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.     

位错与溶质原子间动态相互作用的数值模拟研究

通过Cottrell-Bilby型溶质动力学模型，对位错线周围的溶质原子浓度随应变率的变化进行了研究，并得到了三种不同的位错-溶质相互作用方式：在低应变率时，位错被溶质原子气团充分钉扎，它上面的溶质浓度近似达到饱和；在高应变率时，脱钉作用占主导地位，位错运动几乎不受深质影响；而在中间应变率时，位错反复经历着钉扎和脱钉过程，动态应变时效发生.此外，通过对模型方程的推导，还自然地得到了平衡状态下率相关流动应力与应变率之间的N形关系曲线. 关键词： 位错 溶质原子 动态应变时效 数值模拟     

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.     

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 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.     

Localization of plastic strain under shock-wave loading of titanium alloy with a crack

The effect of shock-wave loading with an amplitude of 4 GPa and a duration of 10 μs on the localization of plastic flow and the dynamic fracture of VT-1 cast titanium alloy containing a disk-shaped crack is considered. It is found that the crack size decreases in the direction of shock wave propagation, the dislocation density grows and adiabatic shear bands appear near the crack, and secondary cracks originate in the areas of localized flow near the crack edges. The strain, strain rate, dislocation density, rate of dislocation generation, and dislocation velocity near and away from the healing crack are estimated.     

不同加载条件下位错和溶质原子交互作用的数值模拟

动态应变时效,即位错和溶质原子的动态交互作用,对合金材料的力学性质产生重要影响. 本文基于蒙特卡罗方法,建立了“多位错-溶质原子” 二维动力学模型,分别模拟了单位错-恒定应力率、多位错-无应力、多位错-恒定应力和多位错-恒定应力率四种条件下位错和溶质原子的演化过程. 单位错-恒定应力率情况下,低应力率时位错被溶质原子钉扎而无法脱钉,高应力率时位错未被钉扎而一直运动,只有在适当应力率范围内,位错才呈现出反复的钉扎和脱钉;多位错-无应力时,溶质原子向正/负位错的下/上方偏聚;多位错-恒定应力时,位错运动受溶质原子钉扎的影响随应力增大而减小;多位错-恒定应力率时,集群化的钉扎和脱钉过程导致了位错总位移呈现阶梯状的演化. 模拟结果表明：“位错-溶质原子”尺度上呈现了动态应变时效微观过程,与其理论描述相一致. 关键词： 动态应变时效 动力学模型 位错运动     

Modelling the yield point phenomena during deformation at elevated temperatures: case study on Inconel 600

The discontinuous yield behaviour (DYB) of Inconel 600 was studied during hot compression tests at temperatures in range of 850–1150°C and strain rates of 0.001–1?s^?1. The yield point phenomena were observed in the temperature range of 850–1000°C and strain rates of 0.001–0.1 s^?1. The DYB was modelled by considering the evolution of dislocation density at the early stages of yielding. The opposite effects of dislocation multiplication, dislocation interaction (work hardening) and dynamic recovery (DRV) were considered. It was shown that the dislocation multiplication and DRV result in flow softening, while the dislocation interaction leads to work hardening. The model was established in a way to consider the effects of various microstructural evolutions on the σ(ε) function. The discontinuous flow curves were fitted by the developed model with acceptable precision. The variations of material constants with temperature and strain rate were found physically meaningful. The dislocation multiplication parameter was determined at various temperatures and strain rates. It was concluded that the rate of dislocation multiplication increases as temperature rises or strain rate declines. Accelerated dislocation multiplication leads to less drop in yield stress between the upper and lower yield points.     

不同速度拉伸变形时高纯铁的正电子湮没研究

本文采用慢拉伸与正电子多普勒展宽方法相结合,研究应变速率对正电子S参数与形变量ε变化规律(S-ε曲线)的影响,获得如下结果:1)高纯铁慢拉伸条件下,其S-ε曲线出现不饱和现象,应变速率越小,不饱和现象越明显;2)高纯铁中S-ε曲线随应变速率变化的原因归结于不同应变速率拉伸所产生的位错组态不同;3)高纯铁拉伸变形时,S参数的增加一部份来源于位错,另一部份来源于空位,空位及其聚合物是导致S-ε曲线不饱和的主要原因。 关键词：     

Initial dislocation density effect on strain hardening in FCC aluminium alloy under laser shock peening

Abstract

The effect of initial dislocation density on subsequent dislocation evolution and strain hardening in FCC aluminium alloy under laser shock peening (LSP) was investigated by using three-dimension discrete dislocation dynamics (DD) simulation. Initial dislocations were randomly generated and distributed on slip planes for three different dislocation densities of 4.21 × 10¹², 8.12 × 10¹² and 1.26 × 10¹³ m^?2. Besides, variable densities of prismatic loops were introduced into the DD cells as nanoprecipitates to study the dislocation pinning effect. The flow stresses as a function of strain rate obtained by DD simulation are compared with relevant experimental data. The results show a significant dislocation density accumulation in the form of dislocation band-like structures under LSP. The overall yield strength in FCC aluminium alloy decreases with increasing initial dislocation density and forest dislocation strengthening becomes negligible under laser induced ultra-high strain rate deformation. In addition, yield strength is enhanced by increasing the nanoprecipitate density due to dislocation pinning effect.     

