A crystal plasticity model of a formation of a deformation band structure

The formation of deformation bands with the typically alternating sign of the misorientation across their boundaries is interpreted as spontaneous deformation instability caused by anisotropy of hardening. To analyse the nature of the fragmentation, a model of a rigid-plastic crystal domain deformed by symmetric double slip in a plane-strain compression is considered. The basic reason for the deformation band existence is that a local decrease in number of active slip systems in the bands is energetically less costly than a homogeneous deformation by multislip. However, such model of the bands predicts their extreme orientation and their width tends to zero. This trend is modified by hardening caused by a build up of the band boundaries and by a dislocation bowing (Orowan) stress. The model provides an explanation of observed orientation of the bands, their width and the significant change in the structural morphology seen as the band reorientation occurs at large strains. The predictions are in a favourable agreement with the available observations.     

Formation and propagation of cracks during cyclic deformation

Summary Starting from observation of the geometric features of formation and propagation of cracks in cycled single crystals of copper a model was developed for fatigue cracking. The only and experimentally well established assumption of the model is that the slip during cyclic deformation tends to be coarse. By the cooperation of stress concentrations at the slip steps and the hardening of slip planes activated locally two slip systems (with different slip planes and Burgers vectors) are activated alternatively so that a crack develops from the slip step. It propagates without monotonically increasing the hardening at the crack tip. The coarse slip produces sharp slip steps at the surface for crack formation and prohibits crack blunting during propagation. In contrast to other models the one described can show how the irreversible process of crack formation and propagation can take place despite completely symmetrical push-pull stresses. The whole crack is formed merely by the motion of dislocations present in the material so that but comparatively small stresses are needed. As, moreover, no thermally activated processes are necessary, fatigue at 4·2°K can be explained too. The strong dependence of fatigue on the state of the surface can also be accounted for since the cracks form at the surface steps. Materials which tend to coarse slip even in unidirectional tests are expected to fatigue easily. This is corroborated experimentally. Finally, many details of crack geometry can be explained in terms of the model.Published in Z. f. Metallkunde58 (1967), 780.     

Slip band formation and mobile dislocation density generation in high rate deformation of single fcc crystals

The mechanisms for the nucleation, thickening, and growth of crystallographic slip bands from the sub-nanoscale to the microscale are studied using three-dimensional dislocation dynamics. In the simulations, a single fcc crystal is strained along the [111] direction at three different high strain rates: 10⁴, 10⁵, and 10⁶?s^??1. Dislocation inertia and drag are included and the simulations were conducted with and without cross-slip. With cross-slip, slip bands form parallel to active (111) planes as a result of double cross-slip onto fresh glide planes within localized regions of the crystal. In this manner, fine nanoscale slip bands nucleate throughout the crystal, and, with further straining, build up to larger bands by a proposed self-replicating mechanism. It is shown that slip bands are regions of concentrated glide, high dislocation multiplication rates, and high dislocation velocities. Cross-slip increases in activity proportionally with the product of the total dislocation density and the square root of the applied stress. Effects of cross-slip on work hardening are attributed to the role of cross-slip on mobile dislocation generation, rather than slip band formation. A new dislocation density evolution law is presented for high rates, which introduces the mobile density, a state variable that is missing in most constitutive laws.     

Dislocation and defect density-based micromechanical modeling of the mechanical behavior of fcc metals under neutron irradiation

A rate-independent dislocation and defect density-based evolution model is presented that captures the pre- and post-yield material behavior of fcc metals subjected to different doses of neutron radiation. Unlike previously developed phenomenological models, this model is capable of capturing the salient features of irradiation-induced hardening, including increase in yield stress followed by yield drop and non-zero stress offset from the unirradiated stress–strain curve. The key contribution is a model for the critical resolved slip resistance that depends on both dislocation and defect densities, which are governed by evolution equations based on physical observations. The result is an orientation-dependent non-homogeneous deformation model, which accounts for defect annihilation on active slip planes. Results for both single and polycrystalline simulations of OFHC copper are presented and are observed to be in reasonably good agreement with experimental data. Extension of the model to other fcc metals is straightforward and is currently being developed for bcc metals.     

Dislocations in plastically deformed Fe-3% Si alloy single crystals

The plastic deformation of Fe-3%Si alloy single crystals made from the melt is studied by the method of etching of dislocations. At a room-temperature and at static stress deformation by slip occurs in the 1/2〈111〉 directions along planes of maximum resolved shear stress. The plastic properties are determined by the motion of screw dislocations which cause the broadening of slip bands.     

