Evolution of Distribution of Dislocations in Ni3Ge Single Crystals During Deformation

The evolution of the distribution of dislocations in Ni₃Ge single crystals subjected to deformation in uniaxial compression is studied. The dislocation ensemble in the material under review is found to be of a chaotic homogeneous type. Contact interactions between dislocations prevail, and a linear relation of the spacing between dislocations to the length of dislocation segments is observed for stoppers of an arbitrary type. An equation is derived for the probability density function of the fraction of mobile dislocation segments. The solution to the equation is the normal distribution law. This solution can be extended to parameters that are functions of the dislocation density or spacing between dislocations. The experimental histograms of the spacing between dislocations and of that between arbitrary stoppers with a high significance level obey the lognormal law for all degrees of reduction studied.     

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.     

Kinetics of accumulation of vacancy complexes in dislocated silicon under 60Co γ-ray irradiation

Abstract

Radiation defect accumulation in ⁶⁰Co γ-ray-irradiated n-type Si single crystals (ρ=150ωcm) with various densities of dislocations (N_D = 1 × 10⁴ to 1 × 10⁷ cm ^?2) introduced at plastic deformation was studied. The temperature dependences of the Hall coefficient were measured. The probabilities of interaction of vacancies with oxygen, phosphorus atoms, and dislocation line elements were determined. It has been established that with the increase of N_D they can increase at the expense of complication of dislocation structure, decrease during formation of impurity atmosphere near dislocations and compensation of deformation fields, and they do not change if complex formation of vacancies with impurities occurs far from dislocations. Kinetics of A- and E-centre accumulation in the crystals containing dislocations with different impurity atmosphere was described.     

On the generation of vacancies by moving dislocations

New experiments of Molenaar and Aarts, Blewitt and others seem to confirm the view of the author, previously based only on the experiments of Gyulai and Hartly and Stepanow on sodium chloride, that vacant lattice sites, and possibly interstitial atoms, are generated during plastic flow in ductile crystals, particularly in metals. It is pointed out that the average temperatures near a moving dislocation are probably not sufficiently high to evaporate vacant lattice sites or interstitial atoms as a result of thermal effects alone. Instead, one apparently must conclude that the imperfections are generated either by purely geometrical means during the looping of dislocations about appropriate obstacles, as the result of dynamical instability in the motion of a dislocation, possibly near a jog, or in the very high thermal pulses or ‘spikes’ which are generated either in the zone where two dislocations of opposite sign annihilate one another or near impediments where dislocations are strongly curved. It is pointed out that a pair of vacancies is probably stable near room temperature and may diffuse more rapidly than a single vacancy. It is also proposed that vacancies retained during quenching of Al-Cu alloys and those generated by cold-work play an important role in the precipitation process. The origin of work hardening in single crystals is discussed and several alternative interpretations, which involve the impediment of Frank-Read generators either directly or indirectly as a consequence of the generation of vacancies, are presented. The importance of prismatic dislocations formed by condensation of vacancies is restated. The role that vacancies formed by cold-work may play in determining the stored energy and decrease in density and in affecting processes such as creep and the hardening of latent slip planes is also discussed. Finally a few experiments are proposed, typical of those which could prove decisive in isolating the influence of vacancies.     

Climb via vacancy diffusion of edge dislocations in 2D dislocation microstructures

The prevention of strength degradation of components is one of the great challenges in solid mechanics. In particular, at high temperatures material may deform even at low stresses, a deformation mode known as deformation creep. One of the microstructural mechanisms that governs deformation creep is dislocation motion due to the absorption or emission of vacancies, which results in motion perpendicular to the glide plane, called dislocation climb. However, the importance of the dislocation network for the deformation creep remains far from being understood. In this study, a climb model that accounts for the dislocation network is developed, by solving the diffusion equation for vacancies in a region with a general dislocation distribution. The definition of the sink strength is extended, to account for the contributions of neighbouring dislocations to the climb rate. The model is then applied to dislocation dipoles and dislocation pile-ups, which are dense dislocation structures and it is found that the sink strength of dislocations in a pile-up is reduced since the vacancy field is distributed between the dislocations. Finally, the importance of the results for modelling deformation creep is discussed.     

