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By William J. Gillich, Gerald L. Moss

PREVIOUS studies of the shock loading of randomly oriented polycrystalline aggregates have firmly established that, after rather short load duration, hydrostatic compression closely approximates the shocked state.' However, McQueen deduced from pressure measurements with good time resolution that, during shock loading, metals begin to undergo a stress relaxation at the yield stress. He suggested that the relaxation is due to plastic deformation accompanying the change from a one-dimensional compression to a three-dimensional, hydrostatic, compression.' Stress relaxation may occur faster as stress is increased above the yield stress, but the existence of unidirectionally compressed states for finite times suggests that the concept of a unidirectionally distorted lattice should furnish considerable insight into the mechanical behavior of materials subjected to shock loading. Here, a crystallographic analysis is presented for the hypothetical situation where atom motion may be considered as unidirectional which, as indicated above, is a useful extension of the macroscopic concept of shock loading to the microscopic domain. Only motion caused by the com-pressive forces is treated; i.e., lattice vibrations upon which this motion is superimposed, as discussed by Fitzgerald, are ignored.3 The purpose of the analysis to be presented is to develop a description for single crystals of the lattice rotations that occur for idealized uniaxial strain deformation. The usefulness of such an analysis in realistic deformation is to give a method of specification of those properties of an initially distorted lattice which would affect the subsequent deformation. Non-axial complications that arise experimentally, such as off-axis rarefaction waves, must be treated in proper context. Consider the material element shown in Fig. 1 and let the compression be uniform at all regions of the element. Then, any interior point of the element is displaced in proportion to its distance from the base of the element. Accordingly, if the top of a unit element is displaced by an amount, (-K), with respect to the base, a point P(X, Y) will be displaced by (-KY). Crystal planes are, therefore, rotated by the compression. Analysis of this rotation may be accomplished from the geometry shown in Fig. 1 where the line OP is the edge of the plane {hkl} and N is its normal. The orientation of the crystal plane with respect to the shock direction is specified by the angle, before deformation. After deformation the edge of plane {hkl}

Jan 1, 1969

By Yoginder P. Chugh

Elastic and viscoelastic behavior of three rocks-Tennessee sandstone, Barre granite, and Indiana limestone-was studied experimentally under uniaxial tensile stress. Cylindrical specimens of these rocks, about 1.0 in. diam and 2.0 in. long, were subjected to incremental constant stress history under uniaxial tension. The stress was held constant for a period of 40 min at each stress level. During this period, longitudinal and transverse strains on specimens were continuously monitored. The straintime history at each stress level was analyzed for elastic and viscoelastic parameters of a generalized Burger model. The viscoelastic parameters under uniaxial tensile stress were compared with those under uniaxial compressive stress. The experimental setup, experimental procedure, analysis techniques, and more significant results are described. This limited research effort clearly indicates the importance of the mechanical behavior of geologic material under tensile stresses.

Jan 1, 1975

By D. J. Varnes

Rocks in mines, quarries, and many outcrops commonly show evidence of being under high stress. Saw cuts and drillholes close in, partly mined coal bursts violently, and pillars crush and rock spalls in mines even at moderate depths. Similarly, strong and massive rocks such as granite and sandstone naturally divide themselves into sheets that lie more or less parallel to their outward topographic form. The sheets may be either convex or concave. Thin plates of bare rock surfaces bow up and buckle. Such effects often cannot be explained by the obvious loads now acting on the rock, that is, by loads resulting from overburden, topographic irregularities, or stress concentration around openings. The stresses exceed those that would result from such loads. Two interpretations of such excess stresses have been made. In one, the stresses are assigned in origin to now active tectonic forces. In the other, they are regarded as leftover and locked in from some previous state at which higher pressures prevailed. These two sources may both operate and they generally cannot be distinguished easily in the field. There are other complicating sources of stress such as temperature gradients and chemical alteration. Nevertheless, some bodies of rock, by exfoliating, show evidence of high internal stress even though they are practically unweathered and so isolated topographically that the presence in them of significant stress due to exterior loads or active tectonic forces seems unlikely (Fig. 1). Moreover, completely isolated rocks are known to change density, shape, or size 1,2 to expand under constant compressive stress;3 and even to disintegrate 4,5 without the intervention of weathering processes. The stresses involved here must be truly residual in the sense long used by metallurgists; that is, residual stresses in a body are those that remain.

Jan 1, 1970

By Fun-Den, Wang

An open pit rock structure usually contains geological planes of weakness. They are formed by joints, faults, bedding planes, fractures, and cleavages. Rock slope failures often occur in the form of sliding of rock blocks along a plane or several planes. Such a rock block has three- dimensional geometry, and consequently a vector method of analysis has been found useful in evaluating its stability. Rock blocks of a tetrahedral shape with one free surface have been analyzed by Londe. Rock blocks formed by sets of parallel joints have been analyzed by Wittke. The present chapter presents the analysis of rock blocks formed by planes of weakness of arbitrary orientation, and of three-dimensional geometry.

