Periodic arrays of partial grain boundary dislocations in a f.c.c. alloy

It is shown that periodic arrays of partial GBDs as well as GBDs with DSC Burgers vectors occur as components of the secondary GBD network in a near ∑ boundary in a f.c.c. Cu-Si alloy. The periodic arrays of partial GBDs separate two different states of translation between the grains which repeat with the periodicity of the network. Matching of theroretical and experimental electron micrographs, together with the determined geometry of the network, are used to identify the Burgers vectors of the GBDs. The results show that the difference between the two translation states is predominantly a relative displacement between the grains normal to the boundary of approximately 0.023 nm.     

The fine structure f.c.c./b.c.c. boundaries in a Cu-0.3% Cr alloy

The interfacial structures of overaged b.c.c. precipitates in a Cu-0.3%Cr alloy have been studied with transmission electron microscopy using weak-beam and lattice imaging techniques and the results have been compared with theoretical structures obtained with the “O”-lattice calculation. Lattice imaging showed that one set of close-packed planes in the structures were accurately parallel and using normal diffraction and Kikuchi line measurements the precipitates were observed to have a range of orientation relationships varying from Nishiyama-Wasserman to Kurdjumov-Sachs and beyond. All precipitates showed at least one fine dislocation array with spacings < 2.5 nm and several examples of arrays with two sets of dislocations were also observed. For three precipitates investigated in detail reasonably good agreement between the theoretical and observed values of the spacings, directions of dislocations and overall habit planes of the interfaces was obtained. Confirmation of the (533)_f.c.c. habit plane of the lath precipitate was also obtained.     

Kinetic path for a relaxation process of an f.c.c. disordered phase

Tetrahedron approximation of the Cluster Variation Method and the Path Probability Method are employed for an f.c.c. disordered system, and the time evolution of spin configuration, which is regarded as the first approximation to an alloy system, is investigated. The convergent values at infinite time exactly coincides with the cluster probabilities independently obtained by the Cluster Variation Method for thermal equilibrium system. Furthermore, the kinetic path is placed on the thermodynamic configurational space spanned by correlation functions.     

Structural bonding contributions and the elastic response of b.c.c. and f.c.c. crystals

The anisotropic elastic response of body centered cubic (b.c.c.) and face centered cubic (f.c.c.) crystals is reviewed within the framework of general elasticity and particular model dependent relations. It is found that important trends in the observed behavior of specific groups of crystals can be reproduced by models that include only structural contributions to crystal binding. In fact, a very simple model, consisting of only nearest and next nearest neighbor interactions, reproduces the salient behavior, including the algebraic signs of Poisson's ratio and the orderings of the shear moduli, Young's moduli, and Poisson's ratios associated with major crystallographic symmetries. The analysis provides insight into the differences between the b.c.c. transition metals and the b.c.c. alkali metals.     

Dislocation dissociation in some f.c.c. metals

The dissociation of a perfect screw dislocation into a stacking fault in an f.c.c. lattice is modeled by the modified lattice statics. The interatomic potentials are obtained from the work of Esterling and Swaroop and differ substantially from those empirical potentials usually employed in defect simulations. The calculated stacking fault widths for aluminum, copper, and silver are in good agreement with weak beam microscopy results.     

Relationship between rolling textures and shear textures in f.c.c. and b.c.c. metals

The rolling and shear textures of aluminium (f.c.c.) and Fe-16% Cr (b.c.c.) have been compared. First a 90° rotation relationship about the transverse direction was found experimentally between the stable orientations of the rolling textures and the shear textures. This was explained with the symmetry of the glide systems and the orientation relationship between both coordinate systems. Second for both kinds of deformation namely rolling and shear a 90° rotation relationship about the transverse direction was also found between the stable b.c.c. and f.c.c. orientations. This was explained with the Taylor theory and the Sachs model making use of the orientation relationship between f.c.c. and b.c.c. glide systems.     

