Investigations of pipe-diffusion-based dislocation climb by discrete dislocation dynamics

A new numerical dislocation climb model based on incorporating the pipe diffusion theory (PDT) of vacancies with 3D discrete dislocation dynamics (DDD) is developed. In this model we hold that the climb rate of dislocations is determined by the gradient of the vacancy concentration on the segment, but not by the mechanical climb force as traditionally believed. The nodal forces on discrete dislocation segments in DDD simulation are transferred to PDT to calculate the vacancy concentration gradient. This transfer establishes a bridge connecting the DDD and PDT. The model is highly efficient and accurate. As verifications, two typical climb-involved examples are predicted, e.g. the activation of a Bardeen-Herring source as well as the shrinkage and annihilation of prismatic loops. Finally, the model is applied to study the breakup process of an infinite edge dislocation dipole into prismatic loops. This coupling methodology provides us a useful tool to intensively study the evolution of dislocation microstructures at high temperatures.     

The dynamic stress intensity factor for a crack due to arbitrary rectilinear screw dislocation motion

The dynamic stress intensity factor for a stationary semi-infinite crack in an elastic plane due to the rectilinear motion of a screw dislocation is obtained analytically. The intensity factor is studied for its dependence on the (initial) dislocation position, orientation and speed. The speed is subsonic and possibly non-uniform. The position and orientation are arbitrary, so that crack-dislocation intersection is considered. It is assumed that a dislocation traveling toward the crack surface arrests upon arrival. It is found that, in general, dislocation motion initiation and arrest cause discontinuities in the intensity factor. In the latter instance, the factor takes on a constant value and, in the case of arrest on the crack surface, this value depends only on the initial dislocation position.     

Modeling of processes of complex plastic deformation of materials along arbitrary temperature and force loading paths

We develop a mathematical model describing the processes of complex plastic deformation of structural materials (metals and their alloys) under multiaxial nonproportional paths of complex temperature and force loading. To obtain qualitative and quantitative assessment of the constitutive relations developed here, we study how the strain path shape affects the plastic behavior of metals. We show that the version of constitutive relations developed here correctly represents the main elastoplastic deformation effects in metals for arbitrary strain paths.     

Stochastic simulation of dislocation glide in tantalum and Ta-based alloys

We employ a kinetic Monte Carlo algorithm to simulate the motion of -oriented screw dislocation on a -slip plane in body centered cubic Ta and Ta-based alloys. The dislocation moves by the kink model: double kink nucleation, kink migration and kink-kink annihilation. Rates of these unit processes are parameterized based upon existing first principles data. Both short-range (solute-dislocation core) and long-range (elastic misfit) interactions between the dislocation and solute are considered in the simulations. Simulations are performed to determine dislocation velocity as a function of stress, temperature, solute concentration, solute misfit and solute-core interaction strength. The dislocation velocity is shown to be controlled by the rate of nucleation of double kinks and the dependence of the double kink nucleation rate on stress and temperature are consistent with existing analytical predictions. In alloys, dislocation velocity depends on both the short- and long-range solute dislocation interactions as well as on the solute concentration. The short-range solute-core interactions are shown to dominate the effects of alloying on dislocation mobility. The present simulation method provides the critical link between atomistic calculations of fundamental dislocation and solute properties and large scale dislocation dynamics that typically employ empirical equations of motion.     

Non-linear elastic non-uniform torsion of bars of arbitrary cross-section by BEM

In this paper an elastic non-uniform torsion analysis of simply or multiply connected cylindrical bars of arbitrary cross-section taking into account the effect of geometric non-linearity is presented employing the boundary-element(BE) method. The torque-rotation relationship is computed based on the finite-displacement (finite-rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometric non-linear term often described as the “Wagner strain”. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross-section's torsional rigidity is evaluated exactly without using the so-called Saint-Venant's torsional constant. The torsional rigidity of the cross-section is evaluated directly employing the primary warping function of the cross-section depending on its shape. Three boundary-value problems with respect to the variable along the beam axis angle of twist, to the primary and to the secondary warping functions are formulated. The first one, employing the Analog Equation Method (a BEM-based method), yields a system of non-linear equations from which the angle of twist is computed by an iterative process. The remaining two problems are solved employing a pure BE method. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The developed procedure retains most of the advantages of a BEM solution over a pure domain discretization method, although it requires domain discretization.     

