Variation of internal stresses as a function of deformation and distance from sources in Cu–Al polycrystalline alloys

Internal stress fields in deformed Cu–Al polycrystalline alloys are studied via TEM. The sources of such stresses are determined. Internal stress fields are measured as a function of distance from different sources. The effect grain size has on the formation of internal stresses is determined.     

Internal friction,Young’s modulus,and electrical resistivity of submicrocrystalline titanium

The variation of the internal friction, Young’s modulus, and electrical resistivity of two grades of polycrystalline titanium (VT1-0 and Grade 4) in the area of low temperatures (100–300 K) as depending on the initial structure and subsequent severe plastic deformation converting the material into the submicrocrystalline structural state in relation to the grain size is studied. The maximum of the internal friction is detected in submicrocrystalline titanium, which is interpreted as a Bordoni peak. All the studied characteristics are sensitive indicators for a nonequilibrium state of the grain boundaries after the deformation. The effect of the initial structure of the metal on its properties after the severe deformation is revealed.     

Effects of grain size on dislocation organization and internal stresses developed under tensile loading in fcc metals

The relationship between deformation and dislocation properties has been studied for pure polycrystalline nickel and austenitic stainless steel AISI 316L in stage III. Special care was taken to study statistically the effects of the grain size and grain orientation on dislocation densities and distribution. It is shown that the nature of dislocation cells depends on grain size and crystallographic orientation. The dimensional parameters, which depend on grain size, i.e. the inter-boundary spacing (λ) and boundary thickness (e), define three domains of crystallographic orientation and depend on the grain size. Scaling hypotheses reveal two physical mechanisms which, at this level of plastic strain, are correlated to a specific value of the noise, associated with distribution functions. Similarities between structural parameters and dislocation densities in each phase (walls and inter-walls spacing) are identified and discussed in terms of kinetic equations describing dislocation density evolution and fluctuations of certain physical parameters. This similarity provides physical signification of the scaling distribution obtained on λ and e in terms of a stochastic approach to dislocation distribution. The origin of Hall–Petch behaviour observed at large strain is interpreted in terms of an interaction between inter- and intra-granular long-range internal stresses, which depends on grain size. We conclude that, at high strain, the Hall–Petch phenomenological relationship is a consequence of plastic strain history and strain gradient in grains. From this last point, a length scale arises naturally, which depends on stacking fault energy.     

A multiscale gradient-dependent plasticity model for size effects

The mechanical behaviour of polycrystalline material is closely correlated to grain size. In this study, we investigate the size-dependent phenomenon in multi-phase steels using a continuum dislocation dynamic model coupled with viscoplastic self-consistent model. We developed a dislocation-based strain gradient plasticity model and a stress gradient plasticity model, as well as a combined model, resulting in a theory that can predict size effect over a wide range of length scales. Results show that strain gradient plasticity and stress gradient plasticity are complementary rather than competing theories. The stress gradient model is dominant at the initial strain stage, and is much more effective for predicting yield strength than the strain gradient model. For larger deformations, the strain gradient model is dominant and more effective for predicting size-dependent hardening. The numerical results are compared with experimental data and it is found that they have the same trend for the yield stress. Furthermore, the effect of dislocation density at different strain stages is investigated, and the findings show that the Hall–Petch relation holds for the initial strain stage and breaks down for higher strain levels. Finally, a power law to describe the size effect and the transition zone between the strain gradient and stress gradient dominated regions is developed.     

Structural mechanisms of fracture of nanocrystalline materials

Structural mechanisms and features of brittle and quasi-brittle fracture of nanocrystalline materials are theoretically analyzed. The role of size effects and internal stresses caused by a nonequilibrium structure during brittle trans-and intercrystallite fracture is studied. The dependence of the nanocrystalline material durability on the working stress and grain size is calculated. The conditions for certain mechanisms of plastic deformation to be operative in nanocrystalline materials are analyzed. The influence of the grain-boundary and dislocation mechanisms of plastic deformation on the conditions of nanocrack formation is studied. The dependence of the fracture toughness of nanomaterials on structure parameters is calculated.     

Resistance to dynamic deformation and fracture of tantalum with different grain and defect structures

This paper presents the results of measurements of the strength properties of technically pure tantalum under shock wave loading. It has been found that a decrease in the grain size under severe plastic deformation leads to an increase in the hardness of the material by approximately 25%, but the experimentally measured values of the dynamic yield stress for the fine-grained material prove to be less than those of the initial coarse-grained specimens. This effect has been explained by a higher rate of stress relaxation in the fine-grained material. The hardening of tantalum under shock wave loading at a pressure in the range 40–100 GPa leads to a further increase in the rate of stress relaxation, a decrease in the dynamic yield stress, and the disappearance of the difference between its values for the coarse-grained and fine-grained materials. The spall strength of tantalum increases by approximately 5% with a decrease in the grain size and remains unchanged after the shock wave loading. The maximum fracture stresses are observed in tantalum single crystals.     

