Hydrostatic Stress Field Research Articles

Identification of the Double Acceptor States of Some Transition Metal Impurities in GaAs

AbstractThe double acceptor states of chromium, cobalt and nickel were identified by means of the optical and transport measurements under external fields such as hydrostatic pressure, uniaxial stress and magnetic field. The axial fields enable us to observe optical line splittings, which give information about defect symmetries. This technique has been used to identify a double acceptor state of nickel in the GaAs energy gap. High pressure eliminates a degeneracy between defect levels and crystal bands. This leads to activation of new charge states of some impurities. In the case of chromium and cobalt impurities, their double acceptor levels were found to be degenerate with the conduction band of GaAs. A trend existing for the energies of the double acceptor levels permits us to conclude that there will be no other acceptors among the transition metal impurities in GaAs.

Slip zones for discontinuities parallel to circular tunnels or shafts

General analytical solutions are presented for calculating the slip zone boundaries around circular tunnels or shafts parallel to sets of weakness planes. The stress distribution for a circular hole in an isotropic linearly elastic material is used. The shear strength of the weakness planes is described by a linear slip criterion. Slip zones are defined as the areas where the strength is exceeded pointwise along weakness planes with given dip and strength and arbitrary location. The maximum slip zone depth in a hydrostatic stressfield is expressed as a function of cohesion, friction, field stress and support pressure. The orientation of the slip zone is determined by the dip and friction of the weakness planes. Zones within which tensile stresses develop across weakness planes—for highly anisotropic stresses or for high internal pressures—strongly depend on the orientation of weakness systems. Examples of slip zones are given to illustrate the influence of discontinuity orientation and strength (cohesion and friction, eventually affected by roughness), virgin stressfield and internal pressure. The analysis complements kinematic stability evaluation, and can assist in the design of rock reinforcement. Slip zones for ubiquitous discontinuity sets that have an arbitrary orientation with respect to a circular excavation are discussed in an Appendix, for the case of an isotropic stressfield.

On the structure of tilt grain boundaries in cubic metals I. Symmetrical tilt boundaries

An atomistic study of tilt grain boundary structures in f.c.c. metals has been made. The principal aim of this study is to understand the structure of long-period (‘general’) tilt boundaries. Boundaries for which Σ< 491 were considered, where Σ is the reciprocal density of coincidence sites. The work is presented in three parts. In this paper three series of atomistic studies of symmetrical tilt boundaries in aluminium and copper are reported. One of the main objectives is to determine whether the stress fields of localized grain boundary dislocations exist in boundaries deviated far from any short-period boundary orientations. On the basis of the results of these studies, a new structural classification of grain boundaries is introduced. Certain boundaries are found to be the fundamental structural elements of other boundaries nearby in the misorientation range. Boundaries that consist of contiguous sequences of one type of fundamental structural elements are called favoured; all other boundaries are called non-favoured. Itis found that favoured boundaries are not always associated with the lowest possible values of Σ and that the same boundaries are not necessarily favoured in all metals with the same crystal structure. With use of the pair interactions to calculate the atomic level stress tensor, the hydrostatic stress fields of the boundaries are displayed. In all cases considered the stress fields of distinct, localized intrinsic grain boundary dislocations were found in non-favoured boundaries. The concept of continuity of boundary structure with misorientation is introduced. It is shown that continuity of boundary structure requires unique boundary structures at all misorientations. With use of this concept it is demonstrated how one can predict the atomic structure and stress field of any non-favoured boundary between two known, successive favoured boundaries. It is also found that an isolated discontinuous change in boundary structure between two successive favoured boundaries may exist, depending on their translation states. Some earlier atomistic studies of tilt boundaries in f.c.c. and b.c.c. metals are reinterpreted in the light of this work.

