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By P. L. Raffo, T. E. Mitchell

Single crystals of Ta-Re alloys have been deformed in tension and compression as a function of solute concentration and temperature. The temperature dependence of the yield stress is decreased by alloying. At low temperatures there is a minimum in the yield stress (at about 2 at. pct) as a function of concentration. Three-stage hardening was not observed in the alloys. Linear hardening rates, where observed, were characteristic of stage II in pure tantalum. At low temperatures and high concentrations, work softening was often prominent at high strains. Electron microscopy revealed that dislocations are mostly of screw orientation, although heavily jogged and cusped, and often occurring in dipole pairs. The alloys become more prone to cleavage with increasing rhenium content, due mostly to an increasing yield stress rather than a change in cleavage strength. Alloying apparently decreases the Peierls stress of bcc metals at low temperatures by facilitating kink nucleation at solule atoms on screw dislocations. Higher solute concentrations further increase the yield stress. Quantitative calculations and comparisons with other bcc alloy systems are made to show that the predominant hardening mechanism is due to the interaction of dislocations with misfitting solute atoms close to their slip planes. The interaction is so localized that the core dilatation of dislocations could be important. CONSIDERABLE interest has arisen in recent years concerning the mechanical properties of unalloyed bcc metal single crystals.'-7 These and similar studies on polycrystalline materials have resulted in a considerable understanding of the macroscopic yielding characteristics8, 9 and the process of work hardening.'' This latter advance is due in a large part to the increased use of transmission electron microscopy in P I RAFFO junior Membar AlMF is Metallyureist Iewis such studies and the general observance of three stages of work hardening in the shear stress-shear strain curves. The properties of substitutional alloy single crystals of bcc metals have not been determined in as much detail as in the pure metals. Insufficient systematic studies have been made on the effect of alloying on the magnitude and temperature dependence of the yield stress or the stress-strain curves. The alloy systems which have been studied to some extent have been Ta-W,11, 12 Ta-Mo," Ta-Nb,12'14 Mo-Re,15 W-Re,16 and alloys of iron with nickel,17 platinum,17 vanadium,18 and aluminum.18 A large body of data exists on Fe-Si alloys, but these have mainly been a result of the experimental convenience of using this material in place of unalloyed iron, rather than a comprehensive study of the mechanical properties of the alloy system per se. The present authors have previously reported additional data on the properties of Ta-Re, Ta-W, and Ta-Mo alloy single crystals.1g Some of the data on Ta-Re alloys will be described later in this paper. Briefly, single crystals of Ta-Re (1.2 to 10.6 pct), Ta-W (6.2 and 10.2 pct), and Ta-Mo (2.9 and 9.0 pct) were grown by the floating zone method in vacuum. Compression tests were performed in the temperature range 77" to 623°K. Slip was found to occur in Ta-Re alloys at 77' and 298°K on the (~ll)[lil] system and slip lines were coarser and straighter than in unalloyed tantalum. No three-stage hardening was observed in any of the alloy systems and the curves were nearly parabolic. At temperatures above 175°K the yield stress* increased monotonically with in- creasing composition while at 77" and 175°K the yield stress initially passed through a minimum after which it began to increase again for concentrations greater than about 2 pct Re. Similar minima were observed in Ta-Mo alloys and to a lesser extent in Ta-W alloys. The minimum was interpreted as being a result of a