Nanocrack nucleation in polycrystalline silicon during grain-boundary sliding

A theoretical model is proposed to describe nanocrack nucleation in polycrystalline silicon. In terms of this model, nanocrack nucleation is stimulated by grain-boundary sliding, which creates sources of local stresses in triple junctions of grain boundaries. The relaxation of these local stresses is the main driving force of nanocrack nucleation near triple junctions in polycrystalline silicon, in which grain-boundary sliding contributes substantially to plastic deformation under cyclic loading at room temperature. The model is used to calculate the critical external stress required for nanocrack nucleation in polycrystalline silicon.     

Potts-Ising model for simulation of polarization switching in polycrystalline ferroelectrics

This paper proposes a scheme based on the Potts and Ising models for simulating polarization switching of polycrystalline ferroelectrics using the Monte Carlo method. The polycrystalline texture with different average grain size is produced from the Potts model. Then Ising model is implemented in the polycrystalline texture to produce the domain pattern and hysteresis loop. The domain patterns and hysteresis loops have been obtained for polycrystalline texture with different average grain size. From the results of domain pattern evolution process under an applied electric field using this scheme, an extended domain, which covers more than one grain with polarization aligned roughly in the same direction, has been observed during the polarization reversal. This scheme can well reproduce the basic properties of polycrystalline ferroelectrics and is a valuable tool for exploring the physical properties of polycrystalline ferroelectrics.     

Grain size effect on twin density in as-deposited nanocrystalline Cu film

Here, we report the formation of twins and grain size dependence of twin density in nanocrystalline (NC) copper films fabricated by pulsed laser deposition. It is found that the percentage of grains containing twins decreases with decreasing grain size in the grain size range of 2–10?nm. Surprisingly, although the twins were formed during the deposition process without mechanical deformation, our analysis suggests that they are most likely deformation twins formed under high internal stress existing in the NC Cu films. This phenomenon may also happen in other NC metallic thin films where internal stresses are high.     

Grain boundary segregation and relaxation in nano-grained polycrystalline alloys

The present study carries out systematic thermodynamics analysis of Grain Boundary(GB)segregation and relaxation in NanoGrained(NG)polycrystalline alloys.GB segregation and relaxation is an internal process towards thermodynamic equilibrium,which occurs naturally in NG alloys without any applied loads,causes deformation and generates internal stresses.The analysis comprehensively investigates the multiple coupling effects among chemical concentrations and mechanical stresses in GBs and grains.A hybrid approach of eigenstress and eigenstrain is developed herein to solve the multiple coupling problem.The analysis results indicate that the GB stress and grain stress induced by GB segregation and relaxation can be extremely high in NG alloys,reaching the GPa level,which play an important role in the thermal stability of NG alloys,especially via the coupling terms between stress and concentration.The present theoretic analysis proposes a novel criterion of thermal stability for NG alloys,which is determined by the difference in molar free energy between a NG alloy and its reference single crystal with the same nominal chemical composition.If the difference at a temperature is negative or zero,the NG alloy is thermal stable at that temperature,otherwise unstable.     

Grain-boundary hardening in polycrystalline copper-based solid solutions

A study is made of the contribution of grain-boundary hardening to the overall hardening in a polycrystalline material on the basis of Ashby's model. Yield curves are used for copper-based solid solutions in polycrystalline and singlecrystal forms. It is shown that the contribution from statistically accumulated dislocations to the yield stress in a polycrystalline specimen reflects the behavior of the corresponding single crystal. The contribution from grain boundaries to the yield stress can be described in terms of the additional dislocation density due to the joint grain deformation in the aggregate up to high strains. At low strains, the main role in hardening of a polycrystalline material is played by the grain boundaries. This extends up to larger strains as the strain temperature is reduced and the alloy-element concentration increases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 47–52, January, 1984.     

Generation of glide split-dislocation half-loops by grain boundaries in nanocrystalline Al

A three-dimensional model for the generation of split dislocations by grain boundaries in nanocrystalline A1 is proposed. In terms of this model, rectangular glide split-dislocation half-loops nucleate at glide lattice dislocation loops pressed to grain boundaries by an applied stress. The level of the applied stress and the grain size at which the emission of such dislocation half-loops becomes energetically favorable are determined. The dependences of the stacking-fault width on the grain size and the applied stress are found. The anomalously wide stacking faults experimentally detected in nanocrystalline A1 are shown to be caused by high internal stresses forming in the stages of preparation, treatment, or local loading of nanocrystalline samples.     

多晶体压剪试样静态加载有限元计算

基于晶体塑性理论研究了晶体织构对数值计算结果的影响,建立了带有织构的多晶体压剪试样(SCS)模型。从材料和试样结构两方面研究了静态加载条件下微观晶粒在有限变形过程中对试样宏观力学性能的影响。由于模型几何结构的特殊性,重点对模型斜槽部分的应力、应变及变形特点进行了分析。考虑到试样在压缩过程中受摩擦的影响,数值分析了不同摩擦系数对变形过程的影响,在此基础上计算了相同摩擦系数下不同晶粒数目、不同单元数目以及单元类型对多晶体压剪模型力学性能的影响,并对试件关键部位不同取向晶粒的应力状态进行了分析。     

Monte Carlo simulation of the kinetics of decomposition and the formation of precipitates at grain boundaries of the general type in dilute BCC Fe–Cu alloys

