V. Vitek

A theory of the anomalous yield behavior in L12 ordered alloys

It has been generally accepted that in many L12 ordered alloys the observed flow stress increase with increasing temperature is due to thermally activated cross slip from the (111) primary slip plane to the (010 cross slip plane. Using the results of recent atomistic studies of screw dislocations in L12 structures, a functional form for the activation enthalpy of cross slip of a 12 [101] (111) dislocation has been derived. This activation enthalpy is principally controlled by the following four phenomena: 1. (i) The difference in antiphase boundary energy on (111) and (010) planes 2. (ii) the resolved shear stress on (010) 3. (iii) the difference of the energy of the superpartial pair due to a stress induced compression or extention of the superpartial splitting before a jump and an equilibrium splitting afterwards 4. (iv) the nature of the core dissociation on {111} planes before and after the cross slip event, the so-called Escaig effect (i)-(ii) lead to a result that can be reduced to the form assumed by Takeuchi and Kuramoto [Acta metall. 21, 415 (1973)] but (iii) and (iv), which have not been included by Takeuchi and Kuramoto, predicts a tension/compression asymmetry of the CRSS that is also orientation dependent and is a prominent feature of the anomalous yield stress behavior. It is shown that recent experimental data can be explained by the model, and furthermore, the model predicts that a maximum tension/compression asymmetry will occur for orientations near [011], a result which has been tested in the following paper in this journal. A model for unpinning is also developed which explains the shape of the CRSS vs temperature curve of [111] oriented samples.

Simple N-body potentials for the noble metals and nickel

Abstract Using the approach of Finnis and Sinclair, N-body potentials for copper, silver, gold and nickel have been constructed. The total energy is regarded as consisting of a pair-potential part and a many body cohesive part. Both these parts are functions of the atomic separations only and are represented by cubic splines, fitted to various bulk properties. For the noble metals, the pair-potentials were fitted at short range to pressure-volume relationships calculated by Christensen and Heine so that interactions at separations smaller than that of the first-nearest neighbours can be treated in this scheme. Using these potentials, point defects, surfaces (including the surface reconstructions) and grain boundaries have been studied and satisfactory agreement with available experimental data has been found.

Plastic anisotropy in b.c.c. transition metals

The anisotropy of plasticity in b.c.c. metals is decomposed into two parts. The first, a variation of the Peierls stress with slip plane and sense of slip, is intrinsic to the b.c.c. structure and is reflected in the geometry of the screw dislocation core and of the generalized stacking fault energy ({gamma}) surface. The second part, a sensitivity of the Peierls stress to non-glide elements of the applied stress, is shown to be due to small edge fractional dislocation components in the screw dislocation core. These edge components and their change in response to non-glide applied stress can be explained by the characteristics of the {gamma}-surface. These concepts are illustrated by means of atomistic calculations, using Finnis-Sinclair interatomic force laws, for the b.c.c. transition elements of groups VB and VIB of the periodic table. Metals in the two groups are shown to fall into two classes of core structure and behavior; the contrasting properties can be explained in terms of the {gamma}-surfaces, and can be traced further to differences in the elastic constants.

The core structure of ½(111) screw dislocations in b.c.c. crystals

Abstract A relaxation-type calculation of the structure of the dislocation core has been made for the ½ 〈111〉 screw dislocation in b.c.c. crystals, using a variety of central-force potentials. Two stable configurations were found, corresponding to the centre of the dislocation being along either the left-hand or the right-hand type of three-fold screw axis in the crystal. These two configurations differed only in the very centre. For both configurations and for all potentials, the core structure possessed three-fold symmetry, the largest displacements being in the directions in which displacements on (211) type planes were in the twinning sense. The structure can be described by a combination of large displacements on {110} type planes, plus ‘stacking faults’, 1–2b wide on {211} type planes in the twinning sense only. An investigation of the effect of boundary conditions showed that any errors caused by incomplete relaxation were negligible, and that changing the initial dislocation position or the positi...

Structural defects in amorphous solids A computer simulation study

Abstract A definition of structural defects in amorphous solids in terms of the distribution of the internal stresses on the atomic level and of the symmetry of the environment of individual atoms is introduced. This definition does not require an ideal reference structure. The concept of the internal stresses on the atomic scale has been previously applied to describe the core structure of crystalline dislocations. In this paper it has been applied to the model amorphous structure generated by a computer simulation. It was found that there is a significant variation in the magnitude and direction of internal stresses, and that there are regions of 10 to 20 atoms over which the stresses remain either high or low. A method of calculating the symmetry coefficients at atomic sites has been proposed, and applied to the same system. It has been shown that there are significant correlations between the internal stresses and the local symmetry. The low-stress, high-symmetry regions resemble microcrystalline clus...