Jan 1, 1972

By L. W. Kempf, K. R. VanHorn

PLASTIC deformation of most commercial metals within a sufficiently low temperature range results in profound changes in structure and properties, of which the causes and effects are not completely understood. One of these effects is the presence of internal residual stresses and strains, which ordinarily do not appear to require specific consideration in most structural applications but which may be quite undesirable in particular instances. For example, in heavy sections that require considerable machining before assembly, residual stresses may be undesirable because of the distortion they cause when their balance is disturbed by machining or otherwise. In addition, the distribution of stresses may be such that it acts in the same direction as the applied load, thus bringing about premature failure or reducing the load-carrying capacity of the member. One source of residual stress in metal structures is the plastic deformation that may occur during rapid cooling from relatively elevated temperatures, as in the cooling of a casting in the mold or the quenching of a heavy section from elevated temperatures during heat-treatment. These residual stresses are usually undesirable because their direction of operation and magnitude cannot be controlled well enough to permit utilization of the changes in properties of the metal that they may bring about. The most convenient manner of controlling such residual stress is by proper selection of the cooling rate or by reheating to a temperature at which plastic flow can take place, resulting in relief of the residual stresses and strains. Both of these methods of control, however, may cause a reduction in the optimum properties obtainable from the previous operation compromise must be struck, and if it is to result in the best possible combinations of properties, specific information must be available regarding the magnitude of the stresses and the rate at which they are affected by variations in cooling rate or in reheating temperature. The complete quantitative estimation of residual stress in complicated metal shapes is exceedingly difficult, if not impossible. In simple sections, however, relatively quantitative analysis may be applied and useful estimations of stress distribution may be made. This paper is concerned largely with the rate of relief, upon reheating, of internal residual stress in simple aluminum-alloy structures. Since even with simple structures quantitative estimation of residual stresses is laborious and costly, an attempt was made to find other means of collecting data upon which commercial heat-treatments might be based. Incidentally, a few data were collected bearing on the problem of relaxation of aluminum alloys. DETERMINATION OF RESIDUAL STRESSES The magnitude and distribution of residual stresses in simple aluminum-alloy shapes rapidly cooled from elevated temperatures has been discussed in a previous paper.1 Fig. I reproduces some of the data

Jan 1, 1941

By S. E. Bronisz, J. O. Brittain

Experiments have been carried out to study the effect of an applied stress on strain aging in steel. It was found that the stress-induced strain aging reaction proceeds rapidly in the temperature range of 0° to 60°C. The variation of stress-induced strain aging with plastic strain, aging time, and temperatures is reported. The activation energy for the stress-induced strain aging was found to be 10,000 cal per mol for the steel used in this investigation. VARIOUS observations1-5 have been made of the influence of an applied stress upon the yielding of iron and steel. However, there have been only cursory studies of the effect of an applied tensile stress upon strain aging in iron and steel1,2 The following represents the results of a preliminary study of strain aging as influenced by the application of an external tensile load during the aging process. For the most part, previous experimental work on strain aging can be classified into two parts. First, the experimental technique involved a direct determination of mechanical properties of a suitable specimen that has been plastically deformed to a constant strain and aged generally at a temperature of the order of 200°C, with the aging times varying from about 1/10 to 2 hr.6-8 The second classification of strain aging experiments involves an indirect determination of strain aging by means of physical property such as electrical resistivity or internal friction as a function of the aging time at a constant temperature and strain.9-12 The latter results have

Jan 1, 1961

By D. K. Crampton

INTERNAL stress and season cracking in brass have been studied for many years and the technical literature contains many data on various phases of the subject. A résumé of the literature shows certain fairly well established points upon which various authors are mostly agreed: 1. Season cracking is primarily caused by the presence of relatively high internal stresses, or possibly in some cases by external stresses, or both. 2. A specific corrosion is also essential to season cracking: Certain agents, particularly mercurous salts, mercuric salts and ammonia salts; have such a specific corrosive effect. 3. The tendency to season crack under given conditions increases with increasing zinc content, brass containing less than 20 per cent zinc being relatively immune. 4. In alpha brass the season cracks are intercrystalline; in alphabeta brass they lie between the two constituents; and in beta brass they are transcrystalline. 5. The ordinary impurities or added elements in special brasses have little or no effect on the tendency to season crack. 6. Internal stresses can be eliminated, or at least reduced to a safe 'limit by annealing treatments at temperatures that do not produce visible microstructural changes or appreciable softening of the worked brasses. There are, however, some points in connection with the phenomenon of season cracking which have not been thoroughly investigated, or wherein different authors and investigators are not entirely in agreement. The investigations described in this paper were undertaken to determine: 1. The correlation between mercurous nitrate tests and actual season cracking on long-time atmospheric exposure. 2. The quantitative effect of type and degree of drawing operations on the intensity of internal stress and on the tendency to season crack in brass tubes. 3. The possibility of drawing high-brass tubes in such a manner as to prevent the occurrence of harmful stresses rather than to find a remedy for such stresses once having obtained them.

