Source Of Internal Stress Research Articles

Negative creep and mechanochemical spinodal in amorphous metals

The observed negative creep behavior in amorphous metals (length shrinkage under a tensile stress) is explained by assuming microstructural instability in which the second-order derivative of the Helmholtz free energy is negative with respect to a variable which contains volume or strain in addition to composition. Hence the system is unstable with respect to spatial variations in such a variable. The decomposition of such “mechanochemical” spinodal could be a source of internal stresses which cause embrittlement on annealing.

Internal Stresses and Relations between Effective Thermoelastic Properties of Stochastic Solids – Some Exact Solutions

AbstractWe consider composites made of two phases and polycrystalline aggregates composed of hexagonal, tetragonal, or trigonal crystals. Within linear elasticity exact relations between effective elastic constants, effective thermal expansion, stored elastic energy, and internal stresses are derived. Two sources of internal stresses are taken into account: external loading and differential or anisotropic thermal expansion. If the fluctuation of elastic constants can be neglected, we obtain solutions for internal stresses and stored energy which are valid for any phase topology.

Calculation of line singularity fields near a crack tip

Near-crack-tip elastic fields are of primary importance in all crack propagation theories. Besides external loads, the near-tip field is determined by internal stress sources such as dislocations and other defectsIn particular, recent works (1-5) have pointed out that dislocations shield crack tips against applied loads, because they remarkably alter the local stress inten- sity. Such investigations have been carried out in anti- plane strain conditions, assuming screw dislocations as typical stress sources. This option presents the advantage of obtaining the basic features of the process through a relatively simple mathematical applicationThe drawback is that only single-mode crack loading (mode III) may be considered. Plane elasticity conditions (e.g. edge dislocations), though mathematically more complicated, appear much less limiting. In fact, with mode I and mode II loading, they allow for the treatment of crack growth under combined stresses. This condition is practically unavoidable in order to model real fracture processes, and also to deal with internal stress sources other than dislocations. The present paper proposes a solution for the prob- lem of an internal stress source located near a crack tip in generalized plane stress or plane strain conditions. The resulting formulae differ from those of Rice (6) in that Cauchy integration is avoided, and only the knowledge of the Laurent's expansion coefficients of the bulk-field potentials is required. Because in many cases of interest only a few and directly available bulk coefficients come into play, it is concluded that the obstacle of the mathematical complications, encountered in dealing with plane elasticity, may be noticeably reduced by using the present results. The geometry of the problem is shown in Fig. la. In the complex plane z = x + iy the crack occupies the negative real axis, and the stress source is at the point Zo = xo + iyo. In Fig. lb the z-plane, deprived of the crack line, is mapped on to the half-plane ~ > 0 of the (-plane by the function

Interaction of an edge dislocation with a lamellar inhomogeneity

The elastic behavior of an edge dislocation parallel to an infinite lamellar inhomogeneity is considered. The elastic field in the matrix and lamella is obtained through the complex variable technique and the image method. The resulting formulas may be employed to solve the elasticity problem for any source of internal stress (plane elasticity) whose bulk field is known. The force on the dislocation is explicitly calculated and discussed. It is found that the behavior of the dislocation near a lamella differs in some important aspects from that of a dislocation near a bimetallic interface.

The lamellar inclusion problem in plane elasticity

Within the framework of linear isotropic plane elasticity, a general method giving the elastic field in an internally stressed three-phase material is determined. The internal stress source may be located either in or near the lamellar component. General closed-form formulas solving the limiting case of a bimetallic interface are also obtained. As an example of application, the interaction between a lamellar inclusion and a dilatation centre is analyzed.

Two R Curves for Partially Stabilized Zirconia

The enhanced fracture toughness due to stress‐induced transformation can be explained from two viewpoints: (1) the increase can be attributed to the need to supply a work of transformation, or (2) the transformation can be considered to result in internal stresses which oppose crack opening. Experimental results for magnesia‐partially‐stabilized zirconia are presented for the two experimental measures of toughness corresponding to these two viewpoints, namely (1) the specific work of fracture, R, and (2) the nominal stress intensity factor, KR. It is observed that these two measures are not equivalent during the initial stage of R‐curve behavior, prior to reaching steady‐state cracking. The theoretical reason for this difference is discussed. In particular, it is noted that the usual definition for the crack extension force does not correspond to the experimentally measured work of fracture in the presence of stress‐induced (or pre‐existing) sources of internal stress.

THE DISPLACEMENT DOMAINS CAUSED BY DEFECTS IN BINARY CRYSTALS

By using the elastic dipole model of strained crystals, we regard every atom in a binary crystal as an elastic dipole, which has various effective moment. On various kinds of atoms, different force will be acted by the stress field due to other stronger internal stress sources such as dislocation, inclusion, etc. Thus different displacement will take place and some domains of various shape depending on the relative magnitude of permanent moment and induced moment will form. In the present paper, the domain patterns produced by internal stress field of edge dislocation, screw dislocation, inclusion and crowdion are obtained by calculation, they look like rosettes Under proper condition the patterns of these domains might be observed. The result also shows the effect of pressure on phase transition.