Kicking Off in Large-Diameter Holes

Abstract We have studied theoretically the stresses in a poorly consolidated sand around a cylindrical well. assuming axial symmetry. Applying theories of elasticity and plasticity on this three-dimensional (3D) model, analytical solutions for all three stress components have been worked out. The existence of a plastic zone around an uncased wellbore is confirmed, and the size of the zone is determined. When allowing an incompressible fluid to flow radially into the wellbore, a stability criterion describing the failure of the sand is found to exist. This criterion relates fluid flow forces to rock strength properties. Consideration also has been given to the stress distribution around a cased hole. It is shown that a decrease in the size of the plastic zone relative to an uncased hole occurs. Introduction Previous Work Knowledge of the stress distribution around a drilled hole is of great importance in several situations, such as while drilling, during production or injection, and when calculating, fracturing pressures. One of the early works contributing to this problem is the study by Westergaard. This study was initiated by Karl Terzaghi, who raised the question: What distributions of stress are possible in the soil around an unlined drill hole for a deep well" Westergaard concluded that at great depths a plastic state exists around the hole, which relieves the stresses. In his work, Westergaard uses the concept of effective stresses. A more detailed discussion of the influence of the pore pressure resulting, from a fluid contained in a porous rock was given by Blot. Blot gave a general theory of 3D consolidation, taking into account also the possibility of a flowing pore fluid. Many of the later works are based on this study. One of these is the work done by Paslay and Cheatham. They studied rock stresses caused by a fluid flowing into the borehole. In their study, they also considered the case where permeability is reduced in a region adjacent to the wellbore. Paslay and Cheatham assumed that the rock behaved elastically all the way up to the wellbore and thus ignored the effect of a plastic zone around the hole. Gnirk realized the existence of a plastic zone around the well. He assumed that the rock was situated in a hydrostatic stress field and that it obeyed the Coulomb criterion of plastic yield. Gnirk calculated the wellbore pressures required to prevent plastic yielding of an uncased wellbore, assuming that no fluid flow would be involved. The same problem was treated later by Geertsma. He studied two specific problems: particle influx in production wells and formation fracturing around injection wells. Geertsma discussed stress and strain solutions and stated that elastic theory is applicable to borehole fracturing, but that sand influx requires accounting for plasticity effects. This study was basically two-dimensional, not taking into consideration the vertical stress. Geertsma discussed the problems in a general way and did not give detailed stress and strain solutions. In another recent paper, Bradley worked out a semiempirical approach to the wellbore stability problem, discussing, especially inclined boreholes. This approach is useful for predicting the limit of elastic behavior: however, it gives no information on the behavior in the plastic state. SPEJ P. 883^

Pattern partitioning for enhanced proximity-effect corrections in electron-beam lithography: Mihir Parikh and Donald E. Schreiber. IBM J. Res. Devel.24 (5), 530 (September 1980)

The depression of the order parameter at grain boundaries in high critical temperature superconducting oxides is determined using two formulations. First, we use the Bardeen-Cooper-Schrieffer formulation and assume formation of Cooper pairs by an attractive interaction potential. The spatial variation of the density of energy states at the Fermi level near the boundary, estimated as a function of hydrostatic stress field, is used to determine the depression of the order parameter. Second, the proximity-effect formulation is used in the form of a boundary condition on the order parameter at the interface. The boundary conditions are solved taking into account the spatial variation of the density of energy states. The depression of the order parameter from the two formulations is used in conjunction with atomic modeling to determine the critical current density associated with the grain boundaries. The model correctly predicts dependence of the critical current density across grain boundaries on the misorientation angle and temperature, in good agreement with experimental observations.

Quality and reliability in hybrid circuits: R. F. Read. Electrocomp. Sci. Technol.7, 155 (1980)

The depression of the order parameter at grain boundaries in high critical temperature superconducting oxides is determined using two formulations. First, we use the Bardeen-Cooper-Schrieffer formulation and assume formation of Cooper pairs by an attractive interaction potential. The spatial variation of the density of energy states at the Fermi level near the boundary, estimated as a function of hydrostatic stress field, is used to determine the depression of the order parameter. Second, the proximity-effect formulation is used in the form of a boundary condition on the order parameter at the interface. The boundary conditions are solved taking into account the spatial variation of the density of energy states. The depression of the order parameter from the two formulations is used in conjunction with atomic modeling to determine the critical current density associated with the grain boundaries. The model correctly predicts dependence of the critical current density across grain boundaries on the misorientation angle and temperature, in good agreement with experimental observations.