Dissociation and core structure of 〈110〉 screw dislocations in L12 ordered alloys I. Core structure in an unstressed crystal

Abstract The core structure of 〈110〉 screw dislocations in ordered alloys with the L12 structure has been studied using computer simulation techniques. Dislocations lying on both {111} arid {100} planes in stress-free crystals were studied using three different interatomic potentials corresponding to different antiphase boundary (ABP) and complex stacking fault (CSF) energies on {111} planes. The superlattice intrinsic stacking fault (SISF) energy on {111} planes was held constant in all calculations. When the APB energy is not too high, the dislocation dissociates on the {111} plane into two ½〈110〉 superpartials separated by APS. The cores of the superpartials are planar and similar to those of dislocations in f.c.c. materials. When the APB energy is high, the dislocation dissociates on {111} into two ⅓〈112〉 superpartials separated by SISF, the cores of which can be highly non-planar. On {100} planes the dislocation always dissociates into two ½〈110〉 superpartials, the cores of which are non-planar, spre...

Structural defects in amorphous solids Statistical analysis of a computer model

Abstract The possibility of defining structural defects in amorphous solids in terms of parameters such as atomic-level internal stresses and local symmetry coefficients was proposed in a previous paper (Egami, Maeda and Vitek 1980). Using a model amorphous structure generated by a computer, these parameters are statistically analysed in the present paper. It is shown that the stress and the symmetry coefficients are closely correlated and that spatial correlations of various kinds exist. The structural defects are then defined as regions in which the corresponding characterizing parameter deviates significantly from its average value. Two distinct classes of defects were found; (i) positive (p-type defects) and negative (n-type defects) local density fluctuations; and (ii) regions of large shear stresses and large deviations from spherical symmetry. Defects consisting of pairs of p-type and n-type defects separated by regions of large shear stresses are also common. The effect of annihilation of p- and n...

An atomistic study of deformation of amorphous metals

Abstract The computer simulation of a shear deformation of a model monoatomic amorphous metal has been performed. The strain was applied incrementally, relaxing the structure at each step. The complete stress-strain curve was thus obtained. A large number of microscopic deformation events have been observed and analyzed using the description of the local atomic structure by the atomic level stresses. Although no temperature effects have been included in the present study the calculated stress-strain curve is in very good agreement with the stress-strain curves measured experimentally at or above room temperature. The common feature of these experiments and present calculations is, however, the homogeneity of the deformation. Hence, it is argued that fundamental microscopic deformation mechanisms are the same at low and high temperatures and the macroscopic differences arise owing to the strain localization in the former case. The regions of inhomogeneous atomic movement which results in plastic deformation, have not been found to be correlated with local density fluctuations in contrast with assumptions of the models based on free volume theory. They are, however, correlated with regions of high shear stresses, called τ-defects. These defects are formed during the deformation, are sustained by the applied stress and appear to act as stress concentrators in the vicinity of which a localized viscous flow develops.

The asymmetry of the flow stress in Ni3(Al,Ta) single crystals

Abstract Flow stress measurements were performed on single crystalline Ni 3 (Al, Ta) as a function of temperature, orientation, strain rate and sense of the applied uniaxial stress to check the predictions of the Paidar et al. model [ Acta metall. 32 , 435 (1984)]. It was found that the critical resolved shear stress (CRSS) for (111)[101] slip depends not only on the test temperature and orientation of the samples, as other investigators have previously observed, but also on the sense of the applied stress. The orientation dependence of the tension/compression asymmetry, including the regions where the asymmetry is a maximum (positive), a minimum, and where it disappears, is as predicted by the model. The applied stress changes the activation enthalpy of cross slip primarily through its effect on constricting the Shockley partials during cross slip and only secondarily on directly promoting (111) to (010) cross slip. A maximum attainable CRSS for (111)[101] slip, the saturation stress, is also in agreement with the model. It was also found that the CRSS for (111)[101] slip is strain rate independent, but the CRSS for (001)[101] slip shows a strong positive strain rate dependence. The temperature at which the peak in the flow stress vs temperature curve occurs increases with increasing strain rate and decreases with increasing ratio of RSS on (001)[110] divided by that on (111)[101]. When the deformation occurs by (001)[110] slip the stress-strain curve exhibits clearly defined, continuous yield points.

A microscopic theory of brittle fracture in deformable solids: A relation between ideal work to fracture and plastic work

A criterion is developed for brittle fracture of a crystalline solid which is capable of being plastically deformed. The theory starts with the experimental fact that during extension of a brittle crack, energy is consumed not only by bond stretching and breaking, but also by dislocation emission from the crack tip. The latter is the “plastic work”. γp, which in the present theory depends on the ideal work of fracture. An empirical relationship between stress and dislocation velocity is employed to calculate the work connected with dislocation emission; then an approximation of the dynamics of bond stretching is made. Combination of the two allows the development of a Griffith-type thermodynamic fracture criterion which is applicable to any deformable solid. This theory contains all the basic features of ductile vs brittle behavior of solids, regardless of whether the brittle mode is transgranular cleavage or intergranular fracture. As a consequence, a relationship between γp and γ is obtained which enables one to estimate γ from measurements of local fracture stress. The use of this is illustrated in the form of estimates of reductions in γ due to segregation of several impurities, calculated from measured local integranular fracture stresses in experimental steels.