Long-range Stress Fields Research Articles

The stored energy of cold work: Predictions from discrete dislocation plasticity

The stored energy of cold work is calculated for planar single crystals under tensile loading with plastic deformation occurring through dislocation glide. Superposition is used to represent the solution of boundary value problems in terms of the singular fields for discrete dislocations and image fields that enforce boundary conditions. Constitutive rules are used which account for the effects of line tension and three-dimensional dislocation interactions including dynamic junction formation. The stored energy is calculated both under load and after load removal and methods are devised to estimate the local plastic dissipation and to separate out the contribution of long-range stresses to the energy stored. Calculations are carried out up to imposed strains of 0.05–0.1 and the effects of strain level, dislocation structure and crystal orientation on the evolution of the stored energy are investigated. Although the flow stress and work hardening rate depend mainly on the dislocation density, the stored energy of cold work depends on details of the dislocation structure that forms, with any long-range dislocation stress field playing a significant role. The calculations exhibit a connection between the stored energy of cold work and the Bauschinger effect. It is also found that local energy storage values can differ substantially from the average value.

A Novel Quantum/Classical Hybrid Simulation Technique

Natural phenomena occur on a variety of length scales. These lengthscales not only tend to define scientific disciplines (physics and chemistry for the very small, biology for intermediate, geology for very long times and large lengthscales, and cosmology for the largest) but can also delineate subfields within a given discipline due to the very different experimental methods and theoretical models that are applicable at each scale. In some cases, these models form a multiscale hierarchy in which the parameters used in the larger scale models can be measured or calculated using modelling carried out on a smaller scale. [1] However, in a large class of problems the length scales cannot be separated in this way because the coupling between them is strong, and “bidirectional”. This occurs, for instance, when microscopic phenomena are not only driven by macroscopic forces but also change these macroscopic forces. In this case, there is a feedback loop between the microscopic and macroscopic scales. Stress-induced defect processes in solids are a good example, and brittle fracture is the prototypical problem. If we wish to simulate such processes, we have to accurately simulate both length scales simultaneously. Crucially, one cannot use the smallest-scale model to simulate the entire system, because it would be too computationally demanding and it would also be hugely wasteful of resources. For instance, a typical quantum mechanical molecular dynamics simulation can deal with hundreds of atoms but the minimum system size that can capture the larger scale aspects of the problem, such as the long-range stress fields, could reach into hundreds of thousands of atoms or more. In the past decade there has been a growing effort to devise socalled hybrid simulation techniques, that seamlessly integrate a wide variety of different models, ranging from first-principles methods to finite elements techniques, into a concurrent simulation. [2, 3] A pioneering work in this field was the quasicontinuum method, [2] which successfully linked classical atomistic and

Environmental effects of H2O on fracture initiation in silicon: A hybrid electronic-density-functional/molecular-dynamics study

A hybrid quantum-mechanical/molecular-dynamics simulation is performed to study the effects of environmental molecules on fracture initiation in silicon. A (110) crack under tension (mode-I opening) is simulated with multiple H2O molecules around the crack front. Electronic structure near the crack front is calculated with density functional theory. To accurately model the long-range stress field, the quantum-mechanical description is embedded in a large classical molecular-dynamics simulation. The hybrid simulation results show that the reaction of H2O molecules at a silicon crack tip is sensitive to the stress intensity factor K. For K=0.4 MPa⋅m, an H2O molecule either decomposes and adheres to dangling-bond sites on the crack surface or oxidizes Si, resulting in the formation of a Si–O–Si structure. For a higher K value of 0.5 MPa⋅m, an H2O molecule either oxidizes or breaks a Si–Si bond.

