The direct observation and analysis of dislocations in experimentally deformed plagioclase feldspars

Transmission electron microscopy has been used to observe and analyse the dislocations in a series of plagioclase feldspars which had been experimentally deformed in compression. The results indicate that a moving dislocation in these materials leaves behind a fault in the structure. Two types of fault are observed but both define the slip plane of the associated dislocation. From these observations, together with stuctural considerations, the visibility of the dislocations and the orientatation of the applied shear stress it has been possible to determine the slip system uniquely for a number of dislocations. The origin of the dislocations and the nature of the faults are also discussed.     

On the formation and stability of dislocation patterns—II: Two-dimensional considerations

We consider the motion and interaction of dislocation species on the slip plane via two-dimensional partial differential equations of the reaction-diffusion type. We distinguish between slow moving dislocations with mobilities along both the slip direction and the direction perpendicular to it (random motion), and fast moving dislocations with mobility along the slip direction only (stress-driven motion). The competition between gradients and nonlinearities leads to stable periodic dislocation structures with wavevector parallel to the slip direction and an intrinsic wavenumber given by the same formula as in the one dimensional analysis of Part I. In addition to the one-dimensional results, however, we find here that splitting of the periodic structures and development of superdefects is possible, according to experimental observations.     

Dislocation-mediated migration of interphase boundaries

Faceted interphase boundaries (IPBs) are commonly observed in lath-shaped precipitates in alloys consisting of simple face-centred cubic (fcc), body centred-cubic (bcc) or hexagonal closed packed (hcp) phases, which normally contain one or two sets of parallel dislocations. The influence of these dislocations on interface migration and possible accompanying long-range strain field remain unclear. To elucidate this, we carried out atomistic simulations to investigate the dislocation-mediated migration processes of IPBs in a pure-iron system. Our results show that the migration of these IPBs is accompanied with the slip of interfacial dislocations, even in high-index slip planes, with two migration modes were observed: the first mode is the uniform migration mode that occurs only when all of the dislocations slip in a common slip plane. A shear-coupled interface migration was observed for this mode. The other interfaces propagate in the stick-slip migration mode that occurs when the dislocations glide on different slip planes, involving dislocation reaction or tangling. A quantitative relationship was established to link the atomic displacements with the dislocation structure, slip plane, and interface normal. The macroscopic shear deformation due to the effect of overall atomic displacement shows a good agreement with the results obtained based on the phenomenological theory of martensite crystallography. Our findings have general implications for the understanding of phase transformations and the surface relief effect at the atomic scale.     

A new fast finite element method for dislocations based on interior discontinuities

A new technique for the modelling of multiple dislocations based on introducing interior discontinuities is presented. In contrast to existing methods, the superposition of infinite domain solutions is avoided; interior discontinuities are specified on the dislocation slip surfaces and the resulting boundary value problem is solved by a finite element method. The accuracy of the proposed method is verified and its efficiency for multi‐dislocation problems is illustrated. Bounded core energies are incorporated into the method through regularization of the discontinuities at their edges. Though the method is applied to edge dislocations here, its extension to other types of dislocations is straightforward. Copyright © 2006 John Wiley & Sons, Ltd.     

Modelling of small fatigue crack growth interacting with grain boundary

The slip band at the tip of a small fatigue crack interacting with grain boundaries is modelled for four cases: a slip band not reaching the grain boundary, a slip band blocked by the grain boundary, a slip band propagated into an adjacent grain, and a slip band propagated through one and then blocked by a second grain boundary. The theory for continuously distributed dislocations is used to calculate the crack-tip sliding or opening displacement and the microscopic stress intensity factor under tensile and shear loading. Assuming that the range of the tip displacement directly determines the propagation rate of both Stage I and II cracks, prediction of the propagation behavior of a small crack is made as a function of the distance between the crack tip and the grain boundary, and of the difficulty to propagate slip into adjacent grains, as well as a function of crack length and stress level. The directions for further development of modelling are discussed.     

