Strain incompatibility and its influence on grain coarsening during cyclic deformation of ARB copper

It is well known that the characteristic length scale in ultra-fine grained and nanocrystalline metals has a significant effect on the mechanical behaviour. The inhibited ability to accommodate imposed strain with conventional dislocation mechanism has led to the activation of unconventional deformation mechanisms. For one, grain coarsening at shear bands has been observed to occur within metals with sub-micron grain size upon cyclic deformation. Such grain coarsening is often linked to the observed cyclic softening behaviour. The purpose of this study was to investigate the relationship between strain localisation associated with shear banding and the observed deformation-induced grain coarsening in ultra-fine grained metals. The investigation was carried out using ultra-fine grained, oxygen-free high conductivity copper processed by accumulative roll-bonding. A close relationship between strain localisation and deformation-induced grain coarsening was revealed. As strain localisation is not only found at shear bands, but also at other places whereby heterogeneous microstructure or geometric discontinuity is present, hence the present study bears a general significance. Such strain localisation sites may also include a hard constituent embedded in a relatively ductile matrix, micro-crack tips and artificial notches. The stress concentration at these sites provides a high input of strain energy for grain boundary motion leading to grain coarsening. Furthermore, when the grain size is very small, the stress gradient leading away from the stress concentration sites is also believed to increase the driving force for grain boundary migration within the affected regions.     

Influence of thermomechanical processing on shear bands formation and magnetic properties of a 3% Si non-oriented electrical steel

The effect of thermomechanical processing on the formation of shear bands and on the magnetic properties of a 3.0 wt% silicon non-oriented steel was investigated by hot rolling samples with different thicknesses at different temperatures, in order to obtain a variation in hot band grain size and cold strain. All the samples were processed in a single-stage cold rolling and finally annealed at 1020 °C. It was found that the increase of the hot band grain size decreases the γ fiber volume fraction and increases the η fiber volume fraction after the final annealing. The increase of the cold strain strongly contributed to this result. A good combination of intense generation of shear bands, and proper crystallographic texture, due to higher nucleation of grains with favorable orientations to magnetization in these bands, can be obtained for the samples hot rolled at 1000 and 1120 °C and submitted to cold strain of 64.3% and 72.2% respectively. However the best combination of B₅₀, W_15/60 and μ_r can be obtained by hot rolling the samples at 1000 °C to the thickness of 1.4 mm, corresponding to 64.3% of cold strain.     

A numerical examination of shear banding and simple shear non-coaxial flow rules

Strain localisation and shear band formation is frequently observed during the handling and flow of dense phase particulate materials. However, a complete understanding of how shear bands form and what happens inside shear bands is still lacking. In order to address this problem, discrete particle simulations have been carried out to examine the detailed processes that occur at the grain scale associated with the initiation and development of shear bands. To reliably identify the continuum model applicable within a shear band is difficult due to the small number of particles/contacts involved. However, it is normally accepted that the mode of deformation within a shear band is one of simple shear. Consequently, simple shear simulations have been performed in order to determine the evolution of the stress tensor, dilation rate, and the principal directions of stress and strain-rate. It is demonstrated that the corresponding non-coaxial flow rule is equivalent to that suggested by Tatsuoka et al. (Géotechnique 38 148 (1988)). Furthermore, at fully developed flow when there is no further change in volume, the stress and strain-rate directions are coaxial and the flow rule is that proposed by Hill (The Mathematical Theory of Plasticity (Oxford University Press, 1950) p. 294).     

A study on anomalous yield drop behaviour in modified beta titanium alloys

ABSTRACT

The yield drop phenomenon observed in the Ti–15V-3Al–3Sn-3Cr (Ti–15–3) beta-titanium alloy and its anomalous behaviour in the boron and carbon added Ti–15–3 alloys have been studied. While the base and the carbon containing alloys exhibit yield drop, the boron containing alloy with smaller grain size than base alloy does not appear to show this phenomenon. Tensile tests were interrupted at different stress levels followed by analyses of slip lines and sub-structural characteristics using scanning and transmission electron microscopes to understand this anomalous yield point phenomenon. Infrared thermal imaging technique was used to map the strain localisation and the spatiotemporal evolution of deformation along the gauge length of the specimens during the tensile tests. Deformation in these alloys initiates only in a few grains. Pile-up of dislocations in these grains subsequently triggers the formation of dislocations in other grains and their rapid multiplications. The spreading of deformation by the generation of dislocations from pile up dislocations in one grain to neighbouring un-deformed grains and their rapid multiplication to new regions influence the yield drop phenomenon and its characteristics. It is shown in this study that microscopic instability in the grain level is a necessary, but not the sufficient condition for the manifestation of macroscopic instability during tensile deformation in polycrystalline materials. The presence of boride particles at grain boundaries restricts the slip transfer across the grains as well as the spreading of deformation to new regions, which causes the suppression of yield drop in the boron containing alloy.     