Jan 1, 1930

By R. P. Carreker, J. C. Fisher

Cheep tests are normally constant load tests. Such tests approximate some types of service conditions and therefore are justified from the engineering point of view. Coupled with this consideration is the advantage of simplicity inherent in constant load tests, as contrasted with the comparatively complex requirements of a constant stress test. It is not surprising that the vast majority of creep tests reported are of the constant load type. Despite the enormous amount of accumulated creep test data, plastic flow is by no means completely understood. The widespread use of constant load tests is at least partly responsible for this lack of understanding. Any attempt to analyze deformation must involve the more fundamental quantity stress, rather than load. It is possible to predict constant load behavior from known constant stress data, but the reverse is much more difficult. When a metal specimen elongates, as in a creep test, the cross section decreases, maintaining constant volume. Thus For a constant stress test the force on the specimen must be decreased as the cross section decreases, that is, this force must be inversely proportional to the elongation of the specimen. An-drade has described three methods of obtaining the constant stress condition,l-3 each of which is relatively complex. The most recent proposal,³ suggests a major simplification which maintains the simplicity of the constant load test while approximating quite closely the desirable condition of constant stress. Andrade's device is admittedly more accurate but the method described below has definite advantages Consider a specimen in the form of a "V" supported at its ends. If a weight be applied at the vertex of the angle, the stress in each leg of the "V" If this stress causes an elongation ?1 in each leg of the "V," the angle decreases from a. to a smaller angle a1. The quantity sec — thus decreases with specimen elongation while the quantity 1/A increases. By selecting proper initial conditions it should be possible to hold S/So very nearly constant at unity. The proper initial conditions are realized when a0 is made equal to approximately 90°. Fig 1 compares the ratios of S/S0 for a0 = 85, 90, 95, 100°, with a0 = 0, that is, a straight speci- men, for true strains up to e = 0.10. It may prove convenient to measure X, the movement of the vertex, rather than the true elongation 1. Contour lines of X/lo are also plotted in Fig 1. The method for obtaining constant stress described above is especially suited to the testing of small wires, but may easily be extended to rods of any diameter through the use of a suitable grip which serves as the vertex joining two identical rods forming the legs of the "V." References 1. E. N. da C. Andrade: On the Viscous Flow in Metals, and Allied Phenomena. Proc. Roy. Soc., A, 84, 1, (1910-11). 2. E. N. da C. Andrade and B. Chalmers: The Resistivity of Polycrystalline Wires in Relation to Plastic Deformation, and the Mechanism of Plastic Flow. Proc. Roy. Soc., A, 138, 348, (1932). 3. E. N. da C. Andrade: A New Device for Maintaining Constant Stress in a Rod Undergoing Plastic Extension. Proc. Phys. Soc., 60, (3). 304, (March, 1948).

Jan 1, 1950

By Gerald Edmunds, R. K. Waring, E. A. Anderson

Brass is liable to failure under the combined influence of stress, certain corrosion media, and time, a phenomenon commonly termed season cracking or stress-corrosion cracking. The consequences of this are serious in applications of brass generally, including the important field of cartridge cases. Cartridge cases (70 Cu: 30 Zn) that fail from this cause may allow the escape of gas from the gun breech, a hazard to the shooter, and may not eject, thus temporarily putting the gun out of action. In loaded cartridge cases, the stress present is partly residual from the, drawing and necking operations and partly applied by the insertion of the projectile. Ammonia, present as a decomposition product of smokeless powder, air and moisture constitute corrosive media. The prevalence of season cracking has been reduced considerably, but not eliminated, during the past quarter of a century by low-temperature annealing to relieve stresses residual from fabrication, a method suggested by Diegel 38 yr. ago(I).2

Jan 1, 1945

By George J. Young

(Cleveland Meeting, October, 1912.) I. GENERAL. THE recurrence of mine-fires in Nevada during the past decade is not only a matter of interest, but also one of considerable concern to engineers and mine-managers. The more important fires may he enumerated as follows: Forman Shaft fire., Gold Hill, April 21, 1903 ; shaft-house, machinery, and shaft, destroyed; loss estimated at $50,000.; Cause Unknown. Union Shaft fire, Virginia City, July 14, 1904; shaft-house, machinery, and shaft in part destroyed; loss estimated it $100,000; cause of fire stated as the careless throwing of a match in the rope-house. Sutro Tunnel fire, Virginia City, Jan. 27, 1909 ; 700 ft. of tunnel-timbering destroyed, and direct damage of $10,000; cause ' probably electric wires." Belcher Shaft fire, Gold Hill, Aug. 9, 1910; shaft-house destroyed, machinery ruined, and upper part of shaft damaged; damage, $25,000; no cause given. Belmont Mine fire, Tonopah, Feb. 23, 1911; fire started in winze ; 17 men killed. Giroux Mine fire, Kimberly, Aug. 23, 1911 ; fire originated iii shaft-station from unknown cause; 7 men killed, and $34,¬521 damage caused. (NOTE 1.-On June 11, 1912, some time after the present paper was written, a fire broke out in the pump-room on the 2475 station of the Ward shaft, Virginia City. This fire was caused by the short-circuiting and exploding of the starting-switch on No. 5 pump. The oil in the switch was scattered about and set fire to the timbers and laming of the pump-room. The pump-roan in charge notified the surface, and the * Professor of Mining and Metallurgy, Mackay School of Mines.