Dislocation junctions as indicators of elementary slip planes in body-centered cubic metals

In body-centered cubic (bcc) metals, an unambiguous determination of the elementary slip planes remains difficult owing to several possible interpretations of the glide activity, of slip steps on the specimen surface or features of the dislocation microstructure. In this article, a method is proposed to determine the elementary slip planes in bcc metals based on the line directions of sessile junctions resulting from the interaction of mobile dislocations with \({a}/2\langle 111\rangle \)  Burgers vector. The proposed method allows to determine slip activity inside a material and not at its surface, where other effects may play a role. It is in principle applicable to determining the elementary slip plane in any crystalline material. Particularly, it may help to resolve a long-standing debate of the nature of the elementary slip planes in bcc metals.     

Plastic deformation of copper thin foils

According to one suggested model, bending of a single crystal introduces edge dislocations of the same sign. In the present study, this model is examined by computer simulation using molecular dynamics. When a notch is present on the tension surface, Heidenreich-Shockley partial dislocations are created near the tip of the notch. In the compression surface, partial dislocations are created due to wrinkling of the crystal plane. The results of simulation shows that dislocations are more easily created in a compressive bending region than in a tension bending region or simple tension region. For shear deformation, partial dislocations are created on the highest resolved shear stress slip plane {1 1 1} and slip in the direction of highest resolved shear stress.     

Contraintes induites dans un support de molybdénite par un dépôt épitaxique de magnésium

Misfit dislocations are often observed between epitaxial layers. The introduction of these dislocations at the interface depends upon the presence of suitable slip planes between the crystals. The aim of this paper is to describe a crystal system in which such slip planes do not occur.Epitaxial Mg films were grown by evaporation onto hot MoS₂ thin platelets in high vacuum. In such a combination there are no slip planes to allow the introduction of interfacial misfit dislocations. Another type of dislocation with curved lines appears in the substrate as a consequence of the stresses induced by the overgrowth.     

Continuous plastic cracks in ordered alloys

A discrete dislocation analysis of the continuous plastic crack is carried out for ordered alloys. The crack is assumed to nucleate and reach a size where it will emit a set of lattice dislocations in order to decrease its energy. Further growth of the crack takes place elastically until it can emit the next set of lattice dislocations. Repeated emission of lattice dislocations, with elastic crack growth in between, leads to the Griffith configuration where the energy variation with size of the crack is zero. It is shown that a crack, either tensile or shear, can be stabilized by the presence of antiphase boundary energy alone. In the absence of frictional stress or with the very low frictional stresses encountered in real materials, the lattice dislocations are generated in pairs on each slip plane. However, when the frictional stress is high, the lattice dislocations are generated as single ones, giving rise to an antiphase boundary between the crack and the lattice dislocation.     

Numerical modelling of plastic forming of aluminium single crystals

The current study focused on modelling of micro-deep drawing of aluminium single crystals using a physically-based crystal plasticity model. The approach consisted in modelling the gauge area located at the centre of the crystals with boundary conditions extracted from displacement fields measured experimentally by digital image correlation. Thanks to three different geometries of samples, three loading paths were considered: uniaxial tension, plane strain tension and equi-biaxial tension. Comparisons between simulations and experimental observations were performed in terms of displacement fields, strain fields and slip traces. Data obtained from the simulations also allowed analysis of the results in terms of crystal rotation, dislocation density evolution and accumulated slip. Reasonable agreement between experimental observations and simulations was generally obtained, except for the prediction of strain localisation which was only correct in the case of uniaxial and plane strain tension. Discrepancies and validity of the modelling approach are then discussed in terms of experimental inaccuracies and numerical approximations.     

Transmission electron microscopic observation of dislocations in x-phthalocyanine crystals

Transmission electron microscopy has been utilized to directly reveal the defects that are present in thin single crystals of x-phthalocyanine polymorph. The bright field images are characteristic of dislocation arrays while the associated diffraction patterns indicate that the parent monoclinic structure of x-phthalocyanine may undergo a stress-induced phase transformation into a daughter orthorhombic structure. The transformation is akin to a martensitic process as a result of the operation of an invariant plane strain. The dislocation arrays observed have been interpreted in terms of slip dislocations.     