A new production technique: ion milling: D. Bollinger and R. Fink. Solid St. Technol. p. 79 (November 1980)

The depression of the order parameter at grain boundaries in high critical temperature superconducting oxides is determined using two formulations. First, we use the Bardeen-Cooper-Schrieffer formulation and assume formation of Cooper pairs by an attractive interaction potential. The spatial variation of the density of energy states at the Fermi level near the boundary, estimated as a function of hydrostatic stress field, is used to determine the depression of the order parameter. Second, the proximity-effect formulation is used in the form of a boundary condition on the order parameter at the interface. The boundary conditions are solved taking into account the spatial variation of the density of energy states. The depression of the order parameter from the two formulations is used in conjunction with atomic modeling to determine the critical current density associated with the grain boundaries. The model correctly predicts dependence of the critical current density across grain boundaries on the misorientation angle and temperature, in good agreement with experimental observations.

D.C. sputtering process: its characterization and its problems when applied to tin-dioxide thin-films: Anant G. Sabnis. Electrocomp. Sci. Technol.7, 19 (1980)

The depression of the order parameter at grain boundaries in high critical temperature superconducting oxides is determined using two formulations. First, we use the Bardeen-Cooper-Schrieffer formulation and assume formation of Cooper pairs by an attractive interaction potential. The spatial variation of the density of energy states at the Fermi level near the boundary, estimated as a function of hydrostatic stress field, is used to determine the depression of the order parameter. Second, the proximity-effect formulation is used in the form of a boundary condition on the order parameter at the interface. The boundary conditions are solved taking into account the spatial variation of the density of energy states. The depression of the order parameter from the two formulations is used in conjunction with atomic modeling to determine the critical current density associated with the grain boundaries. The model correctly predicts dependence of the critical current density across grain boundaries on the misorientation angle and temperature, in good agreement with experimental observations.

Plastic deformation of FeNi invar alloys

We report on the deformation behaviour of FeNi single crystals oriented for single slip in the temperature region between 77 and 610 K. Below the Curie temperature the critical shear stress of the Invar alloys increases much more rapidly than that of any f.c.c. substitutional alloy investigated till now. Simultaneously the activation volume decreases down to 10–20 b 3. Below the Curie temperature the stress-strain curves of the Invar crystals differ from those of other f.c.c. alloys. All results taken together indicate a dependence of the dislocation mobility on the magnetic properties of FeNi Invar. It is shown that the experiments cannot be understood with a simple magnetic friction stress arising from the interaction between the hydrostatic stress field of the edge dislocations and the stress dependence of the magnetization [3]. However, they can be described with an empirical friction law which had been introduced originally [18,19] for the case of strongly localized thermal activation, e.g. kink motion.

The nature of fracturing and stress distribution in quartzite around the 1128-M (3700-FT) level of the crescent mine, Coeur d'Alene mining district, Idaho

