Grain boundary sliding and lattice dislocation emission in nanocrystalline materials under plastic deformation

A theoretical model is proposed to describe the physical mechanisms of hardening and softening of nanocrystalline materials during superplastic deformation. According to this model, triple interface junctions are obstacles to glide motion of grain boundary dislocations, which are carriers of grain boundary glide deformation. Transformations of an ensemble of grain boundary dislocations that occur at triple interface junctions bring about the formation of partial dislocations and the local migration of triple junctions. The energy characteristics of these transformations are considered. Pileups of partial dislocations at triple junctions cause hardening and initiate intragrain lattice sliding. When the Burgers vectors of partial dislocations reach a critical value, lattice dislocations are emitted and glide into adjacent grains, thereby smoothing the hardening effect. The local migration of triple interface junctions (caused by grain boundary sliding) and the emission of lattice dislocations bring about softening of a nanocrystalline material. The flow stress is found as a function of the total plastic strain, and the result agrees well with experimental data.     

Study of the effects of grain size on the mechanical properties of nanocrystalline copper using molecular dynamics simulation with initial realistic samples

Abstract

Molecular dynamics simulations have been performed to study the mechanical properties of a columnar nanocrystalline copper with a mean grain size between 9.0 and 24 nm. A melting–cooling method has been used to generate the initial samples: this method produces realistic samples that contain defects inside the grains such as dislocations and vacancies. The results of uniaxial tensile tests applied to these samples reveal the presence of a critical mean grain size between 16 and 20 nm, for which there is an inversion of the conventional Hall–Petch relation. The principal mechanisms of deformation present in the samples correspond to a combination of dislocations and grain boundary sliding. In addition, this analysis shows the presence of sliding planes generated by the motion of perfect edge dislocations that are absorbed by grain boundaries. It is the initial defects present inside the grains that lead to this mechanism of deformation. An analysis of the atomic configurations further shows that nucleation and propagation of cracks are localised on the grain boundaries especially on the triple grains junctions.     

Theories of Creep in Ceramics

Mathematical models that have been proposed for creep in ceramics are described. Emphasis is on models involving grain boundary motion (sliding or flow). In Lifshitz models the crystalline grains elongate with strain; the elongation results from diffusion, slip, or solution and precipitation. In Rachinger models the grains do not elongate during creep. The sliding strain can be accommodated by viscous flow of a glassy phase at the grain boundaries, or if there is no boundary glass by diffusion or slip in superplastic models. Sliding of a glass-free boundary can result in cavitation, cracking, or formation of boundary dislocations or triple point folds.

Most models of ceramic creep at high temperatures predict a steady state (stage II) creep rate that depends on the applied stress, grain size, and temperature. A general equation for the creep rate as a function of these factors, as well as the elastic modulus and a diffusion coefficient, is used to compare models. The models give different exponents for the functional dependence of creep rate on grain size and strain and different temperature dependencies. These differences are compared in tables, and the main mechanistic features of the models are described in the text.

The purpose of this review is to describe creep models rather than to compare them with experimental results or to select the most applicable models. There are few critical experimental tests that allow selection of the most accurate models; such experiments are suggested as the next step in choosing between the models for specific experimental results.     

The influence of strain rate on the visibility of dislocations in transmission electron microscopy images of deformed Ti–6 wt% Al–4 wt% V and in Timet 550

Samples of Ti–6?wt%?Al–4?wt%?V and Timet 550 (Ti–4?wt%?Al–4?wt%?Mo–2?wt%?Sn–0.5?wt%?Si) have been subjected to strain rates between 10^?1 and 10³?s^?1and detailed examination of the dislocation structure in the α grains has been carried out using transmission electron microscopy (TEM). For samples deformed to a strain of 0.1 at 10^?1?s^?1, detailed analysis of the defects can be carried out using all diffracting vectors and the presence of (c +?a) dislocations and a dislocations thus confirmed. In contrast, for samples strained to the same strain of 0.1 but at 5?s^?1, it is not possible to obtain images of dislocations when using any diffracting vectors other than 0002. Thus the presence of dislocations which have a Burgers vector containing a c component can be confirmed in the samples strained at 5?s^?1 but the presence of a-component dislocations can only be inferred from TEM of these samples because of the difficulty of obtaining images with diffracting vectors other than 0002. Limited observations on samples strained at 10³?s^?1 show that similar difficulties are found in imaging dislocations as are found in samples deformed at 5?s^?1 but at this strain rate, the highest used, the difficulties are reduced since images can be obtained in some grains using diffracting vectors other than 0002. These results are discussed in terms of the nature of damage as a function of strain rate and the factors that influence contrast from dislocations in crystals.     