Loading frequency and microstructure interactions in intergranular fatigue crack growth in a disk Ni-based superalloy

The paper examines the role of the loading frequency on the dwell fatigue crack growth mechanism in the super-solvus nickel-based superalloy, ME3. This is accomplished by carrying out a set of crack growth experiments in air and vacuum at three temperatures; 650 °C, 704 °C and 760 °C using a dwell loading cycle with hold time periods up to 7200 s imposed at the maximum load level. Results of these tests show that the transitional transgranular/intergranular loading frequency is 0.1 Hz, and are used to determine the apparent activation energy of the time-dependent crack growth process. Analysis of this energy in both air and vacuum showed that the intergranular cracking is governed by a mechanism involving grain boundary sliding. This mechanism is explained in terms of absorption of dissociated lattice dislocations into grain boundary dislocations. The gliding of these dislocations under shear loading is assumed to cause grain boundary sliding. A condition for this mechanism to occur, is that a critical minimum distance exists between slip bands impinging the affected grain boundary. This condition is examined by correlating the slip band spacing (SBS) and loading frequency using a model based on minimum strain energy accumulation within slip bands and that a unique configuration of number and spacing of bands exists for a given plastic strain. The model outcome expressed in terms of SBS as a function of loading frequency is supported by experimental measurements at both high and low loading frequencies. Results of the model show that a saturation of SBS, signifying a condition for intergranualr cracking, is reached at approximately 3 μm which is shown to coincide with the transitional loading frequency of 0.1 Hz.     

Deformation mechanisms in oriented high-density polyethylene

The deformation of samples of oriented high-density polyethylene has been analysed in terms of three principal deformation mechanisms,fibrillar slip, lamella slip andchain slip. From a study of small- and wide-angle X-ray diffraction patterns it is possible to deduce which mechanism or mechanisms are operating in particular cases. Material prepared in three different ways has been examined and it appears that in all three cases the primary mechanism for plastic deformation is [001] chain slip.In oriented and annealed material with a well-defined lamella crystal structure it has been possible to show that the recoverable elastic deformation is primarily due to reversible lamella slip. In this material plastic deformation by chain slip starts at a well-defined critical resolved shear stress of about 15 MNm^–2.Deformation of oriented unannealed material, in which the crystal structure is not so well-defined, appears to be more complicated. In material prepared by cold drawing some of the plastic strain may be accounted for by permanent lamella slip. Fibrillar slip does not appear to be a major deformation mechanism in any of the three materials.     

Dislocation structures in deformed Cu-Ni-Zn alloy single crystals

It is known that Cu-Ni-Zn alloy has an ordered structure Cu₂NiZn (Ll₂) by annealing between 573 and 623 K. In the present experiments, the effects of annealing on the dislocation structure were studied on Cu-Ni-Zn single crystals with several compositions. Thin foils cut parallel to the {111} planes were observed in a transmission electron microscope. The results obtained are as follows. (i) In Cu-5Ni-5Zn, Cu-10Ni-10Zn and Cu-15Ni-15Zn (at%), the stress-strain behaviour, slip mode and dislocation structure did not change by annealing at 573 K. However, the slip mode became more concentrated and localized, and dislocations emitted from a source tended to stay on the same slip plane, as the nickel and zinc concentrations increased. (ii) However, those properties in Cu-20Ni-20Zn and Cu-25Ni-25Zn changed drastically by annealing. As the ordering proceeded, uniform distributions of superlattice dislocations were observed. A typical dislocation configuration, with long screw and wavy-edged superlattice dislocations, took the place of piled-up unit dislocations. (iii) The facts that edge-type superlattice dislocations formed dipoles and their clusters, and that the secondary dislocation density was much lower than the primary one, implied that the elastic interaction of the primary edge-type superlattice dislocations on the nearby parallel slip planes would control the work-hardening of ordered Cu₂NiZn alloy single crystals.     