Jan 1, 1969

By M. G. Corson

THE iron-silicon alloy series has always been one of the most puzzling among the binary alloys. Examining the well known mechanical properties of the iron-rich alloys only we meet the following situation: The ultimate strength and yield point of alloys worked and annealed under the usual conditions represent nearly a straight line function of the silicon content up to 4.5 per cent. silicon (Fig. 1). Starting at the ultimate strength of 35,000 lb. and at a yield point of 16,000 lb. for pure electrolytic iron, one reaches a maximum strength of 93,000 lb. and a maximum yield point of 74,000 lb. at 4.5 per cent. silicon. This corresponds to an increase in ultimate strength by 13,000 lb. per each per cent. of silicon added and nearly the same rate applies to the yield point. The data mentioned are taken from the investigation by T. D. Yensen,1 and while they do not exactly corroborate the results obtained by earlier investigators, they seem to be the most correct. Plastic properties of the alloys are controlled by a much more complicated relationship. Up to 2.5 per cent. Si, the elongation stays close to 50 per cent. (in 2 in.) and the area reduction amounts to 85 per cent;, a situation that forms the usual feature of all alloys representing strictly solid solutions. The plasticity of the latter is always nearly equal to that of their base metal. Beyond 2.5 per cent. silicon, the situation becomes much more complicated. Yensen observed an enormous drop in elongation and area reduction at about 2.65 per cent. silicon, where the first hardly reaches 10 per cent. and the second is still lower; he found, however, a considerable recovery in plasticity at about 2.8 per cent. Si and up to 4.5 per cent. Si it is represented by 20 per cent. for the elongation and 30 per cent. for area reduction.

Jan 1, 1928

By Edward Keller

Jan 1, 1906

By B. W. Frazier

Jan 1, 1882

By DR. RICHARD RATHBUN

(Washington Meeting, May, 1965.) THE remarks of Dr. Rathbun in his address of welcome render it unnecessary that I dwell either upon the history or aims of the National Museum, and enable me to proceed at once with a brief descriptive outline of the Department for which I am responsible, and this with particular reference to that division devoted to applied geology. The amount of geological material brought together prior to 1876, under the various Congressional acts quoted, was, though valuable, comparatively small. It consisted mainly of the collections made by Professor J. D. Dana and his assistants during the Wilkes Exploring Expedition; by the various geologists accompanying the surveys of the Pacific railroads in 1854-55; the Surveys West of the 100th Meridian under the direction of the Engineering Corps of the Army; the United States geological surveys under direction of Dr. F. V. Hayden ; and the various Land Office surveys. Prior to 1873 there were no paid assistants to care for these collections. They were studied, if studied at all, by " collabrators," so-called, several of whom had offices and even sleeping apartments in the Smithsonian Institution. In the list of these collaborators are found such names as Conrad, Cope, Gabb, Leidy, Lesquereux, Meek, and Newberry. The building now occupied by the National Museum was designed primarily to make room for the great mass of material secured in 1876 at the close of the Centennial Exposition in Philadelphia. As completed in 1880, it afforded opportunity for expansion and incidental organization on much more practical basis than had previously existed. This found expression in the creation of numerous departments with salaried officials to take charge of the various collections. With the appointment of Dr. George W. Hawes to the position of Curator of Geology and Mineralogy, in 1881, and Dr.

Jul 1, 1905

By W. Geo. Waring

THE growing need of better methods for the recovery of zinc and other elements from complex sulfide ores has suggested an inquiry respecting a possible group separation of the elements by the aid of volatilization at more or less elevated temperatures. It 'is evident that if the zinc content of such ores can be completely separated, for instance, as pure oxide, by a volatilization 'method, there should be no difficulty in recovering the other elements by smelting and refining. Zinc burning" as applied to zinkiferous ores has advanced but little in practice since the invention of the wetherill grate-furnace process in 1852, as may be seen by reference to papers on the subject.' In other words the thermochemical reaction employed in effecting the volatilization of the zinc is essentially one of reduction by means of carbon, whether the ores treated contain their zinc in an oxidized form, or as the sulfide. The zinc vapors, liberated from the ores at a temperature above that required for the reduction of ZnO by C (about ,1100° C.) or for the volatilization of ZnS per se, (about' 1300°-1400° C.) are subsequently burned to ZnO or to ZnO + SOz, by contact with' atmospheric ,oxygen in the upper or posterior parts of the furnace chamber, or in a so-called "combustion chamber" after leaving the .furnace proper.

