Evolution of mechanical response and dislocation microstructures in small-scale specimens under slightly different loading conditions

In small dimensions, the flow stress of metallic samples shows a size-dependence such that smaller is stronger, even in nominally strain gradient-free loading conditions. However, the role of the boundary conditions in miniaturised tension or compression tests on the mechanical response and dislocation structure has not been studied in detail. In simulations performed with a three-dimensional discrete dislocation dynamics tool, initial, well-defined dislocation microstructures are loaded in tension with different boundary conditions including superimposed torsion moments. The influence of the loading conditions on details of the evolving dislocation microstructure was investigated by using identical starting configuration. An additional torsion moment significantly influences the dislocation activity since forest-dislocations are generated, but size effect of the flow stress is found to be unchanged.     

Evidence for a transition in deformation mechanism in nanocrystalline pure titanium processed by high-pressure torsion

Nanocrystalline titanium with an average grain size of about 60–70 nm was prepared by high-pressure torsion. The results of hardness and structural evolutions indicate that a strain-induced hardening–softening–hardening–softening behaviour occurs. For coarse-grained titanium, 〈a〉-type dislocation multiplication, twinning and a high pressure-induced α-to-ω phase transformation play major roles to accommodate deformation, leading to a significant strain hardening. As deformation proceeds, dynamic recrystallisation leads to a decrease in dislocation density, especially for 〈a〉-type dislocations, leading to a slight strain softening. The 〈c〉-component dislocation multiplication dominates the deformation when the grain size decreases to 100 nm and 〈c〉-component dislocation multiplication, grain refinement and the α-to-ω phase transformation contribute to the second strain hardening. The following strain softening is attributed to dynamic recovery.     

Towards a further understanding of dislocation pileups in the presence of stress gradients

This study is an essential complement and extension to the stress-gradient concept recently proposed by Hirth. An analytic method is presented for studying the behaviour of double-ended dislocation pileup in the presence of various stress gradients by solving a singular integral equation based on the continuous approximation of dislocations. Four special cases of double-ended pileup in the presence of stress gradients are discussed in detail. The corresponding dislocation distribution, the length of pileup, the total number of dislocations within the pileup and the force on the leading dislocations at the pileup ends are derived, respectively. It is shown that both the number of dislocations and the force on the leading dislocation in a pileup are sensitive to the relative magnitude of stress near the dislocation source and both are less than that in constant stress case. Of particular importance, it is indicated that the small-scaled materials subjected to a stress involving a gradient would be stronger than that under a constant stress. Applied to wire torsion and foil bending, the stress gradient model predicts an increase in the initial yielding, which is in reasonable agreement with the recent experimental data. The proposed stress gradient concept may provide a new physical insight into the size-dependent plasticity phenomena at small length scale.     

Microstructural instabilities: dislocation substructures with pronounced mechanical effects

Microstructure evolution is largely dominated by the internal stress fields that appear upon the appearance of inhomogeneous structures in a material. The hardening behaviour of metals physically originates from such a complex microstructure evolution. As deformation proceeds, statistically homogeneous distributions of dislocations in grains become unstable, which constitutes the driving force for the development of a pronounced dislocation substructure. The dislocation structure already appears at early stages of deformation due to the statistical trapping of dislocations. Cell walls contain dislocation dipoles and multipoles with high dislocation densities and enclose cell-interior regions with a considerably smaller dislocation density. The presence and evolution of such a dislocation arrangement in the material influence the mechanical response of the material and is commonly associated with the transient hardening after strain path changes. This contribution introduces a micromechanical continuum model of the dislocation cell structure based on the physics of the dislocation interactions. The approximation of the internal stress field in such a microstructure and the impact on the macroscopic mechanical response are the main items investigated here.     

Emergent geometry experienced by fermions in graphene in the presence of dislocations

In graphene in the presence of strain the elasticity theory metric naturally appears. However, this is not the one experienced by fermionic quasiparticles. Fermions propagate in curved space, whose metric is defined by expansion of the effective Hamiltonian near the topologically protected Fermi point. We discuss relation between both types of metric for different parametrizations of graphene surface. Next, we extend our consideration to the case, when the dislocations are present. We consider the situation, when the deformation is described by elasticity theory and calculate both torsion and emergent magnetic field carried by the dislocation. The dislocation carries singular torsion in addition to the quantized flux of emergent magnetic field. Both may be observed in the scattering of quasiparticles on the dislocation. Emergent magnetic field flux manifests itself in the Aharonov–Bohm effect while the torsion singularity results in Stodolsky effect.     

Formation of dislocation patterns under irradiation

The interaction energy between point defects and dislocation patterns (such as the pile-up of dislocation loops and the dislocation wall) is derived. The bias for interstitial absorption by a dislocation in a pattern is shown to be lower than that of an isolated dislocation. The dislocation patterning is proposed to be driven by the dependence of dislocation bias on the dislocation arrangement.     