Molecular dynamics simulations of the effects of defects on martensite nucleation

The effects of various lattice defects, such as a single edge dislocation, dislocation configurations, a low-angle grain boundary, and a high-angle grain boundary, on martensite nucleation and growth were investigated by performing molecular dynamics simulations, using EAM interatomic potentials for Ni–Al alloy. Stress induced and thermally activated martensitic transformations were studied in the cases that various defects were introduced into the simulated system. The simulation results show that the nucleation patterns were closely related to the stresses of the dislocation configurations, in the sense that the locations where stresses assist the lattice distortion of the transformation are favorable for martensite nucleation. A symmetric, tilt low-angle grain boundary is not favorable for martensite nucleation, because the stresses of the constituent dislocations cancel one another and stresses that assist the lattice distortion cannot be produced. The low-angle boundary hinders the martensite growth due to the high stability of this type of dislocation configuration. A relaxed, high-angle grain boundary (coincident site lattice) is also not favorable for martensite nucleation, because of the lack of long-range stress field.

Out-of-plane STM displacement measurements and evaluation of elastic fields in iron silicide islands on silicon

Elastic deformations have been discerned with b-FeSi2 islands grown on Si(111)737 by STM. Anisotropic mismatch between the b-FeSi2 and the surface is 25.3% and 11.4% along FeSi2@101 ¯#iSi@1 1 ¯ 2# and FeSi2@010#iSi@1 10# respectively. STM images of these islands show threefold symmetry and significant deformations of the surface ~the normal to the surface deviates by several degrees from the average substrate normal!, both on the islands and around them. Larger islands exhibit smaller deformation, and when deposited on a surface step the island normal tilts towards the upper terrace. Using finite element method in the framework of linear elasticity, the deformations of small islands were simulated, taking into consideration the surface stress. Best agreement with the experimental deformation is obtained when the islands are made of three domains rotated by 120° with respect to each other. The calculations of the deformation agree qualitatively with the measured displacements, and reproduce the deviation of the surface normal. The quantitative difference between the elastic theory and the experimental results may be utilized to gain additional information about the mechanical properties at the surface in the nm scale. The measured deformation of the island also enabled the calculation of the long-range stress fields it generates.

Hardening and formation of dislocation structures in LiF crystals irradiated with MeV–GeV ions

Material modifications of LiF crystals irradiated with Au, Pb and Bi ions of MeV to GeV energy are studied by means of microindentation measurements and dislocation etching. Above a critical irradiation fluence of 10 9 ions/cm 2, the microhardness can improve by a factor of 2 in the bulk and by more than 3 on the surface. Radiation-induced hardening follows the evolution of the energy loss along the ion path. Annealing experiments indicate that complex defect aggregates created in the tracks play a major role for the hardness change. Evidence for severe structural modifications is found when etching indentation impressions in highly irradiated crystals leading to similar pattern as in amorphous or micro-grained materials. Dislocation etching also reveals long-range stress fields extending far beyond the implantation zone deep into the nonirradiated crystal.

Bulk and Surface Quenching of Structural Steel: Morphological Analysis of the Structure

Structures formed in medium-carbon low-alloy steels during bulk quenching from furnace heating and surface quenching initiated by a low-power high-current electron beam are investigated by the methods of diffraction electron microscopy. The influence of the carbon concentration, initial austenite grain size, and cooling rate on the morphology of martensitic crystals and self-tempered carbide particles, long-range stress fields inside a packet and plates, and their dislocation substructure is analyzed. The temperature intervals for the formation of high-temperature plate martensitic crystals and packet (lath) martensite are estimated. It is demonstrated that the structure formed at ultrahigh heating and cooling rates is determined mostly by the morphology of martensite in the initial steel samples.

A comparison of mode I fracture behavior of fcc and bcc metallic materials: a discrete dislocation analysis

Mode I fracture behavior in fcc and bcc materials is analyzed using the discrete dislocation approach. Dislocations are modeled as line discontinuities residing in an isotropic linear elastic medium and interacting with each other through long-range stress fields. In addition, the short-range reactions underlying dislocation nucleation and annihilation are introduced to enable simulation of the evolution of the dislocation structure during loading. The motion of dislocations and their nucleation is considered to be controlled by thermal activation at higher temperatures and lower stress levels and by phonon-drag at lower temperatures and higher stress levels. A mode I crack is introduced into the model using a cohesive surface formulation. The results obtained show that differences in the orientation of the slip planes, relative to the low-cohesive strength {1 0 0} fracture planes, cause dislocations to promote crack tip blunting and plastic shielding in the case of the fcc material while such effects are only marginal in the case of the bcc material. Furthermore, temperature is found to have a pronounced effect on fracture toughness of the bcc material while its role in the fcc material is very small.