Jan 1, 1925

By Oliver Bowles

AUTOMOTIVE TRANSPORT by highway, which has become indispensable to modern life either in peace or war, involves the use of powerful machines, many of which travel at high speed. To start, accelerate, and stop each motor vehicle demands the use of clutch and brake. Friction is applied intensively to both these mechanisms, and their linings must therefore be of materials that will resist wear and that will not ignite with the heat of friction. Asbestos, that curious fire-resisting: natural fiber that may be woven into unburnable cloth, is eminently suitable for this special' use, and no satisfactory substitute for it has yet been found Because- asbestos is regarded as absolutely essential to all types of motor transport on land, and in addition is indispensable to. many .other kinds of machines and equipment, the situation of the- United State's with respect to supplies of-raw-material-is of special interest: From the standpoint of national self-sufficiency, conditions are far, from satisfactory, for United States mines furnish only three to four percent of the total domestic require-

Jan 1, 1938

By E. J. Eisenach, Edward Matsen

AT the present time the Climax Molybdenum Co. is the largest molybdenum producer in the world and the operator of the largest underground mine in North America. It has grown steadily and rapidly since its beginning in 1917. Only 250,000 lb of MoS2 were produced during the first year from 1917 to 1918 when the company was formed. Operations were suspended shortly thereafter because of the lack of a market and knowledge of the uses of molybdenum. During World War I it was used as a substitute for some rare metals and for minor chemical purposes. After 5 years of intensive research and sales promotion, Climax metallurgists succeeded in finding proper applications for the newly discovered metal and the mine was reopened in 1924. Demand for molybdenum increased gradually and in 1930, 3.5 million lb of MoS2 were produced. In the meantime, research work for additional uses of molybdenum continued until it had established itself as one of the most important alloying elements in producing high quality steels. After the start of World War 11, from January 1942 to October 1953, 43 million tons of molybdenum ore were mined and 484 million lb of MoS2 were produced. Climax mine is located in Colorado, 100 miles southwest of Denver and 12 miles northeast of Leadville on the Continental Divide of the Rocky Mountains. The principal mine workings range from 11,170 to 12,000 ft in elevation. Topographically, it lies in the base of a large cirque that is surrounded by Mt. Bartlett to the north, Clinton Peak and McNamee Peak to the east and Ceresco Ridge to the south. This cirque opens to the west and to the Ten Mile Valley.

Jan 3, 1954

By Mark L. Requa

(San Francisco fleeting, October, 1911.) DURING the past two years California has developed a new and important oil-field : I refer to Midway. This field produced the famous Lake View gusher, which is credited with a total production in excess of 8,000,000 barrels. Fortunately for the oil industry of the State, this well is now a thing of the past, and nothing save a great crater-like opening marks its location. The pipe is entirely worn away and gone ; and it is a matter of serious doubt if there can be anything done that will cause the well to produce again. Fortunately, also, there have been no, other wells in that field or elsewhere throughout the State that in any way compared with the Lake View. Midway is noted for large wells, of from 500 to 2,000 barrels production; but the decline is rapid, and a few months serve to bring the output down to a few hundred barrels. In the oil-territory heretofore blocked out as proved and probable, there have been, during the year, many changes. Some areas which were expected to be fairly productive have apparently failed; others, more strictly "wild-cat," have come in; while in some of the older fields there are properties which are beginning to show evident signs of exhaustion. The total area of proved territory will therefore probably suffer but small increase, when balances are struck off. The increase of new area has come from extensions of the Midway field, the development of a field in Lost Hills and Belridge, and extensions of the Fullerton-Whittier field in southern California. In these later developments, down to date, the fresh area absolutely proved is not much in excess of 3,000 acres. Recent developments in Coalinga indicate the possible extension of that field to the south, but at great depth. Coalinga is still the most northerly field of any consequence in the State. The Kettleman Hills have hitherto brought in nothing, although a