Mechanisms of high-temperature creep of nickel-based superalloys under low applied stresses

[001] single-crystal specimens of the superalloys CMSX-4 and CMSX-10 were tested for creep at 1100°C under tensile stresses between 105 and 135?MPa, where they show pronounced steady creep. The deformed superalloys were analysed by density measurements, scanning electron microscopy and transmission electron microscopy which supplied information about porosity growth, evolution of the γ–γ′ microstructure, dislocation mobility and reactions during creep deformation. It is shown that, under the testing conditions used, steady creep strain mostly results from transverse glide–climb of (a/2) ?011? interfacial dislocations. A by-product of the interfacial glide–climb are vacancies which diffuse along the interfaces to growing pores or to a ?100? edge dislocations climbing in the γ′ phase. Climb of a ?100? dislocations in the γ′ phase is a recovery mechanism which reduces the constraining of the γ phase by the γ′ phase, thus enabling further glide of (a/2) ?011? dislocations in the matrix. Moreover the γ′ dislocations act as vacancy sinks facilitating interfacial glide–climb. The creep rate increases when the γ–γ′ microstructure becomes topologically inverted; connection of the γ′ rafts results in extensive transverse climb and an increase of the number of a?100? dislocation segments in the γ′ phase.     

Point Defect Production Under High Internal Stress Without Dislocations in Ni and Cu

Kiritani et al. have observed a large number of small vacancy clusters without dislocations at the tip of torn portions of fcc metals such as Au, Ag, Cu and Ni. Small vacancy clusters, rather than dislocation cell structures, have also been observed after high-speed compressive deformation, suggesting the possibility of plastic deformation without dislocations. In this paper, in order to investigate the mechanism of deformation without dislocations, change in formation energy of point defects under high internal stress was estimated by computer simulation. Elastic deformation up to - 20% strain was found to provide a remarkable lowering of formation energy of point defects. For example, when Ni is subjected to elastic strain, the formation energy of an interstitial atom decreases to 40% that without strain and the formation energy of a vacancy decreases to 51% that without strain. The number of point defects formed under thermal equilibrium during deformation was evaluated. The number was judged to be insufficient for explaining the formation of vacancy clusters as observed in experiments.     

Subsurface defect evolution and crystal-structure transformation of single-crystal copper in nanoscale combined machining

ABSTRACT

In the paper, molecular dynamics simulation is applied to study the evolution and distribution of subsurface defects during nanoscale machining process of single-crystal copper. The chip-removal mechanism and the machined-surface-generative mechanism are examined through analysis of the dislocation evolution and atomic migration of the workpieces. The findings show that under different stresses and temperatures, the difference of the binding energy leads to a zoned phenomenon in the chip. Owing to elastic deformation, some of the dislocations could be recovered and form surface steps; moreover, the work hardening of the workpiece can be achieved on account of generation of twin boundaries, Lomer-Cottrell dislocations, and stacking fault tetrahedra (SFT) by plastic deformation. A process of evolution of an immobile dislocation group containing stair-rod dislocations into SFT is discovered, which is different from the traditional Silcox-Hirsch mechanism. Furthermore, a growth oscillation phenomenon, which corresponding stacking fault planes growth and retraction during the formation of the stable SFT, is discussed.     

Specific resistivity of dislocations and vacancies for super-pure aluminium at 4.2 K determined in-situ and post-recovery deformation and correlated to flow stress

ABSTRACT

The evolution of dislocations during shape-change of metal forms results from microstructural shear mechanism that is essential to enhance ductility. However, at room temperatures for face-centred cubic metals, this evolution results in the generation of vacancies that tend to form nano-voids, the growth of which leads to ductile failure. The correlated occurrence of dislocations and vacancies may be differentiated using the change of resistivity with plastic strain at 4.2?K, because resistivity is very sensitive to single vacancies compared to the formation of stacking faulted defects and dislocations. In order to assess the microstructure, the specific resistivity of these defect species was measured at 4.2?K, whereby thermal recovery processes are non-existent. The resistivity per dislocation line-length per volume was determined to be 1.87?×?10^?25?Ωm³ for super-pure aluminium. The change in resistivity directly correlated to the shear flow stress squared. Vacancy-like defects formed during plastic flow were correlated to the recoverable resistivity after 298?K anneal and the derived volume fraction (C_V) from mechanical data. The magnitude could be expressed as 12.9?×?10^?9?Ωm per C_V in % or as 1.21?×?10^?25?Ωm³ in terms of line-length of vacancies per volume. The choice of representation depends on the presumed vacancy distribution. However, the recoverable flow stress upon 298?K anneal only appear to be proportional to √ C_V at low strains; that is, at high strains the generated vacancies had transformed to defects that give rise to a small decrease in resistivity but a more notable increase in the flow stress. The possible mechanisms for this transformation are discussed.     