Dislocation Walls in Finite Media: The Case of an Infinite Slab

ABSTRACTThe dislocation microstructure observed in solids exhibits cellular patterns. The interiors of these cells are depleted of dislocations while the walls contain dense bundles including the geometrically necessary dislocations leading to misorientations of the crystal lattice on either side. This clustering is the result of short-range interactions which favor the formation of dislocation dipoles or multipoles and tilt and twist boundaries. While this short-range ordering of dislocations is readily understood, the long-range pattern formation is still being studied. We examine finite tilt boundaries in an infinite medium, a model grain, and a free slab to investigate the conditions for long-range stress interactions. We find that finite tilt walls in a larger medium generally possess a long-range stress field because the local bending at the tilt wall is constrained by the surrounding material.

Interaction of deformation twin and 120 deg-rotational order fault domain boundary in the lamellar structure of two-phase TiAl-based alloys

Interactions between deformation twin and 120 deg-rotational domain boundary were studied by transmission electron microscopy in a two-phase TiAl-based alloy with fully lamellar structure deformed at room temperature. Three types of the interaction were observed, depending on the interaction geometry and crystallography faced by the incident twinning Shockleys. It was found that the incident twinning shear could be accommodated into the barrier domain by a reaction involving emission of 1/2 $$\left. {\left\langle {1\bar 10} \right.} \right]_B $$ {111} B slip in all the three types of interactions presumably since the slip required a small critical resolved shear stress (CRSS) and was always favored by the pile-up stress. Several reaction schemes involving 1/2 $$\left. {\left\langle {1\bar 10} \right.} \right]_B $$ {111} B slip for each type of the interactions were proposed by considering whether the reaction resulted in a reduced elastic energy and if the dissociated dislocations were able to glide away to minimize the total elastic energy associated with a long-range stress field of a pileup of the incident twinning partials. It is suggested that whether a reaction scheme is feasible would depend on behavior of other product dislocation except 1/2 $$\left. {\left\langle {1\bar 10} \right.} \right]_B $$ {111} B .

Non-linear anelasticity due to dislocation–solute atom interactions in solid solutions

A theory for the non-linear, strain-amplitude-dependent internal friction (ADIF) in solid solutions due to dislocation–solute atom interactions has been developed. The suggested model accounts for different modes of dislocation–solute atom interactions: • solute atoms, distributed in the dislocation glide plane, represent short-range obstacles for the dislocation motion; • solute atoms, situated away from the dislocation glide plane, create diffuse weak long-range elastic stress fields, also impeding dislocation motion. Dislocations overcome localised obstacles under the combined action of the applied stress and thermal energy, whereas diffuse long-range obstacles can be surmounted only athermally. Numerical calculations of the ADIF, strain-amplitude-dependent modulus defect, their ratio, and of the fraction of the athermal ADIF component have been performed. The model predicts a complicated multistage behaviour of the parameters of the non-linear anelasticity in the strain amplitude–temperature–solute concentration domain which is in excellent agreement with recent experimental data.

Long-range elastic interactions and equilibrium shapes of curved ferroelastic domain walls in crystals

Dislocation-disclination models of ferroelastic domain walls (twin walls) are developed. These models are used to calculate long-range stress fields created by curved walls and to evaluate the associated elastic energy. For two basic domain-wall configurations (corner and kink), the equilibrium trajectories of the walls are analysed by minimizing the total energy of the system, which is the sum of the domain wall self-energy and the elastic energy stored in the surrounding medium. It is shown that, by introducing a characteristic length, it is possible to reveal universal features of domain-wall trajectories in ferroelastic crystals.

