference in the deformation mode; for compression perpendicular or parallel to the twin boundaries, shear deformation always occurs across them while, for compression at an intermediate angle, shear deformation is parallel to the boundaries. The former mode of deformation is much harder than the...

Deformation of polysynthetically twinned crystals of TiAl with a nearly stoichiometric composition

Using a formalism developed by Stroh (1962), a simple image force theorem for a dislocated anisotropic bicrystal is derived. An extension of the Stroh formalism, shows that the prelogarithmic energy factors depend only on the crystallographic directions of the dislocation line and its Burgers vector relative to each medium constituting the bicrystal. In addition, a formula is developed which allows one to obtain the prelogarithmic energy factor by simple numerical integration. A previous result of Dundurs and Sendeckyj (1965) for the net integrated tractions on any plane parallel to the interface of a dislocated bicrystal is extended to the anisotropic case. Finally, an intimate relation between dislocations moving parallel to the bicrystal interface and Stoneley waves in anisotropic bicrystals is developed.

http://iopscience.iop.org/article/10.1088/0305-4608/4/10/010/pdf

An image force theorem for dislocations in anisotropic bicrystals

The properties of linear defects in crystals (dislocation lines) and of planar defects (stacking faults) are important in almost every branch of solid state physics. This article is intended to give a comprehensive introduction to dislocation theory for the physicist who is not a specialist in crystal plasticity. It begins with a survey of the established theory relating to the geometrical and topological properties of dislocations, the elastic theory of dislocations in a continuum, the atomistic or core properties of dislocations, and the dynamics of moving dislocations. General methods for finding the elastic field of an arbitrary dislocation loop are outlined, and the results of some recent calculations using anisotropic elasticity are summarized. These include the prediction, partially confirmed by experiment, that dislocations in certain ranges of orientation may have negative line tension. The current importance of atomistic calculations of core structure and related problems is emphasized, and the methods available for these calculations are discussed. More detailed descriptions of dislocation and stacking fault configurations are given for some of the common crystal structures, and recent work on complex defects resulting from vacancy aggregation in close-packed structures is included. The experimental and theoretical evidence for the recent conclusion that screw dislocations in body-centred cubic metals have an asymmetric core is also reviewed. The rather controversial theory of thermally activated dislocation motion is described in a separate section, and examples are given of the application of this theory to various models of the obstacles encountered by moving dislocations. The final section is concerned with the theory of dislocations in grain boundaries and interphase boundaries, and includes the concept of the surface dislocation tensor.

https://iopscience.iop.org/article/10.1088/0034-4885/33/1/307/pdf

Dislocations and stacking faults

Nanostructuring of titanium-based implantable devices can provide them with superior mechanical properties and enhanced biocompatibity. An overview of advanced fabrication technologies of nanostructured, high strength, biocompatible Ti and shape memory Ni–Ti alloy for medical implants is given. Computational methods of nanostructure properties simulation and various approaches to the computational, “virtual” testing and numerical optimization of these materials are discussed. Applications of atomistic methods, continuum micromechanics and crystal plasticity as well as analytical models to the analysis of the reserves of the improvement of materials for medical implants are demonstrated. Examples of successful development of a nanomaterial-based medical implants are presented.

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Nanostructured titanium-based materials for medical implants: Modeling and development

Compatibility stresses have been calculated in the model of a bicrystal composed of two semi-infinite crystals. The elastic anisotropy of the component crystals is fully taken into account. Various particular cases chosen for the cubic bicrystals with the 〈100〉 and 〈110〉 rotation axes commonly used in experiments are discussed in detail. The effects of elastic and plastic deformation have also been compared. The model provides compatibility stresses as functions of grain boundary geometrical parameters and of the loading axis orientation.

Compatibility stresses in deformed bicrystals

The general expressions for the stress field of a dislocation situated near a welded, slipping and free boundary are derived employing the method of Fourier transformations. As an example the stress field of a screw dislocation near a simple type of welded boundary is explicitly given.

Dislocations in an inhomogeneous anisotropic medium

The bicrystal composed of two anisotropic half-spaces joined by a planar infinite boundary is uniaxially deformed in tension or compression. The additional elastic stresses due to the accommodation of elastic or plastic deformations differing in the both component crystals are calculated.

J. Gemperlová

Papers

Compatibility stresses in deformed bicrystals

Dislocations in an inhomogeneous anisotropic medium

Stresses in deformed cubic bicrystals with a tilt (001) grain boundary