Microscopical study of the formation of adiabatic shear bands in 4340 steel during dynamic loading

In this study, optical microscopy, scanning electron microscopy, transmission electron microscopy, X-ray diffraction and electron probe microanalyser were used to analyse the changes in microstructure of AISI 4340 steel specimens caused by impact at high strain rates and large strains. The structures of the steel prior to dynamic deformation and after dynamic deformation were examined to understand on a microscale level, the mechanism of formation of adiabatic shear bands (ASBs). The study also includes the structural changes that occur during post-deformation annealing processes which may relate to understanding of the mechanism of formation of ASBs. Prior to deformation, the tempered steel specimens consisted of lenticular laths of α-ferrite with precipitated platelet and spherical M₃C carbides. After impact, the structure inside the shear band was characterized by refined and recrystallized grains immersed in dense dislocation structures. In addition, residual carbide particles were observed inside the shear bands due to deformation induced carbide dissolution. Regions away from the shear bands developed ‘knitted’ dislocation walls, evolving gradually into sub-boundaries and highly misoriented grain boundaries at increasing strains, leading to grain refinement of the ferrite. After impact, annealing the shear bands at 350?°C resulted in an increase in hardness regardless of the heat treatment before impact, amount of deformation and the time of annealing. This is because of the occurrence of extensive reprecipitation of dissolved carbides that existed in the steel structure prior to deformation. It is concluded that dynamic recovery/recrystallization, development of dislocation structures and carbide dissolution all contribute simultaneously to the formation of ASBs in quench-hardened steels.     

Special misorientations in localized deformation regions in Fe-3%Si alloy single crystals

Extended regions located at an angle of 20° to the rolling plane are observed inside deformation bands in a (110)[001] Fe-3%Si alloy single crystal at a high strain (～60%). These regions were interpreted earlier as shear bands. The lattice orientation in these bands is close to (110)[001], and their habit plane is parallel to the {112} planes of the deformed {111}〈112〉 matrix. The misorientations between the bands and the matrix group around special misorientations Σ9, Σ19a, Σ27a, and Σ33a, which are characterized by close angles of rotation about axis 〈110〉. During primary recrystallization, the (110)[001] grains growing from the bands retain segments of the corresponding special boundaries with the deformed matrix.     

Grain refinement in coarse-grained 7475 Al alloy during severe hot forging

Grain refinement taking place in a coarse-grained 7475 Al alloy was studied in multidirectional compression at 490°C and at a strain rate of 3?×?10^?4?s^?1. The integrated flow curve displays significant work softening just after yielding and an apparent steady-state plastic flow at high strains. The structural changes are characterized by the development of deformation or microshear bands in coarse-grain interiors, followed by homogeneous evolution of new grains at high strains. The new grains are considered to be developed by a kind of continuous reaction through grain fragmentation that is similar to continuous dynamic recrystallization (cDRX). The mechanism of fine grain production and the factors controlling grain refinement during hot multidirectional deformation are discussed in detail.     

Plasticity enhancement in 25Cr15Co hard magnetic alloy deformed in bridgman anvils

In the work, we studied the evolution of structural and mechanical properties of 25Cr15Co hard magnetic alloy under shear deformation in Bridgman anvils at different rotation angles. It is shown that at the initial stage, severe plastic strains in a highly coercive (α₁ + α₂) state are localized in shear bands, in which the α₁ and α₂ phases are dissolved and an oversaturated a solid solution is formed. As this takes place, there arises a mixed structure consisting of misoriented fragments of the (α₁ + α₂) phase surrounded by interlayers of the a solid solution. A further increase in strain degree results in a single-phase nanocrystalline structure with a grain size of about 50 nm. It is found that the dissolution of the α₁ phases in the α₂ matrix under severe plastic deformation causes an increase in the strength characteristics and plasticity of 25Cr15Co alloy at all strain degrees under study. Maximum plasticity is found in the alloy with a mixed structure consisting of submicrocrystalline and cellular sites, and formation of nanocrystalline grains causes the plasticity to decrease somewhat.     