Creep behaviour in a discontinuous SiC–Zn-22% Al composite

Creep experiments were conducted on Zn-22%?Al in which SiC particulates were introduced by variable co-deposition of multi-phase materials (VCM). The objective of the investigation is to determine the effect of SiC particulates on the creep behaviour in region I (the low-stress region) and region II (the intermediate-stress or superplastic region) of the sigmoidal plot between stress and strain rate, which was previously reported for the reinforcement-free Zn-22%?Al. The creep data show that the presence of SiC particulates has no effect on the sigmoidal trend between stress and strain rate; and that in region II, the stress exponent, n, and the activation energy for creep, Q, agree well with those reported for SiC-free grades of Zn-22%?Al; n?=?2.5 and Q?～?Q _gb, where Q _gb is energy for grain boundary diffusion in the alloy. However, the data indicate that the presence of the particulates results in narrowing region II and reducing maximum ductility. An analysis of the creep data reveals the presence of a threshold stress that depends strongly on temperature. The microstructural data inferred from an examination of the crept specimens by the means of transmission electron microscopy (TEM) suggest that the origin of τ ₀ may be related to the interaction between moving dislocations and dispersion particles. These particles are introduced in the material as a result of processing the material by thermal spray and deposition.     

Grain Growth During Superplastic Deformation

Significant grain growth occurring during superplastic deformation is related to the micro-mechanism of superplastic flow. Observations performed on the deformed surface of superplastically deformed tensile and shear Pb-62%Sn samples and bi-axially formed AA7475 samples directly indicate that cooperative grain boundary sliding, i.e. sliding of grain groups, is accompanied by cooperative grain boundary migration that can result in an enhanced grain growth. Such a long range correlation in migration of sliding grain boundaries is related to movement of grain boundary dislocations having a step associated with its core. Observed correlation between grain size and strain measured in different regions of a superplastically formed Ti-alloy part and alignment of grain boundaries along shear surfaces support coupling of grain boundary sliding and migration. A model of grain growth considering climb of cellular dislocations, topological defects in a grain array, has been expanded to incorporate gliding and mixed cellular dislocations.     

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.     

A study on anomalous yield drop behaviour in modified beta titanium alloys

ABSTRACT

The yield drop phenomenon observed in the Ti–15V-3Al–3Sn-3Cr (Ti–15–3) beta-titanium alloy and its anomalous behaviour in the boron and carbon added Ti–15–3 alloys have been studied. While the base and the carbon containing alloys exhibit yield drop, the boron containing alloy with smaller grain size than base alloy does not appear to show this phenomenon. Tensile tests were interrupted at different stress levels followed by analyses of slip lines and sub-structural characteristics using scanning and transmission electron microscopes to understand this anomalous yield point phenomenon. Infrared thermal imaging technique was used to map the strain localisation and the spatiotemporal evolution of deformation along the gauge length of the specimens during the tensile tests. Deformation in these alloys initiates only in a few grains. Pile-up of dislocations in these grains subsequently triggers the formation of dislocations in other grains and their rapid multiplications. The spreading of deformation by the generation of dislocations from pile up dislocations in one grain to neighbouring un-deformed grains and their rapid multiplication to new regions influence the yield drop phenomenon and its characteristics. It is shown in this study that microscopic instability in the grain level is a necessary, but not the sufficient condition for the manifestation of macroscopic instability during tensile deformation in polycrystalline materials. The presence of boride particles at grain boundaries restricts the slip transfer across the grains as well as the spreading of deformation to new regions, which causes the suppression of yield drop in the boron containing alloy.     

