The size effects upon shock plastic compression of nanocrystals

For the first time a theoretical analysis of scale effects upon the shock plastic compression of nanocrystals is implemented in the context of a dislocation kinetic approach based on the equations and relationships of dislocation kinetics. The yield point of crystals τ_y is established as a quantitative function of their cross-section size D and the rate of shock deformation as τ_y ~ ε^2/3 D. This dependence is valid in the case of elastic stress relaxation on account of emission of dislocations from single-pole Frank–Read sources near the crystal surface.     

Size effects under plastic deformation of microcrystals and nanocrystals

A theoretical analysis of size effects in plastically deformed crystals with transverse sizes in micro and nanometer ranges has been performed in the framework of the dislocation-kinetic approach. The analysis is based on the evolution equation of the dislocation density in these crystals and takes into account the generation of dislocations from surface dislocation sources and the escape of dislocations from the crystal through the crystal surface. It has been established that the generation of dislocations from the sources leads to a strong strain hardening of the crystal and that the escape of dislocations through the crystal surface results in a fast equilibration of these two kinetic processes. As a result, there occurs a strong “exhaustion” of strain hardening of thin crystals at the early stage of their plastic deformation in accordance with experiments. According to the theory, the flow stresses σ and transverse sizes D of microcrystals and nanocrystals are related by the expressions σ ∼ D ⁻ⁿ (n = 0.625–1.0), which are in agreement with the experiment.     

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.     

Elastic constitutive laws for incompatible crystalline media: the contributions of dislocations,disclinations and G-disclinations

Linear higher-grade higher-order elastic constitutive laws for compatible (defect-free) and incompatible (containing crystal line defects) media are presented. In the proposed model, the free energy density of a body subjected to elastic deformation under the action of surface tractions, moments or hyper-traction tensors (second-order tensors whose anti-symmetric part corresponds to moments) has contributions coming from the first two gradients of displacements. Thermodynamic considerations reveal that only the symmetric component of the gradient of elastic displacement, i.e., compatible elastic strain tensor, and the anti-symmetric component of the second gradient of elastic displacement, i.e., compatible third-order elastic curvature tensor, contribute to the free energy density during compatible deformation of the body. The line crystal defect contributions are accounted for by incorporating the incompatible components of elastic strains, curvatures and symmetric 2-distortions as state variables of the free energy density. In particular, the presence of generalized disclinations (G-disclinations) is acknowledged when the medium is subjected to surface hyper-traction tensors having a non-zero symmetric component along with surface-tractions on its boundary. Mechanical dissipation analysis provides for the coupling between the Cauchy stresses and third-order symmetric hyper-stresses. The free energy density and elastic laws for a defect-free and line crystal defected medium are proposed in a linear setting. In the special case of isotropy, the cross terms between elastic strains and curvatures contribute to the free energy density through a single elastic constant. More interestingly, the Cauchy and couple stresses are found to have contributions coming from both, elastic strains and curvatures.     

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.     

Evolution of the concentration of point defects at the tip of a crack

The evolution of the distribution of interstitial impurity atoms in the plastic zone around the tip of a tension crack is analyzed. The transport of point defects is determined by: 1) the hydrostatic component of the elastic stress at the crack tip, created by the superposition of the elastic fields of the crack and dislocations; 2) the elastic field of moving dislocations (“sweeping out” of interstitial impurity atoms); 3) the dislocation-driven transport of point defects present in the dislocation cores. The contributions of each mechanism of transport of point defects to the crack tip are calculated over the entire time from the start of loading of a sample containing a crack until an equilibrium distribution of plastic deformation is established after the cessation of loading. Numerical calculations are carried out for interstitial hydrogen atoms dissolved in an α-Fe crystal. Fiz. Tverd. Tela (St. Petersburg) 39, 1580–1585 (September 1997)     

α-Fe裂纹的分子动力学研究

通过分子动力学方法，模拟了α-Fe裂纹的单轴拉伸实验中的形变过程.研究了不同晶体取向裂纹的形变特点和断裂机理，观察到各种形变现象，如位错形核和发射，位错运动，堆垛层错或孪晶的形成，纳米空洞的形成与连接等.计算结果表明，裂纹扩展是塑性过程和弹性过程相结合的过程，其中塑性过程表现为由裂尖发射的位错导致的原子切变行为，而弹性过程的发生则是由无位错区中的原子断键所导致.同时还研究了α-Fe裂纹的形变特点和断裂机理与温度场和应力场的依赖关系.     

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.     

Formation of a misorientation band in the elastic field of a disclination dipole

The formation of a misorientation band in the elastic field of a disclination dipole is considered and simulated using a kinetic approach. The dipole is artificially located on a grain boundary or induced by plastic deformation on a double ledge in a grain boundary in a bicrystal. The simulation results agree well with the results obtained earlier in a continuum approximation. The dislocation structure of the misorientation band that forms during accommodation slip is shown to be a dynamic steady-state structure, and its appearance has a kinetic nature.     