Oct 1, 1912

By A. Brown

RAPIDLY rising world demand for mineral products has accelerated depletion of the more readily accessible ores, particularly those of premium grade. Operations must proceed at a faster rate to deeper horizons, where there are problems of ground control that restrict economic recovery of the mineral and introduce new hazards to mine personnel. For some of the new Canadian mining fields severe problems of ground stress are still in the future, but much of Canada's mineral output comes from well established mines that have reached considerable depths. It must also be anticipated that the depletion of premium grade ores will eventually necessitate mining low grade material at competitive cost, and unsolved problems of ground control can materially increase costs. Studies of ground stress phenomena in underground workings are therefore considered a present-day necessity, especially since these investigations must be a long-term effort owing to the highly complex nature of the problem and the difficulty of making full-scale observations. In recent years the Mines Branch of the Department of Mines and Technical Surveys in Canada has conducted such an investigation. This report of the work is primarily concerned with stress problems in some Canadian coal mines and, in particular, with mine bumps. Mines Branch investigations of this and related problems are carried out by a small team of mining engineers and physicists who, with assistance from geologists, pool their special skills in an integrated program. These Canadian investigations combine a field and laboratory approach. Since data obtained under contrasting mining conditions allow useful comparisons of ground behavior under stress, this article will present data gathered under a wide range of Canadian coal mining conditions. Two contrasting longwalls in eastern Canada will be discussed and two dissimilar pillar extraction operations in western Canada. Locale of Observations In eastern Canada observations are being made in the collieries at Springhill, Nova Scotia. The district's No. 2 mine, which has a history of bump occurrences dating back to 1917, is currently being worked at a depth of 4200 ft. The mining method is longwall retreating along the strike and the practice is to retreat three walls in line, each about 350 ft long. There is no machine cutting or shooting—the coal is hand-picked and hand-loaded onto face conveyors. There are three rows of hardwood chock block supports parallel to the coal face. These supports are built during the two daily coal loading shifts, and the rear line is withdrawn during the midnight shift. The goaves are partially packed by stone midwalls 12 ft wide which are built forward daily in step with the face advance. The seam dips at 15° and averages 9 ft of strong, well cleated bituminous coal enclosed in competent beds of shales, sandy shales, and sandstones of Carboniferous age. The bumps rarely disturb the retreating longwall faces but manifest themselves as violent upthrusts of pavement in the levels leading to the walls. Observations have also been made in Springhill's No. 6 mine, which operated in a 5-ft seam of coal at a depth of about 2500 ft. Although No. 6 mine was

Jan 1, 1959

By Charles E. Heinrichs

IN the last decade one of our oldest and largest non-metallic metallic mineral industries has been the subject of persistent technical research, the results of which are another example of the benefits following the systematic application of scientific principles. The consequent improvement in the technique of phosphate recovery represents the greatest material advance in the industry since the discovery of phosphate in Florida in 1881. Moreover, these successes have stimulated interest and development in numerous other nonmetallic industries. Strange as it may seem, and despite the fact that the phosphate deposits of Giles County, Tennessee, together with those of Polk and Hillsborough Counties, Florida, have yielded more than 50,000,000 long tons in the last twenty years, the mineralogy of phosphates has been given scarcely any space in our technical literature. For many years it was the general consensus that these so-called phosphate rocks represented a physical mixture composed principally of tri-calcium phosphate, together with smaller quantities of calcium carbonate, calcium fluoride, iron phosphate, aluminum phosphate and other less important constituents. More recent investigations, however, led to the conclusion that these phosphates really represent a complex mineral in which calcium, iron, aluminum, phosphorus pentoxide, carbon dioxide, and fluorine all form a definite part of the molecule. Colony, after a careful study, utilizing chemical, microscopic, and X-ray diffraction methods, reported that American phosphates consist principally of calcium-carbono-phosphate of the staffalite type.