The kinetics of decomposition of a polycrystalline Fe–Cu alloy and the formation of precipitates at the grain boundaries of the material have been investigated theoretically using the atomistic simulation on different time scales by (i) the Monte Carlo method implementing the diffusion redistribution of Cu atoms and (ii) the molecular dynamics method providing the atomic relaxation of the crystal lattice. It has been shown that, for a small grain size (D ~ 10 nm), the decomposition in the bulk of the grain is suppressed, whereas the copper-enriched precipitates coherently bound to the matrix are predominantly formed at the grain boundaries of the material. The size and composition of the precipitates depend significantly on the type of grain boundaries: small precipitates (1.2–1.4 nm) have the average composition of Fe–40 at % Cu and arise in the vicinity of low-angle grain boundaries, while larger precipitates that have sizes of up to 4 nm and the average composition of Fe–60 at % Cu are formed near grain boundaries of the general type and triple junctions.     

Size effects and magnetoelastic couplings: a link between Hall–Petch behaviour and coercive field in soft ferromagnetic metals

Size effects regarding Hall–Petch (HP) relation are studied in this work for cobalt, nickel and Fe–3wt.%Si (FeSi), from polycrystalline to multicrystalline states. The materials show a breakdown in HP plot for thickness (t) to grain size (d) ratio less than a critical value. This appears in the beginning of plasticity for cobalt and FeSi whereas a plastic strain threshold must be overcome for nickel. Measurements of the coercive field on strained samples are able to depict such modification for low t/d ratio. Values of the coercive field in the polycrystalline domain allow an estimation of the magnetocrystalline anisotropy energy, related to the grain volume fraction concerned by reversal mechanisms for magnetic domains. Multicrystalline samples of cobalt and FeSi becomes magnetically softer at the yield stress. This is linked to a delay of the maximum intergranular stress towards higher strains for FeSi. For cobalt, non-linear elasticity and strong basal texture modify the magnetoelastic effects in coarse grain samples. For nickel, size effect on the coercive field appears after a few per cent of plastic strain as for HP relationship. A mean internal stress can be captured by magnetic measurements on polycrystals, related to the intragranular part of the kinematic stress. The softening of the magnetic properties for strained nickel multicrystals is due to a competition between the apparition of dislocation cells, which increases the coercive field by mechanisms of magnetic domain wall pinning, and surface softening of multicrystals, which tends to decrease the value of H_c.     

Evolution of structural and magnetic properties of sputtered nanocrystalline Co thin films with thermal annealing

Ultrafine grain films of cobalt prepared using ion-beam sputtering have been studied using X-ray diffraction (XRD), X-ray reflectivity (XRR), atomic force microscopy (AFM) and magneto-optical Kerr effect (MOKE) measurements. As-prepared films have very smooth surface owing to the ultrafine nature of the grains. Evolution of the structure and morphology of the film with thermal annealing has been studied and the same is correlated with the magnetic properties. Above an annealing temperature of 300 °C, the film gradually transforms from HCP to FCC phase that remains stable at room temperature. A significant contribution of the surface energy, due to small grain size, results in stabilisation of the FCC phase at room temperature. It is found that other processes like stress relaxation, grain texturing and growth also exhibit an enhanced rate above 300 °C, and may be associated with an enhanced mobility of the atoms above this temperature. Films possess a uniaxial anisotropy, which exhibits a non-monotonous behaviour with thermal annealing. The observed variation in the anisotropy and coercivity with annealing can be understood in terms of variations in the internal stresses, surface roughness, and grain structure.     

晶界弛豫研究50年

文章综述了我国科学工作者５０年来关于晶界弛豫研究的早期开拓和近期发展．前者包括扭摆内耗仪的发明、晶界内耗峰的发现和无序原子群晶界模型的提出．后者包括澄清了关于晶界内耗峰来源的争论,揭示了晶界弛豫具有一个临界温度,从而提出了一个适合于各种温度的综合的晶界模型．一个最重要的进展是关于竹节晶界内耗峰的发现与其机理的阐明,从而揭示了晶界附近的位错亚结构能够影响晶界本身的性质和结构．这对于研究多晶金属的力学性质提供了一个广阔的途径．另外,晶界与邻域位错的非线性交互作用的发现,为奠定非线性滞弹性这门新学科提供了实验基础     

On the micromechanical modelling of the effective diffusion coefficient of a polycrystalline material

This study focuses on calculation of the effective diffusion coefficient of a polycrystalline material accounting for the grain size and shapes. Polycrystal is modelled as a composite consisting of a matrix with high diffusivity (grain boundaries and triple junctions) and inhomogeneities with low diffusivity (bulk grains including crystal defects like dislocations). The segregation at the grain boundaries is accounted for. Typical micromechanical models are re-written for diffusivity assuming that the grains have the shape of ellipsoids of revolution (spheroids). The results are compared with (1) numerical results for hydrogen diffusion in an imaginary polycrystalline material and (2) experimental results for diffusion of hydrogen in nickel polycrystal available in the literature. The approach can be used for extraction of information on diffusivity along the grain boundaries.