A DISCUSSION OF THE IMPORTANCE OF LINE TENSION ON COTTRELL'S THEORY OF THE SHARP YIELD POINT
Tension yield point of dislocation in atmosphere of impurity atoms
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Tension yield point of dislocation in atmosphere of impurity atoms
The fine structure of the slip bands observed on the surface of a deformed Cu3Au single crystal is examined. The separation distance determined between the resolved individual slip lines is used to examine the calculations of other authors relating the passing stress of a dislocation past a dislocation pileup on a nearby parallel glide plane.
A transmission electron microscopy study is being conducted on the microstructure of beta-SiC films grown epitaxially on 001-plane silicon by chemical vapor deposition. Observations have been made in plain view and in cross-section. A high density of stacking faults has been found in the bulk of the epilayer which are bounded by partials of the Shockley type with Burgers vectors 1/6 211-line. Cross-sectional high resolution electron microscopy of the interface has shown it to be semicoherent with misfit dislocations to accommodate the lattice parameter difference between the substrate and the epilayer. In addition to misfit dislocations, a high density of twins and some stacking faults are present in the SiC near the interface. Mechanisms for the nucleation and growth of these defects are discussed.
TEM and cathodoluminescence (CL) imaging and spectroscopy have been performed on In(0.2)Ga(0.8)As/GaAs MQW structures. Cross-sectional and plan-view TEM demonstrates that misfit dislocations (MDs) are confined to the MQW-to-GaAs interfacial regions. The observed large variation in the exciton luminescence intensity is interpreted as due to the presence of nonradiative recombination centers spread homogeneously in the MQW region away from interface MDs. These nonradiative recombination centers compete with exciton and midgap radiative centers at wavelengths of 950 nm and 1000-1600 nm, respectively, resulting in spatiallty correlated dark line defects for all CL imaging wavelengths.
Single crystal specimens of a nickel-base superalloy with axes near 001, 011, and -112 were tested in tension at room temperature, 760, and 980 C. The alloy Rene N-4, was developed for gas turbine engine blades and has the nominal composition 3.7 Al, 4.2 Ti, 4 Ta, 0.5 Nb, 6 W, 1.5 Mo, 9 Cr, 7.5 Co, balance Ni, (all in weight percent). Analysis of slip band traces, specimen axis rotation, and dislocation Burgers vectors showed that at 760 and 980 C primary cube slip supplanted normal octahedral slip for the -112 line-oriented specimens. The other two orientations, which have lower resolved shear stresses on the cube system, exhibited octahedral slip at all three temperatures. The critical resolved shear stress is considerably greater on the cube system than on the octahedral system at room temperature. However, at 760 and 980 C the critical resolved shear stresses on the two systems are about the same. While the room temperature and 980 C yield strengths for the two orientations exhibiting octahedral slip could be rationalized on the basis of resolved shear stress, those at 760 C could not. Such violations of Schmid's law have previously been observed in other superalloys and single phase gamma-prime.
The general plane elastostatic problem of interaction between a crack and an inclusion is considered. The Green's functions for a pair of dislocations and a pair of concentrated body forces are used to generate the crack and the inclusion. Integral equations are obtained for a line crack and an elastic line inclusion having an arbitrary relative orientation and size. The nature of stress singularity around the end points of rigid and elastic inclusions is described and three special cases of this intersection problem are studied. The problem is solved for an arbitrary uniform stress state away from the crack-inclusion region. The nonintersecting crack-inclusion problem is considered for various relative size, orientation, and stiffness parameters, and the stress intensity factors at the ends of the inclusion and the crack are calculated. For the crack-inclusion intersection case, special stress intensity factors are defined and are calculated for various values of the parameters defining the relative size and orientation of the crack and the inclusion and the stiffness of the inclusion.
