Multiscale dislocation dynamics simulations of shock-induced plasticity in small volumes

Multiscale dislocation dynamics plasticity (MDDP) was used to investigate shock-induced deformation in monocrystalline copper. In order to enhance the numerical simulations, a periodic boundary condition was implemented in the continuum finite element (FE) scale so that the uniaxial compression of shocks could be attained. Additionally, lattice rotation was accounted for by modifying the dislocation dynamics (DD) code to update the dislocations’ slip systems. The dislocation microstructures were examined in detail and a mechanism of microband formation is proposed for single- and multiple-slip deformation. The simulation results show that lattice rotation enhances microband formation in single slip by locally reorienting the slip plane. It is also illustrated that both confined and periodic boundary conditions can be used to achieve uniaxial compression; however, a periodic boundary condition yields a disturbed wave profile due to edge effects. Moreover, the boundary conditions and the loading rise time show no significant effects on shock–dislocations interaction and the resulting microstructures. MDDP results of high strain rate calculations are also compared with the predictions of the Armstrong–Zerilli model of dislocation generation and movement. This work confirms that the effect of resident dislocations on the strain rate can be neglected when a homogeneous nucleation mechanism is included.     

Features of slip-band formation during the plastic straining of layered crystals

The effects of the narrowing and branching of screw slip bands during the plastic straining of nonuniformly doped or nonuniformly irradiated (layered) crystals are discussed theoretically on the basis of the equations of dislocation kinetics. Band formation is treated as a process involving the self-organization of dislocations in a dislocation ensemble at the mesoscopic level. The distributions of the densities of mobile and immobile dislocations, as well as of the local plastic strain rate, in a slip band propagating in a layered crystal are obtained. It is found that the narrowing of bands is due to the lower rate of broadening of the bands in stiff layers than in soft layers, which have not been hardened by doping or irradiation, and that branching is due the low local strain rate in stiff layers compared with the strain rate per slip band assigned by the straining machine. In the latter case the nucleation of new bands or the branching of existing bands is required to restore the balance between these rates. Fiz. Tverd. Tela (St. Petersburg) 41, 252–258 (February 1999)     

On the conditions of strain localization and microstructure fragmentation under high-rate loading

The paper reports on research in the deformation and fragmentation mechanisms of coarse- and fine-grained materials under high-rate loading. The study was performed by an experimental procedure based on collapse of thick-walled hollow cylinders and by molecular dynamics simulation. The key issue was to study the formation of plastic strain localization bands. It is found that the pattern of plastic deformation is governed by loading conditions and characteristic grain sizes. For a coarse-grained material, the governing mechanism is dislocation deformation resulting in localization bands. For a fine-grained material, the governing mechanism is grain boundary sliding with attendant fragmentation of the material. A dependence of the strain rate and degree on the critical grain size was disclosed. The computer simulation revealed mechanisms of grain boundary sliding on the scales studied.     

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.     

Modelling the dynamic deformation and patterning in fcc single crystals at high strain rates: dislocation dynamics plasticity analysis

The deformation process in copper and aluminium single crystals under shock loading is investigated using a multiscale model of plasticity that couples discrete dislocation dynamics and finite element analyses. Computer simulations are carried out to mimic loading condition of high strain rates ranging from 10⁵ to 10⁷?s^?1, and short pulse durations of few nanoseconds involved in recent laser based experiments. The effects of strain rate, shock pulse duration and the nonlinear elastic properties are investigated. Relaxed configurations using dislocation dynamics show formation of dislocation micro bands and weak dislocation cells. Statistical analyses of the dislocation microstructures are preformed to study the characteristics of the local dislocation densities and the distribution of the instantaneous dislocations velocities.     

Effect of cyclic stresses on the microstructures of hexagonal close packed metals

Slip band extrusions are formed in cadmium, magnesium and titanium, but not in zinc. The extrusions form preferentially in untwinned crystals. Filamentary growths occur at {10¯12} and {11¯21} twin interfaces during cyclic twinning.Possible dislocation interactions at these twin interfaces are described. The dislocation debris produced during cyclic strain in the slip bands and by cyclic twinning is shown to be similar and composed of a high density of dipole loops. It is therefore concluded that the occurrence and distribution of slip band extrusions in metals and the formation of twin boundary filamentary growths can be accounted for by a model based upon the glide of interstitial type dipole loops. Vacancy type loops will then cause crack nucleation in slip bands and deformation twin boundary regions.Twin boundary debris can also cause the observed fragmentation of twins by acting as a barrier to twin boundary movement.The author is grateful to Dr. A. G. Crocker, University of Surrey, for many discussions on the twinning mode in h.c.p. metals and to P. J. E. Forsyth for his interest and encouragement. The paper is published by permission of the Controller, H. M. Stationery Office. Crown copyright is reserved.     

