Neutron and X-ray diffraction studies and cohesive interface model of the fatigue crack deformation behavior

The crack-tip deformation behavior during a single overload, fatigue test of ferritic stainless steel, and Ni-based HAYNES 230 superalloy is studied at different structural levels using (1) neutron-diffraction, from which both the elastic-lattice strain and volume-averaged total dislocation densities are obtained, (2) polychromatic X-ray microdiffraction to probe the geometrically necessary dislocations and boundaries distribution, and (3) an irreversible and hysteretic cohesive interface model which has been implemented into a finite element framework to simulate the stress/strain evolution near the fatigue crack tip. Neutron strain measurements and finite element simulations are in qualitative agreement on the macroscopic length scale. Large plastic deformation induced by the overload and the resulting compressive residual strains are observed in front of the crack tip after the overload, and are the principal reason for the fatigue-crack-growth retardation. Strong strain gradients surrounding the crack propagation result in the formation of a high density of geometrically necessary dislocations near the fractured surface and cause local lattice rotations on the submicron level.     

The surface topography of cracks in strained In0.72Ga0.28P films

Cracks in a 2% tensile strained In_0.72Ga_0.28P film grown on an InP substrate by molecular-beam epitaxy have been studied by cross-section transmission electron microscopy and scanning probe microscopy. A dislocation analogue (i.e. replacing the crack by an array of equivalent infinitesimal edge dislocations) is employed to account for the ratio of the crack-opening displacement to the normal surface displacement associated with the crack.     

Dislocations and cracks at Vickers indentations in (0 0 0 1) GaN single crystals

Single-crystal (0 0 0 1) GaN samples have been deformed with a Vickers indenter at room temperature using loads in the range from 0.02 to 4.90 N. Dislocations and cracks at the indentations were examined by means of scanning electron microscopy, cathodoluminescence, light microscopy and transmission electron microscopy. Geometrical relations could be found between the dislocation arrangement, cracks and the orientation of the indenter. The orientation of the indenter has only a slight effect on the dislocation pattern, but the crack system is predominantly determined by the symmetry and the orientation of the indenter.     

The displacement field of a rectangular Volterra dislocation loop

The displacement field of a rectangular Volterra dislocation loop having three non-zero Burgers vector components is obtained in an analytical closed form. The solution is obtained via integrating the Burgers equation for the displacement field of any closed dislocation curve and is expressed in a relatively compact form. The current solution has utility in a number of problems including dislocation-particle interaction problems, where the boundary condition involved imposes certain restrictions on the displacements in the medium, and modelling of cracks of arbitrary shapes. The solution is also useful in benchmarking newly emerging dislocation dynamics codes which discretize a curved dislocation line in some form or another. Several verification steps of the solution correctness are made including a comparison with the displacement and stress fields of a circular Volterra dislocation loop of equal Burgers vector and comparable size.     

Creep behaviour of ice single crystals loaded in torsion explained by dislocation cross-slip

Torsion creep experiments are carried out in order to understand the physics of ice plasticity. A dislocation spreading mechanism based on double cross-slip of basal dislocations is proposed to explain the strong plastic anisotropy and the power law relationship between stress and strain rates. The scenario is tested using three-dimensional dislocation dynamics simulations. Numerical investigations give a stress exponent n?=?2.3 in agreement with experimental measurements. This dislocation spreading mechanism sheds a new light on the interpretation of former experimental observations.     

Investigation of jog motion in γ-TiAl via molecular dynamics

The elastic displacement field of a jogged screw dislocation is obtained analytically from Burgers equation. With this analytic solution, a pair of jogs in a screw dislocation is implemented into molecular-dynamics simulations. The dislocation line bows out between two jog pinning points and breaks away when the line tension of the dislocation exceeds a certain critical value. The creation of vacancies and interstitials is observed during the non-conservative motion of the jogged screw dislocation in γ-TiAl. The structures of vacancies and interstitials are discussed.     

Application of electron channelling contrast to the investigation of strain localization effects in cyclically deformed fcc crystals

The dislocation substructure and the glide activity in cyclically deformed nickel single crystals have been studied using the channelling contrast of backscattered electrons in a scanning electron microscope. Dislocation arrangements which arise in the saturation region after cyclic loading at room temperature and at one elevated temperature are considered. The electron channelling contrast technique is shown to be a useful instrument for the qualitative and quantitative characterization of the dislocation pattern on a macroscopic and a mesoscopic scale. The correlation between the specific dislocation structure in persistent slip bands PSBs and the localized glide activity of PSBs and PSB macrobands are considered.     