Geometric dynamic recrystallization of austenitic stainless steel through linear plane-strain machining

ABSTRACT

Type 316L austenitic stainless steel was severely plastically deformed at room temperature using linear plane-strain machining in a single pass that imparted shear strains up to 2.2 at strain rates up to 2?×?10³ s^?1. The resulting microstructures exhibited significant grain size refinement and improved mechanical strength where geometric dynamic recrystallization was identified as the primary microstructural recrystallization mechanism active at high strain rates. This mechanism is rarely observed in low to medium stacking fault energy materials. The critical stress required for twin initiation is raised by the combined effects of refined grain size and the increase in stacking fault energy due to the adiabatic heating of the chip, thus permitting geometric dynamic recrystallization. The suppression of martensite formation was observed and is correlated to the significant adiabatic heating and mechanical stabilisation of the austenitic stainless steel. A gradient of the amount of strain induced martensite formed from the surface towards the interior of the chip. As the strain rate is increased from 4?×?10² s^?1–2?×?10³ s^?1, a grain morphology change was observed from a population of grains with a high fraction of irregular shaped grains to one dominated by elongated grain shapes with a microstructure characterised by an enhanced density of intragranular sub-cell structure, serrated grain boundaries, and no observable twins. As strain rates were increased, the combination of reduction in strain induced martensite and non-uniform intragranular strain led to grain softening where a Hall-Petch relationship was observed with a negative strengthening coefficient of ?0.08?MPa m^1/2.     

Multiscale model of deformed polycrystals. Hall-Petch problem

The paper puts forward a multiscale model of deformed polycrystals according to which the basis for self-consistent deformation of grains is rotational wave flows of planar structural transformations at their boundaries. Computer-aided engineering of grain boundaries reveals two types of rotational wave flows defined by the misorientation angle of adjacent grains. Grain boundary flows of the first type develop at low-angle boundaries and feature low curvature. These flows generate dislocations in the grain bulk and the Hall-Petch equation for them has the form σ=σ₀+kd^?1/2. Grain boundary flows of the second type develop at high-angle boundaries and feature high curvature. These flows generate curvature bands in near-boundary zones and inject them into the grain bulk, resulting in fragmentation of grains and breakdown of translation invariance. For such self-consistency of grains in a polycrystal, the Hall-Petch equation has the form σ=σ₀+kd^?1. Experimental data in support of the proposed multiscale model are presented.     

Low-temperature deformation of nanocrystalline niobium

The strain characteristics of nanocrystalline niobium are measured in the temperature range 4.2–300 K. It is shown that the development of a strong local deformation with clearly delineated macroscopic slip bands occurs at 4.2 K and 10 K. The thermal effects at a stress jump observed upon transition of the sample (or a niobium strip placed close to the sample) from the superconducting state to the normal state are estimated. It is demonstrated that the temperature dependence of the yield point σ_s(T) can be divided into three portions: two portions (T<10 K and T>70 K) with a slight change in σ_s and the third portion with a strong dependence σ_s(T). The strain characteristics of polycrystals with nano-and larger-sized grains are compared with those of single crystals.     

The influence of shear bands on final structure and magnetic properties of 3% Si non-oriented silicon steel

The presence of shear bands in the deformed material before final annealing is very important for Goss and Cube textures formation in silicon steel [S.C. Paolinelli, M.A. Cunha, J. Magn. Magn. Mater. 255 (2003) pp. 379. [1]; J.T. Park, J.A. Szpunar, Acta Mater., 51 (2003) 3037. [2]]. The increase of the hot-band grain size can increase the number of shear bands, which favor the nucleation of these orientations. In this work, the effect of the hot band grain size variation, promoted by varying the hot rolling finishing temperature, on final structure and magnetic properties was investigated for 3% Si alloy. It was found that the increase of the hot-band grain size increases the occurrence of shear bands and promotes an increase of η fiber fraction and a reduction of γ fiber fraction, improving the magnetic induction. On the other hand, the final grain size is reduced when the hot-band grain size is larger than 190 μm, deteriorating the core loss values in spite of the texture benefits. The reduction of final grain size was explained by the increase of the number of nuclei at the beginning of the recrystallization caused by the increase of shear bands in the deformed material.     

Effect of thermomechanical processing on microstructural evolution and deformation behaviour of polycrystalline magnesium under quasi-static and high strain rate conditions

Abstract

The effect of thermomechanical processing on microstructure evolution and room temperature flow behaviour of polycrystalline magnesium in compression at strain rates of ~10^?2 and ~10³ s^?1 was investigated. Different initial microstructures were produced by optimising rolling and annealing cycles. Prior to annealing for 1 h at 350 °C, Mg samples were processed by two different treatments such as (i) hot rolling at 350 °C and (ii) hot rolling at 350 °C plus cold rolling at room temperature. Introduction of cold working step led to an increased fraction of hard oriented grains with a marginal grain size difference in post-annealed samples. A profound effect of thermomechanical processing on strain hardening rate as well as rate-sensitive flow behaviour of Mg was observed. The influence of prior processing history and strain rate on flow behaviour of Mg was clearly reflected in terms of texture strengthening/weakening phenomena and formation of microstructural deformation bands.     