Dislocation structure and dynamics govern pop-in modes of nanoindentation on single-crystal metals

ABSTRACT

There are two types of pop-in mode that have been widely observed in nanoindentation experiments: the single pop-in, and the successive pop-in modes. Here we employ the molecular dynamics (MD) modelling to simulate nanoindentation for three face-centred cubic (FCC) metals, including Al, Cu and Ni, and two body-centred cubic (BCC) metals, such as Fe and Ta. We aim to examine the deformation mechanisms underlying these pop-in modes. Our simulation results indicate that the dislocation structures formed in single crystals during nanoindentation are mainly composed of half prismatic dislocation loops. These half prismatic dislocation loops in FCC metals are primarily constituted of extended dislocations. Lomer–Cottrell locks that result from the interactions between these extended dislocations can resist the slipping of half dislocation loops. These locks can build up the elastic energy that is needed to activate the nucleation of new half dislocation loops. A repetition of this sequence results in successive pop-in events in Al and other FCC metals. Conversely, the half prismatic dislocation loops that form in BCC metals after first pop-in are prone to slip into the bulk, which sustains plastic indentation process after first pop-in and prevents subsequent pop-ins. We thus conclude that pop-in modes are correlated with lattice structures during nanoindentation, regardless of their crystal orientations.     

Instability of interstitial dislocation loops in electron-irradiated dielectrics

The experiments on electron irradiation of yttrium-stabilized zirconium oxide samples show the formation of strong elastic fields near interstitial dislocation loops. The fields increase with an increase in the loop radius and, when the loop radius reaches a certain critical value, the loops became unstable due to the beginning of plastic deformation and the formation of a dislocation network. The mechanism of the occurrence of this instability is suggested. It is based on the accumulation of charges at dislocation loops due to ionization processes in an electron-irradiated dielectric. It is shown that the accumulation of the electric charge at growing dislocation loops in dielectrics may be responsible for an increase in elastic stresses near dislocation loops and for their instability because of the beginning of plastic deformation near the loops when stresses at growing loops become close to the theoretical yield stress of the material.     

Two Stages of Impact Fracture of Polycrystalline ZnS and ZnSe Compounds

Mechanoluminescence (ML) in ductile solids is caused by the motion of charged dislocations in the deformable material. Interatomic bond ruptures followed by electronic structure reconfiguration are the main source of ML in brittle bodies. We studied ML in ceramics composed of mixed ionic/covalent ZnS and ZnSe compounds, which are generated during impact loading higher than the limit deformation. Depending on synthesis method and thermal treatment, the resulting ceramics had different size and geometry of grains and intergrain boundary structure, which presumably may have a significant effect on the dislocation glide. In both materials, the time sweeps of ML pulses have two well-resolved peaks. The position of the peaks along the time axis is substantially dependent on the size of ceramic-forming grains and, to a smaller extent, on the barrier properties of intergrain boundaries. The first peak is associated with plastic deformation preceding disintegration of the crystal structure. The second peak emerges upon crack nucleation as interatomic bonds are ruptured and the material is undergoing local deformation in tips of propagating cracks. The distributions of ML pulse amplitudes (the dependences between the number of pulses and their amplitude) calculated for both peaks individually follow the power law, which demonstrates that the electronic processes having different excitation mechanisms (dislocation motion vs bond rupture) are correlated.

     

A New View of Incipient Plastic Instability during Nanoindentation

Whether the dislocation nucleation or the sudden dislocation multiplication dominates the incipient plastic instability during the nanoindentation of initial defect-free single crystal still remains unclear. In this work, the dislocation mechanism corresponding to the incipient plastic instability is numerically investigated by coupling discrete dislocation dynamics with the finite element method. The coupling model naturally introduces the dislocation nucleation and accurately captures the heterogeneous stress field during nanoindentation. The simulation results show that the first dislocation nucleation induces the initial pop-in event when the indenter is small, while for larger indenters, the incipient plastic instability is ascribed to the cooperation between dislocation nucleation and multiplication. Interestingly, the local dislocation densities for both cases are almost the same when the sudden load drop occurs. Thus it is inferred that the adequate dislocations generated by either nucleation or multiplication, or both, are the requirement for the trigger of incipient plastic instability. A unified dislocation-based mechanism is proposed to interpret the precipitate incipient plastic instability.     