Apr 1, 1912

By O. P. Quist, S. H. Carpenter

The internal friction of single-crystal LiF has been investigated as a function of crystal orientation, while simultaneously applying a static compressive load. Three different crystal orientations were used, these being samples with the (100), (110), and (111) directions along the sample length. Results show the internal friction measured to be similar in appearance but different in magnitude for the (100) and (110) samples. With both orientations, application of a static stress caused an increase in the amplitude-independent damping, which recovered with time. The amplitude-dependent damping was found to first decrease with load up to the yield stress and then increase rapidly. Samples of the (111) orientation were found to have no measurable internal friction even when loaded up to 3.0 kg per sq mm. These results are discussed in terms of current theories of internal friction in ionic crystals. This paper presents the results of an investigation of the dislocation mobility and dislocation motion in high-purity single-crystal LiF at applied stress levels up to the yield stress. Internal friction measurements of the dislocation damping while simultaneously applying a static compressive load was the experimental technique used. LiF crystals much prefer to slip on the (110) set of slip planes. However, with a suitable stress distribution they can be forced to slip on the {100} set of slip planes.' For both sets of slip planes the slip direction is the same, namely (110). The object of this investigation was to try and learn more about the dynamical properties of dislocations on the different slip systems in LiF crystals. EXPERIMENTAL PROCEDURE Dislocation damping was measured, in terms of the log decrement, using a five-component marx2 composite piezoelectric oscillator. The apparatus used allows one to measure the dislocation damping while simultaneously applying a static compressive load on the sample. A schematic of the apparatus used is shown in Fig. 1 and a complete discussion of its construction and operation is given elsewhere.3 All measurements were made at room temperature with a longitudinal resonant frequency of approximately 50 kc per sec. Damping measurements were made using longitudinal vibrations with strain amplitudes from up to 10. Static loads up to 3.0 kg per sq mm were applied to the sample while the damping was being measured. Samples used in this investigation were high-purity single crystals of LiF purchased from the Harshaw Chemical Co. All samples were approximately of an in. square and were hand-ground in length to one-half wavelength to match the resonant frequency of the driver and gage quartz crystals. Samples of three different crystallographic orientations were used, namely, crystals with the (loo), (110), and (111) direction parallel to their length. The magnitude of the damping is a direct measure of the area on the slip planes swept out by dislocations during a complete oscillatory cycle. With a sample of the (100) orientation the maximum applied shear stress, due to longitudinal vibrations, is on the (110) slip planes with zero shear stress on the (100) slip planes. Thus, damping measured from a (100) sample is due entirely to dislocation motion taking place on the (110) set of slip planes. Similarly, for a sample of the (111) orientation there is zero shear stress on the (110) set of slip planes and the damping measured from a sample of this orientation is due entirely to dislocation motion on the (100) set of slip planes. Samples of the (110) orientation will have a component of shear stress on both sets of slip planes and

