E. Schafler

Deformation Induced Vacancies with Severe Plastic Deformation: Measurements and Modelling

In discussing hardening characteristics in terms of crystalline lattice defects, in most cases the properties and kinetics of dislocations and their arrangement have been considered. However, during plastic deformation also vacancies and/or vacancy type defects are produced in very high densities which are typically close to those of vacancies in thermal equilibrium at the melting point. The effect of high vacancy concentrations on the hardening characteristics is twofold: (i) direct effects by impeding the movement of dislocations (ii) indirect one by inducing climbing and annihilation of edge dislocations leading to softening or even absolute decreases in strength. This paper presents first measurements of deformation induced vacancies in SPD materials which have been achieved by combined evaluation of resistometry, calorimetry and X-ray diffraction. The density of vacancies during and after SPD deformation is found to be markedly higher than in cases of conventional deformation and/or coarse grained material which may be partly attributed to the particular conditions of SPD namely the enhanced hydrostatic pressure as well as the changes in deformation path. It is suggested to make this high vacancy concentration responsible for both dynamic and static recovery and/or recrystallisation processes recently found during and after SPD, being potential reasons for enhanced ductility and superplasticity which only occur with nanomaterials originating from SPD. Recent publications show that in alloys, SPD induced vacancies can also enable the existence of phases which do not appear in the equilibrium diagram.

Measurement of screw and edge dislocation density by means of X-ray Bragg profile analysis

Abstract The type of dislocations produced during plastic deformation is necessary to know for the fundamental understanding anisotropy of hardening processes. By studying X-ray line broadening in several reflections, the fraction of certain dislocation types can be determined experimentally. The contribution of strain to line broadening is generally anisotropic. On the basis of the dislocation model, the modified Williamson–Hall and Warren–Averbach procedures have been suggested where g and g2 are replaced by g C and g2 C , with C as the average dislocation contrast factor. C can be evaluated theoretically for different crystal systems and different dislocation types, i.e. edges and/or screws, by numerical methods. On the other hand, by analyzing strain anisotropy C can be determined from experiment. Comparing experimental with theoretical C-values the specific fraction of dislocation types can be determined. In the present paper this procedure has been carried out for fine grained Cu 99.9% for deformation well into stage III. The ratio starts with a high fraction (90%) of screw dislocations. During deformation up to e=0.3 this picture changes in favor of edge dislocations (75%).

Work hardening and microstructure of AlMg5 after severe plastic deformation by cyclic extrusion and compression

Deformation by cyclic extrusion/compression in AlMg5 leads to the same stages of work hardening as unidirectional deformation. The analogy is confirmed by studies of the microstructure, by analysis of long range internal stresses and by evaluation of dislocation densities. The strains leading to the various stages of work hardening are much higher than those in conventional deformation modes while the dislocation densities in the stages are about the same. The strain shift in cyclic extrusion/compression is attributed to the reversal of strain path. The resulting subgrain size is smaller than that resulting from conventional deformation modes which seems to be a consequence of the higher hydrostatic pressure of cyclic extrusion/compression.

Structural anisotropy in a Zr57Ti5Cu20Al10Ni8 bulk metallic glass deformed by high pressure torsion at room temperature

Fully amorphous Zr57Ti5Cu20Al10Ni8 bulk metallic glass specimens were subjected to deformation by high pressure torsion at room temperature. Consecutive high resolution synchrotron x-ray diffraction mapping has revealed the variation of the average atomic bond length and shown no evidence of crystallization in this excellent glass former. Difference in the sign of the atomic distortion obtained in direction parallel to the sample surface and along the cross section indicates strong structural anisotropy.

Vacancy concentrations determined from the diffuse background scattering of X-rays in plastically deformed copper

The background intensity of X-ray diffraction patterns is analysed in terms of point defects, especially vacancies, in poly- and single-crystalline copper specimens. The samples have been deformed by compression in-situ in a synchrotron peak profile experiment. Systematic comparative analysis of X-ray, electrical resistivity, and calorimetric measurements indicate that (i) point defects, especially vacancies, are produced during plastic deformation and (ii) that the point defect concentration is increasing concomittantly with the actual dislocation density. The point defect production rate in poly- and single-crystalline specimens is observed to be drastically different. This difference is interpreted as different vacancy production rates in the grain interior and in the grain-boundary regions. With increasing deformation, the vacancy concentration in the grain-boundary regions is found to approach the equilibrium values corresponding to the melting temperature of copper. This result would support the assumption that in severely deformed metals the grain boundary region is a highly distorted, almost amorphous phase of the material.