Superplasticity in a Zn-1·1 wt.% Al alloy

In the paper the results of the deformation behaviour study in a Zn-1·1 wt. % Al alloy are presented. The influence of temperature ranging from 223 K (0·34T_m) to 645 K (0·98 T_m) on the flow stress, strain rate sensitivity parameterm and activation energy was investigated at various strain rates. The superplastic behaviour was observed in a very broad temperature interval the limits of which were dependent on the strain rate. The best superplastic properties—ductility A>1000 % and parameterm0·7—were established at strain rates at temperatureT=520 K. Superplastic characteristics were found in coarser-grained samples with grain sizes up to 50 m. An intensive grain growth occurring at temperaturesT370 K was found to be probably responsible for the origin of anomalies in temperature dependences of the flow stress and parameterm. The activation energy established in the region of superplastic behaviour was much lower than the activation energy measured in the non-superplastic region. The valueQ90 kJ/mol obtained in the non-superplastic region at very high temperatures is comparable with the activation energy of lattice selfdiffusion in pure Zn or heterodiffusion of Al in Zn along the hexagonalc-axis. This result suggests that the deformation mechanism in the non-superplastic region has a nature similar to the high-temperature dislocation creep. The activation energyQ 20;40 kJ/mol obtained in the superplastic region cannot be compared with activation energies of any known diffusion types in Zn. The explanation of this discrepancy could be find in the presence of other temperature dependent terms the contributions of which to the temperature dependence of the flow stress were neglected. The structure study confirmed the decrease in the contribution of grain boundary sliding when passing from the superplastic to the non-superplastic region.     

Multiscale modelling of dislocation/grain boundary interactions. II. Screw dislocations impinging on tilt boundaries in Al

The interaction of dislocations with grain boundaries (GBs) determines a number of important aspects of the mechanical performance of materials, including strengthening and fatigue resistance. Here, the coupled atomistic/discrete-dislocation (CADD) multiscale method, which couples a discrete dislocation continuum region to a fully atomistic region, is used to study screw-dislocations interacting with Σ3, Σ11, and Σ9 symmetric tilt boundaries in Al. The low-energy Σ3 and Σ11 boundaries absorb lattice dislocations and generate extrinsic grain boundary dislocations (GBDs). As multiple screw dislocations impinge on the GB, the GBDs form a pile-up along the GB and provide a back stress that requires increasing applied load to push the lattice dislocations into the GB. Dislocation transmission is never observed, even with large GBD pile-ups near the dislocation/GB intersection. Results are compared with experiments and previous, related simulations. The Σ9 grain boundary, composed from a more complex set of structural units, absorbs screw dislocations that remain localized, with no GBD formation. With increasing applied stress, new screw dislocations are then nucleated into the opposite grain from structural units in the GB that are nearby but not at the location where the original dislocation intersected the boundary. The detailed behaviour depends on the precise location of the incident dislocations and the extent of the pile-up. Transmission can occur on both Schmid and non-Schmid planes and can depend on the shear stresses on the GB plane. A continuum yield locus for transmission is formulated. In general, the overall dissociation and/or transmission behaviour is also determined by the Burgers vectors and associated steps of the primitive vectors of the grain boundary, and the criteria for dislocation transmission formulated by Lee et al . [Scripta Metall. 23 799 (1989); Phil. Mag. A 62 131 (1990); Metall. Trans. A 21 2437 (1990)] are extended to account for these factors.     

纳米单晶与多晶铜薄膜力学行为的数值模拟研究

通过对不同温度下单晶薄膜的拉伸性能的分子动力学模拟，从微观角度揭示了温度效应对材料性能的影响. 结果表明温度效应对材料的变形机理影响很大.0K温度下由于缺乏热激活软化的影响, 粒子运动所受到的阻碍较大, 薄膜的强度较高, 塑性变形主要来自于粒子的短程滑移.温度升高，粒子的热运动加剧，屈服强度降低, 塑性变形将主要来自于大范围的位错长程扩展.多晶薄膜的模拟结果表明, 虽然其晶粒形状较为特殊, 但是它仍然遵循反Hall-Petch关系.在模拟过程中，侧向应力最大值比拉伸方向应力的最大值滞后出现.位错只会从晶界产生并向晶粒内部传播，晶粒间界滑移是多晶薄膜塑性变形的主要来源. 关键词： 纳米薄膜 变形机理 温度效应 分子动力学     