Jan 1, 1969

By D. Walton

The effect of small solute additions of Cu on the activation energies for creep A1 single crystals were determined over the range from 78° to 850° K. Below 240°K and above 800°K activation energies were unchanged. Between 240°K and 400°K strain aging causes the creep rate to become vanishingly small and the flow stress was independent of the temperature. Between 500° and 50°K the activation energy was increased to 41,000 cal per mole. NUMEROUS investigationsL have shown that solid solution alloying invariably increases the flow stress. A typical example is documented in Fig. 1. Such increases in flow stress can arise from two general effects: Alloying can increase the long-range stress fields through which dislocations must move by causing appropriate clustering; modification of dislocation densities, and so forth. Alloying can also modify the short-range stress fields that determine the activation energies for thermally stimulated migration of dislocations, such as occurs in some solute atom pinning processes, and so forth. Actually both long- and short-range stress-field effects can occur simultaneously. It was the purpose of this investigation to evaluate the effect of alloying on the short-range stress fields by determining the effect of alloying on the activation energies for creep. The resulting observations also shed some light on the effect of long-range stress fields on dislocation processes. EXPERIMENTAL TECHNIQUE Single-crystal bars (6 in. long 3/8 in. wide and l/4 in. thick) of dilute solutions of Cu in A1 were seeded, so as to provide extensive single slip, with the pole of the tensile axis located in the standard stereographic projection as shown in Fig. 2. Each crystal was grown under an argon atmosphere in a graphite mold containing a large reservoir of molten alloy for the purpose of obtaining rather uniform composition of Cu along the length of the bar. The nominal compositions of the alloys which were produced from 99.99 pct Cu and high-purity A1 containing 0.001 pct Fe and 0.001 pct Si, are given in Table I. Strains, measured by linear variable transformers attached by quartz rods to a 3 in. gage section were sensitive to and the stresses were ap- plied by direct loading of the specimen. Temperatures were determined by thermocouples attached to the gage section of the specimens. Below 400°K the apparent activation energies for creep, Q, were determined by the effect of small, rapid changes in temperature of about + 10°K from T1 to T2 on the corresponding creep rates ?1 and ?2 during primary creep according to where R is the gas constant.' Above 400°K, Q was evaluated from Eq. [1] for the secondary creep rate using temperature changes of about ±20K. A typical set of results is shown in Fig. 3. RESULTS AND DISCUSSION The previously obtained effect of temperature on the apparent activation energy for creep of single crystals of high-purity A12 is shown by the broken curve of Fig. 4. The datum points on the same graph illustrate the effect of dilute a solid solution alloying with Cu on the activation energy between 600" and 750°K. Each plotted point is the average of not less than five independent test values between 600° and 750°K and not less than three at other tempera-

Jan 1, 1962

By M. King Hubbert, David G. Willis

A theoretical examination of the fracturing of rocks by means of pressure applied in boreholes leads to the conclusion that, regardless of whether the fracturing fluid be of the penetrating or non-penetrating type, the fractures produced should be approximately perpendicular to the axis of least stress. The general state of stress underground is that in which the three principal stresses are unequal. For tectonically relaxed areas characterized by normal faulting, the least stress should be horizontal; the fractures produced should be vertical with the injection pressure less than that of the overburden. In areas of active tectonic compression, the least stress should be vertical and equal to the pressure of the overburden; the fractures should be horizontal with injection pressures equal to or greater than the pressure of the overburden. Horizontal fractures cannot be produced by hydraulic pressures less than the total pressure of the overburden. These conclusions are compatible with field experience in fracturing and with the results of laboratory experimentation. INTRODUCTION The hydraulic-fracturing technique of well stimulation is one of the major developments in petroleum engineering of the last decade. The technique was introduced to the petroleum industry in a paper by J. B. Clark,' of the Stanolind Oil and Gas Co. in 1948, and since then its use has progressively expanded so that by the end of 1955 more than 100,000 individual treatments had been performed. The technique itself is mechanically related to three other phenomena concerning which ah extensive literature had previously developed. These are: (1) pressure parting in water injection wells in secondary-recovery operations, (2) lost circulation during drilling, and (3) the breakdown of formations during squeeze-cementing operations, all of which appear to involve the formation of open fractures by pressure applied in a wellbore. The most popular interpretation of this mechanism has been that the pressure had parted the formation along a bedding plane and lifted the overburden, notwithstanding the fact that in the great majority of cases where pressures were known they were significantly less than those due to the total weight of the overburden as determined from its density. Prior to 1948, this prevalent opinion had already been queried by Dickey and Andresen,2 in a study of pressure parting; and by Walker,"' who, in studies of squeeze cementing, pointed out that the pressures required were mostly less than those of the overburden, and inferred that the fractures should be vertical. J. B. Clark,' in his paper introducing hydraulic fracturing, and later Howard and Fast," and Scott, Bearden, and Howard," also of Stanolind, postulated that the entire weight of the overburden need not be lifted in producing horizontal fractures, but that it was only necessary to- lift an "effective overburden," requiring a correspondingly lower pressure. Hubbert,7 in discussing the paper by Scott and associates, pointed out that the normal state of stress underground is one of unequal principal stresses; and in tectonically relaxed areas, characterized by normal faults, the least stress should be horizontal. Therefore, in most cases, fracturing should be possible with pressure less than that of the overburden and, moreover, such fractures should be vertical. Harrison, Kieschnick, and McGuire,8 also on the expectation that the least principal stress should be horizontal, argued strongly in favor of vertical fracturing. Scott, Bearden, and Howard6 observed that, when