Silver and copper are the principal ores mined from the quartzite at the Crescent mine. Both the main ore-bearing veins and foliation in the quartzite are parallel to the nearly vertical formational contacts. Anisotropy of the quartzite is indicated by both dynamic and static tests. Disking and breakage of core from holes perpendicular to the foliation are about twice what they are in core from holes parallel to foliation. Natural cleavage as well as slabbing and blasting fractures around the tunnels are also controlled by the foliation. Extensive overcore deformation measurements indicate that most of the influence of the tunnels on the “free” stress field is between the rib and a depth of 2.7 m (1 tunnel diameter). The maximum principal stress axis in the free field is nearly horizontal; its magnitude is not much greater than the vertical component and calculations indicate a nearly hydrostatic free stress field. Stress considerably greater than the free field was measured between about 0.3–2.7 m behind the rib and is caused by a transfer of load from above the tunnel opening. Peak stress is in the vertical direction and about 1.7 m behind the rib. An air-injection survey shows that high permeabilities are confined to the highly fractured annulus around a tunnel to a depth of at least 0.6 m. Air-injection measurements could be taken in the interval of about 0.6–1.8 m, but more fractures with high permeabilities may also be present in the annulus from about 0.6–1.2 m. Permeabilities measured deeper than about 1.8 m by the air-injection technique are either very low or nonexistent. The absence of open and noncontinuous fractures beyond about 1.8 m is also indicated by very low porosities and permeabilities of core, very high stresses (which presumably would close fractures), the lack of stains or secondary fillings in disking fractures, a conspicuous lack of ground water in the tunnels, and the fact that fractures encountered in an experimental 0.9-m tunnel did not extend into the 1.8-m tunnel that was mined over it. Air-injection techniques exceed the accuracy of any field deformation measurement now in use, and they are sensitive to permeabilities as small as one microdarcy and to fracture widths as small as 250 nanometers. This technique was applied for future reference in mining design and, perhaps, to be used later to detect microfracturing prior to rockbursts.

A model for hydrogen-assisted crack initiation on planar shear bands in near-alpha titanium alloys

A model was proposed which explains subsurface cleavage facet formation in large grained, planar slip titanium alloys by the buildup of large hydrostatic stresses at the tip of long, blocked shear bands. These shear bands can result from creep deformation. Hydrogen is attracted to the hydrostatic stress field and can initiate a cleavage facet possibly by the locally increased hydrogen concentration or more likely by actual hydride formation and subsequent cracking of the hydride. The model is qualitatively consistent with several experimental results and implies that the evaluation of dwell debits in alloys must be conducted at stresses where some creep deformation is possible.

The alignment error of the hole-drilling method

The hole-drilling method is one technique for measuring residual stresses. All the existing equations for the calculation of residual stresses are based on the assumption that the hole is located at the rosette center. In this paper, the stress-strain relationship for the eccentric hole case has been derived and expressed in terms of the off-center distance and the polar angle. The alignment error is studied and demonstrated by two examples, namely, a uniaxial-stress field and a hydrostatic-stress field. The error analysis yielded the following typical result: ten percent of hole radius off-center will yield about five-percent measurement error for the standard rosette (EA-09-062-RE-120).

Finite element analysis of static and dynamic stresses around suddenly punched holes in plates and shells

The magnitude and distribution of stresses around suddenly punched holes in initially stressed plates and shells is of interest to insure that cracks will not precipitate from stress concentration. This problem is of practical interest to pressure vessel designers to preclude catastrophic failure when holes are punched in vessels to release gas. This paper presents a finite element analysis of several problems investigating static and dynamic stress fields around suddenly punched circular holes. The first problem deals with the investigation of the radial and tangential stress fields in the vicinity of a suddenly punched hole in a stretched, elastic, isotropic plate subjected to an initial hydrostatic stress field. The wave propagation from a punched hole in the plate under a hydrostatic state of stress was solved analytically, using transform techniques, by Miklowitz; the finite element analysis of this problem presented in this paper confirms the analytical solution. Two grid meshes were investigated and results are presented to show the effect of grid mesh on solution accuracy and the power of finite element techniques for solving stress unloading problems. A formula for determining integration step size is found to be a function of the minimum element length and the wave propagation velocity. A similar investigation into the stress effects around a suddenly punched hole in the plate subjected to an initial uniaxial state of stress was also carried out as a prerequisite for the final problem studied. The last problem is an anisotropic composite shell of varying thickness under an initial stress field due to internal pressure. The static and dynamic stress fields are computed from an unloading wave that radiates outward from a reinforced circular hole that is cut in the shell in 20 μs. A finite-element model of the shell is developed using quadrilateral and triangular plate elements and both in-plane and bending stiffness is included in the analysis as is nonlinear differential stiffening incorporated into the analysis as a single step approximation. Both bending and in-plane waves radiate outward from the cut hole and the dynamic stresses around the hole edge are computed for both unloading waves. The effects of the unloading waves are temporally spaced due to different wave velocities. The paper demonstrates that fast response stress problems are readily amenable to finite-element analysis. For holes other than circular, the power of finite-element methods is apparent since these shapes lead to mathematically intractable problems if closed form solutions are attempted.

