Showing papers on "Stress field published in 1975"

Microfracture beneath point indentations in brittle solids

Abstract: The microfracture patterns observed around point indentations in brittle solids are investigated. A description is first given of the stress field in an elastic half-space loaded normally at a point in its surface. This field is then used as a basis for analysing the crack geometry. A localized zone of irreversible deformation forms about the contact point, thereby removing a singularity in the elasticity solutions and providing nucleation centres for the ensuing microcracks. Generally, two main types of ‘vent’ cracks are observed to propagate from the deformation zone: median vents, formed during indenter loading, spread downward below the point of contact on planes of symmetry, and lateral vents, formed during unloading, spread sideways toward the specimen surface. Of these, the median vent is relatively well-behaved, and is amenable to standard fracture-mechanics analysis. From such an analysis we derive the means for predetermining, in principle, the depth of fracture damage under given point loading conditions. The significance of the results in relation to important practical applications, such as glass cutting and surface fragmentation processes, is discussed.

Stress−induced diffusion of point defects to spherical sinks

Abstract: Radiation damage in metals at elevated temperatures produces small dislocation loops and voids. The growth of these sinks is determined by the steady−state diffusion of point defects migrating in the stress field of these sinks. To obtain the steady−state current of point defects to these spherical sinks a perturbation method is developed to deal with the drift term of the diffusion equation. It is shown that the contribution of the drift term to the current can be expressed by a bias factor which differs from unity if the point defects interact with the spherical sink. Explicit expressions of the bias factors for voids and infinitesimal dislocation loops are given. If the metal is subject to external loads the bias factors of voids depend on the elastic dilatation, whereas the bias factors for dislocation loops depend on the deviatoric elastic strain. These results then provide the basis for stress−induced swelling and irradiation creep of metals. Both of these phenomena are briefly discussed.

A short-time diffusion correlation for hydrogen-induced crack growth kinetics

Abstract: Analysis of hydrogen-stress field interactions have led to kinetic criteria for slow crack growth. Using both elastic and plastic stress fields under opening-mode loading, criteria for stage I, II, III growth are developed in terms of the pressure tensor gradient at the crack tip. It is proposed that stage I (stress-intensity dependent) growth kinetics are predominantly controlled by the elastic stress field while stage II (nearly stress-intensity independent) kinetics are controlled by the plastic stress field. Measurements of slow crack growth in cathodically-charged AISI 4340 steel verify the overall aspects of the correlation. Detailed measurement and analysis of the increase in crack-tip radius with increasing applied stress intensity have led to a proposed decrease in crack growth rate during stage II growth. Some experimental evidence corroborates this later hypothesis and is consistent with long range diffusional flow of hydrogen as the controlling mechanism for crack growth kinetics.

Stress fields in central portions of the Pacific Plate: Delineated in time by linear volcanic chains