Steady state vacancy concentration around a plastic crack

The vacancy chemical potential associated with the crack region and with the lattice dislocations representing the plastic zone are identified in terms of the energy of the dislocation configuration. In order to determine the steady state vacancy concentration, the configuration is considered as made up of several internal sources of stress. The diffusion equation under steady state is solved for a crystal containing each source of stress. Further, superposition of the concentration of vacancies around each source is used to determine the total concentration of vacancies for small scale deformation at the crack tip. On the other hand, for large scale deformation at the tip, matching boundary conditions are applied to determine the concentration in each region containing an internal source. Both the discrete dislocation and the single lattice dislocation representations of the crack are employed to determine the crack growth rate. The results are used to emphasize the influence of the plastic zone on the crack growth rate by vacancy diffusion mechanism.

Investigation of Structural Defects in the Amorphous Ferromagnetic Alloy Fe40Ni40P14B6

AbstractStructural defects in the amorphous ferromagnetic alloy Fe40Ni40P14B6 are investigated by measuring the magnetic polarization in the region of approach to ferromagnetic saturation. From the field dependence of the high‐field susceptibility it is concluded that the main source of internal stresses may be characterized as quasi‐dislocation dipoles. These structural defects are shown to be rather stable under annealing treatments and may be produced by small plastic deformations.

Dual-career couples: Conflicts and treatment

Abstract This paper integrates clinical data gathered through psychotherapy with dual-career couples and research findings from social psychology and sociology. The paper's main focus is the clinical understanding and therapeutic interventions most appropriate for these couples' marital and individual difficulties. The paper briefly describes characteristics of the dual-career lifestyle and personalities. The analysis provides case examples illustrating external and internal sources of stress generated by a lack of time or the need for an effective system for handling housework and childcare.

A Model of Stress and Counseling Interventions

Current popular interest in stress and its effects on physical and psychological functioning has implications for counselors and clients. Although many counselors have not been trained in the physiological and medical aspects of stress, they do have skills that can be appropriately applied to the alleviation and modification of environmental and internal sources of stress. This article describes a model to aid counselors in understanding stress and in designing and implementing counseling interventions to mediate its effects.

Stress field in a semi-infinite elastic medium due to internal stress sources, and an interpretation of tectonics in and around Japan.

This paper investigates the stress field in the interior of a semi-infinite elastic medium due to internal stress sources. Importance of strain nuclei as sources of the internal stress is emphasized. Patterns of the stress changes induced by introducing a simple strain nucleus are illustrated with the aid of equal area projection. The internal stress field in and around Japan is calculated by distributing double couple point sources on the deep-seismic plane with their compressional axes parallel to the dip of the descending plates, and the results obtained are projected on a Mercator map. Such a model may explain the actual stress field in this region at least to some extent.

The Entropy of Internal Stress Fields

AbstractIn the strictly linear elasticity theory (no third order terms in the expansion of the free energy) or in the harmonic approximation for a crystal, there is no entropy change when an internal stress field is introduced into a body. When higher order terms are considered it is shown that in the expressions given by Zener and DiMelfi et al. terms are missing which in the hierarchy of perturbation are of the same order however due to the magnitude of the material parameters generally make a small contribution. In addition there exists an entropy of interaction between two internal stress sources.

Internal stresses due to an oblate spheroidal inclusion: Misfit, inhomogeneity and plastic deformation effects

Internal stress in and around an oblate spheroidal inclusion is evaluated by using Eshelby theory. We consider three different sources of internal stress as a function of the aspect ratio and elastic moduli ratio; these are 1. (1) misfit effect, 2. (2) inhomogeneity effect 3. (3) plastic deformation effect. The misfit effect arises from the difference of thermal expansion coefficients of the matrix and inclusion. Normal stresses within the inclusion (or the principal stresses), maximum shear stress inside the inclusion, total strain energy and the normal stress at the matrix-inclusion boundary are determined. The inhomogeneity effect arises from the difference of the elastic moduli of the matrix and inclusion, which perturbs otherwise uniform applied stress. The direction of applied stress is parallel to the axis of revolution of the inclusion. Normal stresses within the inclusion and at the matrix-inclusion boundary are obtained. Plastic deformation of the matrix in the presence of a plastically non-deformable inclusion produces internal stresses, as shown by Ashby and by Tanaka and Mori. The approach developed by Tanaka and Mori is extended here to evaluate the internal stresses for the inclusion geometries appropriate to the analysis of technically important cases. The results of the present calculations in limiting cases agree with previously published calculations. Implications of the results are discussed in connection with several experimental studies.

