Effect of Small Preliminary Deformation on the Evolution of Elastoplastic Waves of Shock Compression in Annealed VT1-0 Titanium

The evolution of an elastoplastic waves of shock compression in VT1-0 titanium in the as-annealed state and after preliminary compression is measured. A preliminary strain of 0.6% and the related increase in the dislocation density are found to change the deformation kinetics radically and to decrease the Hugoniot elastic limit. An increase in the preliminary strain from 0.6% to 5.2% only weakly changes the Hugoniot elastic limit and the compression rate in the plastic shock wave. The measurement results are used to plot the strain rate versus the stress at the initial stage of high-rate deformation, and the experimental results are interpreted in terms of dislocation dynamics.     

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.     

Evaluating the effects of loading parameters on single-crystal slip in tantalum using molecular mechanics

This study is aimed at developing a physics-based crystal plasticity finite element model for body-centred cubic (BCC) metals, through the introduction of atomic-level deformation information from molecular dynamics (MD) investigations of dislocation motion at the onset of plastic flow. In this study, three critical variables governing crystal plasticity mediated by dislocation motion are considered. MD simulations are first performed across a range of finite temperatures up to 600K to quantify the temperature dependence of critical stress required for slip initiation. An important feature of slip in BCC metals is that it is not solely dependent on the Schmid law measure of resolved shear stress, commonly employed in crystal plasticity models. The configuration of a screw dislocation and its subsequent motion is studied under different load orientations to quantify these non-Schmid effects. Finally, the influence of strain rates on thermal activation is studied by inducing higher stresses during activation at higher applied strain rates. Functional dependence of the critical resolved shear stress on temperature, loading orientation and strain rate is determined from the MD simulation results. The functional forms are derived from the thermal activation mechanisms that govern the plastic behaviour and quantification of relevant deformation variables. The resulting physics-based rate-dependent crystal plasticity model is implemented in a crystal plasticity finite element code. Uniaxial simulations reveal orientation-dependent tension–compression asymmetry of yield that more accurately represents single-crystal experimental results than standard models.     

Stochastic dislocation patterning during cyclic plastic deformation

A dislocation dynamical theory is developed for the formation of dipole dislocation patterns during cyclic plastic deformation in single glide. The stochastic dislocation dynamics adopted is suitable to account, in terms of a fluctuating effective medium, for the effects of long-range dislocation interactions on a mesoscopic scale. The theory can explain the occurrence of a matrix structure and persistent slip bands as a result of evolutionary processes, it gives the intrinsic strain amplitudes and the characteristic wavelength of these structures, and it allows for an interpretation of the structural changes associated with changes of the deformation conditions. Quantitative results are in good agreement with experimental observations.     

Strain-rate-induced bcc-to-hcp phase transformation of Fe nanowires

Using molecular dynamics simulation method, the plastic deformation mechanism of Fe nanowires is studied by applying uniaxial tension along the [110] direction. The simulation result shows that the bcc-to-hcp martensitic phase transformation mechanism controls the plastic deformation of the nanowires at high strain rate or low temperature; however,the plastic deformation mechanism will transform into a dislocation nucleation mechanism at low strain rate and higher temperature. Furthermore, the underlying cause of why the bcc-to-hcp martensitic phase transition mechanism is related to high strain rate and low temperature is also carefully studied. Based on the present study, a strain rate-temperature plastic deformation map for Fe nanowires has been proposed.     

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.     

Mechanism of Strain Rate Effect Based on Dislocation Theory

Based on dislocation theory, we investigate the mechanism of strain rate effect. Strain rate effect and dislocation motion are bridged by Orowan＇s relationship, and the stress dependence of dislocation velocity is considered as the dynamics relationship of dislocation motion. The mechanism of strain rate effect is then investigated qualitatively by using these two relationships although the kinematics relationship of dislocation motion is absent due to complicated styles of dislocation motion. The process of strain rate effect is interpreted and some details of strain rate effect are adequately discussed. The present analyses agree with the existing experimental results. Based on the analyses, we propose that strain rate criteria rather than stress criteria should be satisfied when a metal is fully yielded at a given strain rate.     