Jan 1, 1958

By J. T. Cherry

A fundamental goal of the Plowshare Program is to predict crater dimensions when an explosive of known yield is buried at a given depth in a given medium. In this paper a technique is presented that seems to calculate adequately, from first principles, the mound and cavity growth that occur during nuclear and high-explosive cratering events. The technique features a standard, numerical approach to high- intensity stress-wave propagation coupled with a unique model of material behavior in brittle failure. A schematic of stress-wave propagation is presented in Fig. 1. The equation of motion provides a functional relation between the applied stress field and the resulting acceleration of each point in the medium. Accelerations, when allowed to act over a small time increment [A]t, produce new velocities, velocities produce displacements, displacements produce strains, and strains produce a new stress field. Time is incremented by [A]t, and the cycle is repeated. The time increment [A]t is determined by an independent stability condition which requires the increment to be smaller than the time necessary far a compressional wave to travel across the smallest zone. We assume that failure occurs in a brittle material when either the tensile strength or the maximum allowable strain energy of distortion is exceeded. When either of these two conditions is violated, the code uses the cracked equation of state to determine the stress. A preshot testing program is used to determine the consolidated and cracked equations of state. In situ properties to be determined by field logging are density and elastic velocity (compressional and shear ve-

Jan 1, 1967

By M. Gensamer

THE stresses which initiate deformation processes in metals are funda-mentally important in the study of the mechanical properties of metals. A point of inflection in the load-elongation curves obtained for single crystals1 has been rather too readily interpreted as a true yield point, and the critical resolved shearing stress on the plane of slip taken as a material constant. Even early work showed that the stress at this point varies with rate of loading, but it has not been generally appreciated that creep tests under static loads alone are suited for determining the existence or nonexistence of a yield point.2 It has now been shown by Miller that single crystals of zinc3 when loaded statically begin to yield at loads too small to measure; as a result there is no case now known, apart from that cited in the present paper, in which a true critical stress for yielding has been demonstrated for single crystals of metals. The case of iron has especial interest: the existence of an upper and lower yield point and of an elongation at the yield point in ordinary iron and steel marks this substance as unusual, though the effects have been found to a very minor degree in other metals and alloys. ? Most alloys do not show such marked phenomena when appreciable yielding begins, and accordingly modern practice is to speak of the yield strength of such materials, a stress read from the load-elongation curve after elongation has begun, rather than yield point. The special behavior of iron suggests that it is more likely that single crystals of iron should have a true yield point than other metals.

Jan 1, 1938

By Toshihisa Adachi, Shosei Serata, Shunsuke Sakurai

The present state of knowledge of three-dimensional rock properties does not provide an adequate basis for evaluating the safety of under- ground structures in situ. Most of the triaxial studies reported in the past have dealt with crushing strength, but have failed to consider the intergranular behavior and triaxial strain state of rocks. Without this information, the structural competence of rocks cannot be accurately assessed. The absolute three-dimensional testing method (ATT) was conceived for the purpose of analyzing the three-dimensional states of stresses and strains in aggregate rocks under conditions commonly encountered in underground structures. In-situ stress-strain states are not simple, even in the simplest possible form of opening, excavated in a homogeneous and isotropic rock medium. In general, there are four basic stress-strain states which are present in underground openings, regardless of the complexity of their geological conditions. They are the yielded, brittle-fractured, stress-relieved, stress-concentrated states, as illustrated in the schematic diagram, Fig. 1. The ATT machine was designed to create and study all these states in the laboratory. A theory describing the aggregate behavior of rocks under these diversified states is essential to evaluate the safety of underground structures. The Griffith theory is limited to tensile failure of ductile materials and therefore does not apply to behavior of aggregate rocks under compression. The Griffith theory also fails to consider the grain boundary characteristics of aggregates, which is the determining factor of rock behavior. The Mohr-Coulomb theory of failure ignores the importance of the intergranular behavior of rocks. An application of the continuum theory to