A quantitative assessment of forest-hardening in f.c.c. metals

Macroplastic deformation results from the long-distance movement of dislocations. In singlephase crystals it implies cutting the dislocation forest traversing the slip plane of the running dislocations and, as a consequence of the non-regular distribution of the “trees”, dislocation loops are left around the harder islands in their slip planes. The dislocation length so stored represents an increment of the obstacle density already present in other non-coplanar slip systems and thus contributes to their work-hardening. This work presents quantitative results on the contribution by forest cutting in a f.c.c. metal upon flow stress and work hardening rate. It has been obtained by computer simulation of dislocation glide through a mixture of punctual and linear obstacles whose strengths reproduce approximately the strength spectrum of a f.c.c. forest as derived by Shoeck and Frydman. Simulations have been conducted for random arrays of obstacles and for more realistic spatial dislocation distributions (cells, subgrains). Both the flow stress (and its temperature and strain rate dependence) and the athermal work-hardening rate so obtained are in good agreement with those measured for f.c.c. polycrystals in experiments covering up to large strains.     

Ground state of f.c.c. alloys with multiatom interactions

The ground state of a binary f.c.c. alloy with nearest neighbor interactions and tetrahedral multiatom interactions (characterized by two parameters α and β) is derived and presented in a chart which shows classification of phases in the space of α and β. Where non-stoichiomctric phases can occur, the phase boundaries at T = 0 are computed using the tetra̧hedron approximation of the cluster variation method. Duality of the composition and the chemical potential is emphasized and results are presented and/or interpreted in the dual approaches.     

An explanation of labyrinth walls in fatigued f.c.c. metals

The occurrence of labyrinth dipolar walls in fatigued f.c.c. metals is explained as resulting from double pseudo-polygonization (DPP) arrangements of dipole loops essentially edge in character. From the orientations of the edge dislocations of two Burgers vectors on any two slip systems, a three-dimensional regular stacking network of dipole loops can be constructed from which a dipolar wall is obtained by restricting stacking in one of two directions, since the third possible stacking direction appears to be mechanistically favoured. The experimentally demonstrated {100} and {210} walls are shown to be obtained from the same dipole networks. Some experimental evidence also exists suggesting the presence of geometrically predicted {110}, {111} and {211} and/or {311} DPP walls. The present model for f.c.c. metals explains the main aspects of the existing experimental evidence on the orientations of labyrinth walls and also appears to explain that on walls produced at intersections of persistent slip bands. Apparent rotations of simple polygonization {100} walls and the occasional presence of dipolar walls along persistent slip band interfaces can also be rationalized by this model.     

Grain reorientation during the plastic deformation of f.c.c. metals

The theory of Renouard and Wintenberger, which can be used to remove the ambiguities inherent in the Taylor and Bishop and Hill theories of polycrystal deformation, is reviewed in detail and reformulated in a more convenient notation. This theory is based on the minimization of the texture based component of the macroscopic work hardening rate. It is employed to predict the rotation of

• 1.(i) single crystals deformed in pure plane strain compression under conditions of full constraint;
• 2.(ii) extremely coarse grained multicrystals deformed in rolling, for which relaxed constraint conditions apply.

For each of these cases, the extent of the possible ambiguities is specified. The RW predictions are compared with the experimental results of Driver and coworkers, as well as with the predictions obtained from the classical BH theory modified so as to resolve the ambiguity problem by means of averaging or a rate sensitive approach. It is shown that in the case of fully constrained deformation, the RW theory gives results which are in better agreement with the experimental observations than either the averaging or rate sensitive methods. By contrast, in the case of deformation under relaxed constraints, the extent of the ambiguities is so limited that the techniques being compared generally give similar results. An exception concerns nearly symmetric orientations, for which the averaging technique is the only one that predicts the small rotations observed experimentally. This is interpreted to signify that the deformation of symmetrically oriented crystals is likely to involve the concurrent operation of 6 or 8 slip systems, instead of three, four or five.     

On the origin of planar slip in f.c.c. alloys

The origin of planar slip in single-phase and precipitation-hardened f.c.c. alloys is discussed in detail. It is shown that pronounced short range order (SRO) or short range clustering (SRC) in solid solutions are the main reasons causing planar slip. Since the leading dislocations destroy SRO (SRC), glide plane softening occurs; therefore, a yield point or a point of inflection is observed on the stress-strain curve. In precipitation-hardened alloys finely dispersed particles with an atomic order also give rise to planar slip. Distinct planar slip occurs when cross slip is planar too. Other parameters, like a low value of the stacking fault energy or a high value of the yield stress, seem to be only of minor importance for the formation of pronounced planar slip.     