Stochastic dislocation patterning during cyclic plastic deformation

A dislocation dynamical theory is developed for the formation of dipole dislocation patterns during cyclic plastic deformation in single glide. The stochastic dislocation dynamics adopted is suitable to account, in terms of a fluctuating effective medium, for the effects of long-range dislocation interactions on a mesoscopic scale. The theory can explain the occurrence of a matrix structure and persistent slip bands as a result of evolutionary processes, it gives the intrinsic strain amplitudes and the characteristic wavelength of these structures, and it allows for an interpretation of the structural changes associated with changes of the deformation conditions. Quantitative results are in good agreement with experimental observations.     

Scanning probe microscopy on superconductors: Achievements and challenges

A dislocation dynamical model of the reaction-diffusion type is used to describe the spatio-temporal dynamics of Lüders band propagation in polycrystals. The diffusive nature of dislocation glide is traced back to the random crystallographic orientation of the active slip systems. The role of pile-ups in dislocation multiplication is accounted for by a dynamical generalization of the Hall-Petch law. It is argued that Lüders bands in polycrystals are related to a bistable dynamics of mobile dislocations. Further results obtained cover the dependences on material parameters and deformation conditions of (1) the occurrence, (2) the strain, propagation velocity and width of Lüders bands, and (3) the upper and lower yield stresses. These results are in good agreement with experimental findings.     

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.     

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.     

强流脉冲电子束作用下金属纯Cu的微观结构状态——变形结构

为了研究金属的超快变形机理,利用强流脉冲电子束(HCPEB)技术对多晶纯Cu进行了辐照处理,并利用透射电子显微镜对HCPEB诱发的表面微结构进行了表征.实验结果表明,HCPEB轰击多晶纯Cu后,在轰击表层诱发了幅值极大的应力和极高的应变速率.1次HCPEB轰击材料表层的变形结构以交滑移形成的位错胞和位错缠结结构为主;多次轰击后平行的位错墙和孪晶是该区域的主要变形结构特征;原子面的扩散乃至位错攀移可在晶界和孪晶界上形成台阶结构.根据各自区域的变形结构特征,对相应的变形机理进行了探讨. 关键词： 强流脉冲电子束 多晶Cu 变形结构 孪晶     

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.     

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.     

Micromechanistic origin of irradiation-assisted stress corrosion cracking

A multi-scale study of the micromechanics of dislocation–grain boundary interactions in proton and ion-irradiated stainless steels is presented. Interactions of dislocation channels with grain boundaries result in slip transfer, discontinuous slip without or with slip along the grain boundary. The presence of the irradiation damage enhances the importance of the magnitude of the resolved shear stress on the slip system activated by the grain boundary to transfer slip across it. However, the selected slip system is still determined by the minimization of the grain boundary strain energy density condition. These findings have implications for modelling the mechanical properties of irradiated metals as well as in establishing the mechanism for disrupting the grain boundary oxide, which is a necessary prerequisite for irradiation-assisted stress corrosion cracking.     

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.     

The effect of the location of stage-I fatigue crack across the persistent slip band on its growth rate – A 3D dislocation dynamics study

Abstract

A 3D dislocation dynamics study to ascertain the probable path of stage-I fatigue crack propagation across the persistent slip band (PSB) in austenitic stainless steel is presented. Cyclic plasticity and the resulting crack tip slip displacement (CTSD) are evaluated for cracks of varying length introduced at PSB-center and at two PSB-matrix interfaces. CTSD attains high value at either of the two interfaces irrespective of the proximity of crack front to the grain boundary. Further, a difference in microcrack propagation rate is also observed among the two interfaces. The present results assert microcrack propagation preferrentially along one of the two PSB-matrix interfaces rather than at the PSB-center. A pre-existing PSB dislocation structure localises the cyclic slip for crack lengths up to approximately half of the grain depth for an applied strain range of 2 × 10^?4.     

Influence of boundary structure and near neighbor crystallographic orientation on the dynamic damage evolution during shock loading

The role of crystallographic orientation on damage evolution in ductile metals during shock loading has been investigated. By utilizing large-grained copper specimens, it has been shown that the development of intragranular damage, in the form of void growth and coalescence, is influenced by the grain orientation with respect to the applied load. Additionally, strain incompatibility and the inability to promote transmission or activation of secondary dislocation slip across a grain boundary, are proposed as the likely cause for intergranular failure. Finally, the free surface velocity profiles of each grain, specifically the decay of the oscillations after the pull-back, correlated well with the amount of damage measured within the respective grain.     

Evolution of mechanical response and dislocation microstructures in small-scale specimens under slightly different loading conditions

In small dimensions, the flow stress of metallic samples shows a size-dependence such that smaller is stronger, even in nominally strain gradient-free loading conditions. However, the role of the boundary conditions in miniaturised tension or compression tests on the mechanical response and dislocation structure has not been studied in detail. In simulations performed with a three-dimensional discrete dislocation dynamics tool, initial, well-defined dislocation microstructures are loaded in tension with different boundary conditions including superimposed torsion moments. The influence of the loading conditions on details of the evolving dislocation microstructure was investigated by using identical starting configuration. An additional torsion moment significantly influences the dislocation activity since forest-dislocations are generated, but size effect of the flow stress is found to be unchanged.