Modeling of thermally activated dislocation glide and plastic flow through local obstacles

A unified phenomenological model is developed to study the dislocation glide through weak obstacles during the first stage of plastic deformation in metals. This model takes into account both the dynamical responses of dislocations during the flight process and thermal activations while dislocations are bound by obstacle arrays. The average thermal activation rate is estimated using an analytical model based on the generalized Friedel relations. Then, the average flight velocity after an activation event is obtained numerically by discrete dislocation dynamics (DD). To simulate the dynamical dislocation behavior, the inertia term is implemented into the equation of dislocation motion within the DD code. The results from the DD simulations, coupled with the analytical model, determine the total dislocation velocity as a function of the stress and temperatures. By choosing parameters typical of the face centered cubic metals, the model reproduces both obstacle control and drag control motion in low and high velocity regimes, respectively. As expected by other string models, dislocation overshoots of obstacles caused by the dislocation inertia at the collisions are enhanced as temperature goes down.     

The transient motion of a nonuniformly moving dislocation

The solution to the transient subsonic motion of a nonuniformly moving screw dislocation starting from rest is obtained.

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Résumé On étudie le mouvement quelconque d'une dislocation se propageant à une vitesse nonuniforme subsonique à partir d'une position de repos.

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This research was conducted while the author held a visiting appointment at Brown University.     

Guided motion of short carbon nanotube driven by non-uniform electric field

The molecular dynamics simulations are performed to show that in aque- ous environments, a short single-walled carbon nanotube （SWCNT） guided by a long SWCNT, either inside or outside the longer tube, is capable of moving along the nanotube axis unidirectionally in an electric field perpendicular to the carbon nanotube （CNT） axis with the linear gradient. The design suggests a new way of molecule transportation or mass delivery. To reveal the mechanism behind this phenomenon, the free energy profiles of the system are calculated by the method of the potential of mean force （PMF）.     

A crystal plasticity theory for latent hardening by glide twinning through dislocation transmutation and twin accommodation effects

Imagine a residual glide twin interface advancing in a grain under the action of a monotonic stress. Close to the grain boundary, the shape change caused by the twin is partly accommodated by kinks and partly by slip emissions in the parent; the process is known as accommodation effects. When reached by the twin interface, slip dislocations in the parent undergo twinning shear. The twinning shear extracts from the parent dislocation a twinning disconnection, and thereby releases a transmuted dislocation in the twin. Transmutation populates the twin with dislocations of diverse modes. If the twin deforms by double twinning, double-transmutation occurs even if the twin retwins by the same mode or detwins by a stress reversal. If the twin deforms only by slip, transmutation is single. Whether single or double, dislocation transmutation is irreversible. The multiplicity of dislocation modes increases upon strain, since the twin finds more dislocations to transmute upon further slip of the parent and further growth of the twin. Thus, the process induces an increasing latent hardening rate in the twin. Under profuse twinning conditions, typical of double-lattice structures, this rate-increasing latent hardening combined with crystal rotation to hard orientations by twinning is consistent with a regime of increasing hardening rate, known as Regime II or Regime B. In this paper, we formulate governing equation of the above transmutation and accommodation effects in a crystal plasticity framework. We use the dislocation density based model originally proposed by Beyerlein and Tomé (2008) to derive the effect of latent hardening in a transmuting twin. The theory is expected to contribute to surmounting the difficulty that current models have to simultaneously predict under profuse twinning, the stress-strain curves, intermediate deformation textures, and intermediate twin volume fractions.     