Jan 1, 1933

By J. K. Edgar

For a number of years the production and use of super-purity aluminum (better than 99.99 pct) has been steadily increasing. High-grade lots of. such aluminum show certain outstanding characteristics not found in lower grades containing principally silicon, iron and copper as impurities. One such characteristic is the so-called "self annealing," that is, the re-crystallization of the heavily cold worked metal at room temperature.' Interest therefore is aroused as to the effects of the impurities. It is well known that the amounts of silicon and copper which occur in aluminum of better than 99.95 pct are completely soluble, at least at elevated temperatures (above 200°C). Iron, on the other hand, is known to be fairly insoluble in solid aluminum. Thus, a knowledge of the limits of this solubility would he of considerable use in studying the characteristics of the high purity metal. All investigators have agreed that iron has very low solubility in solid aluminum. Rosenhain, Archbutt and Hanson2 reported traces of an aluminum-iron phase in the "purest samples of aluminum obtainable." Gwyer and Phillips3 reported that an iron constituent was visible under the microscope in metal containing ".0088 per cent iron." Roth4 found that in the solid state the solubility of iron in high purity aluminum was 0.01, 0.01, 0.017 and 0.022 pct at 225, 320, 500 and 600°C respectively. Dix5 working with alloys containing less than 0.03 pct impurities, concluded from microscopic and chemical analyses of eutectic areas that the eutectic composition was close to 1.7 pct iron. Dix placed the eutectic temperature at 65s°C. Archer and Fink,6 using high purity aluminum-iron alloys, found that the hypoeutectic liquidus intersects the eutec-tic horizontal at 1.7 pct. This is in fair agreement with the investigation of the aluminum-iron system by Gwyer and Phillips who placed the eutectic at 1.89 pct iron with a freezing point of 653'C. Preparation and Chemical Analysis oP Alloys Electrolytically refined aluminum (99.991 pct aluminum) and a high purity alumi-num-iron alloy (11.45 Pet iron) were used in the preparation of the alloys for this investigation. To aid in controlling the iron content of the experimental alloys, an alloy of lower iron content was prepared first from these materials. The high purity aluminum was melted and heated to about 700°C in a plumbago crucible coated with alundum cement and the aluminum-iron alloy was then added. The alloy was thoroughly stirred, fluxed and skimmed and then chill-cast into notch bars. The aIlalyses of the three materials are given in Table I. The alloys for the determination of the solid solubility of iron in aluminum were prepared by melting 600 g total of the aluminum plus the required quantity of the aluminum-iron alloy (No. 92531). These

Jan 1, 1949

By Shosei Serata

Conventional roof bolting may be giving ground to a new technique that utilizes only the ground itself to stabilize mine openings. This newly developed stress control technique (SCT) has initially been used in sedimentary ore bodies that are both overlain and underlain by weak strata. The technique is also suited to the design of production panels and main entry systems, and is readily adaptable to room and pillar as well as total- extraction mining, including both shortwall and longwall coal mining. In applications where the technique has been used, the requirements for roof bolting and floor renewal were virtually eliminated. The SCT comprises three basic methods and covers a wide range of problems associated with failing roofs and heaving floors in underground mines (see Table 1).

Jan 5, 1976

By C. E. Sims, C. A. Zapffe

MANY hundreds of publications have appeared during the past 78 years that treat the subject of hydrogen in iron and steel,105 but conclusions regarding the functions of hydrogen in causing some important defects in steel are still unsatisfactory to many; and other hydrogen-caused phenomena yet remain to be identified with this gas. The most widely discussed of these defects is hydrogen embrittlement, but the conception, perhaps the popular one, that embrittlement is due to hydride formation does not conform to the known facts.104 The true identity of hydrogen embrittlement seems instead to lie in a mosaic nature of metal crystals, which is a concept not yet accepted by most metallurgists. A study of hydrogen embrittlement therefore provides new viewpoints in regard to the crystalline substructure of steel. A second widely discussed hydrogen-caused defect is the "flake" or "shatter crack." Although it is generally agreed that the presence of hydrogen is a prerequisite for their appearance, it is also realized that internal stress plays a decisive part. The relationship of hydrogen to internal stress has not been explained very clearly; nor is it always clear what the relationship is between a "flake" and a "snowflake," or between a "fish eye" and a "shatter crack." More importantly, the relationships among hydrogen embrittlement, hydrogen-caused fissures such as "flakes" and the ultramicroscopic structure of steel have scarcely been recognized. The present investigation attempts to provide an explanation for the embrittlement of steel by hydrogen by showing cause for accepting the "block" concept of metal crystals, and then to show how the numerous hydrogen-caused defects are interrelated in the light of this concept. EVIDENCE OF SUBSTRUCTURE IN METAL CRYSTALS It appears that the concept of a crystal as an aggregate of smaller multi-atom units must be accepted in some form if the behavior of metals is to be understood. The abundant literature on the evidence of an ultramicroscopic "mosaic" structure in metals and other crystalline substances suggests that the physicist has provided the metallurgist with an invaluable new insight. The exact picturization that any one physicist provides may be open to question, but the fact that there is some such fundamental substructure seems undeniable. The present work makes no pretense of comprehensively treating the imperfection structure theories. Nor will conclusions be drawn here regarding the exact nature of the substructure of crystals. However, the acceptance of some imperfection theory of fundamental attributes seems so necessary to an understanding of the behavior of hydrogen in steel that the following brief