Localization of plastic deformation in calcium fluoride crystals at elevated temperatures

The strain distribution was experimentally studied in CaF₂ crystals subjected to compression tests along [110] and [112] at a constant strain rate at temperatures T = 373–1253 K. At T > 845 K, the plastic deformation in deformed samples is found to be strongly localized in narrow bands, where the shear strain reaches several hundred percent. The physical deformation conditions are determined under which the plastic flow loses its stability and, as a result, the deformation is localized. The temperature dependence of the critical stress of the transition to a localized flow is found. A scenario is proposed for the nucleation and development of large localized shears during high-temperature deformation of single crystals.     

High‐energy transmission Laue micro‐beam X‐ray diffraction: a probe for intra‐granular lattice orientation and elastic strain in thicker samples

An understanding of the mechanical response of modern engineering alloys to complex loading conditions is essential for the design of load‐bearing components in high‐performance safety‐critical aerospace applications. A detailed knowledge of how material behaviour is modified by fatigue and the ability to predict failure reliably are vital for enhanced component performance. Unlike macroscopic bulk properties (e.g. stiffness, yield stress, etc.) that depend on the average behaviour of many grains, material failure is governed by `weakest link'‐type mechanisms. It is strongly dependent on the anisotropic single‐crystal elastic–plastic behaviour, local morphology and microstructure, and grain‐to‐grain interactions. For the development and validation of models that capture these complex phenomena, the ability to probe deformation behaviour at the micro‐scale is key. The diffraction of highly penetrating synchrotron X‐rays is well suited to this purpose and micro‐beam Laue diffraction is a particularly powerful tool that has emerged in recent years. Typically it uses photon energies of 5–25 keV, limiting penetration into the material, so that only thin samples or near‐surface regions can be studied. In this paper the development of high‐energy transmission Laue (HETL) micro‐beam X‐ray diffraction is described, extending the micro‐beam Laue technique to significantly higher photon energies (50–150 keV). It allows the probing of thicker sample sections, with the potential for grain‐level characterization of real engineering components. The new HETL technique is used to study the deformation behaviour of individual grains in a large‐grained polycrystalline nickel sample during in situ tensile loading. Refinement of the Laue diffraction patterns yields lattice orientations and qualitative information about elastic strains. After deformation, bands of high lattice misorientation can be identified in the sample. Orientation spread within individual scattering volumes is studied using a pattern‐matching approach. The results highlight the inability of a simple Schmid‐factor model to capture the behaviour of individual grains and illustrate the need for complementary mechanical modelling.     

Effects of grain size on dislocation organization and internal stresses developed under tensile loading in fcc metals

The relationship between deformation and dislocation properties has been studied for pure polycrystalline nickel and austenitic stainless steel AISI 316L in stage III. Special care was taken to study statistically the effects of the grain size and grain orientation on dislocation densities and distribution. It is shown that the nature of dislocation cells depends on grain size and crystallographic orientation. The dimensional parameters, which depend on grain size, i.e. the inter-boundary spacing (λ) and boundary thickness (e), define three domains of crystallographic orientation and depend on the grain size. Scaling hypotheses reveal two physical mechanisms which, at this level of plastic strain, are correlated to a specific value of the noise, associated with distribution functions. Similarities between structural parameters and dislocation densities in each phase (walls and inter-walls spacing) are identified and discussed in terms of kinetic equations describing dislocation density evolution and fluctuations of certain physical parameters. This similarity provides physical signification of the scaling distribution obtained on λ and e in terms of a stochastic approach to dislocation distribution. The origin of Hall–Petch behaviour observed at large strain is interpreted in terms of an interaction between inter- and intra-granular long-range internal stresses, which depends on grain size. We conclude that, at high strain, the Hall–Petch phenomenological relationship is a consequence of plastic strain history and strain gradient in grains. From this last point, a length scale arises naturally, which depends on stacking fault energy.     

Is the Pauli exclusion principle the origin of electron localisation?

ABSTRACT

In this work, we inquire into the origins of the electron localisation as obtained from the information content of the same-spin pair density, γ^{σ, σ}(r₂∣r₁). To this end, we consider systems of non-interacting and interacting identical Fermions contained in two simple 1D potential models: (1) an infinite potential well and (2) the Kronig–Penney periodic potential. The interparticle interaction is considered through the Hartree–Fock approximation as well as the configuration interaction expansion. Morover, the electron localisation is described through the Kullback–Leibler divergence between γ^{σ, σ}(r₂∣r₁) and its associated marginal probability. The results show that, as long as the adopted method properly includes the Pauli principle, the electronic localisation depends only modestly on the interparticle interaction. In view of the latter, one may conclude that the Pauli principle is the main responsible for the electron localisation.