Influence of f.c.c. rolling textures on biaxial sheet stretching

The behaviour of sheet metals initially having f.c.c. rolling textures is simulated under biaxial stretching conditions. A rate-sensitive crystal plasticity model together with the full-constraint Taylor theory is used. Closed-form analytical solutions for the stress states, slip distributions and lattice spins are obtained for the ideal orientations of f.c.c. rolling textures. The three-dimensional lattice rotation fields at these ideal orientations, and their evolution paths in Euler space, are predicted for various biaxial stretching ratios. Similar simulations are also carried out for polycrystalline textures. It is shown that, for a copper-type initial texture (the β-fibre) and a strain ratio ϱ < 0.5, the corresponding biaxial-stretching texture will not be much different from the initial texture. However, for ϱ > 0.5 the β-fibre deteriorates and the α-fibre increases relatively quickly. If the initial texture is the R-recrystallization texture (cube + S₁), the main component of the simulated biaxial-stretching textures is the fibre near β for ϱ < 0.5, but the α-fibre for ϱ > 0.5. The simulated equibiaxial-stretching texture is an agreement with the published measured textures for aluminum sheets.     

Kinetics of f.c.c. deformation twinning and its relationship to stress-strain behaviour

The kinetics of f.c.c. deformation twinning,i.e. the amount of twins vs applied strain were determined by quantitative microscopy at various temperatures in a Co-33Ni alloy. The kinetic curve has a quite parabolic shape and approaches saturation below 50% transformation; however twinning occurs only after a critical strain which is an increasing function of temperature. Assuming that f.c.c. twins nucleate from perfect slip dislocations as proposed by Mahajan and Chin, the volume fraction of twins can be expressed as an implicit function of strain. The approach to saturation is described by two parameters which are temperature dependent through the temperature variation of stacking fault energy. Good agreement with experimental results was obtained.An increase of the flow stress was observed at temperatures where twinning plays an important role in the deformation as compared to slip. This extra contribution is experimentally observed to vary as the inverse of the mean size of matrix cells between neighbouring twins. This dependence has been attributed to the fact that twins can act as strong obstacles to dislocation propagation.     

On a proposed theory for the disappearance of serrated flow in f.c.c. Ni alloys

The disappearance of serrated flow was investigated for Inconel 718 and 600. The activation energy for the disappearance was found to be 2.7 eV for both alloys. It is proposed that the mechanism leading to the disappearance of serrated flow is a reaction occurring between carbide-forming substitutional atoms and carbon atmospheres which are forming on the arrested dislocations. This leads to the subsequent depletion of atmospheres and formation of finely dispersed carbides along dislocation lines and to the disappearance of serrated flow. The rate controlling step for the process is the rate of diffusion of the substitutional carbide-forming species to the arrested dislocation lines. The disappearance occurs when a critical balance is reached between the rate of atmosphere formation and the rate at which carbon is drained from arrested dislocations by the carbide-forming species. This behavior manifests itself by the disappearance of serrations off the outer end of the flow curve at progressively lower strain as the temperature is increased or the strain rate decreased. In contrast, the disappearance of serrated flow in age-hardened Waspaloy took place by a progressively larger delay to the onset of serrations as the temperature is increased or the strain rate decreased. It was proposed that the mechanism leading to the disappearance in age-hardened Waspaloy is due to the draining of carbon down the dislocation line to the Ni₃(Al,Ti) percipitate while the line is arrested at the precipitate. The rate controlling step was proposed to be the reaction rate at the carbide-forming sink (ΔH = 1.3 to 1.6eV). Thus, in each case, it is proposed that the underlying mechanism for the disappearance of serrations at higher temperatures and lower strain rates is a precipitation reaction. The continuous and reproducible pattern of an increase in stress decrement (σ_D) with either decrease in strain rate or increase in temperature was also investigated. With either of the above conditions the atmosphere size increases, thus more than offsetting the decrease in binding energy which occurs simultaneously with increasing temperature. This increase in σ_D continues progressively right up to the point at which the serrations disappear.