Size-dependent interaction between a screw dislocation and an inhomogeneity of arbitrary shape in an applied stress field

We present a general approximate solution for a screw dislocation interacting with an inhomogeneity of arbitrary shape in an applied stress field. The analysis is based on the Eshelby inhomogeneity theory. As special cases, explicit solutions for some common inhomogeneity shapes are obtained, from which size-dependent effects of dislocation stress field and the applied stress field on the interaction can be identified.     

Dislocation multiplication in bcc molybdenum: A dislocation dynamics simulation

Plastic deformation of Mo single crystals is examined by direct simulation of dislocation dynamics under stress. Initial dislocation populations are made to mimic real dislocation microstructures observed in transmission electron microscopy cross-sections of pure annealed Mo single crystals. No a priori sources for dislocation multiplication are introduced, and yet multiplication takes place through a sequence involving aggregation of grown-in superjogs, bowing of screw dislocation segments and fast lateral motion of edge segments, producing a large number of elongated loops and a characteristic cross-grid pattern of screw dislocations.     

Stacking fault and dislocation glide on the basal plane of graphite

Generalized stacking-fault energies for the basal plane of graphite are calculated from first principles for slip along two high-symmetry directions. The rhombohedral fault energy compares well with experiment and the anisotropy in behaviour is consistent with observed dislocation network geometry. Utilizing these calculated fault energies within a modified Peierls-Nabarro model, we estimate the barrier for basal dislocation motion based on lattice friction. This is found to be extremely small, from which we conclude that dislocation network interaction and pinning, rather than the Peierls barrier, must determine the practical shear strength of graphite. However, at low dislocation densities or over small crystallite regions, the shear strength should tend to this lower limit. We discuss the relevance of this to the mechanism of lubrication.     

Quantification of dislocation structures at high resolution by atomic force microscopy of dislocation etch pits

Atomic force microscopy of dislocation etch pit structures is a convenient means of characterising the dislocation structure in etchable materials at high resolution for dislocation spacing extending down to 25 nm . This is demonstrated for single crystals of CaF₂. The local deformation zone generated around nanoindents at ambient temperature and the low-angle boundaries generated in the bulk during uniaxial compression at elevated temperatures are presented as examples.     

The atomic structure of the dislocation cores in a small-angle grain boundary in BaTiO3 thin films

The atomic structure of the cores of the dislocations forming a [110] tilt boundary of 10^o misorientation in a BaTiO₃ film is characterized by means of focal-series reconstruction. Along the small-angle grain boundary, facets with different inclinations are accompanied by different types of dislocation. The dislocation with a Burgers vector of a [001] appears as a perfect edge type. Those with a Burgers vector of a [111] are dissociated into three partials with a Burgers vector of (a/3)[111], leading to two segments of stacking faults. Structural models of these dislocation cores are suggested on the basis of the phase of the reconstructed wavefunction and tested by simulation of the wavefunction.     

Shuffle-set dislocation nucleation in semiconductor silicon device

We have found that a shuffle-set dislocation is nucleated in a semiconductor silicon device subjected to severe thermal processing. The dislocation transforms into a dissociated glide-set dislocation after annealing at 500°C. A possible mechanism for the nucleation of a perfect shuffle-set dislocation during thermal processing is that the dislocation nucleus was nucleated at a low temperature during prior ion-implantation processing.     

A continuum model of deformation-twin dominant crack growth in fcc metals

A continuum model is proposed to address the effects of deformation twinning on ductile versus brittle fracture behaviour of low strain-hardening fcc metals after exhaustion of work hardening. Instead of discrete twin nucleation, a number of partial dislocations ahead of the tip exhibit themselves as twins at the final stage of failure. The crack-tip plasticity is amended for deformation twinning and the constitutive form for the flow strength of arrays of twins of the same sign is expressed as a second gradient of microrotation for their coupling. The twins not only shield the crack tip but also inhibit further dislocation emission to form a dislocation-free zone (DFZ) in the immediate vicinity of the tip. The stress fields induced by deformation twinning lead to fracture branching under Mode I loading. The model is borrowed from the conceptual model presented by Beltz et al. [Acta Mater. 44 3943 (1996)], based on the equivalence of the stresses derived from twin-based crack-tip plasticity, macroscopic plasticity and elasticity on the DFZ boundary. The DFZ size and the crack-tip shielding ratio are obtained, as well as the branching angle. The branching angle is noteworthy for low strain-hardening metals. A strong dependence of the toughness on intrinsic surface energy and hardening index is examined. The toughness reduction due to crack-tip constraints and in the ductile-to-brittle transition (DBT) temperature region is revisited and found to be in agreement with experimental observations and available predictions.     