Jan 1, 1941

By Paul H. Lu, Fred D. Wright

Numerous laboratory tests and field measurements conducted by different persons have indicated that most mine rocks behave viscoelastically rather than elastically. Hence, for an accurate and realistic design of underground structure, the time factor should be taken into account, and the theory of viscoelasticity can be used. By considering the time factor, the time-safe-strength may be used for economical design instead of liberal safety factors with design based on the elasticity theory. The deflection and moment distributions on an elastic roof slab resting on elastic pillars have already been studied.l In this chapter, the stress- strain analysis for a viscoelastic mine roof resting on pillars of the same material or on supports of different material is first considered theoretically. Viscoelastic solutions for deflections, moments, and shears are de- rived from the elastic plate theory on the basis of the elastic-viscoelastic correspondence principle. The Laplace transformation technique is employed as the operational method in the mathematical treatment. The roof slab materials are represented by four different rheological models and four different loading histories are considered. The method of finite difference equations is employed for solving the partial differential equations, using FORTRAN programs to calculate roof deflections, moments, and shears. Numerical examples are given for one of the four models under two of the four loading histories with regular and staggered pillar patterns. The results are discussed in terms of the variance with time of deflections, moments, and shears as well as their variation in space due to the dimensions and configuration of the structure system. A viscoelastic slab resting on viscoelastic pillars or on elastic supports

Jan 1, 1972

By A. R. Gregory, A. L. Podio, K. E. Gray

Dynamic elastic properties of dry and water-saturated Green River shale samples were computed from compressional- and shear-wave velocity measurements. P- and 5-wave velocity measurements were made in three mutually perpendicular directions with respect to the bedding planes. Measurements were also made in several different directions by varying the angle between the bedding planes and the direction of propagation of the wave for angles of 0, 30, 45, 60 and 909 The oriented samples were subjected to both confining pressure and axial loads, in excess of the confining stress, in the direction of propagation. In general, P- and S-wave velocities increased with increasing stress levels, with a corresponding increase in Young's modulus. Water saturation caused the P-wave velocity to increase and the S-wave velocity to decrease. Elastic moduli decreased upon saturation, except for Pois son's ratio, which increased, indicating some degree of weakening of the material. The samples showed a moderate degree of anisotropy; this was to be expected from the laminated nature and shallow occurrence of Green River shale. INTRODUCTION This paper presents some results of an experimental determination of the elastic coefficients of anisotropic materials (in particular, finely layered rocks and minerals such as Green River shale) from measurements of dilatational and shear-ultrasonic-wave velocities. Ultrasonic techniques have been used extensively in nondestructive testing. Several methods have been proposed by Mcskimmin, 1 and some of these have been used successfully to measure ultrasonic velocities in rocks. Hughes and Cross, 2 Wyllie et al., 3 and Birch 4,5 developed pulse first-arrival techniques for the measurement of dilatational and shear velocities. Williams and Lamb 6 used the method of cancellation of a traveling wave, which was later modified by Myers et al.' and perfected by McSkimmin. 8 Although this method is highly accurate, it has not been used as widely as the pulse-transmission methods recently reported by Jamieson and Hoskins 9 King,10 and Mattaboni and Schreiber. 11 It has been common practice to use some form of crystal transducers, either quartz or ceramic, that has been cut or polarized in different directions in order to generate either compressional or shear waves. However, accurate determination of shear wave velocities has been difficult due to problems that arise in obtaining a pure shear wave from cross-polarized crystals, which usually also generate a small amount of compressional energy. As reported by Gregory, 12 this energy can be seen as a long precursor preceding the sharp break of the shear first arrival. The need for generating pure shear waves led to interest in mode-conversion techniques, which are based upon conversion of the mode of vibration through wave reflection or refraction at a discontinuity. Arenberg13 showed that for certain materials and for certain angles of incidence it is possible to generate pure shear modes by reflection at a boundary. Jamieson and Hoskins 9 used a pyrex glass-air interface for generating pure shear waves, and King 10 used this method successfully for measuring shear-wave velocities in rocks. Gregory l4 arrived at a similar result by refraction of a wave at an aluminum-oil interface. A plane compressional wave, traveling in the oil phase, is incident on the aluminum at an angle larger than the critical angle for compressional waves, and thereby generates a purely transverse, plane-polarized wave in the aluminum. During the last few years methods have been developed that allow the simultaneous determination of shear and compressional velocities in solids.

