Kinetic mechanism of the formation of fragmented dislocation structures upon large plastic deformations

The mechanism of formation of fragmented (banded, block) dislocation structures (FDSs) in crystals subjected to large plastic deformations are discussed. The theoretical analysis is based on the kinetic equations for the density of geometrically necessary dislocations (GNDs). The equations include the processes of multiplication, immobilization, annihilation, and diffusion of GNDs. The formation of an FDS is considered a synergetic process of self-organization of GNDs obeying the principle of similitude of dislocation structures at various degrees of plastic deformation. Conditions for the formation of the structures at hand have been determined, as well as their parameters and the dependence of these parameters on the degree of deformation. The theoretical results are compared with the available experimental data.     

Modelling work hardening of aluminium alloys containing dispersoids

The influence of dispersoids on tensile deformation behaviour has been studied by comparison of aluminium alloys containing different dispersoid densities. It was found that a fine dispersion of non-shearable particles led to an increased work hardening at the initial plastic deformation, but the effect was opposite at higher strains. The reason has been attributed to the generation of geometrically necessary dislocations (GNDs). A new model has been proposed for the evolution of GNDs based on a balance of storage and dynamic recovery of GNDs. The model predicts a rapid saturation of GNDs and a reduced work hardening at small strains, consistent with the experimental results.     

Plastic flow localization upon stretching Zr-1% Nb alloy

The stages in the plastic flow curve and the localization of plastic strains upon stretching Zr-1% Nb alloy are considered. The localization pattern is found to correlate with a strain hardening law upon plastic flow. Data for the dislocation structure in strain localization regions are reported.     

Analysis of the parameters of a submicron dislocation structure in metals subjected to severe plastic deformation

Equations of dislocation kinetics are used to quantitatively compare the mechanisms of formation and evolution (with deformation) of cellular dislocation structures at moderate strains and of submicron block dislocation structures at high plastic strains. In both cases, the formation of nonuniform dislocation structures is a result of dislocation self-organization, more specifically, the self-organization of statistically random dislocations during the formation of cellular structures and the self-organization of geometrically necessary dislocations (which appear due to the nonuniform character of plastic deformation on the micron scale) during the formation of block structures.     

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.     

高应变率压缩下纳米孔洞对金属铝塑性变形的影响研究

本文利用分子动力学模拟方法研究了含纳米孔洞金属铝在[110]晶向高应变率单轴压缩下弹塑性变形的微观过程. 对比单孔洞和完整单晶的模型, 讨论了多孔金属的应力应变关系及其位错发展规律. 研究结果表明, 对于多孔模型的位错积累过程, 位错密度随应变的增加可大致分为两个线性阶段. 由同一个孔洞生成的位错在相互靠近过程中, 其滑移速度越来越小; 随着位错继续滑移, 源自不同孔洞的位错之间开始交叉相互作用导致应变硬化. 达到流变峰应力之后又由于位错密度增殖速率升高发生软化. 当应变增加到11.8%时, 所有孔洞几乎完全坍缩, 并观察到在此过程中有棱位错生成.     

Cellular dislocation substructure in polycrystals of FCC solid solutions: quantitative characteristics,laws of formation,and role in hardening

A cycle of investigations carried out by the authors and devoted to the most important cellular dislocation substructure is generalized. Laws of formation of this substructure upon plastic strain of FCC Cu–Mn and Cu–Al alloy polycrystals are considered. The influence of the grain size, strain temperature, and alloy concentration on the parameters of evolving cellular dislocation substructures (DSS) is quantitatively analyzed by the transmission electron microscopy (TEM) method. Special attention is given to the kinetic phase transition in the defect subsystem leading to the formation of the cellular DSS. Based on modern dislocation models, it is demonstrated that hardening by the cellular DSS obeys the main dislocation laws.     