Analysis of a 69.3° Vicinal HAGB in Pure Titanium

A transmission electron microscopy study and geometric analysis has been performed on a vicinal 69.3° high angle grain boundary in pure Ti which exhibits a characteristic dislocation arrangement. The dislocation configuration was modelled using the usual CSL/DSC/O-lattice approach and the predicted arrangement required to accommodate the deviation from a 37 three-dimensional CSL matched well with the arrangement observed experimentally. It was, however, also shown that an identical arrangement would be required to accommodate the deviation from a 37 two-dimensional CSL. Thus the analysis of such boundaries does not constitute a good test to distinguish between the two- and three-dimensional models of the low-energy reference structures adopted high-angle grain boundaries.     

The effect of size on dislocation cell formation and strain hardening in aluminium

The formation of dislocation cells has a significant impact on the strain hardening behaviour of metals. Dislocation cells can form in metals with a characteristic size defined by three-dimensional tangles of dislocations that serve as “walls” and less dense internal regions. It has been proposed that inhibiting the formation of dislocation cells could improve the strain hardening behaviour of metals such as Al. Here we employ in situ scanning electron microscope compression testing of pure Al single crystal pillars with physical dimensions larger, close to and smaller than the reported cell size in Al, respectively, to investigate the possible size effect on the formation of dislocation cell and the consequent change of mechanical properties. We observed that the formation of dislocation cells is inhibited as the pillar size decreases to a critical value and simultaneously both the strength and the strain hardening behaviour become strongly enhanced. This phenomenon is discussed in terms of the effect of dimensional restriction on the formation of dislocation cells. The reported mechanism could be applied in polycrystalline Al where the tunable physical dimension could be grain size instead of sample size, providing insight into Al alloy design.     

Gravitational geometric phase in the presence of torsion

We investigate the relativistic and non-relativistic quantum dynamics of a neutral spin-1/2 particle subject to an external electromagnetic field in the presence of a cosmic dislocation. We analyze the explicit contribution of the torsion in the geometric phase acquired in the dynamics of this neutral spinorial particle. We discuss the influence of the torsion in the relativistic geometric phase. Using the Foldy–Wouthuysen approximation, the non-relativistic quantum dynamics is studied and the influence of the torsion on the Aharonov–Casher and He–McKellar–Wilkens effects are discussed. An erratum to this article can be found at     

Atomistic simulation of the stacking fault energy and grain shape on strain hardening behaviours of FCC nanocrystalline metals

ABSTRACT

Ultra-fine grained copper with nanotwins is found to be both strong and ductile. It is expected that nanocrystalline metals with lamella grains will have strain hardening behaviour. The main unsolved issues on strain hardening behaviour of nanocrystalline metals include the effect of stacking fault energy, grain shape, temperature, strain rate, second phase particles, alloy elements, etc. Strain hardening makes strong nanocrystalline metals ductile. The stacking fault energy effects on the strain hardening behaviour are studied by molecular dynamics simulation to investigate the uniaxial tensile deformation of the layer-grained and equiaxed models for metallic materials at 300?K. The results show that the strain hardening is observed during the plastic deformation of the layer-grained models, while strain softening is found in the equiaxed models. The strain hardening index values of the layer-grained models decrease with the decrease of stacking fault energy, which is attributed to the distinct stacking fault width and dislocation density. Forest dislocations are observed in the layer-grained models due to the high dislocation density. The formation of sessile dislocations, such as Lomer–Cottrell dislocation locks and stair-rod dislocations, causes the strain hardening behaviour. The dislocation density in layer-grained models is higher than that in the equiaxed models. Grain morphology affects dislocation density by influencing the dislocation motion distance in grain interior.     

Resonances of the Spatial Distribution of Dislocations upon Interaction with the Structural Order Parameter

The interaction of a structural subsystem with dislocations under the superposition of an elastic torsion strain and an additional uniaxial spatially nonuniform time-constant pressure is studied. The analysis is carried out within of Landau’s phenomenological theory with refusal of the approximation of constant magnitudes of irreducible vectors. The rise of spatial resonances of the dislocation density in these conditions is shown.     

Torsion and noninertial effects on a nonrelativistic Dirac particle

We investigate torsion and noninertial effects on a spin-1/2$1/2$ quantum particle in the nonrelativistic limit of the Dirac equation. We consider the cosmic dislocation spacetime as a background and show that a rotating system of reference can be used out to distances which depend on the parameter related to the torsion of the defect. Therefore, we analyse torsion effects on the spectrum of energy of a nonrelativistic Dirac particle confined to a hard-wall potential in a Fermi–Walker reference frame.     

X-ray line profiles analysis of plastically deformed metals

The theoretical basis of X-ray line profile analysis and its application to microstructural characterization of plastically deformed metallic alloys is presented. The microstructure is described in terms of coherent domain size, planar fault density, dislocation density and a dislocation arrangement parameter. Two evaluation methods are introduced: the momentum method and the extended Convolutional Multiple Whole Profile fit procedure. Their use is exemplified on plastically deformed single crystals, single grains residing in the bulk of a polycrystal and family of grains making up texture components. The selected examples show the potential of X-ray line profile analysis applied to diffraction patterns recorded with laboratory or synchrotron sources.     