On the measurement of dislocation core distributions in a GaAs/ZnTe/CdTe heterostructure by high-resolution transmission electron microscopy

Tensorial maps of misfit dislocations at the strained GaAs-ZnTe-CdTe interfacial zone are reconstructed by use of digital processing of high-resolution transmission electron micrographs. Large distortions of the crystal lattice around Lomer dislocations are measured using the geometric phase technique. The integration of the dislocation distribution tensor field over a dislocation core region gives the in-plane components of their Burgers vectors. The accuracy of the method for the dislocation map reconstruction is tested by comparing the theoretical values of the so-called true Burgers vectors with those obtained from the integration of tensorial maps.     

Modeling of Dislocation Generation and Interaction During High-Speed Deformation of Metals

Recent experiments by Kiritani et al. [1] have revealed a surprisingly high rate of vacancy production during high-speed deformation of thin foils of fcc metals. Virtually no dislocations are seen after the deformation. This is interpreted as evidence for a dislocation-free deformation mechanism at very high strain rates. We have used molecular-dynamics simulations to investigate high-speed deformation of copper crystals. Even though no pre-existing dislocation sources are present in the initial system, dislocations are quickly nucleated and a very high dislocation density is reached during the deformation. Due to the high density of dislocations, many inelastic interactions occur between dislocations, resulting in the generation of vacancies. After the deformation, a very high density of vacancies is observed, in agreement with the experimental observations. The processes responsible for the generation of vacancies are investigated. The main process is found to be incomplete annihilation of segments of edge dislocations on adjacent slip planes. The dislocations are also seen to be participating in complicated dislocation reactions, where sessile dislocation segments are constantly formed and destroyed.     

Collective effects in an ensemble of dislocations and vacancies with the formation of the localized deformation zone

Abstract

Paperi have reported about the formation of the superplastic zone as the result of defect production in high strength alloys with the fine precipitates of a non-metalic phase under the intensive stress of about (10^-2 ÷ 10^-1)μ, where μ is a shear modulus. It turned out, that the stopping of slipping dislocations near the precipitates leaded to vacancy influx, which promoted dislocations climbing, on the one hand, and increased its concentration on the other. The higher vacancy concentration, the higher dislocation density increases     

Current problems of superplasticity

The possibility of conversion of intermetallic materials (Ti-Al, Fe-Cr-Co and Mn-Al-C) into the superplastic state is shown. The microstructural changes occurring during the superplastic flow in the Ti-Al intermetallics are analysed. A very important role of grain boundary structure in the superplastic deformation of intermetallics is shown. The experimental results obtained are interpreted on the basis of a model taking into account interactions between lattice dislocations and grain boundaries during the superplastic deformation.     

Influence of copper solute on the creep rate sensitivities of aluminium

The presence of copper atoms as continuous networks at the grain boundaries of an aluminium-copper alloy has been considered not preventing the moving of dislocations during creep (or at least partially). The dislocations can bs absorbed by these boundaries and penetrate through them. That leads to changés of shape and structure of grains and also to the sliding of grains against each other. This was deduced from the accelerating increase in the sensitivity of the steady state creep rate to the applied stress of an aluminium 2·8 wt% copper alloy examined at wide range of temperatures (50–350 °C) and applied stresses (7–170 MPa). This rapid increase in the sensitivity parameter of the steady state creep rate occurs in Al-Cu alloys at quite higher ranges of applied stresses and may be attributed mainly to the contribution of the grain boundary movements to the creep strain.     

Observations of glide and decomposition of a⟨101⟩ dislocations at high temperatures in Ni-Al single crystals deformed along the hard orientation