Dislocation densities and internal stresses in large strain cold worked pure iron

Abstract Polycrystalline samples of Fe-0.005%-C were deformed by torsion at 300 K far into stage IV of deformation and investigated by X-ray peak profile analysis (XPA) for the microstructural evolution. The long-range internal stresses Δτ w −δτ c (τ w , τ c are the shear stresses in the cell wall and cell interior regions) pass through a maximum at the onset of stage IV, but reincrease within stage IV at higher deformation. A similar maximum is observed in the formal dislocation density derived directly from XPA which, however, is not seen in residual electrical resistivity. These results can be consistently explained by the assumption that in stages II and III the cell walls are formed as polarized dipole walls (PDW) which in stage IV change into polarized tilt walls (PTW), similarly to recent findings in cold rolled Cu. The significant constancy of total volume fraction of cell walls as well as of specific internal stresses in stage IV confirm the importance of the PTW s for stage IV strengthening.

On the Microstructure of HPT Processed Cu under Variation of Deformation Parameters

The evolution of strength characteristics and the microstructure of copper subjected to high pressure torsion (HPT) are studied under variation of strain and hydrostatic pressure. Measurements of Multiple X-ray Bragg Profile Analysis (MXPA) yield microstructural parameters like dislocation density and arrangement, as well as crystallite (domain) size and distribution, and long-range internal stresses. TEM investigations are carried out to analyse the structural elements and to compare them with the results of MXPA. The strength behaviour is studied by microhardness measurements. The investigations are performed within wide ranges of resolved shear strains = 1 to 400 and of applied pressures p = 0.8 to 8 GPa. The onset of the deformation stages IV and V is strongly affected by the hydrostatic pressure i.e. shifted to higher values of stress and strain with increasing pressure. The experimental results indicate the occurrence of recovery effects, which seem to be of static as well as of dynamic nature, and to be responsible for extended ductility in SPD materials.

Footprints of deformation mechanisms during in situ x-ray diffraction: Nanocrystalline and ultrafine grained Ni

In situ x-ray diffraction demonstrates that in ultrafine grained Ni synthesized by high pressure torsion with a coherent scattering domain size of 80nm, a dislocation network is still built up during tensile deformation whereas this is not the case for electrodeposited nanocrystalline metals with a coherent scattering domain size of 30nm. Simultaneously, the technique shows for the first time important differences in macroscopic stress accommodation during plastic deformation between the nanocrystalline and ultrafine grained Ni, such as the origin of the reduction in flow stress.

Coincidences of hypercubic lattices in 4 dimensions

Summary We consider the CSLs of 4-dimensional hypercubic lattices. In particular, we derive the coincidence index Σ and calculate the number of different CSLs as well as the number of inequivalent CSLs for a given Σ. The hypercubic face centered case is dealt with in detail and it is sketched how to derive the corresponding results for the primitive hypercubic lattice.

Microstructural parameters in large strain deformed Ni polycrystals as investigated by synchrotron radiation

Dislocation densities, arrangements and long-range internal stresses in cold worked polycrystalline nickel were determined by X-ray diffraction profile analysis using synchrotron radiation. Torsionally deformed samples were scanned across the diameter of the specimens with a focal spot of 300 μm providing strain dependent results in good correlation with residual electrical resistivity data. On cold rolled specimens with different deformations, scanning measurements across single grains with a focal spot of less than 50 μm were carried out, in order to inform on the features of the deformation induced substructure. At small deformations including stage III, the dislocation densities and internal stresses are uniform within single grains while at higher deformations in stages IV and V. the dislocation density and internal stresses exhibit correlated fluctuations. In analogy to Cu, in stage IV these fluctuations could be identified as polarized tilt walls (PTW) formed from polarized dipole walls (PDW) whereas in stage V, as a difference to Cu, only PDWs and pile-ups of dislocations at the grain boundaries were found. It is suggested that the differences to Cu arise from the enhanced presence of deformation induced vacancies in Ni, enabling stronger effects of static recovery through dislocation climb to take place in between single passes of rolling deformation.