Abstract: Many linear island chains in the Pacific appear to consist of individual volcanic shields that lie on relatively short, curved loci sometimes of sigmoidal form. These loci, in turn, lie at an angle to the directions of propagation of the chains. Those chains that now trend just south of east (the Pratt-Welker, Hawaiian, Tuamotu, and Austral chains) consist of en echelon sets of loci with right lateral (clockwise) sense of stepwise overlap, whereas the supposed older extensions of these chains that lie nearly north-south (the Emperor and Ellice-Gilbert-Marshall chains) consist of sets of loci with left lateral (counterclockwise) sense of stepwise overlap. Rift zones of isolated volcanoes in the chains, that is, those volcanoes whose local stress fields were not influenced by the buttressing effects of near-neighbor volcanoes at the time of their formation, show the same orientation as the loci. First-motion studies of earthquakes in the Pacific lithosphere to date are few in number and give a variety of solutions with inferred directions of maximum principal compression (P) nearly horizontal and trending in both northeasterly-southwesterly and northwesterly-southeasterly directions. However, the number of such solutions is small, in some cases related to edifice effects, and interpretations relating compression and dilatation to principal stress directions in magmatic source regions are open to question. We consider it likely that the dominant orientation patterns have been due to dynamic effects related to the overall kinematic patterns of Pacific plate motions. Although a large number of different factors can influence the inherent and transmitted stresses in the lithosphere, and thereby influence the locally dominant stress field, we conclude that the effective stress orientations in the very recent past and for about the last 40–50 m.y. can be considered to have been caused by dynamic forces reflected in a right lateral rotational couple acting within the plane of the Pacific plate. These forces have induced maximum (S1) principal compressional stress directions that have had surface traces trending about northwest-southeast, relating to minimum (S3) principal stress directions that have trended northeast-southwest. Prior to 40–50 m.y. ago the dominant stress orientations in the plate were caused by a tendency for left lateral stress rotations, which induced maximum (S1) principal compressional stress directions with surface traces that trended just west of north and minimum (S3) principal stress directions that trended just north of east. These data and interpretations are independent of whether or not a change in direction of motion of the Pacific lithospheric plate took place roughly at the time represented by the bends in the island chains and are also independent of arguments as to whether melting anomalies of the Pacific are rigidly fixed or whether they are better explained in terms of thermal plumes or gravitational anchors. We conclude that the trends and age correlations of volcanic loci in the Pacific accurately track and identify the evolution of states of stress in the Pacific lithosphere with time. As more age data for linear island edifices become available, it should be possible to construct a Pacific-wide chronology of volcanism independent of but similar to that developed from magnetic reversals. Further, it appears that changes in stress directions in the plate have been episodic and that they may correlate with episodic magma generation not only in the central part of the Pacific plate but also around its margins.

On the Three-Dimensional Theory of Cracked Plates

Abstract: This paper discusses a method for solving three-dimensional mixed-boundary-value problems which arise in elastostatics. Specifically, the method is applied to a plate of finite thickness which contains a finite, through the thickness, line crack. The analysis shows that (a) in the interior of the plate only the stresses sigma-x, sigma-y, sigma-z, and tau-xy are singular of order 1/2; (b) in the vicinity of the corner point all the stresses are singular of order ((1/2) plus 2 nu); as the thickness h approaches infinity the plane strain solution is recovered and; (d) as nu approaches o the plane stress solution is recovered. Finally, it is found that in the neighborhood of the corner points, even though the displacements are singular for certain values of the Poisson's ratios, the derived stress field satisfies the condition of local finite energy. /Author/

Dasht-e Baȳaz Fault, Iran: Earthquake and Earlier Related Structures in Bed Rock

Abstract: An 18-km-long segment of bed rock of the Dasht-e Baȳaz earthquake fault was studied in detail to define the 1968 earthquake-related and earlier tectonic deformations. Ground displacements that accompanied the earthquake coincided precisely with the pre-existing east-trending fault trace. Maximum components of offset were 4 m left-lateral and 1 m south side relatively down. The bedrock displacement occurred along new tension fractures that strike on average at 50°, as well as along reactivated pre-existing structures. Earlier tectonic deformation also produced tension fractures (post-Pliocene), conjugate shears (Pliocene), and tension joints (pre-Pliocene), and all are consistent with 47° to 55° tectonic compression. The study covered three points: (1) the 40° to 45° angle measured between the major principal stress direction indicated by the earthquake fractures and the fault; (2) the apparent constancy of the stress field direction during the three early phases and the 1968 deformation; and (3) the “gap” and “anti-Riedel” structure shown by the overall fault trace, which, we suggest, are characteristic of situations of kinematic restraint and are associated with a nonuniformly propagating rupture.

Relationship of mine tremors to induced stresses and to rock properties in the focal region

Abstract: Focal coordinates for a suite of tremors associated with deep-level tabular mining were determined with uncertainties of about 35 m and the tremor positions were analyzed in terms of the stress field induced by mining in the immediate vicinity. All tremors occurred in a region of 300 m in extent and at depths near 3.1 km; their magnitudes ranged from −1.5 to 2.5. The source rock in this region has no groundwater, whatsoever. The two major factors governing the occurrence of tremors appear to be the change in the stress field from its virgin state and the strength of the rock. The positions of tremor foci coincide closely with the region where changes in the stress field due to mining are maximal. Most of the tremors were located in regions where the maximum principal stress induced by mining exceeded 1 kb or where the minimum principal induced stress was less than −160 bars, compressive stresses taken as positive. Nearly all of the tremors were located above the gold-bearing reef. Strength tests in uniaxial compression indicated that the rock above the reef is about 1.4 kb stronger than that below; Young9s modulus is also higher for rock above the reef. These results suggest that tremors tend to occur in regions where the rock is capable of storing the most elastic strain energy before failure. Underground observations of shear failure indicate that tremors are the result of the rupture of previously intact rock. The fact that the majority of seismic foci occurred in regions where the stress field is calculated to be well below that required for rock fracture argues for the existence of localized residual stresses of large magnitude.