Point defect-dislocation interaction in a crystal under tension

Abstract The influence of an external uniaxial stress on the interaction between mobile defects and individual network dislocations is studied theoretically. The point defects are described within the lattice Green function formalism. Their interaction energy with a source of internal stress is deduced. This energy is calculated between intrinsic point defects and a dislocation in a strained f.c.c. crystal. The work aims at examining the foundations of the irradiation creep theory that explains the phenomena as a preferential drift of interstitials and vacancies to dislocations with particular orientations to the external stress axis. The drift to edge dislocations is discussed using an expression that includes the discrete character of the jump. It is concluded that the proposed model of irradiation creep can be sustained only if the dipole tensors of the defects at the equilibrium and saddle point configurations fulfill some specific relations.

Elastic interactions between ’’voids’’ induced by solute segregation

Expressions are derived for the elastic interaction energy between void-solute shell composites. These composites consist of spherical void cores surrounded by spherically symmetric solute shells containing a uniform concentration of irradiation segregated solute. The solutes are assumed ’’misfitting’’ and as such represent sources of internal stress. The elastic interaction energy between composites arises because of the so-called inhomogeneity interaction and has minimum values at certain composite separations and solute shell thickness. The existence of these minima obtains largely because the misfit of the composites increases as the composite separation R increases. For a constant misfit, the interaction energy would decrease monotonically approximately as R−6. The surface stress of voids is taken to be zero in the calculations so that the only source of interaction between composites is the stress induced by solute segregation. The calculations are performed for both two-composite and N-composite interactions, and we show that, primarily, only nearest-neighbor interactions are significant. The calculations are compared with experimental investigations of void ordering in an Ni ion-irradiated Nb-1Zr alloy containing 0.0038 atom fraction of oxygen as an impurity. Given experimentally determined void sizes and auxiliary data, the correct void lattice parameter is predicted when the solute shell thickness is ∼30% of the composite radius. In pure Nb, it is found the O, C, or N impurities are necessary for void ordering, which supports the main thesis of the present paper, viz., solutes/impurities are a primary cause of void ordering.

Dislocation processes during plastic deformation of Si and Ge in the range 0.50 to 0.95 of the melting temperature

Dislocation processes occurring during plastic deformation of Si and Ge for θ = 0.50 to 0.95 (θ = T/Tm is the relative temperature) have been studied both by etch pit method and TEM. A similarity of dislocation processes in Si and Ge when compared in terms of θ has been found. In low-temperature deformation (θ = 0.5 to 0.8) dislocation glide is realized and cross slip is activated. The cross slip gives rise to a multiplication of dislocations. The interaction and multiplication of dislocations are accompanied by the formation of dipoles including faulted ones, multipoles, and bundles in slip bands. A system of Lomer dislocations is the main source of long-range internal stresses in low-temperature deformation. In high-temperature deformation (θ > 0.8) gliding of dislocations combined with climb is realized. This results in decreasing the number of dipoles and Lomer dislocations. At θ > 0.8 a main mechanism of dislocation interaction is their intersection with the degeneration of a quadrupole node into two triple ones. [Russian Text Ignored].

Mutual annihilation of unlike dislocations by cross slip in ordered and disordered alloys

Under the action of an external applied stress, unlike dislocations on parallel slip planes either pass one another, or cross slip or climb and annihilate each other. A detailed numerical analysis of cross slip of unlike screw dislocations was carried out and the conditions under which cross slip was more favorable compared to passing were determined in both ordered and disordered alloys for infinite straight dislocations. It was further shown that cross slip could preferentially occur near the vicinity of an unlike dislocation which acted as a source of internal stress. The presence of such internal stresses was found to reduce the energy barrier for cross slip to an extent that cross slip became spontaneous if the vertical separation between the unlike dislocations was below a critical value. The implication of this was that in the absence of any other internal stresses, the passing dislocation of separation less than the critical value could not be stable, and this critical separation set the limit for the strengthening that could be obtained by passing dislocations. The effects of the applied stress, and its orientation on the cross slip process have also been discussed in detail.

Sub-grain boundary migration in aluminium

Abstract Observations on the migration of sub-grain boundaries during high-temperature testing of aluminium are presented. It is shown that the migration contributes significantly to the overall strain rate of the specimen and that the stress dependence and temperature dependence are in accord with the macroscopic strain rate, and are strictly related to the deformation contribution from fine slip. The mobility of the sub-boundaries leads to a new understanding of the dynamic equilibrium of the sub-structure and its stability with respect to recrystallization. It further leads to the possibility of sub-boundaries acting both as effective obstacles to deformation and as sources of internal stress.

Focal mechanism in connection with energy storage before crack formation

The pattern of internal energy storage depends on distribution of the internal failures, fractures and local stress sources. A simple model of energy storage along a tectonic plane is represented by an array of dislocations. Stress concentration leads to crack formation of tensile, shear or transverse type depending on the confining pressure and stress components prevailing at the tectonic plane. The conditions of energy storage and conditions of crack formation vary with depth. Hence it is expected that the focal mechanism is also subject to transformation with depth.