Formation of fragments with medium-angle boundaries in shear bands: Computer simulation

The conditions for the formation of fragments with medium-angle boundaries in shear bands are analyzed using computer simulation. It is shown that the main condition for the transformation of weakly disoriented dislocation structures into a fragmented structure is the suppression of active plastic deformation in a subgrain by the elastic fields of disclinations appearing at subgrain boundary junctions as a result of mismatch of plastic rotations in individual subgrain boundaries. Under these conditions, during continued straining in the surrounding matrix, such a subgrain behaves as an undeformed inclusion and experiences a crystallographic rotation. The disorientation of the subgrain continuously increases, thereby transforming initial small-angle dislocation boundaries into medium-angle and (in the limit) large-angle boundaries.     

On the foundations of stochastic dislocation dynamics

A stochastic approach to dislocation dynamics is proposed that starts off from considering the geometrically necessary fluctuations of the local stress and strain rate caused by long-range dislocation interactions during plastic flow. On a mesoscopic scale, a crystal undergoing plastic deformation is thus considered an effective fluctuating medium. The auto- and cross-correlation functions of the effective stress and the plastic strain rate are derived. The influences of dislocation multiplication, storage and cross slip on the correlation functions are discussed. Various analogies and fundamental differences to the statistical mechanics of thermodynamic equilibrium are outlined. Application of the theory of noise-induced transitions to dislocation dynamics gives new insight into the physical origin of the spontaneous formation of dislocation structures during plastic deformation. The results demonstrate the importance of the strain-rate sensitivity in dislocation patterning.     

Mathematical model of successive plastic deformations in three mutually perpendicular directions

A mathematical model is formulated for successive plastic deformations in three mutually perpendicular directions when dislocation annihilation is negligible. In some slip systems, the motion of the dislocations changes sign when the deformation axis changes. This results in markedly slower strain hardening of the crystal. Comparison of the theoretical and experimental hardening curves shows that they agree qualitatively at small deformations. The sharp divergence of the curves at large deformations results from neglect of dislocation annihilation in the calculations. Tomsk State Architectural and Construction Academy. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 80–86, September, 1997.     

Sheared solid materials

We present a time-dependent Ginzburg-Landau model of nonlinear elasticity in solid materials. We assume that the elastic energy density is a periodic function of the shear and tetragonal strains owing to the underlying lattice structure. With this new ingredient, solving the equations yields formation of dislocation dipoles or slips. In plastic flow high-density dislocations emerge at large strains to accumulate and grow into shear bands where the strains are localized. In addition to the elastic displacement, we also introduce the local free volumem. For very smallm the defect structures are metastable and long-lived where the dislocations are pinned by the Peierls potential barrier. However, if the shear modulus decreases with increasingm, accumulation ofm around dislocation cores eventually breaks the Peierls potential leading to slow relaxations in the stress and the free energy (aging). As another application of our scheme, we also study dislocation formation in two-phase alloys (coherency loss) under shear strains, where dislocations glide preferentially in the softer regions and are trapped at the interfaces.     

一个单滑移取向铜单晶体疲劳位错结构的热稳定性研究

利用扫描电镜电子通道衬度(SEM-ECC)技术观察研究了[4 18 41]单滑移取向铜单晶体在不同塑性应变幅下的疲劳饱和位错结构及其在不同温度等时退火条件下的热稳定性. 结果表明, 在退火温度为300 °C时, 疲劳位错结构(如脉络结构、驻留滑移带PSB楼梯结构、PSB胞结构和迷宫结构等)均发生了明显回复. 当退火温度高于500 °C, 上述这些疲劳位错结构基本消失, 均发生了明显的再结晶现象, 并大都伴随有退火孪晶的形成. 分析认为, 再结晶的发生和退火孪晶的出现不仅与退火温度和外加塑性应变幅有关, 还与累积循环塑性应变量有着密切的关系.     

Modeling of macroscopic strain localization in alloys with the <Emphasis Type="Italic">L</Emphasis>1<Subscript>2</Subscript> structure

Results of mathematical modeling of plastic strain superlocalization are presented with allowance for dislocation redistribution into dislocation walls. The model based on the concept of hardening and rest is used to construct equations describing kinetics of dislocations and substructure transformations. It is demonstrated that depending on the scenario of the strain model evolution in the microvolume of a deformable body, different types of localization are possible under the influence of stress concentrators.     