Molecular Dynamic Simulation of High Speed Deformation Effect on Microstructure Change in Thermal Heated Metals

In the present paper computer simulation of high-speed deformation (shock wave propagation) by molecular dynamic method is performed in thin copper sample, having the form of rectangular parallelepiped (10 a ‐ 10 a ‐ 20 a , where a is the lattice constant) with 8000 atoms. On the surfaces Z 0 =0 and Z max =20 a the mirror boundary conditions with rigid walls and the periodic boundary conditions along X and Y directions corresponding to short sides of deformed crystal are used, which allows to investigate the reflection of shock wave from the surfaces in Z direction. The changes of microstructure have been investigated up to 12 ps. The numerical calculations of microstructure changes have been performed here taking into account the effect of thermal heating of crystal lattice before shock wave front. The numerical results show that comparing with the propagation of shock waves under room temperature in thermal heated structure additional displaced atoms (vacancies and interstitials) are produced. The obtained results show that the production of point defects during high-speed deformation is determined by the thermal softening of microstructure and generation rate of point defects very strong increases with an increasing of high speed deformation rate. The peculiarities of microstructure changes in deformed copper are analyzed here at the different initial temperatures and various high-speed deformations (average ion velocities behind shock wave).     

Grain-boundary dislocations and enhanced diffusion in nanocrystalline bulk materials and films

A theoretical model is suggested which describes the transformations of grain-boundary dislocation walls and their influence on diffusion processes in nanocrystalline materials fabricated under highly non-equilibrium conditions. It is shown that the decay of boundary dislocation walls of finite extent, occurring via the climb of boundary dislocations and the corresponding emission of vacancies, is capable of highly enhancing the grain-boundary diffusion in nanocrystalline materials. The enhanced diffusion, in turn, strongly affects the deformation behaviour of nanocrystalline materials. In the case of nanocrystalline films deposited on to substrates, the effects of misfit stresses on the transformations of boundary dislocation walls and the diffusion are analysed. It is demonstrated that the mean diffusion coefficient in a nanocrystalline film may increase by approximately several orders of magnitude owing to misfit stresses.     

Size dependent deformation behaviour and dislocation mechanisms in 〈1 0 0〉 Cu nanowires

Abstract

Molecular dynamics simulations have been performed to understand the size-dependent tensile deformation behaviour of 〈1 0 0〉 Cu nanowires at 10 K. The influence of nanowire size has been examined by varying square cross-section width (d) from 0.723 to 43.38 nm using constant length of 21.69 nm. The results indicated that the yielding in all the nanowires occurs through nucleation of partial dislocations. Following yielding, the plastic deformation in small size nanowires occurs mainly by slip of partial dislocations at all strains, while in large size nanowires, slip of extended dislocations has been observed at high strains in addition to slip of partial dislocations. Further, the variations in dislocation density indicated that the nanowires with d > 3.615 nm exhibit dislocation exhaustion at small strains followed by dislocation starvation at high strains. On the other hand, small size nanowires with d < 3.615 nm displayed mainly dislocation starvation at all strains. The average length of dislocations has been found to be same and nearly constant in all the nanowires. Both the Young’s modulus and yield strength exhibited a rapid decrease at small size nanowires followed by gradual decrease to saturation at larger size. The observed linear increase in ductility with size has been correlated with the pre- and post-necking deformation. Finally, dislocation–dislocation interactions leading to the formation of various dislocation locks, the dislocation–stacking fault interactions resulting in the annihilation of stacking faults and the size dependence of dislocation–surface interactions have been discussed.     

Dislocations and the mechanical properties of stabilized ZrO2

Abstract

The dislocation substructures and mechanical properties of cubic ZrO₂ single crystals are analyzed. The temperature dependence of the dislocation velocity is complex, the edge segments moving faster than screw segments at low temperatures, while the screws are faster at high temperatures. Using the loop shrinkage technique, the diffusion coefficient of the slowest diffusing species can be determined. The mechanical properties are analyzed in terms of the Peierls mechanism and of interaction of dislocations and point defects.     

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.     