Ni-44 at.% Al and Ni-50 at.% Al single crystals were tested in compression in the hard d001 ¢orientation. The dislocation processes and deformation behaviour were studied as a function of temperature, strain and strain rate. A slip transition in NiAl occurs from a?111? slip to non-a?111? slip at intermediate temperatures. In Ni-50 at.% Al single crystals, only a?010? dislocations are observed above the slip transition temperature. In contrast, a a?101?{101} glide has been observed to control deformation beyond the slip transition temperature in Ni-44 at.% Al. a?101? dislocations are observed primarily along both ?111? directions in the glide plane. High-resolution transmission electron microscopy observations show that the core of the a?101? dislocations along these directions is decomposed into two a?010? dislocations, separated by a distance of approximately 2 nm. The temperature window of stability for these a?101? dislocations depends upon the strain rate. At a strain rate of 1.4 210^?4 s^?1, a?101? dislocations are observed between 800 and 1000 K. Complete decomposition of a?101? dislocations into a?010? dislocations occurs beyond 1000 K, leading to a?010? climb as the deformation mode at higher temperatures. At lower strain rates, decomposition of a?101? dislocations has been observed to occur along the edge orientation at temperatures below 1000 K. Embedded-atom method calculations and experimental results indicate that a?101? dislocations have a large Peierls stress at low temperatures. Based on the present microstructural observations and a survey of the literature with respect to vacancy content and diffusion in NiAl, a model is proposed for a?101?{101} glide in Ni-44 at.% Al, and for the observed yield strength versus temperature behaviour of Ni-Al alloys at intermediate and high temperatures.     

Grain-boundary sliding in elongated microstructures during diffusion creep

In diffusion creep, the contribution of grain-boundary sliding to the overall strain os can be evaluated in arbitrary polycrystals, if the angular distribution of grain boundaries is known. A os value of 0.5 is obtained for two-dimensional (2D) equiaxed microstructures consisting of regular hexagonal grains, equiaxed grains grown from a Voronoi structure or grains having a circular distribution of grain-boundary angles. The os value is also evaluated for uniaxially deformed 2D microstructures, both diffusionally and uniformly deformed. For the former, the deformed microstructure is obtained by the simulation of microstructural evolution in polycrystals with straight grain boundaries. The os value increases gradually with increasing or decreasing strain and is larger in the diffusionally deformed microstructures than in the uniformly deformed microstructures for a given grain aspect ratio. The os value for three-dimensional (3D) polycrystalline microstructures is also obtained from an ellipsoidal distribution of grain-boundary angles. The resultant os value is 0.60 for 3D equiaxed polycrystals and increases gradually with increasing strain.     

Theory of diffusional rotation about the common boundary of a bicrystal

During the creep of polycrystals, individual grains may undergo shape changes, grain boundary sliding and grain rotation. Theoretical studies have focused on the first two of these processes but only recently has the theory of rotation received detailed attention. Diffusional rotation was analysed by Burton [Phil. Mag. A 82 51 (2002); Phil. Mag. 83 2715 (2003)], for a bicrystal with orthorhombic grains of dimensions X, Y and Z with the common boundary in the yz plane and with Z???X,Y. Rate equations were derived and the stress profile over the common boundary predicted, for cases where grain boundary and lattice diffusion predominate. In this paper, the analyses are extended using numerical methods, to the full two- and three-dimensional cases for boundary and lattice diffusion, respectively. For boundary diffusion, the results for Z/Y???1 reproduce those obtained by analytical means and this is regarded as a verification of the numerical method. When Z/Y?=?1, the rotation rates are shown to be about 30% faster, due to the additional diffusion contribution in the z direction. This contribution increases with decreasing values of Z/Y. The stress patterns at the rotating boundary are derived. For lattice diffusion, the stress pattern at the boundary, the shapes of the vacancy potential contours and the variation of the rotation rate with the ratios X/Y and Z/Y are presented.     

Acoustoplastic effect and internal friction of aluminum single crystals in various deformation stages

The dependences of the acoustoplastic effect and the internal friction on the oscillatory strain amplitude are measured in various deformation stages of low-purity aluminum single crystals. It is discovered that the acoustoplastic effect is observed not only in the macroscopic plastic region of the stress-strain diagram, but also for microplastic deformation in the “elastic” loading and unloading stages. The sign of the effect reverses during unloading. An increase in the strain rate leads to enhancement of the acoustoplastic effect and the absorption of the energy of ultrasonic vibrations causing this effect with a frequency of about 100 kHz. It is concluded that the acoustoplastic effect observed during both macro-and microplastic deformation is caused by the irreversible high-speed motion of dislocations through the long-range stress field of the other dislocations after breaking through the Cottrell atmospheres. Fiz. Tverd. Tela (St. Petersburg) 39, 1794–1800 (October 1997)