Stimulation and Suppression of Grain Boundary Sliding by Intragranular Slip in Zinc Bicrystals

The influence of intragranular slip on grain boundary sliding is studied in originally compatible zinc bicrystals with symmetric tilt boundary. The experiment is designed to separate different effects of intragranular slip on the boundary sliding and establish their mechanisms. Grain boundary sliding with and without development of intragranular slip is observed. The rate of sliding accompanied by slip is more than five times of that without slip. A good correlation between the boundary sliding and intragranular slip prior to slide hardening is established. Slide hardening followed by the negative sliding near one end of the boundary and strain hardening in the boundary vicinity, are observed at the last stages of deformation. For the case of formation of slip induced glissile grain boundary dislocations of opposite signs the possibility of their contribution to total grain boundary sliding, is analyzed. The effect of the increase in the rate of sliding is explained in terms of the accommodation of sliding by slip and appearance of additional glissile grain boundary dislocations of one sign due to strain incompatibility. Contribution of these different dislocation mechanisms to the increase in the sliding rate is determined for the stage of deformation preceding slide hardening. It is supposed that the effect of slide hardening and negative sliding as well as boundary curving is created by non-smooth boundary and small degree of incompatibility caused by straining.     

On slip in AgCl crystals at room temperature

At moderately wavy and branched slip bands on the surfaces of sheets of AgCl crystals the distribution of slip lines has been observed by means of the electron microscope. From the results it can be deduced that the cross slip of screw dislocations takes place. The divergence of the ends of slip bands has also been observed, which can be as well explained by the cross slip. From the active slip direction and the directions of straight slip lines in the cross-slip regions the microscopic slip planes have been determined. They lie in the region roughly limited by the {113} and {331} planes and the problem is discussed whether these planes are low-index crystallographic planes.     

Dislocation structures. Part II. Slip system dependence

Part I established, via extensive transmission electron microscopy investigations, that the type of dislocation structure formed in metals of medium-to-high stacking fault energy upon deformation in tension or rolling to moderate strain levels (≤0.8) depends strongly on crystallographic grain orientation. This paper analyzes the grain orientation-dependent structures in terms of the active slip systems, focusing on the crystallographic plane of extended planar boundaries (geometrically necessary boundaries). The analysis establishes slip systems as the factor controlling the dislocation structure. Five fundamental slip classes, consisting of one to three active slip systems, have been identified. Multiple activation of these slip classes is also considered. The slip classes give rise to different types of dislocation structure, of which all except one contains geometrically necessary planar boundaries aligning with unique crystallographic planes (not necessarily slip planes). A slip class leads to the same type of structure, irrespective of the macroscopic deformation mode, as also demonstrated by successful predictions for shear deformation.     

Heating of slip lines and bands as a quasi-athermic mechanism of plastic deformation of crystals at low temperatures

We discuss theoretically a mechanism of violation of the Arrhenius law for the rate of plastic deformation, on the one hand, and of the appearance of plateau-like segments in the temperature dependence of the thermal-activation parameters, on the other, during deformation of crystals at low (<10 K) temperatures, which is associated with heating of the crystal by slip lines and bands. Via a self-consistent solution of the heat-conduction equation with allowance for variation of its coefficients and the rate of plastic deformation with temperature it is found that both a stable and an unstable regime (in the thermal sense) of propagation of slip lines and expansion of slip bands are possible depending on the ratio between the heating level and the level of strain hardening of the strain localization sites. The first regime is associated with the appearance of quasi-athermic plateaus in the temperature dependences of the thermally-activation parameters, and the second one leads to an instability (stepped) in the plastic deformation that is characteristic at low temperatures. Fiz. Tverd. Tela (St. Petersburg) 40, 1479–1485 (August 1998)     

Microstructural instabilities: dislocation substructures with pronounced mechanical effects

Microstructure evolution is largely dominated by the internal stress fields that appear upon the appearance of inhomogeneous structures in a material. The hardening behaviour of metals physically originates from such a complex microstructure evolution. As deformation proceeds, statistically homogeneous distributions of dislocations in grains become unstable, which constitutes the driving force for the development of a pronounced dislocation substructure. The dislocation structure already appears at early stages of deformation due to the statistical trapping of dislocations. Cell walls contain dislocation dipoles and multipoles with high dislocation densities and enclose cell-interior regions with a considerably smaller dislocation density. The presence and evolution of such a dislocation arrangement in the material influence the mechanical response of the material and is commonly associated with the transient hardening after strain path changes. This contribution introduces a micromechanical continuum model of the dislocation cell structure based on the physics of the dislocation interactions. The approximation of the internal stress field in such a microstructure and the impact on the macroscopic mechanical response are the main items investigated here.     