Theory of dislocation-solute atom interactions in solid solutions and related nonlinear anelasticity

A theory for dislocation-solute atom interactions in solid solutions has been developed which allows one to calculate the nonlinear dislocation strain-amplitude-dependent internal friction. The suggested model accounts for different modes of dislocation-solute atom interactions: (i) Solute atoms distributed in the dislocation glide plane interact with the dislocation core and represent short-range obstacles for the dislocation motion; (ii) Solute atoms situated away from the dislocation glide plane create relatively weak long-range elastic stress fields, also impeding dislocation motion. We assume that dislocations move in a two-component system of obstacles which differ with respect to the thermodynamics of dislocation--point-defect interactions. Namely, dislocations overcome short-range obstacles under the combined action of applied stress and thermal energy, whereas relatively weak long-range obstacles are surmounted athermally. The model predicts a complicated multistage behavior of the nonlinear internal friction in the strain amplitude--temperature--solute concentration domain, which is in excellent agreement with recent experimental data.

Synthesis and characterization of Ti-Si-C-N films

This study represents one of the first attempts to deposit multicomponent (more than three components) thin films by magnetron sputtering of multiphase composite targets (three phases or even more). Films of Ti-Si-C-N were synthesized through dc magnetron sputtering of xTiC+yTi3SiC2+zA composite targets (A was TiSi2, SiC, or a mixture of these phases) in an argon atmosphere or in a gaseous mixture of argon and nitrogen. The as-deposited films were characterized using Auger electron spectroscopy, X-ray diffraction, transmission electron microscopy using selected area electron diffraction and high-resolution techniques, and microhardness. It was shown that the substrate temperature and the nitrogen concentration in the reactive gas had a strong influence on the structure and the composition of the as-deposited films. The films deposited from the Si-poor targets were either polycrystalline or contained a mixture of nanocrystalline and amorphous phases. An amorphous phase formed as individual grains rather than as intergrain amorphous layers. All films deposited from the Si-rich target were amorphous in nature. Particular attention has been paid to the atomic structure of grains and grain boundaries in the crystalline films. Polycrystalline grains contained a high density of dislocations and exhibited a curved appearance of the lattice fringes that is probably due to the presence of the long-range stress fields. The measurements of the lattice parameters using the selected area electron diffraction pattern (SA EDP) method indicated, with a high probability, that the polycrystalline grains consist of clusters of atoms with varying compositions. The grain boundaries in the nanocrystalline Ti-Si-C-N films had both ordered and disordered regions, although some regions close to the interface exhibited neither a fully crystalline nor a homogeneously amorphous structure. The atomic structure of an interface was shown to depend on the orientation relationship between adjacent grains. The atomic planes were perfectly matched when the two grains were oriented close to the [110]fcc1//[110]fcc2 zone axis. However, the interface dislocations were frequently observed at or near the grain boundary when [110]fcc1//[001]fcc2. The contribution of compressive stress as determined by an increase in the fcc lattice parameter is also discussed.

Local Segregation at the Grain Junction: Elastic Singularity and its Effect on Radiation Embrittlement

Under consideration are the long-range stress field generated in deformed polycrystals by grain boundaries and junction lines and corresponding re-distribution of impurity atoms due to their elastic interaction with this stress field. Evaluation of the effect is made for deformed bcc polycrystals at 270°C containing the phosphorus impurity. It is assumed that under neutron irradiation the impurity atoms are in interstitial positions and form mixed P-Fe dumb-bells having a relaxation volume of about an atomic volume of host crystal. Corresponding re-distribution results in the impurity conglomeration around grain junction lines; in the areas as wide as 10% of the grain size the local P concentration is more than 50% higher then its mean concentration. Respective local segregations are considered to facilitate the brittle fracture origination, and the impurity-dependent component of radiation embrittlement is discussed within this framework.

Imperfect low-angle boundaries and fracture in hydrothermally grown berlinite crystals

We present evidence for finite and/or imperfect low-angle grain boundaries and associated long-range stress fields, formed during the hydrothermal growth of berlinite (α-AlPO 4) crystals on multiple-seed-plate arrays. These defective boundaries originate at angularly misaligned junctions between adjacent seed plates as a result of the failure of some component sets of dislocations to propagate epitaxially into the new growth. Lacking a full complement of dislocations, the newly grown boundary may be imperfect and generate long-range stresses, leading to fracture and/or plastic flow.