Jan 1, 1969

By D. S. Tomalin, D. F. Stein

The effect of reducing oxygen to low concentrations on the fracture of high-purity iron single crystals has been examined at 78° and 20°K. It is found that iron single crystals grown by the strain-anneal method usually contain a few occluded grain boundaries which may become embittled in the presence of oxygen, thereby nucleating cleavage fractures. High purity with respect to interstitial elements was found to inhibit twinning and evidence is presented for an orientation dependence of the resolved yield stress. Deformation occurred by slip rather than twinning at both temperatures of testing with elongations of as much as 9 pct at 20°K. THE fracture properties of iron single crystals have been observedl-3 to be a function of temperature, orientation, and purity. Allen, Hopkins, and McLennan1 demonstrated that at 78°K iron single crystals became increasingly brittle as the tensile axis approached the (001) pole of the stereographic unit triangle. Iron crystals with the tension axis near a (001) pole were completely brittle and orientations near the (011)-(111) boundary were very ductile, achieving a 100 pct reduction in area prior to fracture. Later work of Biggs and pratt2 and of Edmondson3 demonstrated that by reducing the carbon content of the single crystals the transition between brittle and ductile failure at 78°K could be shifted to orientations nearer the (001) pole. Ed-mondson went further and pointed out that any mechanism which tended to increase the yield strength of the iron (i.e., carbon addition, pre-strain) also increased the tendency for brittle behavior at 78°K. Thus by a reduction of carbon content Biggs and Pratt were able to obtain ductile behavior to within 20 deg of the (001) pole, and Ed-mondson was able to obtain ductile behavior to within 26 deg of the (001) pole. Edmondson's material had a total interstitial content (carbon, oxygen, and nitrogen) of approximately 60 ppm and, although Biggs and Pratt reported no analysis, indications were that their iron contained comparable impurities. Stein, Low, and seybolt4 purified iron single crystals to a total carbon, oxygen, and nitrogen content of approximately 20 ppm. They observed a lowering of the yield stress with this increased purity, and thus one might have expected an observation of increased ductility. Although they tested specimens of orientations which the previous workers had indicated should be ductile, the crystals failed at a 78°K in a brittle manner with little elongation. Stein noted,' however, that about 90 pet of the failures could be traced in origin to occluded grains. Allen et al.1 and Edmondson3 do not report examination of their cleavage surfaces, but Biggs and pratt2 reported that microscopic examination of the cleavage surfaces of many of their specimens revealed the presence of small occluded grains. Honda and cohen6 and Keh7 have also observed the initiation of fracture at occluded grains in iron single crystals. Therefore, the additional complication of occluded grains must be considered in studying the properties of iron single crystals and the origin of fractures determined if the ductility exhibited by the crystals is to be considered meaningful. Various investigators8-12 have studied the effects of impurities on grain boundaries in high-purity polycrystalline iron. Rees and Hopkins10 showed that the addition of oxygen to low-carbon (0.002 pet) iron weakened the grain boundaries, causing a shift from transcrystalline to intercrystalline fracture and a progressive decrease on the brittle-fracture stress with increasing oxygen content. In addition, it has been shown by Low and Feustel11 that the addition of carbon to polycrystalline iron containing oxygen eliminated grain boundary brittleness. Thus, oxygen can embrittle grain boundaries in high-purity polycrystalline iron, but the addition of an appropriate amount of carbon can eliminate the oxygen-induced brittleness. The oxygen content (19 ppm) of the iron "single crystals" employed by Stein el al. was large enough to suspect impurity effects at the occluded grain boundaries. Allen et al.1 Biggs and pratt,2 and Edmondson3 may have masked any occluded grain problem in their specimens considering the relatively high carbon levels they employed. stein13 demonstrated that the addition of as little as 0.9 ppm C to previously purified (less than 5 x 10-3 ppm C) "single crystals" would increase the elongation from a few percent to more than 20 pet at 78°K and the fracture was not associated with grade boundary initiation.

Jan 1, 1965

By Amitava Gangulee, Michael B. Bever

The effects of changes in short-range order on some thermodynamic, electrical, and mechanical properties of the silver-rich Ag-Mg solid solutions have been investigated. The heats of formation at 273°K of several alloys after two different thermal treatments were measured by liquid metal solution calorimetry. Their electrical resistivities were measured at temperatures ranging from 4° to 773°k. Tensile tests and microhard-ness measurements were carried out at room temperature. An effective short-range order parameter and an effective interaction energy are defined. The measured changes in the properties are interpreted in terms of these quantities. The short-range order parameter is evaluated separately from calorimetric and X-ray data; the results are in fair agreement. Increasing short-range order lowers the resistivity of- the silver-rich Ag-Mg alloys but does not measurably affect the temperature dependence of the resistivity. Short-range order increases the yield stress of these alloys but does not affect the ultimate tensile stress. Changes in the effective short-range order parameter independently obtained from measured changes in the heat of formation, resistivity, and yield stress are in fair agreement. THE thermodynamic, electrical, and mechanical properties of solid solutions have been investigated as functions of composition in many alloy systems, but the effects of configurational variables, such as short-range or long-range order, on these properties have received much less attention. The silver-rich terminal solid solutions in the system Ag-Mg are well-suited for the investigation of the effects of order. The composition of these solid solutions may be varied over a range extending to about 27 at. pct Mg.1 Appreciable short-range ordering is likely to take place in these solid solutions; the degree of short-range order can be varied by suitable thermal treatments. In the alloy Ag3Mg long-range ordering is possible.2 This paper is primarily concerned with the effects of short-range order on some thermodynamic, electrical, and mechanical properties of the silver-rich Ag-Mg solid solutions.-The long-range ordering transition is the subject of a concurrent paper.3 1) EXPERIMENTAL PROCEDURES 1.1) Preparation of Specimens. Ag-Mg alloys containing up to 26.4 at. pct Mg were prepared by melting 99.99 pct pure Ag (obtained from Baker Chemical Co.) and 99.99 pct pure Mg (obtained from Eastman Chemi- cal Co. or Johnson Mathey & Co.) in graphite crucibles under molten potassium chloride. The solidified ingots were homogenized at 823°K for 10 days in evacuated Vycor capsules. A surface layer 6 in. thick was then removed by machining. The ingots were swaged into rods (2.5 mm diam) which were drawn into wires (1.0 mm diam). The wire specimens were annealed at 773°K for 24 hr in vacuum and either quenched into iced brine or cooled to room temperature over a period of 15 days. The average grain diameter (obtained from the linear intercepts) was about 0.1 mm. 1.2) Calorimetry. The heats of formation of the alloys were measured in a tin solution calorimeter as the difference in the heat effects of alternate additions of samples of an alloy and the mechanical mixture of its component elements. The additions were made from 273°K to the bath at about 623°K. The heat effect on addition of the alloys was approximately 5.5 kcal per g-atom. The procedure and the method of calculation have been described.4 1.3) X-Ray Diffraction. Short-range order parameters of two alloys were calculated from diffuse scattering intensities,' obtained with briquettes made from powdered specimens. A GE-XRD 5 diffractometer with filtered copper radiation was used. The absolute intensities were based on calibrations with paraffin. 1.4) Resistivity Measurements. The electrical resistivities were measured by a potentiometric method in which the potential drop across the specimen was compared with that across a standard resistance. For measurements below room temperature, the specimens were immersed in liquid helium (4°K), liquid nitrogen (78°K), dry ice and trichloroethylene (195°K), or ice and water (273°K). Measurements above room temperature were made on specimens held in a furnace under helium or in vacuum. The resistivity measurements were reproducible to ±0.5 pct or less. 1.5) Mechanical Tests. Tensile tests were carried out at room temperature with a Tinius-Olsen XY elec-tromatic Universal testing machine. Wire specimens (nominal gage length 1 in.) were used. The strain was measured with an extensometer, which had a sensitivity of 4 x 10-5; the strain rate was 10-3 min-1. Microhard-ness measurements were made with a square-pyramid indenter and a 100-g load.11 2) RESULTS AND DISCUSSION All measurements were made on two parallel sets of specimens, one quenched and the other slowly cooled from 773°K. The reported values are the averages of at least three measurements. In the range of magnesium concentration substantially below that of the composition Ag3Mg, quenched alloys have less short-range order than slowly cooled alloys. As the magnesium concentration approaches that of Ag3Mg, slow cooling develops long-range order. Quenching sup-