Low-temperature fatigue behaviour and development of dislocation structure in aluminium single crystals with single-slip orientation

Al single crystals oriented for single slip were cyclically deformed under constant plastic strain amplitudes between 1?×?10^?3 and 5?×?10^?2 at 77?K. Al single crystals showed hardening to saturation at all applied shear stress amplitudes. The resultant cyclic stress–strain curve (CSSC) showed a stress plateau in a range of plastic strain amplitude from 2?×?10^?3 to 2?×?10^?2. Surface observation revealed that multiple slip systems were active even at the strain amplitude in the plateau region. At plastic strain amplitudes corresponding to the plateau of the CSSC, persistent slip bands (PSBs) were formed parallel to the primary slip plane. In the PSBs, well-developed dislocation walls parallel to the {100} planes were observed. The microstructure in the PSBs was explained by the fact of multiple activation of the primary and critical slip systems. The above results indicate that the high stacking fault energy of Al is an important factor affecting the fatigue behaviour even at 77?K.     

On lattice and material-frame rotations and crystal hardening in high-symmetry axial loading

A diverse range of experimental behaviour in high-symmetry tensile loading of fcc crystals has been reported in a number of classic papers in the literature (1960–1982). This behaviour includes: (i) axis stability and axisymmetric deformation in ?111? and ?100? load orientations; (ii) axis rotation toward a ?111? orientation in coplanar double-slip in ?110? loading; and (iii) axis rotations toward (from an initial misalignment) or away from precise ?111? and ?100? load orientations, with a reduced number of active slip planes. In this paper extensive kinematic analyses of coincident and relative rotations among material, lattice, and loading frames in each of these orientations, together with additional kinematic solutions for load-axis rotations, are combined with experimental information and perspectives connecting relative hardening and geometric slip-system interactions to determine probable active systems and slip rates in this diverse set of experiments. It is found that a set of basic hardening inequalities, which follow from classic latent hardening experiments in single slip, is consistent with the full range of experimental behaviour in high-symmetry axial-load orientations.     

强流脉冲电子束诱发纯钛表面的微观结构及应力状态

利用强流脉冲电子束(HCPEB)装置对金属纯钛进行轰击,采用X射线衍射,扫描电子显微镜及透射电子显微镜技术详细分析了轰击样品表层的结构和缺陷. X射线衍射分析表明, HCPEB能够在材料表层诱发幅值为 GPa量级的压应力,并在(100), (102)和(103)晶面出现择优取向.表层微观结构的观察表明: HCPEB轰击后材料表层发生了马氏体相变,形成了大量的片状马氏体组织; 此外, HCPEB轰击还在辐照表面诱发了强烈的塑性变形,一次轰击后,晶粒内部的塑性变形以(100)晶面的位错滑移为主,位错密度显著提高;多次轰击后,样品变形结构发生变化,变形孪晶的数量明显增多. 这些变形微结构不仅影响表层的织构演化行为,而且还能细化晶粒,进而提高材料表面硬度, 为HCPEB技术进行纯钛表面强化提供了一条有效的途径.     

Temperature dependence of development of slip bands and of strain hardening in AgCl crystals

The dependence of the flow stress and the slip band density on the plastic strain has been measured at 201 K, 293 K and 363 K. The growth of deformation concentrated in an average slip band has been stated. The types of obstacles acting against the rise and development of a slip band and the temperature dependence of the strain hardening in AgCl crystals are discussed. An equation stating the dependence of the flow stress on the slip band density is presented. The hardening in AgCl crystals is classified as the stage III — hardening.     

Strain hardening under structural superplasticity conditions

A model is proposed for describing the hardening of fine-grained materials deformed under structural superplasticity conditions. Under these conditions, the strain dependence of the flow stress is shown to be caused by the internal stress fields induced by the defects introduced into grain boundaries during intragranular slip. Expressions describing the dependences of the flow stress on the rate and temperature of superplastic deformation and the structural parameters of the material are obtained.     