Dislocations at ductile/plastic crack tips: in-situ TEM observations

In-situ observations of dislocation structures ahead of crack tips in TEM metal foils are reviewed. Two cases are compared in particular: Structure development during in-situ straining to failure of (i) electron-transparent foils ahead of the tip of a growing crack that spreads from the thinnest regions or perforations and (ii) initially non-transparent thick foils. In the latter case cracks formed only after substantial in-situ straining, and they propagated along dislocation cell walls via repeated stimulated crack nucleation ahead of the tip. This behavior was shown to adequately simulate bulk behavior and such cracks do not exhibit dislocation-free zones at their tips. By contrast, dislocation-free regions along ligaments formed by crack propagation and observed in thin (e.g. about 100 nm or less) TEM foils are found to be artifacts due to strong dislocation image forces. These image forces at the same time limit mutual dislocation interactions to the thickness of the foil, and rotate the dislocations to be normal to the foil plane, meanwhile straightening them. This behavior has no correspondence to conditions at real cracks in bulk materials. Theoretical expressions are derived for the dislocation densities ahead of crack tips that give rise to long-range and shorter range stress fields in mode I crack tip configurations, respectively.

Film quality effects associated with formation of misfit dislocations at semiconductor interfaces

The influence of the interface orientation on the strain state and structure properties of epitaxial layers is theoretically investigated for semiconductor films grown on (001) misoriented substrates. The analysis shows that for two intersected MD arrays, the film energy strongly depends on the type of the screw component of their Burgers vector. The energy is much lower if for both mutually perpendicular MD arrays the components are left-screw or right-screw. Identification of these components for 60° misfit dislocation arrays lying in a (001) interface may explain some experimental results of deteriorated epitaxial film structures. If the plastic relaxation process occurs in quasi-equilibrium; the whole multitude of vicinal (001) orientations can be classified into two types: orientations of type 1, when the conditions for threading dislocation formation are present, but the long-range stress field does not appear, and orientations of type 2, when the probability of threading dislocation formation is small, but the field is present.

Effect of temperature on the amplitude dependences of the acoustoplastic effect and internal friction during deformation of crystals

Abstract Oscillatory strain amplitude dependences of the acoustoplastic effect and absorption of ultrasonic vibrations (frequency of about 100 kHz) causing this effect were measured in a wide temperature range in situ during quasistatic deformation of NaCl and Al single crystals. An increase in efficiency of the ultrasonic effect on the plastic deformation process has been found with an increase in temperature. The data obtained provide evidence for the distinction in basic mechanisms of the acoustoplastic effect and amplitude-dependent internal friction. The absorbtion of ultrasound is largely due to dislocation-point-defect interactions under reversible movement of mobile dislocations. Mechanical activation of irreversible movement of the same mobile dislocations through long-range internal stress fields of other dislocations and dislocation pileups is suggested as the basic mechanism of the acoustoplastic effect. Mechanisms are discussed determining the temperature dependences of the acoustoplastic eff...

Acoustoplastic effect and internal friction of aluminum single crystals in various deformation stages

The dependences of the acoustoplastic effect and the internal friction on the oscillatory strain amplitude are measured in various deformation stages of low-purity aluminum single crystals. It is discovered that the acoustoplastic effect is observed not only in the macroscopic plastic region of the stress-strain diagram, but also for microplastic deformation in the “elastic” loading and unloading stages. The sign of the effect reverses during unloading. An increase in the strain rate leads to enhancement of the acoustoplastic effect and the absorption of the energy of ultrasonic vibrations causing this effect with a frequency of about 100 kHz. It is concluded that the acoustoplastic effect observed during both macro-and microplastic deformation is caused by the irreversible high-speed motion of dislocations through the long-range stress field of the other dislocations after breaking through the Cottrell atmospheres.