The transient motion of a dislocation in a solid of general anisotropy

The transient motion of a dislocation starting from rest and moving in an arbitrary rectilinear motion in an anisotropic solid is analyzed by transform techniques and inversion according to the Cagniard-de Hoop technique.     

Non-linear non-planar vibrations of geometrically imperfect inextensional beams, Part I: Equations of motion and experimental validation

The non-linear equations and boundary conditions of non-planar (two bending and one torsional) vibrations of inextensional isotropic geometrically imperfect beams (i.e. slightly curved and twisted beams) are derived using the extended Hamilton's principle. The assumptions of Euler-Bernoulli beam theory are used. The order of magnitude of the natural geometric imperfection is assumed to be the same as the first order of vibrations amplitude. Although the natural imperfection is small, in contrast to the case of straight beams (i.e. geometrically perfect beams), this study shows that the vibration equations are linearly coupled and have linear and quadratic terms in addition to cubic terms. Also, in the case of near-square or near-circular beams, coupling terms between lateral and torsional vibrations exist. Furthermore, a problem of parametric excitation in the case of perfect beams changes to a problem of mixed parametric and external excitation in the case of imperfect beams. The validity of the model is investigated using the existing experimental data.     

The interaction of an edge dislocation with an inhomogeneity of arbitrary shape in an applied stress field

A general, approximate solution is presented for an edge dislocation interacting with an inhomogeneity of arbitrary shape under combined dislocation and applied stress fields. The solution shows that the contributions of the dislocation stress field and the applied stress field to the interaction follow a simple superposition principle. The dislocation stress field has a short range effect, while the applied stress field has a long range effect. As special cases, explicit solutions for some common inhomogeneity shapes are obtained for the interaction induced by the applied stress field.     

The slow motion of two spherical particles along their line of centres

The motion of spherical, solid particles, liquid droplets or gas bubbles along their line of centres is considered. Conditions are limited to quasi-steady creeping flow and results are presented for drag coefficients and streamlines in these systems. Various interactions between two particles are reviewed and applications to gravity settling and droplet coalescence discussed.     

Finite amplitude,periodic motion of a body supported by arbitrary isotropic,elastic shear mountings

The undamped, finite amplitude, periodic motion of a load supported symmetrically by arbitrary isotropic, elastic shear mountings is investigated. Conditions on the shear response function sufficient to guarantee periodic motions for finite shearing with arbitrary initial data are provided. Some general results applicable for all simple shearing oscillators in the class are derived and illustrated graphically. The mechanical response of the general nonlinear shearing oscillator is compared with the response of a certain linear oscillator of comparable design. As consequence, certain static and dynamic aspects of the motion of an arbitrary nonlinear oscillator supported by shear springs are compared with those of a simple, linear oscillator for which the response is well-known and readily determined for the same initial data. The effect of a finite static shear deformation on the frequency equation for superimposed, small amplitude vibrations of the load is examined. The general analysis is applied to a class of hyperelastic biological tissues; and the frequency relation for finite amplitude oscillations of a load supported by soft tissue is derived. The finite amplitude oscillatory shearing of a general isotropic elastic continuum is described; and three universal relations connecting the stress and the oscillatory shearing deformation for every isotropic elastic material are presented.     

The slow motion of two touching fluid spheres along their line of centers

The creeping motion along their line of centers of two fluid spheres in contact is analyzed. An exact solution is presented. Corrections to the Hadamard—Rybezynski equation are tabulated for various particle radii ratios and particle fluid to external fluid viscosity ratios. In the limit of infinite particle viscosity, these corrections are shown to agree with previous calculations for rigid spheres.     

An approximate solution of the interaction between an edge dislocation and an inclusion of arbitrary shape

An approximate solution of the interaction force between an edge dislocation and an inclusion of arbitrary shape is derived, from which a set of succinct formulas for several special inclusion shapes are obtained. As compared with several classical solutions to special inclusion shapes, the present approximate solution has fairly good accuracy.