温度和应变速率耦合作用下纳米晶Ni压缩行为研究

本文利用低温力学测试系统研究了电化学沉积纳米晶Ni在不同温度和宽应变速率条件下的压缩行为. 借助应变速率敏感指数、激活体积、扫描电子显微镜及高分辨透射电子显微镜方法, 对纳米晶Ni的压缩塑性变形机理进行了表征. 研究表明, 在较低温度条件下, 纳米晶Ni的塑性变形主要是由晶界位错协调变形主导, 晶界本征位错引出后无阻碍的在晶粒内无位错区运动, 直至在相对晶界发生类似切割林位错行为. 并且, 在协调塑性变形时引出位错的残留位错能够增加应变相容性和减小应力集中; 在室温条件下, 纳米晶Ni的塑性变形机理主要是晶界-位错协调变形与晶粒滑移/旋转共同主导. 利用晶界位错协调变形机理和残留位错运动与温度及缺陷的相关性揭示了纳米晶Ni在不同温度、不同应变速率条件下力学压缩性能差异的内在原因.     

Dislocation dynamics in cyclic plastic deformation

The paper presents a theoretical investigation of the slip avalanches (so-called strain bursts) which occur in single-glide-orientated face-centered cubic or hexagonal close-packed metals during stress-amplitude-controlled cyclic plastic deformation. The study is based on a model of the dynamics of dislocations that has been developed in a companion paper (Part I). It is shown that this model allows for a quantitative treatment of the strain-burst phenomenon. In particular, the scaling relations between different strain-burst-characteristic parameters which have been found by experiment are connected to the evolution of the dislocation microstructure and thus find a natural explanation.     

Molecular dynamics investigation of plastic deformation mechanism in bulk nanotwinned copper with embedded cracks

The plastic deformation of bulk nanotwinned copper with embedded cracks under tension has been explored by using molecular dynamics simulations. Simulation results show that the cracks mainly act as dislocation sources during the plastic deformation and occasionally as sinks at later stage. The dislocation pile-up, accumulation and transformation at twin boundaries (TBs) control the plastic hardening and softening deformations. The TB dislocation pile-up zone is estimated to be 5.6–8 nm, which agrees well with previous experimental and simulation results. Furthermore, it is found that the flow stress vs. dislocation density at the hardening stage follows the Taylor-type relationship.     

Projecting low and extensive dimensional chaos from spatio-temporal dynamics

We review the spatio-temporal dynamical features of the Ananthakrishna model for the Portevin-Le Chatelier effect, a kind of plastic instability observed under constant strain rate deformation conditions. We then establish a qualitative correspondence between the spatio-temporal structures that evolve continuously in the instability domain and the nature of the irregularity of the scalar stress signal. Rest of the study is on quantifying the dynamical information contained in the stress signals about the spatio-temporal dynamics of the model. We show that at low applied strain rates, there is a one-to-one correspondence with the randomly nucleated isolated bursts of mobile dislocation density and the stress drops. We then show that the model equations are spatio-temporally chaotic by demonstrating the number of positive Lyapunov exponents and Lyapunov dimension scale with the system size at low and high strain rates. Using a modified algorithm for calculating correlation dimension density, we show that the stress-strain signals at low applied strain rates corresponding to spatially uncorrelated dislocation bands exhibit features of low dimensional chaos. This is made quantitative by demonstrating that the model equations can be approximately reduced to space independent model equations for the average dislocation densities, which is known to be low-dimensionally chaotic. However, the scaling regime for the correlation dimension shrinks with increasing applied strain rate due to increasing propensity for propagation of the dislocation bands. The stress signals in the partially propagating to fully propagating bands turn to have features of extensive chaos.     

Mechanoluminescence induced by elastic and plastic deformation of coloured alkali halide crystals at fixed strain rates