Change of the kinetics of shock-wave deformation and fracture of VT1-0 titanium as a result of annealing

The paper presents the results of measurements of shock-wave compression profiles of VT1-0 titanium samples after rolling and in the annealed state. In the experiments, the pressure of shock compression and distance passed by the wave before emerging to the sample surface were varied. From measurements of the elastic precursor decay and compression rate in a plastic shock wave of different amplitudes, the plastic strain and the corresponding shear stresses in the initial and subsequent stages of high-rate deformation in an elastoplastic shock wave are determined. It is found that the reduction in the dislocation density as a result of annealing reduces the hardness of the material but significantly increases its dynamic yield strengh, corresponding to the strain rate above 10⁴ s^–1. With a reduction in the strain rate, this anomalous difference in the flow stresses is leveled off.     

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.     

Experimental verification of Foreman dislocation model

We present a strain analysis of an edge dislocation core, and a detailed discussion of the Foreman dislocation model. In order to examine the model, the quantitative measurement of strain field around an edge dislocation in aluminum is performed, and high-resolution transmission electron microscopy and geometric phase analysis are employed to map the strain field of the edge dislocation core in aluminum. The strain measurements are compared with the Foreman dislocation model, showing that they are in good agreement with each other when 0.7 ≤ a ≤ 1.5.     

Modelling the dynamic deformation and patterning in fcc single crystals at high strain rates: dislocation dynamics plasticity analysis

The deformation process in copper and aluminium single crystals under shock loading is investigated using a multiscale model of plasticity that couples discrete dislocation dynamics and finite element analyses. Computer simulations are carried out to mimic loading condition of high strain rates ranging from 10⁵ to 10⁷?s^?1, and short pulse durations of few nanoseconds involved in recent laser based experiments. The effects of strain rate, shock pulse duration and the nonlinear elastic properties are investigated. Relaxed configurations using dislocation dynamics show formation of dislocation micro bands and weak dislocation cells. Statistical analyses of the dislocation microstructures are preformed to study the characteristics of the local dislocation densities and the distribution of the instantaneous dislocations velocities.     

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.     

剪切应变下刃型位错的滑移机理的晶体相场模拟

针对刃型位错的滑移运动, 构建包含外力场与晶格原子密度耦合作用的体系自由能密度函数, 建立剪切应变作用体系的晶体相场模型. 模拟了双相双晶体系的位错攀移和滑移运动, 计算了位错滑移的Peierls势垒和滑移速度. 结果表明: 施加较大的剪切应变率作用, 体系能量变化为单调光滑曲线, 位错以恒定速度做连续运动, 具有刚性运动特征; 剪切应变率较小时, 体系能量变化出现周期波动特征, 位错运动是处于低速不连续运动状态, 运动出现周期“颠簸”式滑移运动, 具有黏滞运动特征; 位错启动运动, 存在临界的势垒. 位错启动攀移运动的Peierls势垒要比启动滑移Peierls势垒大几倍. 位错攀移和滑移运动特征与实验结果相符合.     

层厚度和应变率对铜-金复合纳米线力学性能影响的模拟研究

采用分子动力学模拟方法, 研究了层厚度和应变率对铜-金多层复合纳米线在均匀拉伸载荷下力学性能的影响, 并分析了铜-金位错成核机理. 研究结果表明, 随着铜-金层厚度的增加, 复合材料的屈服强度也随之增大; 高应变率时复合材料的力学性能比低应变率时要强, 低应变率的塑性形变主要是位错运动和孪晶形变, 而高应变率主要以单原子运动为主, 表现出了非晶化. 该研究对制备高性能的多层复合材料提供了一定的理论依据.     

Simulation of the interaction between an edge dislocation and ⟨111⟩ interstitial dislocation loops in α-iron

ABSTRACT

The dependence of the interactions of intermediate-size ½<111> self-interstitial atom (SIA) loops with an edge dislocation on strain rate and temperature was investigated by molecular dynamics (MD) simulations for the interatomic potential derived by Ackland et al. (A97). For low temperatures (T?=?1?K), the mechanisms of the interactions were in agreement with recent literature. It was shown that a second passing of the dislocation through the loop led to a different mechanism than the one that occurred upon first passing. Since these mechanisms are associated with different SIA loop sizes, and since the loop lost a number of SIAs upon first interaction, it was deduced that the dividing threshold between large and small loops (rendering them strong or weak obstacles, respectively) is at the vicinity of the loop size studied (169 SIAs). For higher temperatures (T?=?300?K), the strain rate dependence proved strong: for low strain rates, the dislocation absorbed the loop as a double super-jog almost immediately and continued its glide unimpeded. For a high strain rate, the dislocation was initially pinned due to the formation of an almost sessile segment leading to high critical stress.     

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.     

铁在范性形变过程中的低频内耗

在改装了的拉力试验机上测量了纯铁在范性形变过程中的内耗。研究了拉伸速率(在0.73×10^-6-50×10^-6/秒范围内)、测量频率(在0.3—3.6/秒范围内)、应变退火及含碳量等对纯铁范性形变过程中内耗的影响。所得结果表明,在屈服平台上,范性形变过程中内耗基本不变,且其值随范性形变速率的增加和测量频率倒数的增加而线性增加。将实验结果与范性形变过程内耗的位错动力学模型所得出的定量关系式进行了对比,得到了满意的符合。求得了退火纯铁在屈服平台上的位错动力学指数为10 关键词：