Manifestation of rock pressure in diatomaceous clays

1. Laboratory investigations and full-scale observations showed the weak strength and high deformability of diatomaceous clays. The full-scale observations showed in connection with this that in the case of short cuts for the given tunnel section these clays remain stable for 24–36 h. Thus, it was possible to drive the tunnel in short two-meter cuts without bracing with the construction of 2-m-long concrete lining rings. 2. Full-scale measurments of the earth pressure with dynamometric sections showed that the distribution of the pressure in the diatomaceous clays is close to uniform over the tunnel contour. 3. The magnitude of the active pressure under the given geologic conditions is many times smaller than in a calculation for a hydrostatic stress field on the basis of the weight of a earth column above the tunnel.

A thermodynamic analysis of hydrogen in metals in the presence of an applied stress field

The thermodynamics of a two component system of metal-hydrogen, oriented towards obtaining a suitable relationship for the evaluation of the pmv of the mobile component (H), in presence of an externally applied uniform hydrostatic stress field has been considered in detail. In the present analysis the central difficulty of maintaining constancy of the amount of the mobile component (H) in the system for obtaining the pmv has been overcome, for those metals which have very small solubility of hydrogen.

Direct Observations of Ferroelectric Domains in Lithium Niobate

AbstractFerroelectric domain walls have been observed in LiNbO3 by transmission electron microscopy. The antiparallel nature of the polar transition has been confirmed by contrast analysis. The pinning of domain walls by lattice dislocations is attributed to an interaction with the hydrostatic stress field of an edge dislocation. It is suggested that this interaction may impede the formation of single‐domain crystals using applied electric fields near the Curie temperature.

Spherical flaw instability in hydrostatic tension

Fracture initiation due to a hydrostatic tensile stress field is studied by considering an idealized solid containing a small spherical cavity. Finite elastic deformation theory assuming Neo-Hookean material behavior is combined with an energy criterion to determine the critical cavity and applied stress at instability. It is found that the critical stress is a monotonically increasing function of a parameter, k = 6T/Eao, that is proportional to specific surface energy and inversely proportional to initial cavity size and modulus. For large cavities, the critical applied stress has the familiar Griffith form pc (k → 0) + (/43) (ET/ao)1/2, while for small cavities the critical stress tends to a constant pc (k →) = 2T/ao. Some final comments pertain to the relation between applied stress and local stress and strain at the point of fracture.

Energy barriers controlling creep processes in metals with special reference to β-cobalt

Abstract The minimum, second stage, creep rate ϵ of polycrystalline cobalt (99·999%), subjected to constant stresses in vacuo at 430–750°C, is shown to obey the relation ϵ = A(T) exp [(-H + qσ)/kT] over the entire range of strain rates employed, extending from 10-9 to 10-4 per sec. As in copper and α-brasses, two sets of the parameters A, H and q are however required to describe any given log ϵσ isotherm, depending on whether the tensile stress σ is greater or less than a critical value σc(T) at which an abrupt change occurs in the creep mechanism. The increase of the activation volume 1/2q with temperature is governed by an activation energy Q = 0·55 ev which, as in other metals, is close to the theoretical value of the interaction energy between the hydrostatic stress field of dislocations and vacancies. H, determined by thermal cycling, was found to be equal to 2·2 ± 0·25 ev and 1·9 ± 0·25 ev for σ < σc and σ > σ;c respectively, but at about 550°C rose steeply with temperature in both cases to a common constant level of 2·9 ev, numerically equal to H sd, the activation energy of self-diffusion. The first two values are ascribed to the movement of jogs in mixed dislocations, the respective barriers being H sd - Q and H sd - 2Q. The barrier at higher temperatures is considered to arise from the non-conservative migration of jogs in dislocations of predominantly screw character. Corresponding energy spectra of other metals are reviewed.