Temperature dependence of the mechanical properties of equiatomic solid solution alloys with face-centered cubic crystal structures

The origin of the Peierls model and its relation to that of Frenkel and Kontorova are described. Within this model there are three essentially different formulae for the stress required to move a dislocation rigidly through a perfect lattice, associated with the names of Peierls, Nabarro and Huntington. There are also three distinct approaches to experimental estimates of the Peierls stress, depending on the Bordoni internal friction peak, the flow stress at low temperatures and Harper-Dorn creep. The results in the case of close-packed metals can be reconciled with the aid of ideas due to Benoit et al. and to Schoeck. The analytical elegance of Peierls's solution depends on the assumption of a sinusoidal law of force across the glide plane. This is physically unrealistic. Foreman et al. and others have obtained interesting results using other laws of force, while still operating in the framework of the Peierls model. The locking-unlocking model extends the ideas to the case in which the dislocation core has two mechanically stable configurations.

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Fifty-year study of the Peierls-Nabarro stress

Experimental evaluation of the Peierls stresses in a variety of crystals and their relation to the crystal structure

It is a long outstanding question whether or not the Peierls stress for a given slip system of a crystal can be quantitatively determined. This paper concerns the prediction of this stress for a wide range of crystals, using a new theoretical Peierls stress equation. It is shown that the prediction is in reasonable agreement with experimental data. Comparison with atomistic calculations illustrates that the accuracy of the prediction may degenerate greatly in the cases where the spreading of the dislocation core is non-planar and the application of an external stress changes the core structure significantly. It is suggested that the magnitude of the Peierls stress is determined primarily by the geometrical configuration of the dislocation core.

Prediction of Peierls stresses for different crystals

This article describes a new computation-based approach for designing ductile Nb-Ti-Cr-Al solid-solution alloys. The proposed approach is based on computation of the surface energy and the Peierls-Nabarro (P-N) barrier energy as a function of alloy composition. The surface energy is used as a measure of the resistance to cleavage fracture, while the P-N barrier energy is used as a measure of dislocation mobility. The ratio of the surface energy to the P-N barrier energy is utilized as a material index which can be adjusted by alloying additions. Analytical relations are developed for computing (1) the elastic constants in terms of the d+s electrons per atom in the alloys and (2) the lattice parameter, surface energy, and P-N barrier energy in terms of alloy composition. Design of a ductile solid-solution alloy is achieved by manipulating the number of d+s electrons, through alloying additions, to obtain a high value of the ratio of the surface energy to P-N barrier energy by reducing the misfit energy of the dislocation core. Applications of the methodology to designing binary, ternary, and quaternary Nb-based solid-solution alloys with Ti, Cr, and Al alloying additions are illustrated with promising results, demonstrating that the proposed methodology is a viable approach for alloy design.

A computational approach to designing ductile Nb-Ti-Cr-Al solid-solution alloys

The Peierls stress is calculated for a discrete Peierls—Nabarro model of a dislocation. Unlike the original continuum model where a continuous distribution of infinitesimal dislocations was considered, the discreteness of the slip plane is maintained throughout the calculation, and the Peierls stress τp is determined as the critical applied stress beyond which the stability of the system breaks. Results for three types of interatomic shear potential are well approximated by the relation τp G∞ exp(−Ah/b), as predicted by the continuum model, G being the shear modulus, b the spacing between slip planes, b the length of the Burgers vector and A a constant depending on the potentials. The magnitude of τp of the discrete model is larger than that of the continuum model for the same sinusoidal potential. Long-range potentials give low τp although they are still larger than experimental values.

H. Koizumi

Papers

The critical stress in a discrete Peierls–Nabarro model