The initiation of oscillatory ripple marks and the development of plane-bed at high shear stresses under waves

Abstract: Data on the development of oscillatory ripple marks under waves are utilized as a further check on the equations that have been proposed for the threshold of sediment motion. If the threshold curve is correct, the data on ripple occurrence should lie in a stress field above the curve for threshold. Analysis of the data shows this mainly to be true but suggests that the curve for the threshold should be lowered slightly to smaller stress values as a number of ripple occurrences would otherwise fall below the threshold curve. As the stress of the wave orbital motion increases, the ripple heights progressively decrease and ultimately disappear at a critical stress value. Data on this disappearance and plane-bed sheet sand transport development are examined and compared with the data on the high-stress presence of ripples. There is good agreement of the two data sets and also confirmation of the theoretical criterion of Bagnold for the disappearance of ripples.

The interaction of gas bubbles in an anisotropic elastic solid

Abstract: The problem of finding the stress field induced in the neighbourhood of two spherical gas bubbles or voids in an anisotropic matrix is formulated in terms of an integral equation for the “transformation stress” in equivalent homogeneous inclusions. An iterative method of solution is outlined, involving the solution of a class of problems for a single spherical inclusion perturbing a polynomial field of stress. Explicit solutions are obtained for polynomials up to second degree. Estimates of the energy of interaction between gas bubbles in α-U and between voids in Mo are deduced as examples, and the results are discussed in relation to earlier calculations and to observations.

Interfacial edge dislocations and dislocation walls in anisotropic two−phase media

Abstract: Explicit expressions are obtained for the displacement and stress fields of an edge dislocation in the plane interface in a two−phase anisotropic medium. These expressions are used to calculate the stress field of an infinite vertical array of equally spaced interfacial edge dislocations. It is shown that in a two−phase medium, either anisotropic or isotropic, an edge−dislocation wall at or near the interface has a long−range stress field, in contrast to the result for a single−phase medium.

Creep and swelling deformation in structural materials during fast-neutron irradiation. Discussion

Abstract: Radiation-induced creep and swelling is formulated in terms of the segregation of vacancies and interstitials to the microstructural sinks, such as voids, dislocations, and dislocation loops, in order to provide the physical basis for the effect of stress on swelling, radiation-induced creep, and the interrelationship between swelling and irradiation creep. It is first shown that the segregation is caused by the interaction between the point defects and the sinks and that the size interaction as well as the inhomogeneity interaction have to be considered. The latter interaction depends both on the external and the internal stresses. The segregation is then expressed in terms of bias factors for each sink type, and these factors are given for voids, small dislocation loops, and edge dislocation multipoles. The bias factors for voids are shown to depend on the hydrostatic stress leading to a stress-dependent incubation time for void nucleation as well as a stress-dependent swelling rate. The bias factors for dislocation loops depend on the deviatoric stress. Thus, the loop growth rate becomes orientation-dependent in a stress field, which gives rise to irradiation creep. The comparison between the bias factors of voids and dislocation multipoles reveals that void nucleation is suppressed in cold-worked materials until sufficient recovery has occurred. By including the bias factors for voids, dislocations, and dislocation loops into the models for swelling and irradiation creep, a constitutive law for radiation-induced deformation is obtained which includes the rates for stress-free swelling, stress-induced swelling, swelling-independent and swelling-dependent irradiation creep.

Evidence for earthquake triggering stress

Abstract: Earthquake time series are constructed by making counts per unit time of earthquakes with magnitudes greater than a chosen threshold. The time series from widely separated regions show strong correlations with one another, and it is suggested that tectonic plates are subjected to a fluctuating stress field that results in these changes in seismic activity.

