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At least 19 records

Dislocation Theory of the Fatigue of Metals

A dislocation theory of fatigue failure for annealed solid solutions is presented. On the basis of this theory, an equation giving the dependence of the number of cycles for failure on the stress, the temperature, the material parameters, and the frequency is derived for uniformly stressed specimens. The equation is in quantitative agreement with the data. Inasmuch as one material parameter is indicated to be temperature-dependent and its temperature dependence is unknown, it is impossible to predict the temperature dependence of the number of cycles for failure. A predicted quantitative correlation between fatigue and creep was found to exist, which suggests the practical possibility of obtaining fatigue data for annealed solid solutions and elements from steady-state creep-rate data for these materials. As a result of this investigation, a modification of the equation for the steady-state creep rate previously developed on the basis of the dislocation theory is suggested. Additional data are required to verify completely the dislocation theory of fatigue.

Machlin, E S↗

Crack Growth Behavior in the Threshold Region for High Cyclic Loading

The present studies show that fanning in the threshold regime is likely caused by other factors than a plastic wake developed during load shedding. The cause of fanning at low R-values is a result of localized roughness, mainly formation of a faceted crack surface morphology , plus crack bifurcations which alters the crack closure at low R-values. The crack growth behavior in the threshold regime involves both crack closure theory and the dislocation theory of metals. Research will continue in studying numerous other metal alloys and performing more extensive analysis, such as the variation in dislocation properties (e.g., stacking fault energy) and its effects in different materials.

Forman, R.↗

On the distribution of stacking faults at dissociated medium-angle grain boundaries: Crystallographic geometry and metastability

Grain boundaries in FCC metals with low stacking-fault energy can form in dissociated configurations of stacking faults. Perhaps the most studied example is 9R stacking at boundaries near Σ3{112}, where the distribution of stacking faults is related to the emission of Shockley partial dislocations. Here, we combine atomic-resolution electron microscopy, atomistic simulations, and dislocation theory to demonstrate that boundaries vicinal to Σ33a support the stabilization of dissociated 9R stacking within a narrow range of inclinations. This boundary is interesting since its misorientation (20.05°) lies in the medium-angle regime, just past the upper misorientation limit for low-angle boundaries, motivating questions for how best to describe it in terms of dislocations. Our HAADF-STEM observations of thin film bicrystals, supported by atomistic modeling, reveal that this inclination dependence arises from specific geometric constraints on the arrangement of Shockley partial dislocations at the interface. Quantification of stacking-fault distributions across multiple boundaries indicates that the density and spacing of faults closely follow the ideal 9R motif, with subtle variations reflecting the complex energy landscape of these boundaries. Through energetic analysis, we establish the presence of competing metastable states enabled by variations in stacking sequences, emphasizing the significant role of crystallographic geometry. We generalize our analysis as a function of misorientation, showing how 9R at the Σ33a boundary is related to previous observations and calculations of HCP at a 29.7° boundary. This study provides a crystallographically grounded framework connecting dislocation structures, stacking-fault distributions, and metastability at grain boundaries in FCC metals.

Atomistic modeling↗

Quantitative treatment of the creep of metals by dislocation and rate-process theories

An equation for the steady-state rate of creep has been derived by applying the theory of dislocations to the creep of pure metals. The form of this equation is in agreement with empirical equations describing creep rates. The theory was also used to predict the dependence of steady-state rate of creep on physical constants of the material and good agreement was obtained with data in the literature for pure annealed metals. The rate of creep was found to decrease with increasing modulus of rigidity. This relation suggest that one of the requirements for a heat-resisting alloy is that its matrix be a metal that has a high modulus of rigidity and therefore a high modulus of elasticity.

Nowick, A S↗

Vertical movements following a dip-slip earthquake

The results of finite element (FEM) computations based on elastic dislocation theory are presented. It is shown that the ratio of fault depth to the lithospheric thickness is a significant factor in the sign of the rebound. Subsidence occurs if the fault penetrates less than approximately 0.68 of the way through the lithosphere. An uplift occurs if the fault cuts deeper. The FEM employed consisted of a 546 node, 500 element grid and a quasi-plane strain algorithm. The situation modeled consisted of a 30 deg dip fault in an initially planar elastic lithosphere overlying a Maxwell viscoelastic asthenosphere. It is suggested that postseismic rebound may be measurable over a several year interval, thus providing data on lithosphere thicknesses.

Melosh, H. J.↗

A synthetic seismicity model for the Middle America Trench

A novel iterative technique, based on the concept of fault segmentation and computed using 2D static dislocation theory, for building models of seismicity and fault interaction which are physically acceptable and geometrically and kinematically correct, is presented. The technique is applied in two steps to seismicity observed at the Middle America Trench. The first constructs generic models which randomly draw segment strengths and lengths from a 2D probability distribution. The second constructs predictive models in which segment lengths and strengths are adjusted to mimic the actual geography and timing of large historical earthquakes. Both types of models reproduce the statistics of seismicity over five units of magnitude and duplicate other aspects including foreshock and aftershock sequences, migration of foci, and the capacity to produce both characteristic and noncharacteristic earthquakes. Over a period of about 150 yr the complex interaction of fault segments and the nonlinear failure conditions conspire to transform an apparently deterministic model into a chaotic one.

Ward, Steven N.↗

An application of synthetic seismicity in earthquake statistics - The Middle America Trench

The way in which seismicity calculations which are based on the concept of fault segmentation incorporate the physics of faulting through static dislocation theory can improve earthquake recurrence statistics and hone the probabilities of hazard is shown. For the Middle America Trench, the spread parameters of the best-fitting lognormal or Weibull distributions (about 0.75) are much larger than the 0.21 intrinsic spread proposed in the Nishenko Buland (1987) hypothesis. Stress interaction between fault segments disrupts time or slip predictability and causes earthquake recurrence to be far more aperiodic than has been suggested.