Surface size effects under plastic deformation of microcrystals and nanocrystals

The size effects associated with the crystal surface as an effective sink for moving dislocations in a thin crystal and as a barrier for these dislocations in the presence of a high-strength film or a special hardened layer on the surface, which favor the accumulation of dislocations in the crystal, have been considered theoretically in terms of the kinetic equation for the density of dislocations concentrated in the crystal in the critical lengths of single-ended (unipolar) dislocation sources. The theoretical results have been illustrated by the experimental data available in the literature for microcrystals and nanocrystals of copper and aluminum. It has been found in accordance with these data that the dependence of the yield stress ??_2% of the crystal on the crystal transverse size D has the form ??_2% ?? D ^?0.75 when there is a free crystal surface for the escape ofthe dislocations and ??_2% ?? D ^?0.5 when there is a high-strength layer on the lateral surface of the crystal..     

Molecular dynamics simulation on elastoplastic properties of the void expansion in nanocrystalline copper

Influences of different factors on the elastic-plastic properties of nanocrystalline copper containing a void are studied by the molecular dynamics method. The radius of the circular plate is 30a, while the radius of the void is 5a (a is 0.3615 nm for the lattice constant of bulk copper). The effects of crystal orientation, the void ellipticity, loading rate, and temperature of nanocrystalline copper are discussed. The elastic-plastic deformation of nanocrystalline under inner pressure is investigated in this research. The plastic zone is determined according to the dislocation nucleation from the edge of the void. The simulation results show that there are different deformation mechanisms under different crystal orientations, and the nanocrystalline copper can be strengthened by changing the void shape, decreasing the loading rate, and lowering the temperature. And the plastic zone initiation and growth are further explained. The change of different conditions has a great influence on plastic zone.     

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.     

Effects of void shape and orientation on the elastoplastic properties of spheroidally voided single-crystal and nanotwinned copper

ABSTRACT

Void nucleation, growth and coalescence have been identified as the leading cause of ductile damage in metallic materials. To understand the underlying deformation and damage mechanisms, extensive theoretical, experimental and simulation efforts have been attempted on spherically voided metals. In this work, molecular dynamics simulations are performed to analyze the uniaxial straining deformation behaviours of both single-crystal and nanotwinned copper materials embedded with a preexisting spheroidal void. The coupling effects among twin boundary, spheroidal void aspect ratio and orientation on unidirectional elastoplastic behaviours are systematically examined. The dislocation-induced plastic deformation mechanism is also examined and compared with the one due to a perfectly spherical cavity. Simulation results show that elastic modulus increases with both spheroidal void aspect ratio and orientation. So do the yield stress, the first peak stress and the plasticity index. Another peak stress exists for most cases, except for a prolate void embedded in nanotwinned specimens. The slope between peak stresses decreases with both the spheroidal aspect ratio and orientation. The incorporation of a twin boundary results in lower elastic modulus, higher yield strength and smaller plasticity index. For an oblate void, the twin boundary gives rise to more severe strain softening behaviour. The dislocation extraction algorithm illustrates that the continuous nucleation, propagation and reaction of dislocations emanated from both the void front and twin boundary are responsible for the ductile damage of spheroidally voided crystals. The lower dislocation densities found in nanotwinned specimens indicate the desired suppression effects of twin boundary on dislocation activities.     

Face-centered-cubic to body-centered-cubic phase transformation of Cu nanoplate under [100] tensile loading

ABSTRACT

Molecular dynamics simulation was used to stretch Cu nanoplates along its [100] direction at various strain rates and temperatures. Under high strain rate and beyond the elastic limit, the Cu nanoplates underwent an unusual deformation mechanism with expansion along free surface lateral direction and contraction along the other lateral direction, which leaded to the face-centred-cubic phase transforming into unstressed body-centred-cubic phase. Under low strain rate, the deformation of the nanoplate went back to well-known dislocation mechanism. The face-centred-cubic to body-centred-cubic phase transformation mechanism was further discussed in terms of elastic stability theory and free surface stress effect.     

Influence of the transverse size of samples with micro- and nano-grained structures on the yield and flow stresses

The effects of reduction in the strength and deviation from the Hall-Petch relationship under plastic deformation of specimens with micro- and nano-grained structures with decreasing size of their cross section have been considered theoretically. The analysis is based on the kinetic equation for the dislocation density, which takes into account that the surface of the specimen serves as both the source and the sink for dislocations, whereas the grain boundaries are barriers limiting the mean free path of dislocations. It has been found that, when the ratio of the transverse size of the specimen D to the grain size d becomes less than 3, in the dependence of the yield stress on the size of the specimen there appears a minimum as a result of the increase in the number of near-surface grains that exhibit a weak resistance to plastic deformation due to the withdrawal of dislocations through the external surface of the fine-dimensional specimen. The minimum of the strength in the range d < D < 3d is a consequence of the competition and nonlinear interaction of the size factors D and d.