Dislocation nucleation and vacancy formation during high-speed deformation of fcc metals

Recently, a dislocation-free deformation mechanism was proposed by Kiritani et al. on the basis of a series of experiments where thin foils of fcc metals were deformed at very high strain rates. In the experimental study, they observed a large density of stacking fault tetrahedra but very low dislocation densities in the foils after deformation. This was interpreted as evidence for a new dislocation-free deformation mechanism, resulting in a very high vacancy production rate. In this paper we investigate this proposition using large-scale computer simulations of bulk and thin films of copper. To favour such a dislocation-free deformation mechanism, we have made dislocation nucleation very difficult by not introducing any potential dislocation sources in the initial configuration. Nevertheless, we observe the nucleation of dislocation loops, and the deformation is carried by dislocations. The dislocations are nucleated as single Shockley partials. The large stresses required before dislocations are nucleated result in a very high dislocation density, and therefore in many inelastic interactions between the dislocations. These interactions create vacancies and a very large vacancy concentration is quickly reached.     

Pop-in phenomenon in MgO and LiF: Observation of dislocation structures

This letter is based on recent progress in the observation of dislocation distributions around nanoindentations by chemical etching. This so-called nanoetching technique is used to determine the dislocation mechanisms associated with the pop-in phenomenon in MgO and LiF. Successive stages of highly controlled chemomechanical polishing have revealed that these dislocations are half-loops lying in the classical slip systems of MgO or LiF. However, they do not extend on the surface in the classical rosette-arms pattern but stay concentrated around the imprint. A mechanism of dislocation interactions, enhanced by the fact that the dislocations are suddenly nucleated in a small volume, is proposed to explain this specific distribution.     

high-resolution electron microscopy at a (113) symmetric Thermally activated step motion observed by tilt grain-boundary in aluminium

Grain-boundary migration is demonstrated to proceed by lateral propagation of a small step in a (113), [110] symmetric Al tilt grain-boundary. In-situ high-resolution (transmission) electron microscopy (HREM) at 523K allowed the study of atomic-scale detail at video rates during the migration process. The grain-boundary translational states on both sides of the step are identical, which leads to a step dislocation. This defect can move laterally by a combination of climb and glide. Dynamic HREM images indicate considerable atomic agitation within the dislocation core. A detailed temporal analysis of the step movements shows small random displacements of the dislocation core.     

Dislocation evolution in twins of cyclically deformed copper

The evolution of dislocation structure in twins of different thicknesses has been investigated in polycrystalline copper fatigued at room temperature under constant plastic axial strain amplitude control. The dislocation structure and its evolution strongly depend on twin thickness. Three critical thicknesses must be distinguished, i.e. (i) characteristic size of fatigue dislocation structures, about 1?µm; (ii) critical height of stable dislocation wall structure, about 200?nm; (iii) critical spacing of dislocation dipole, about 20?nm. It is considered that the size effect is mainly caused by twin boundaries (TBs) which play different roles on slip behaviors in twins.     

Long-term natural ageing of a dissociated dislocation in a Cu-13.43 at.% Al alloy

The nature of impurity-dislocation interactions is one of the key questions governing the strength and plasticity of solid-solution materials. To investigate the influence of impurities on the mechanical properties of intermetallic NiAl, the electronic structure and energy of NiAl with a <100>{010} edge dislocation and transition-metal impurities was calculated using the real-space tight-binding linear muffin-tin orbital method. The localized electronic states, appearing in the core of the dislocation, are found to lead to strong impurity-dislocation interactions via two mechanisms: firstly, chemical locking, due to strong hybridization between impurity electronic states and dislocation localized states; secondly, electrostatic locking, due to long-range charge oscillations caused by the electron localization in the dislocation core. The results obtained explain qualitatively why the solid-solution hardening effect in NiAl correlates with the electronic structure of impurities rather than with size misfit, as expected according to traditional views.     

Dislocation density evolution upon plastic deformation of Al-Pd-Mn single quasicrystals

Dislocation density studies have been performed on icosahedral Al-Pd-Mn single quasicrystals after plastic deformation and after subsequent heat treatment. The deformation tests were carried out at a constant strain rate of 10- 5 s-1 at temperatures between 695 and 820 C. The heat treatments were performed at 730 C, corresponding to one of the deformation temperatures. The development of the dislocation density during heat treatment and that during plastic deformation are compared. The experimental data are interpreted using a kinetic equation, which describes the evolution of the dislocation density during deformation. Numerical values for the dislocation multiplication constant and the annihilation rate for icosahedral Al-Pd-Mn are presented.