Ward, Steven N.↗

Computationally efficient method for determining limiting velocities of edge dislocations in anisotropic crystals

The continuum-limit theory of dislocations in crystals predicts divergences in the elastic energy at crystal-geometry dependent limiting velocities vL, which separate subsonic, transsonic, and supersonic dislocation glide regimes and are therefore import for material strength models at high strain rates. Although it is known how to calculate those limiting velocities, there is one special case - edge dislocations with reflection symmetry, but non-vanishing elastic constants c16 or c26 - where previous methods have been notoriously slow. In this letter, we address this deficiency by deriving a computationally efficient method for determining the limiting velocities of edge dislocations with reflection symmetry which is two orders of magnitude faster than the previous method.

36 MATERIALS SCIENCE↗

Prediction of dislocation generation during Bridgman growth of GaAs crystals

Dislocation densities are generated in GaAs single crystals due to the excessive thermal stresses induced by temperature variations during growth. A viscoplastic material model for GaAs, which takes into account the movement and multiplication of dislocations in the plastic deformation, is developed according to Haasen's theory. The dislocation density is expressed as an internal state variable in this dynamic viscoplastic model. The deformation process is a nonlinear function of stress, strain rate, dislocation density and temperature. The dislocation density in the GaAs crystal during vertical Bridgman growth is calculated using a nonlinear finite element model. The dislocation multiplication in GaAs crystals for several temperature fields obtained from thermal modeling of both the GTE GaAs experimental data and artificially designed data are investigated.

Tsai, C. T.↗

Morphological instability in epitaxially strained dislocation-free solid films - Linear stability theory

The morphological instability of a growing epitaxially strained dislocation-free solid film is analyzed. An evolution equation for the film surface is derived in the dilute limit of vacancies based on surface diffusion driven by a stress-dependent chemical potential. From the time-dependent linear stability problem the conditions for which a growing film is unstable are determined. It is found that the instability is driven by the lattice mismatch between the film and the substrate; however, low temperatures as well as elastically stiff substrates are stabilizing influences. The results also reveal that the critical film thickness for instability depends on the growth rate of the film itself. Detailed comparison with experimental observations indicates that the instability described exhibits many of the observed features of the onset of the 'island instability'.

Spencer, B. J.↗

DiscoFluxM version 1.x

DiscoFluxM is software for modeling the deformation behavior of crystalline materials within the third-party finite-element based software, MOOSE. The software enables full-field crystal plasticity finite element simulations of deformation processes of metals and other crystalline materials. DiscoFluxM is an implementation of the DiscoFlux theoretical and algorithmic framework for coupling single-crystal plasticity with dislocation transport. The continuum mesoscale modeling framework is founded upon a nonlocal dislocation-density based crystal plasticity theory. The nonlocal theory couples continuum dislocation transport with an otherwise spatially-local single-crystal model employing nonlinear thermoelasticity and crystallographic plasticity. Dislocation transport is modeled by enforcing dislocation conservation at a slip-system level through the solution of advection-diffusion equations. The configuration of geometrically necessary dislocation density gives rise to a back-stress that inhibits or accentuates the flow of dislocations.

Luscher, Darby↗

Chemical complexity suppresses interstitial solute segregation to screw dislocation cores in the bcc NbTaTiHfZr high-entropy alloy

Recent reports suggest that interstitial solute additions to body-centered cubic (bcc) high-entropy alloys (HEAs) may enhance their mechanical properties. However, details of interactions between interstitial atoms and dislocations in these HEAs remain incompletely understood. Using first-principles calculations, we examine the energetics of C, N, and O interstitial solutes in elemental bcc metals and NbTaTiHfZr, focusing on their segregation in screw dislocation cores. We examine two types of core sites and show that the low-energy configuration and associated segregation energy depend on the transition metal group. In NbTaTiHfZr, we find that chemical complexity substantially suppresses interstitial segregation in dislocation cores, as fluctuations in bulk solute energies induce energetically favorable sites that disfavor segregation to core sites. Local chemical order further enhances this effect by promoting solute clustering away from dislocation cores. These findings reveal fundamental differences between the behavior of interstitial atoms in elemental metals and HEAs, with implications for high-temperature plasticity and dynamic strain aging.

Body-centered cubic transition metals↗

Inversion of dislocation-impurity interactions in α -Fe under magnetic state changes

Here, in this work, we investigate the dislocation-impurity interaction energies and their profiles for various 3d elements —V, Cr, Mn, Cu, Ni, and Co —in and around 1/2 $\langle111\rangle$ screw dislocations in α -Fe using ab initio methods. We consider the ferromagnetic and paramagnetic states, with the latter being modeled through both the disordered local moment model and a spin-wave approach. Our findings reveal that (1) magnetic effects are large compared to size misfit effects of substitutional impurities, and (2) dislocation-impurity interactions are dependent on the magnetic state of the matrix and thermal lattice expansion. In particular, Cu changes from core-attractive in the ferromagnetic state to repulsive in the paramagnetic state.

36 MATERIALS SCIENCE↗

Three-dimensional deformation analysis of two-phase dislocation substructures

Three-dimensional deformation analysis of two-phase dislocation substructures was carried out, extending the Qian and Fan (1991) approach to 3D stress-strain fields by using the Budiansky and Wu (1962) criterion for strain compatibility between the 'hard' and 'soft' regions. The result is a rate-dependent viscoplastic theory, named the dislocation substructure viscoplasticity (DSV), which incorporates a self-consistent effect of dislocation substructure on material response. An algorithm developed for numerical implementation of the DSV theory is presented.

Freed, Alan D.↗