Search Documents

By R. W. Hyde, B. S. Old, S. E. Eaton

INTRODUCTION ONE of the most important problems facing the steel industry at the present time is that of maintaining at a minimum the sulphur content of many grades of steel where sulphur is known to have harmful effects on both quality and yield. The present outlook in this struggle to reduce the amount of sulphur in steel is rather gloomy since the sulphur content of the raw materials available in the United States is gradually rising, with little relief in sight. A flow sheet of sulphur in the steel process is shown in Fig I. The values used here were obtained by averaging coke oven and blast furnace data at No. 5 furnace in Cleveland and are considered typical for high top pressure practice. The sulphur evolved in the blast furnace top gas was obtained by difference and since the amount is relatively small, little significance should be attached to this particular value. From Fig I it is apparent, however, that coals used in the production of metallurgical coke represent by far the largest single source of sulphur in steelmaking. As an indication of the decrease in quality of these coals as regards sulphur content the weighed average annual sulphur analysis of the coals supplied to two different steel plants, since 1925, is plotted in Fig 2.1 The sharp rise since 1940 is strikingly apparent. Another indication of this trend is found in estimates of coking coal reserves. Thus in the case of Pittsburgh seam coals available in Allegheny, Fayette, Greene, Washington, and Westmoreland Counties in Pa. as of Jan. 1937 only 25 pct of the coal reserves would contain less than 1.50 pct sulphur after washing.2,3 Many of these lower sulphur reserves have been seriously depleted in recent years because of accelerated war demands. Still another demonstration of the increasing sulphur content of coals on a country-wide basis is found in a report by the Bureau of Mines4 which shows a steady increase in the sulphur content of coke made in the United States, It should be noted that this increase continues in spite of the wider use of coal washing in recent years. Sulphur occurs in coal in three forms, pyritic (FeS2), organic sulphur, and a small amount of sulphate sulphur (CaSO4), The sulphur is subsequently found in the coke in combination with carbonaceous material of unknown composition and as calcium and iron sulphides: In considering the general problem of sulphur elimination, the Republic Steel Corp. was interested in determining which, if either, of the two major forms of sulphur in coal contributes the greater portion of sulphur to the coke, Since the ratio of pyritic to organic sulphur varies widely in different coals, it was thought that if it could be shown definitely that the major part of the sulphur occurring in coke originates from one of the two major forms of sulphur in the coal, it would then be possible to select with confidence coal which, although high in total sulphur, would yield coke of fairly low sulphur content, Using the new

Jan 1, 1948

By S. P. Burke

OUTBURSTS in coal mines have contributed greatly to the hazard of mining operations in localities in which they occur. They have been responsible for many casualties and fatalities and much property damage. An excellent review and symposium on the subject appeared recently1. From a study of the papers included in this symposium, and other litera-ture on this subject2, the following conclusions or statements seem justified: 1. Outbursts are more likely to occur in deep mines; that is, where the coal seam being mined has considerable overburden. 2. Outbursts usually occur when hard, dense, nonfractured coal is being mined. It is believed that in most cases a fault or a pocket of friable or soft or pulverized coal existed some distance behind the dense coal at the time of the outburst. 3. The outburst involves a rending or pushing of the solid material of the coal face, the roof, or the floor outwards and often is accompanied by the discharge of large quantities of very fine coal. 4. Drill holes or borings into the coal ahead of the workings have failed to yield information either from evidence of increased gas pressure or increased gas flow that makes possible the prediction of outbursts. 5. Mines in which outbursts occur are usually considered "nongassy," or only very slightly "gassy"; yet large volumes of gas may be produced at the time of the outburst. Despite the varied conditions and varied locations in which outbursts have occurred, the foregoing general statements appear to be applicable in whole or in part to all the recorded cases. These observations there-fore should be significant and any explanation of the mechanism of the phenomena should be consistent with them. The following suggestion seems to be in accord with this requirement, and is offered in the hope that it may assist in the further elucidation of this phenomenon.

Jan 1, 1935

By Thomas V. Falkie, Robert Stefanko

Much has been said and written recently about the manpower problem in the mining industry. The coal segment of the industry has been scrambling to staff and man its companies and operations in order to accommodate the current boom, and there are some interesting side- lights and developments which deserve further attention from coal mining people. This column will deal with the manpower problem in general and the plight of the professional-the mining engineer-in particular. At this point in the game, it is desirable and perhaps necessary to ask ourselves if there really is a manpower problem and, if so, how serious it is. Suprisingly, there are varying and conflicting answers to this question. If we are talking about warm bodies, then in most mining areas there is no problem. If, however, we are talking about skilled or trained people-at all levels-there are apparently serious shortages, especially in the coal industry and in the U. S. Bureau of Mines. To define quantitatively the present and future need for mining professionals is a formidable task, to say the least. Without pretending that these figures are anything but an educated guess, we feel there is an immediate need for about 1000 mining engineers right now and a continuing need for about 300 mining school graduates per year (double last year's number) for the next ten years in order to take up the slack, provide for attrition and maintain a normal growth rate. Mining companies, large and small, are just now beginning to realize that the industry is undergoing a revolution, It is no longer possible to design, build and operate coal mines by the "seat of the pants." Production demands, the new health and safety law and the inevitable new legislation on surface mining will require more engineering, more planning and new technology. There are mine operators who need mining engineers and don't even know that they need them. This could mean rough going for the small operator. It surely means that there will be a trend toward increasing the ratio of technical to nontechnical employees and the ratio of technical employees to dollars of capital towards levels comparable with other highly mechanized industries.