A review of slip transfer: applications of mesoscale techniques

In this review article, we present and discuss recent mesoscale modeling studies of slip transmission of dislocations through biphase interfaces. Specific focus is given to fcc/fcc material systems. We first briefly review experimental, atomistic, and continuum-scale work that has helped to shape our understanding of these systems. Then several mesoscale methods are discussed, including Peierls–Nabarro models, discrete dislocation dynamics models, and phase field-based techniques. Recent extensions to the mesoscale mechanics technique called phase field dislocation dynamics are reviewed in detail. Results are compiled and discussed in terms of the proposed guidelines that relate composite properties to the critical stress required for a slip transmission event.     

Dislocation energies and mobilities in B2-ordered Fe-Al alloys

Anisotropic elasticity theory was used to calculate the energies and mobilities of dislocations belonging to the slip systems {1 1 0} < 1 1 1 > and {1 1 0} <1 0 0> in B2-ordered Fe-Al alloys. Based only on the energy values, it was not possible to predict the experimentally observed room-temperature slip system {1 1 0} <1 1 1>. However, when the mobility parameter, as modified by the consideration of atomic radii ratioR _Fe/R _Al was taken into account, the operative slip system could be predicted correctly.     

The dislocation structure of slip bands in deformed high entropy alloy nanopillars

Remarkable diversity is observed in dislocation interactions that are responsible for intermittent and sud-den crystal slips.While large crystal slips can be easily observed on the surface of deformed crystals,unraveling the underlying dislocation interaction mechanisms,however,has been a longstanding chal-lenge in the study of single-crystal plasticity.A recent study demonstrated that the sluggish dislocation dynamics in the high entropy alloy (HEA) of Al0.1CoCrFeNi enables the observation of slip bands for a direct link to dislocation avalanches in a nanopillar.Here,we further examined the dislocation structure of slip bands in the HEA nanopillars oriented for single slip.Experimental evidence was provided on the dislocation organization in a slip band based on groups of primary dislocations,secondary dislocations,and dislocation pileups.The results were compared with the previously proposed slip band models.The unique aspects of the HEA that enable such observations were also investigated through an examination of the dislocation microstructure and its response to applied forces in the HEA nanopillars.     

Computer simulation of deformation and fracture of small crystals by molecular dynamics method

Body-centred cubic iron whiskers having [100] and [110] axes were pulled in a molecular dynamics simulation using a supercomputer. The upper yield stress close to the theoretical strength was found. Above the upper yield stress, phase transformation was observed; at the same time the stress was greatly reduced. A new possible mechanism of twinning is proposed. The whiskers were pulled until they had broken into two pieces. Copper small crystals with and without a notch were sheared. It was observed that the edge dislocations were created at the surface and moved through and escaped from the crystals. Copper small single crystals with a notch were pulled. A half-dislocation was created near the tip of the notch. Sharp yield stress was observed. In medium deformation dislocations on different slip planes were created. Due to the cutting of dislocations the tensile stress increased.     

Hydrogen-induced Modification in the Deformation and Fracture of a Precipitation-hardened Fe-Ni Based Austenitic Alloy

Hydrogen-induced modification in the deformation and fracture of a precipitation-hardened Fe-Ni based austenitic alloy has been investigated in the present study by means of thermal hydrogen charging experiment, tensile tests, scanning electron microscopy （SEM） and transmission electron microscopy （TEM）. It is found that the γ＇ particles are subjected to the multiple shearing by dislocations during plastic deformation, which promotes the occurrence of the dislocation planar slip. Moreover, the alloy will be enhanced by hydrogen resulting in the formation of strain localization at macroscale. So, the mechanisms of deformation and fracture in the alloy have been proposed in terms of serious hydrogen-induced planar slip at microscale which can lead to macroscopic strain localization.