The general plane elastostatic problem of interaction between a crack and an inclusion is considered. The Green's functions for a pair of dislocations and a pair of concentrated body forces are used to generate the crack and the inclusion. Integral equations are obtained for a line crack and an elastic line inclusion having an arbitrary relative orientation and size. The nature of stress singularity around the end points of rigid and elastic inclusions is described and three special cases of this intersection problem are studied. The problem is solved for an arbitrary uniform stress state away from the crack-inclusion region. The nonintersecting crack-inclusion problem is considered for various relative size, orientation, and stiffness parameters, and the stress intensity factors at the ends of the inclusion and the crack are calculated. For the crack-inclusion intersection case, special stress intensity factors are defined and are calculated for various values of the parameters defining the relative size and orientation of the crack and the inclusion and the stiffness of the inclusion.
At temperatures above 1/2 T(sub m), the generation and movement of dislocations may result due to the load created by the weight of the crystal itself The deformation may be expected to increase the line defect density and may result in generation of low angle grain boundaries, especially in the regions of the crystal attached to the ampule. It has often been suspected that elimination of this effect in space can improve crystallinity of crystals grown under microgravity conditions, however, a direct experimental proof of such relation is still missing. In this work we have designed and built a system of in-situ optical detection and measurement of the mechanical deformations of a crystal wafer under its own weight, and studied the deformation effects as a function of temperature. The results of the measurements for ZnSe and ZnTe crystal wafers will be presented.
Optical and electrical characterization of defects has been started in EFG ribbon grown in a system that will be used to test the stress model. Temperature and stress field modeling aimed at defining low stress growth configuration is also in progress, and results will be used to guide development of the experimental system. The baseline defect configuration for ribbon grown at speeds of approx. 1 cm/min consists of dislocation densities of the order of 10 to the 5th power to 10 to the 6th power/sq cm, as well as saucer type etch pits and line defects. All these defects are inhomogeneously distributed. EBIC measurements indicate that diffusion lengths are in the range 20 to 60 microns, and significant spatial inhomogeneities occur through the ribbon thickness. Growth speed changes in the range 0.7-1.0 cm/min do not produce significant variations in ribbon defect configurations.
The high temperature cyclic stress softening response of the single crystal nickel-base superalloy PWA 1480 was investigated. Specimens oriented near the 001- and 111-lines were tested at 1050 C in low-cycle fatigue and then microstructurally evaluated. The 001- and 111-line specimens had dissimilar flow behavior in monotonic tensile tests, but comparable softening in low-cycle fatigue. This softening was accompanied by rapid generation of dislocation networks at the gamma-gamma-prime interfaces and by a slower time-dependent coarsening of gamma-prime precipitates. Due to the rapid formation of a dislocation substructure at the gamma-gamma-prime interfaces, the cyclic stress softening could be modeled with an existing theory which related cyclic stress to the evolving microstructure and dislocation structure.
The fracture behavior and deformation of He-charged (at 22 C) single crystals of PWA 1480E Ni-base superalloy were investigated using SEM and TEM techniques to observe the behavior of tensile fractures in notched single crystals with seven different crystal growth orientations: 100-line, 110-line, 111-line, 013-line, 112-line, 123-line, and 223-line. To identify the cleavage plane orientation, a stereoscopic technique, combined with the use of planar gamma-prime morphologies, was applied. It was found that gamma-prime particles were orderly and closely aligned with edges along the 100-line, 010-line, and 001-line-oriented directions of the gamma matrix. Different crystal growth orientations were found not to affect the morphology of gamma-prime particles. The accumulation of dislocations around gamma/gamma-prime interfaces formed strong barriers to subsequent dislocation movement and was the primary strengthening mechanism at room temperature.