Creep and Swelling Deformation in Structural Materials During Fast-Neutron Irradiation

Abstract: Radiation-induced creep and swelling is formulated in terms of the segregation of vacancies and interstitials to the microstructural sinks, such as voids, dislocations, and dislocation loops, in order to provide the physical basis for the effect of stress on swelling, radiation-induced creep, and the interrelationship between swelling and irradiation creep. It is first shown that the segregation is caused by the interaction between the point defects and the sinks and that the size interaction as well as the inhomogeneity interaction have to be considered. The latter interaction depends both on the external and the internal stresses. The segregation is then expressed in terms of bias factors for each sink type, and these factors are given for voids, small dislocation loops, and edge dislocation multipoles. The bias factors for voids are shown to depend on the hydrostatic stress leading to a stress-dependent incubation time for void nucleation as well as a stress-dependent swelling rate. The bias factors for dislocation loops depend on the deviatoric stress. Thus, the loop growth rate becomes orientation-dependent in a stress field, which gives rise to irradiation creep. The comparison between the bias factors of voids and dislocation multipoles reveals that void nucleation is suppressed in cold-workedmore » materials until sufficient recovery has occurred. By including the bias factors for voids, dislocations, and dislocation loops into the models for swelling and irradiation creep, a constitutive law for radiation-induced deformation is obtained which includes the rates for stress-free swelling, stress-induced swelling, swelling-independent and swelling-dependent irradiation creep.« less

Elastic Energy, Stress Field and Interaction of Dislocations in Bismuth Crystal

Abstract: The energy factor, K, and the elastic energy of dislocations at temperatures between 4.2 K and the melting point in a bismuth crystal are obtained by numerical calculations in terms of anisotropic elasticity theory. The results are applied to the stress fields around edge dislocations and the possible dislocation interactions. It is found that the temperature dependence of K's is analogous to those of the elastic constants and dislocations in each slip plane may be most stable if its line is along a direction. The experimental fact that the {001} slips have been active in our previous work is verified by the criterion of a minimum dislocation energy. The stress fields around an edge dislocation in a {001} and a {11} slip systems show a distinct anisotropic effect.

Three-Dimensional Analysis of Laminar Composites with Through Cracks

Abstract: The variational principle of minimum complementary potential energy is employed to develop an approximate three-dimensional model for the stress distribution in laminar composites. This approximate theory is applied to the problem of a symmetric composite plate containing a through crack subjected to in-plane loading. Asymptotic solutions are obtained for the stress components in the vicinity of the leading crack edge. These solutions are in complete agreement with information obtained from an exact three-dimensional asymptotic analysis; that is, the in-plane variation of the stress components within each layer is described by the singular portion of the elastic, plane-strain crack solution. However, because of the three-dimensional character of the problem, the amplitude of the singular solution for the stress components varies along the leading crack edge. A two-parameter model incorporating the concept of surface and interfacial boundary layers is used to describe this transverse variation. Results from the modeling and analysis performed here include a description of the through-the-thickness-variation of the near-tip stress field, which has already proven to be of use in conjunction with photoelastic measurements, and an average or effective stress intensity factor for finite thickness homogeneous plates and laminates.

Threeui-Dimensional Solution for a Through-Thickness Crack with Crack Tip Damage in a Cross-Plied Laminate

Abstract: A three-dimensional finite-element solution is given for the stress field of a 0/90 laminate containing a sharp through-thickness edge crack with crack tip damage consisting of subcracks parallel to the fibers of each ply. The solution is compared to that for a sharp crack with no subcracks given in an associated paper, and the introduction of the subcracks is shown to significantly alter the stress field. Outside of a core zone at the main crack tip, the two stress distributions are nearly identical. Inside of the core zone, the subcracks serve to relax the in-plane stresses in a manner similar to the action of a plastic zone in a metal; the mechanisms of stress transfer around the subcracks are identified. The results also indicate that the fundamental fracture mechanics concept of a zone of relaxed stresses near the main crack tip, surrounded by an undisturbed singular stress field, is preserved, and that the subcracks cause no shift in the singular stress field which would require a crack length correction.