Theoretical study of defect formation processes in metals

Abstract

The equilibrium solute atmosphere around a straight edge dislocation in interstitial solid solutions has been investigated. A long-range deformation interaction among impurities is accounted for. Quantitative estimations have been given for the example of carbonaceous martensite. The impurity concentrations in an atmosphere around the dislocation core are calculated for a given temperature in dependence on its mean value in the specimen. For a dislocation with an impurity atmosphere stationary fluxes of interstitial atoms and vacancies on the dislocation are calculated; a concentration dependence of impurity parameters indicating a dislocation capture efficiency of the self-interstitial atoms and vacancies and the parameter of dislocation preference B are received; a radiation-induced deformation rate (swelling and creep) is determined.     

Generation and accumulation of atomic vacancies due to dislocation movement and pair annihilation

Generation and accumulation of atomic vacancy due to pair annihilation of edge dislocations during plastic slip deformation of metallic materials are numerically evaluated by crystal plasticity analysis. Dislocation density-based models are utilised in the deformation analysis and a theoretical model for the generation of atomic vacancies is introduced. Purely uniform single- and double-slip deformations are analysed and results show that the evolution of the vacancy density depends largely on the microstructure length scale and multiplication of slip activity on different slip systems.     

Effects of torsional deformation on the microstructures and mechanical properties of a CoCrFeNiMo0.15 high-entropy alloy

Abstract

The effects of torsional deformation on the microstructures and mechanical properties of a CoCrFeNiMo_0.15 high-entropy alloy have been investigated. The torsional deformation generates a gradient microstructure distribution due to the gradient torsional strain. Both dislocation activity and deformation twinning dominated the torsional deformation process. With increasing the torsional equivalent strain, the microstructural evolution can be described as follows: (1) formation of pile-up dislocations parallel to the trace of {1 1 1}-type slip planes; (2) formation of Taylor lattices; (3) formation of highly dense dislocation walls; (3) formation of microbands and deformation twins. The extremely high deformation strain (strained to fracture) results in the activation of wavy slip. The tensile strength is very sensitive to the torsional deformation, and increases significantly with increasing the torsional angle.     

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.     

Modelling and simulation of dynamic recrystallisation based on multi-phase-field and dislocation-based crystal plasticity models

ABSTRACT

The mechanical properties of metals used as structural materials are significantly affected by hot (or warm) plastic working. Therefore, it is industrially important to predict the microscopic behaviour of materials in the deformation process during heat treatment. In this process, a number of nuclei are generated in the vicinity of grain boundaries owing to thermal fluctuation or the coalescence of subgrains, and dynamic recrystallisation (DRX) occurs along with the deformation. In this paper, we develop a DRX model by coupling a dislocation-based crystal plasticity model and a multi-phase-field (MPF) model through the dislocation density. Then, the temperature dependence of the hardening tendency in the recrystallisation process is introduced into the DRX model. A multiphysics simulation for pure Ni is conducted, and then the validity of the DRX model is investigated by comparing the numerical results of microstructure formation and the nominal stress–strain curve during DRX with experimental results. The obtained results indicate that in the process of DRX, nucleation and grain growth occur mainly around grain boundaries with high dislocation density. As deformation progresses, new dislocations pile up and subsequent nucleation occurs in the recrystallised grains. The influence of such microstructural evolution appears as oscillation in the stress–strain curve. From the stress–strain curves, the temperature dependence in DRX is observed mainly in terms of the yield stress, the hardening ratio, and the change in the hardening tendency after nucleation occurs.     

Alternate dissociation of the screw dislocations in a (0 0 1) buried small-angle twist boundary in silicon

The square dislocation network of a (0 0 1) buried small-angle boundary in silicon was observed by dark-field transmission electron microscopy to examine the structures of more than 100 dissociated dislocation segments. Images were taken with g = (2 2 0), using a many-beam case along the reciprocal lattice row. Dissociation occurs on alternate close-packed planes without systematic rule, although a degree of ordering is taking place. Most of the dislocation segments have lengths equal to half of the square network period. Image simulation studies revealed that their experimental contrasts cannot be explained from the usual assumption of straight dislocations running in an infinite crystal. However, if these dislocations are supposed close and parallel to a nearby free surface, a reasonable agreement is found between the micrographs and the simulated images. A three-dimensional elastic model is proposed to explain the contrasts of the dislocation network.