Fundamental differences in mechanical behavior between two types of crystals at the nanoscale

We present differences in the mechanical behavior of nanoscale gold and molybdenum single crystals. A significant strength increase is observed as the size is reduced to 100 nm. Both nanocrystals exhibit discrete strain bursts during plastic deformation. We postulate that they arise from significant differences in the dislocation behavior. Dislocation starvation is the predominant mechanism of plasticity in nanoscale fcc crystals, while junction formation and hardening characterize bcc plasticity. A statistical analysis of strain bursts is performed as a function of size and compared with stochastic models.     

Localization of twinning plastic strain in doped γ-Fe single crystals

The patterns of plastic flow localization in high-manganese γ-Fe fcc single crystals oriented for twinning upon stretching are obtained. Basic space-time features of strain localization at the stages of yield plateau, easy glide, and linear hardening are established. The velocity of strain localization sites during stretching is determined. Conditions under which plasticity autowaves appear in the strained medium are discussed. It is demonstrated that the local strain distributions in the case of twinning are similar to those due to dislocation glide.     

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.     

Structural changes in Hadfield steel under cold deformation

The influence of cold deformation on the structure of Hadfield (110G13L) steel is analyzed. The steel hardening is demonstrated to be caused by the formation of dislocation clusters and the generation of stacking faults and twins. It is found that regions with nanocrystalline structures with FCC and hexagonal close-packed lattices are created at large degrees of compression.     

From dislocation junctions to forest hardening

The mechanisms of dislocation intersection and strain hardening in fcc crystals are examined with emphasis on the process of junction formation and destruction. Large-scale 3D simulations of dislocation dynamics were performed yielding access for the first time to statistically averaged quantities. These simulations provide a parameter-free estimate of the dislocation microstructure strength and of its scaling law. It is shown that forest hardening is dominated by short-range elastic processes and is insensitive to the detail of the dislocation core structure.     

On the homogeneous nucleation and propagation of dislocations under shock compression

The dynamic response of crystalline materials subjected to extreme shock compression is not well understood. The interaction between the propagating shock wave and the material’s defect occurs at the sub-nanosecond timescale which makes in situ experimental measurements very challenging. Therefore, computer simulation coupled with theoretical modelling and available experimental data is useful to determine the underlying physics behind shock-induced plasticity. In this work, multiscale dislocation dynamics plasticity (MDDP) calculations are carried out to simulate the mechanical response of copper reported at ultra-high strain rates shock loading. We compare the value of threshold stress for homogeneous nucleation obtained from elastodynamic solution and standard nucleation theory with MDDP predictions for copper single crystals oriented in the [0 0 1]. MDDP homogeneous nucleation simulations are then carried out to investigate several aspects of shock-induced deformation such as; stress profile characteristics, plastic relaxation, dislocation microstructure evolution and temperature rise behind the wave front. The computation results show that the stresses exhibit an elastic overshoot followed by rapid relaxation such that the 1D state of strain is transformed into a 3D state of strain due to plastic flow. We demonstrate that MDDP computations of the dislocation density, peak pressure, dynamics yielding and flow stress are in good agreement with recent experimental findings and compare well with the predictions of several dislocation-based continuum models. MDDP-based models for dislocation density evolution, saturation dislocation density, temperature rise due to plastic work and strain rate hardening are proposed. Additionally, we demonstrated using MDDP computations along with recent experimental reports the breakdown of the fourth power law of Swegle and Grady in the homogeneous nucleation regime.     

Strain-dependent deformation behavior in nanocrystalline metals

The deformation behavior as a function of applied strain was studied in a nanostructured Ni-Fe alloy using the in situ synchrotron diffraction technique. It was found that the plastic deformation process consists of two stages, undergoing a transition with applied strain. At low strains, the deformation is mainly accommodated at grain boundaries, while at large strains, the dislocation motion becomes probable and eventually dominates. In addition, current results revealed that, at small grain sizes, the 0.2% offset criterion cannot be used to define the macroscopic yield strength any more. The present study also explained the controversial observations in the literature.