Mechanoluminescence (ML) emission from coloured alkali halide crystals takes place during their elastic and plastic deformation. The ML emission during the elastic deformation occurs due to the mechanical interaction between dislocation segments and F-centres, and the ML emission during the plastic deformation takes place due to the mechanical interaction between the moving dislocations and F-centres. In the elastic region, the ML intensity increases linearly with the strain or deformation time, and in this case, the saturation region could not be observed because of the beginning of the plastic deformation before the start of the saturation in the ML intensity. In the plastic region, initially the ML intensity also increases linearly with the strain or deformation time, and later on, it attains a saturation value for large deformation. When the deformation is stopped, initially the ML intensity decreases at a fast rate; later on, it decreases at a slow rate. The decay time for the fast decrease of the ML intensity gives the relaxation time of dislocation segments or pinning time of the dislocations, and the decay time of the slow decrease of the ML intensity gives the diffusion time of holes in the crystals. The saturation value of the ML intensity increases linearly with the strain rate and also with the density of F-centres in the crystals. Initially, the saturation value of the ML intensity increases with increasing temperature, and for higher temperatures the ML intensity decreases with increasing temperature. Therefore, the ML intensity is optimum for a particular temperature of the crystals. From the ML measurements, the relaxation time of dislocation segments, pinning time of dislocations, diffusion time of holes and the energy gap between the bottom of the acceptor dislocation band and interacting F-centre level can be determined. Expressions derived for the ML induced by elastic and plastic deformation of coloured alkali halide crystals at fixed strain rates indicates that the ML intensity depends on the strain, strain rate, density of colour centres, size of crystals, temperature, luminescence efficiency, etc. A good agreement is found between the theoretical and experimental results.     

Investigation on dislocation-based mechanisms of void growth and coalescence in single crystal and nanotwinned nickels by molecular dynamics simulation

Abstract

Molecular dynamics simulations were conducted to elucidate dislocation mechanisms of the void growth and coalescence in single crystal and nanotwinned nickels subjected to uniaxial tension. The simulation results reveal that twin boundary is capable of decreasing the critical stress, suppressing the emission of dislocations and reducing the overall stiffness of the crystal. A size-scale dependence of critical stress is definitely illustrated through stress–strain response, where the larger void size leads to the lower critical stress and strain. It is the successive emissions of leading partials and the subsequent trailing partials that cause the atoms on the void surfaces to escape from the void surfaces continually, and consequently the voids grow to be larger and larger with increasing strain. The voids in the nanotwinned nickel coalesce earlier than those in the single crystal nickel even though the initiation of dislocations in the former is later than that in the latter. Void fraction remains a constant during elastic deformation, while it presents a linear increase with increasing strain during plastic deformation. Evolution of void fraction during void growth and coalescence is independent on void size.     

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.     

Universality and scaling of unstable plastic flow

The statistics of the jumplike plastic deformation of a Cu–Be alloy under the conditions of a low-temperature unstable plastic flow is studied experimentally. At a high strain rate, the parameters of the load jumps are found to be related by power laws, which corresponds to a scale-invariant behavior. A comparison with the data obtained for another mechanism of plastic instability, namely, the Portevin–Le Chatelier effect, points to the existence of universal laws governing the dynamics of a dislocation ensemble in the conditions of plastic instability.     

Modeling of the evolution of a dislocation structure and development of microplastic deformation in single crystals of fcc substitutional solid solutions

An analysis is made of evolution of a dislocation structure during the initial stage of plastic deformation and the stress-strain diagrams are derived theoretically for single crystals of fcc substitutional solid solutions. The example of Cu-Al alloys is used to confirm the theoretically predicted relationship between the stress and strain, and also between the flow stress and the resistance to the motion of a single dislocation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 93–97, July, 1980.     

Strain Rate Sensitivities of Face-Centred-Cubic Metals Using Molecular Dynamics Simulation

We use dislocation theory and molecular dynamics （MD） simulations to investigate the effect of atom properties on the macroscopic strain rate sensitivity of f cc metals. A method to analyse such effect is proposed. The stress dependence of dislocation velocity is identified as the key of such study and is obtained via 2-D MD simulations on the motion of an individual dislocation in an fcc metal. Combining the simulation results with Orowan＇s relationship, it is concluded that strain rate sensitivities of fcc metals are mainly dependent on their atomic mass rather than the interatomic potential. The order of strain rate sensitivities of five fcc metals obtained by analysing is consistent with the experimental results available.     

On the conditions of strain localization and microstructure fragmentation under high-rate loading

The paper reports on research in the deformation and fragmentation mechanisms of coarse- and fine-grained materials under high-rate loading. The study was performed by an experimental procedure based on collapse of thick-walled hollow cylinders and by molecular dynamics simulation. The key issue was to study the formation of plastic strain localization bands. It is found that the pattern of plastic deformation is governed by loading conditions and characteristic grain sizes. For a coarse-grained material, the governing mechanism is dislocation deformation resulting in localization bands. For a fine-grained material, the governing mechanism is grain boundary sliding with attendant fragmentation of the material. A dependence of the strain rate and degree on the critical grain size was disclosed. The computer simulation revealed mechanisms of grain boundary sliding on the scales studied.