Some features of the macrolocalization of the plastic deformation of copper single crystals in alternating torsion

Copper single crystals of various orientations have been plastically deformed in alternating torsion, and observations have been made of the appearance of fine slip traces in the initial stage of deformation, the longitudinal elongation, and the transformation of the circular cross section into oval-tetragonal, cruciform, triangular, elliptical, and other sections. Analysis of the slip traces has shown that, with a symmetrical arrangement of the octahedral slip planes with, respect to the axis of torsion, not all of the planes are active, but only a certain number sufficient to convert the elastic deformations into plastic slip. The axial elongation and the nature of the change in shape of the cross section depend on the number and orientation of the active slip planes.It has been found that, in addition to the accumulation of macroslips of opposite sign observed during the deformation of polycrystalline aggregates [1–3], there is in single crystals incomplete recovery of the displacements along the crystallographic slip planes. During deformation a single crystal breaks up into thin plates which are displaced by alternating rotation and translation with respect to one another. The failure of the plates to return completely to their original positions leads to an accumulation of slips of opposite sign between adjacent plates and to a corresponding change in the shape of the cross section. The elements of the ratchet mechanism [4,5] of accumulation of macroslips are regarded as a manifestation of the incomplete reversibility of dislocation movement.     

The distribution of dislocations in slip bands of Fe-3% Si alloy single crystals deformed by bending

The distribution of dislocations at the ends of slip bands was studied by etching on surfaces parallel to the slip plane. In these places the slip band is formed by groups of asymmetric dislocation loops several hundred microns wide. The long mixed-type parts of these loops running nearly equidistantly and lying in near planes, are the equilibrium arrangement of dislocations of the same sign in the shear stress gradient. From the results we can judge that the dislocation sources are at larger distances from the ends of the slip bands and that the dislocation groups at the ends of the slip bands are sources of large stress fields.     

强流脉冲电子束作用下金属锆的微观结构与应力状态

利用强流脉冲电子束 (HCPEB) 技术对金属纯锆进行表面处理, 采用X射线衍射, 扫描电子显微镜及透射电子显微镜详细分析了辐照诱发的表层微观结构和缺陷. X射线分析结果表明, HCPEB辐照后在材料表层诱发幅值为GPa量级的压应力, 并形成{0002}, {1012}, {1120}及{1013}织构. 表层微观结构观察表明, 与其他金属材料不同, HCPEB辐照在材料表层诱发的熔坑数量极少, 多次轰击甚至几乎没有表面熔坑的形成. 此外, 在快速的加热和冷却状态下, 在表面熔化层形成大量的超细晶粒结构, 同时诱发马氏体相变和强烈的塑性变形. 1次HCPEB辐照后表层内形成的变形微结构以位错为主, 孪晶数量较少; 5 次辐照样品的位错密度迅速增高, 孪晶数量也显著增加; 10次辐照后样品中的变形微结构以变形孪晶为主, 且出现二次孪晶现象. 表层晶粒内部变形的晶体学特征不仅决定了表层的织构演化行为, 而且还起到细化晶粒的作用, 为纯锆及锆合金表面强化提供了一条有效的途径. 关键词： 强流脉冲电子束 纯锆 微观结构 应力状态     

Hydrogen-induced strain localisation in oxygen-free copper in the initial stage of plastic deformation

Single crystals of oxygen-free copper oriented to easy glide of dislocations were tensile tested in order to study the hydrogen effects on the strain localisation in the form of slip bands appearing on the polished specimen surface under tensile straining. It was found that hydrogen increases the plastic flow stress in Stage I of deformation. The dislocation slip localisation in the form of slip bands was observed and analysed using an online optical monitoring system and atomic force microscopy. The fine structure of the slip bands observed with AFM shows that they consist of a number of dislocation slip offsets which spacing in the presence of hydrogen is markedly reduced as compared to that in the hydrogen-free specimens. The tensile tests and AFM observations were accompanied with positron annihilation lifetime measurements showing that straining of pure copper in the presence of hydrogen results in free volume generation in the form of vacancy complexes. Hydrogen-enhanced free-volume generation is discussed in terms of hydrogen interactions with edge dislocation dipoles forming in double cross-slip of screw dislocations in the initial stage of plastic deformation of pure copper.     

脆性断裂的统计理论

本文试图从位错理论出发来探索晶体脆性断裂的统计理论。脆性断裂过程,实质上是微裂缝在极小的范性形变过程中形成长大和传播的随机过程。本文导出了描述这种随机过程的微分方程,利用微裂缝形成长大的位错机理,解出了微裂缝大小的统计分布函数。文中给出了范性形变、加工硬化和活动位错源数目与微裂缝数目和大小之间的函数关系。过去研究脆性断裂时,范性变形只是含糊地包括在有效表面能之内,而加工硬化和活动位错源数目则一向被略去。从微裂缝大小的统计分布函数和微裂缝的传播条件,导出了强度的统计分布函数,从而求得了脆性断裂判别式、脆性断裂强度及脆性-范性转变温度。