We explore the burst energy distribution of fast radio bursts(FRBs)in the low-twist magnetar model ofWadiasingh & Timokhin(WT19). Motivated by the power-lawfluence distributions of FRB121102, we proposean elementary model for the FRB luminosity function of individual repeaters with an inversion protocol thatdirectly relates the power-law distribution index of magnetar short burstfluences to that for FRBs. The protocolindicates that the FRB energy scales virtually linearly with crust/field dislocation amplitude, if magnetar shortbursts prevail in the magnetoelastic regime. Charge starvation in the magnetosphere during bursts(required inWT19)for individual repeaters implies the predicted burstfluence distribution is narrow,3 decades for yieldingstrains and oscillation frequencies feasible in magnetar crusts. Requiring magnetic confinement and chargestarvation, we obtain a death line for FRBs, which segregates magnetars from the normal pulsar population,suggesting only the former will host recurrent FRBs. We convolve the burst energy distribution for individualmagnetars to define the distribution of luminosities in evolved magnetar populations. The broken power-lawluminosity function’s low-energy character depends on the population model, while the high-energy index tracesthat of individual repeaters. Independent of the evolved population, the broken power-law isotropic-equivalentenergy/luminosity function peaks at∼1037–1040erg with a low-energy cutoff at∼1037erg. Lastly, we considerthe localfluence distribution of FRBs andfind that it can constrain the subset of FRB-producing magnetarprogenitors. Our model suggests that improvements in sensitivity may reveal aflattening of the global FRBfluencedistribution and saturation in FRB rates.
Correlations between critical current density (j(sub c)) critical temperature (T(sub c)) and the density of edge dislocations and nonuniform strain have been observed in YBCO thin films deposited by pulsed laser ablation on (001) LaAlO3 single crystals. Distinct maxima in j(sub c) as a function of the linewidths of the (00 l) Bragg reflections and as a function of the mosaic spread have been found in the epitaxial films. These maxima in j(sub c) indicate that the magnetic flux lines, in films of structural quality approachingthat of single crystals, are insufficiently pinned which results in a decreased critical current density. T(sub c) increased monotonically with improving crystalline quality and approached a value characteristic of a pure single crystal. A strong correlation between j(sub c) and the density of edge dislocations ND was found. At the maximum of the critical current density the density of edge dislocations was estimated to be N(sub D) approximately 1-2 x 10(exp 9)/sq cm.
Transmission electron microscopy has been used to study the bulk deformation characteristics of seven nickel-base superalloys tested in fatigue and creep-fatigue at 650 C. The alloys were Waspalloy, HIP Astroloy, H plus F Astroloy, H plus F Rene 95, IN 100, MERL 76, and NASA IIB-7. The amount of bulk deformation observed in all the alloys was low. In tests with inelastic strain amplitudes less than about 0.003, only some grains exhibited yielding and the majority of those had the 110 line near the tensile axis. Deformation occurred on octahedral systems for all of the alloys except MERL 76 which also showed abundant primary cube slip. Creep-fatigue cycling occasionally produced extended faults between partial dislocations, but otherwise deformation was much the same as for fatigue cycling.
The plane interaction problem for a circular elastic inclusion imbedded into an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations as Green's functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equation with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress intensity factors representing the strength of the stress singularities are obtained in terms of the asymptotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress intensity factors are given.
The plane interaction problem for a circular elastic inclusion embedded in an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations as Green's functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equations with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress-intensity factors representing the strength of the stress singularities are obtained in terms of the asymptotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress-intensity factors are given.
Numerical calculation of 111-plane 110-line slip activity in silicon web crystals generated by thermal stresses is in good agreement with etch pit patterns and X-ray topographic data. The data suggest that stress redistribution effects are small and that a model, similar to that proposed by Penning (1958) and Jordan (1981) but modified to account for dislocation annihilation and egress, can be used to describe plastic flow effects during silicon web growth.
The objectives are to: (1) demonstrate the mechanisms of deformation in body centered cubic (BCC), face centered cubic (FCC), and hexagonal close-packed (HCP)-structure metals and alloys and in some ceramics as well; (2) examine the deformed microstructures (slip lines and twin boundaries) in different grains of metallic and ceramic specimens; and (3) study visually the deformed macrostructure (slip and twin bands) of metals and alloys. Some of the topics covered include: deformation behavior of materials, mechanisms of plastic deformation, slip bands, twin bands, ductile failure, intergranular fracture, shear failure, slip planes, crystal deformation, and dislocations in ceramics.