Curvature from spin

We show that, considering the dislocation defect induced by torsion in spacetime, which behaves like a string with tension, we are lead also to defect angle and then to curvature of spacetime. The space with torsion and curvature is then equivalent to an elastic continuum which has undergone plastic deformations and, following Sakharov idea of the spacetime as a elastic continuum, we are lead to a gravitational constant, which occurs in the Einstein action, as the metrical elasticity of spacetime with the exact value without introducing any arbitrary cutoff, when also torsion is considered.     

铝-0.5%铜合金中反常振幅效应内耗峰的进一步实验和位错弯结气团模型

用低频扭摆进一步研究了在Al-0.5％Cu合金中观察到反常位错内耗峯的条件。结果指出,对于完全退火的试样来说,需要有适当的冷加工量,但是对于高温淬火试样则不需要冷加工。用位错气团模型定性地解释了过去所观测到的表现反常振幅效应的时效内耗峯和温度内耗峯;同时指出,简单的气团模型在作定量的解释时,遇到了下述的困难:(i)在测量内耗所用的交变应力的作用下,位错线所能够拖着气团移动的距离太短。(ii)为了气团能够被位错拖着移动,组成气团的溶质原子必须具有比通常大很多个数量级的扩散系数。(iii)根据气团模型,从理论上计算出来的使位错拖着气团以临界速度而移动时,所需的临界应力比观测值大几百倍。提出了溶质原子沿着位错弯结而扩散的气团模型,这个改进模型能够初步解决上述困难,并能定性地解释所观测的结果。这个模型所依据的基本假设是,要观测到反常内耗现象,位错线上必须具有一定数目的弯结。要得到这种弯结,可以对于退火试样进行适量的冷加工,或者把试样从高温淬火。带着弯结的位错线能够通过弯结的沿边运动而实现垂直于位错线方向的移动。可以假定,气团只在弯结两端的直位错段处形成,在弯结本身上并不形成气团。在弯结的沿边振动的过程中,聚集在弯结两端的溶质原子可以沿着位错管道进行来回的短程扩散。已知沿着位错管道的扩散具有比在正常晶体点阵中扩散时大得多的扩散系数。     

Molecular dynamics simulation on the elastoplastic properties of copper nanowire under torsion

Influences of different factors on the torsion properties of single crystal copper nanowire are studied by molecular dynamics method. The length, torsional rate, and temperature of the nanowire are discussed at the elastic-plastic critical point. According to the average potential energy curve and shear stress curve, the elastic-plastic critical angle is determined. Also, the dislocation at elastoplastic critical points is analyzed. The simulation results show that the single crystal copper nanowire can be strengthened by lengthening the model, decreasing the torsional rate, and lowering the temperature. Moreover, atoms move violently and dislocation is more likely to occur with a higher temperature. This work mainly describes the mechanical behavior of the model under different states.     

铝-银合金在疲劳过程中所表现的一些特点

本工作进行了淬火Al-7.27％Ag合金的扭转疲劳试验,测定了各种扭应变下的△E-N曲线,并且观察了经过各种循环数以后试样的表面金相变化。实验结果指出,当扭应变较小时,△E随着循环数N的增加而逐渐下降,△E-N曲线的变化类似Al-Cu和Al-Mg合金在较低扭应变下的情况。但当扭应变较大时,△E开始略有下降,随后上升到某一较高值后再下降,直至试样断裂。△E-N曲线的形状与Al-Cu和Al-Mg合金完全不同。试样表面的金相变化分为两个明显不同的阶段。在疲劳的起始阶段,滑移痕迹细而均匀,但经过一定循环数后,少数滑移痕迹变得集中而深化。随着循环数的增加,新的滑移带在原有滑移带之间不断地出现,没有纯Al和Al-Mg合金中滑移带变宽的情况。还看到了裂纹沿晶界的形成和发展。根据溶质银原子与位错的电交互作用和位错切割银原子簇的观点,对所得到的结果进行了讨论。 关键词：     

Dislocation arrangement in deformed very dilute Cu-Cd alloy single crystals

The influence of the precipitation annealing on the CRSS and dislocation arrangement of the Cu-0·03 at. % Cd single crystals is observed experimentally. Dislocation distributions are determined by TEM of sections (111) and (101) in stage I and in the transition region. The CRSS increases due to precipitation annealing. There are not observed any second phase particles, but nevertheless there exist some differences in the dislocation arrangement of the solution annealed single crystals and the precipitation annealed ones.     

Damping in metals under combined stress loading

Studies have been made of damping behaviour under conditions of combined stress (i.e., biaxial loading) for six high damping metals—two alloys of manganese-copper and four grades of cast iron. Measured values of damping are presented from tests covering a range of combined stress states and the damping behaviour is interpreted in terms of dependence on stress state. The measured values were obtained from a new experiment in which various combined stress conditions are generated by coupled torsion/bending vibration of a cantilever. The range covered is from all torsion to all bending, i.e., principal stress ratios from ?1 to 0. Damping is determined from energy input during steady state resonant vibration, but frequency response and free decay methods can also be used. Details of the apparatus are given.