Jan 1, 1972

By H. Foster Bain

Steel for any large structure must be imported, the Hanyang works being entirely unable to supply local demand. The United States Steel Products Co. has warehouses and small stocks at Shanghai and at normal times there are heavy importations from Europe. It is difficult to obtain any accurate index of prices, but comparison of customs valuations with Pittsburgh quotations shows angles, bars and plates to have averaged $10 gold per ton higher in China in 1914, while on galvanized and tinned plates the excess was- $38 per ton. The margin since has been greater. Previous to the war little machinery was manufactured in China. There were shipyards at Shanghai and at Hong Kong which built a small number of engines, and small foundry and repair works are found at a number of ports. Their capacity was limited and the difficulties and delays incident to transport in China so numerous that in practice every important mine has a small foundry, boiler works, and machine shop. This must be taken into account in plans for work in the country. While skilled workmen can be found it is to be noted that most of them have been trained

Jan 1, 1921

By N. J. Grant, I. S. Servi, A. Chaudhuri

IN a recent paper by Servi and Grant,' it was illustrated that the slip band spacing and stress based on creep test data were related by the equation: d =1/ where d is the spacing in millimeters and v is the stress in psi, based on a more complete equation proposed by Orowan. It was shown further,' that for a. given grain size, the slip band spacing became larger with decreasing stress (and was independent of temperature), until such time that the slip band spacing becomes greater than about one-half the grain diam- eter. When this occurred, the mechanism of deformation in creep of 2s aluminum at high temperature changed from slip to grain boundary deformation (sliding). Additional metallographic evidence is now available which confirms this in a most interesting fashion.

Jan 1, 1954

By Zden[e]k P. Bažant

Due to their heterogeneity, most rocks fracture with a zone of distributed cracking ahead of the fracture front. This makes linear elastic fracture mechanics inapplicable. The present study describes a mathematical model in which the progressive microcracking is taken into account by strain-softening stress-strain relation. In a simpler version of the model, the triaxial strain-softening stress- strain relation is obtained by direct adjustment of the elements of the compliance matrix. This formulation is rigorous only if the principal stress directions do not rotate during fracture formation within the fracture process zone. As a more sophisticated and generally applicable model, the so-called microplane model which is an analogue of the slip theory of plasticity is outlined. Comparison with fracture data for various rocks are given.

Jan 1, 1984

By G. W. R. Kuzyk, John D. Smith

Tantalum Mining Corporation of Canada Limited has been mining tantalum ore from the Bernic Lake pegmatite dyke since 1968. The shallow nature of the dyke and relatively high strengths of the various rock types led to the choice of a room and pillar mining method. Rock mechanic studies have indicated that the original pillar dimensions of 50 feet x 50 feet are conservative for existing rooms. Therefore, a plan to reduce the size of pillars using rock mechanics instrumentation to monitor the resulting stress on pillar remnants and stope backs was devised. The paper describes the test work done on the rock types within the pegmatite dyke. The use of Irad stress cells and extensometers in monitoring the stress in pillars is described. The actual results of the program to date are presented.

Jan 1, 1983

By Michael M. Maier, Charles B. Brumleve

The Henderson mine uses the panel caving method to extract molybdenum ore from a deep ore body in an igneous intrusive. Research into caving mechanics and its related problems has yielded fundamental relationships concerning the response of a stressed rock mass to the caving method. The relationships studied through a variety of programs include the following: the evaluation of time and distance related stress fields; the monitoring of the deformation of underground openings and the design implications; ground and mining sequence classifications compared to past support requirements; the response of finite rock masses to zones of high stress concentrations; the evaluation of the subsidence induced by caving; and the microseismic monitoring of cave growth. The cumulative objective of this research is to better understand, predict, and control rock mass response.

Jan 1, 1981