Jan 1, 1969

By W. G. Bearden, G. C. Howard, J. W. Spurlock

An investigation of the factors af-fec.ting the inter-zonal flow of fluids in the casing-wellbore annrc1rt.s of an oil or gas ivell is presented Laborntory tests revealed that failure of the caring-cement bond allows communi-cation of fluid at pressure differentials near 1.000 psi. Perforating with a 11011011: carrier gun does not shatter or crack the cement sufficiently to allow communication through these cracks and does not seriously affect the casing-cement bond failure pressure. The pressure to cause communication at the casing-cement bond can he increared to 3,000 psi by. limiting pipe deformation during cementing and subsequent operations. Communication can be prevented, however. up to pressures sufficient to cause the cement to fail or the casing to col-lapse, by attaching to the casing a seal ring of deformable ruhber molded between two steel flanges. When installed, one flange is attached rigidlv to the casing to serve as back-up for the gasket While tile other flange is movable. To date, these gasket seal rings have been field-tested in 27 Wells. Althotrgh communication has been noted in two wells, inter-zonal flow has been prevented in other wells in the same area by installing more seal rings between the communicaring zones. INTRODUCTION The inter-zonal flow of fluids behind casing cemented in oil wells during normal production or stimulation operations is a major operating problem. If it cccurs during production operations. it can seriously limit the pressure to which a reservoir may be depleted without harmful invasion of unwanted fluids. If it occurs during stimulation operations, it may preclude the possibility of stimulating the desired zone. This communication can be caused by failure of the bond between the casing and cement, failure of the bond between the cement and formation, or failure of the cement itself. This paper presents the results of an investigation of factors affecting com-munication at the casing-cement bond and methods which aid in preventing it. LABORATORY INVESTIGATIONS The laboratory tests performed in this study were divided into three phases. The first phase consisted of tests to determine if perforating would shatter and crack the cement sheath so severely that communication would occur through the cement itself. The second phase consisted of tests to determine more precisely the cause for the casing-cement bond failure. The third phase consisted of tests to evaluate the effectiveness of various de-formable seals attached to the casing in preventing communication. EFFECT OF PERFORATING, The effect of perforating was invest~gated in tests performed with apparatus shown on Fig. 1. Cement was poured into the annulur space hetween 5%-in. casing and 8%-in. casing and allowed to cure for 72 hours. The apparatus was then perforated with a hollow carrier gun containing eight duPont 26-A shaped charges. Bull plugs were placed over the perforations in the 8 5/8-in. casing and hydraulic pressure was applied inside the 5 1/2i-in. casing. The pressure to cause fluid communication past the cement sheath was observed and termed the "bond failure pressure". Several different cement compositions were included in these tests, the results of which are shown in Table 1. In Tests 1 through 4 of Table 1, bond failure occurred at- the inter- .

Jan 1, 1966