Jan 1, 1971

By W. Bonfield

The temperature dependence of the microscopic yield stress (the stress to produce a plastic strain of 2 x 10-6 in. per in.) and the stress-plastic strain curve of polycrystalline Cu 1.9 wt pct Be have been measured for the solution treated condition, an intermediate condition containing G.P. zones and ?' precipitate and the overaged ? precipitate condition, in the range from -58° to 200° C. A transition in micro -yield behavior and a large temperature dependence were noted for the intermediate condition, which are interpreted in terms of the interaction of glide dislocations with two differently sized zones. In comparison the microscopic yield stresses of the solution treated and overaged conditions were less sensitive to temperature variations and are satisfied by the Mott-Nabarro and dislocation bowing theories, respectively. A determination of the temperature dependence of the yield stress of a precipitation hardening alloy has provided a powerful tool for evaluation of the operative deformation mechanism. There is a marked contrast between the effect of temperature on the yield behavior of a metal containing coherent zones or intermediate precipitates, which can be "cut through" by mobile dislocations, and a metal containing a dispersion of noncoherent particles, through which dislocation "bowing out" is the dominant role of deformation.' These studies have in general been confined to single crystals, as it was considered that similar experiments on polycrystalline material did not produce good data because of the lack of sensitivity with which the yield stress could be determined. However, this objection has been removed by the introduction of mi-crostrain techniques, with which the yield stress in polycrystalline materials can be measured to a strain sensitivity of 10-6. Such measurements have not only shown that the deformation of polycrystalline precipitation hardening alloys can be examined with the same detail as single crystals, but also that some unexpected results are obtained.' In this paper the results obtained from a study of the temperature dependence of the microscopic yield stress (the stress to produce a plastic strain of 2 x 10-6 in. per in.) and the stress-plastic strain curve of a polycrystalline Cu 1.9 wt pct Be precipitation hardening alloy (Berylco 25) are discussed. The temperature dependence of the alloy was measured for three different conditions: 1) The solution treated condition (a supersaturated solid solution of a containing ~12 at. pct Be3) which is obtained by water quenching the alloy from 800° C. 2) The condition of y' intermediate precipitate, to- gether with some G.P. zones,' which is produced after an aging treatment of 2 hr at 315°C from the solution treated condition. (The alloy was cold rolled to 40 pct reduction prior to aging to minimize grain boundary precipitation effects.)4 3) The condition with equilibrium ? precipitate structure2 which is developed after an aging treatment of 24 hr at 425° C. EXPERIMENTAL PROCEDURE Tensile specimens of gage length 1 in. and with rectangular cross section of 0.18 by 0.06 in. were prepared from the solution treated, cold rolled alloy and were either resolution treated for 1 hr at 800°C, followed by water quenching, or aged for 2 hr at 315°C and 24 hr at 425° C to produce the desired precipitate structures. The microstrain characteristics of the aged specimens were determined at temperatures from —58" to 200° C and those of the solution treated specimens from -58° to 30° C. Each temperature was controlled to ± 0.2°C, which was a level of stability sufficient to eliminate thermal expansion effects from the measurements (~1.2°C temperature increase produced an extension of 2 x 10-6 in.). The microplastic behavior of the specimens in the temperature range below 82" C was measured with a standard Tuckerman strain gage,5 while at temperatures above 82°C a modified Tuckerman gage with a reduced strain sensitivity (4 x10-6 in. per- in.) was used. A load-unload technique was used to establish values of the microscopic yield stress. The specimen was strained at a constant cross head speed of 2 x 10-2 in. per min to a given stress level, at which the total strain was measured. Then the specimen was immediately unloaded at the same rate and any residual plastic strain determined. This procedure was repeated for an increasing series of stress levels until the microscopic yield stress was established by a direct measure of the stress to produce a residual plastic strain of 2 x 10-6 in. per in. (It should be noted that, as reversible dislocation motion occurs at stresses less than the microscopic yield stress,2 the plastic strain rate at this level was not constant.) In an ideal test, the microscopic yield stress would be determined from a continuous stress-strain measurement, rather than from a load-unload sequence, in order to eliminate mechanical recovery effects.6 However, it was found experimentally that mechanical recovery was negligible in Cu 1.9 wt pct Be at small plastic strains for all the temperatures investigated, as the microscopic yield stress was independent of the number of load-unload cycles employed (i.e., the values measured for specimens subjected to different numbers of cycles was within the experimental scatter determined for specimens tested in an identical manner). Therefore, it is reasonable to consider the microscopic yield stress determined in the load-unload

Jan 1, 1969

By E. G. Williams

Manganese-ore has been found upon the Isthmus of Panama throughout' a region of nearly three hundred square miles, over the greater part of which, however, it is known only in small bodies without commercial value. Only six mines, controlled by two companies, have actually shipped ore, although a large area has been taken up in miningelaims. The ore-bearing region extends along the coast of the Carib. bean Sea, beginning on the west near Puerto Bello and extending easterly about 35 miles toward Point San Blas. Ore has been discovered in the interior, at a maximum distance of about 10 m. from the coast. Fig. 1 is a map of a portion of the Isthmus

Jan 1, 1903

By R. V. Norris

THE wage rates and working conditions in the anthracite. region of Pennsylvania have been governed for nearly 20 years by the award of the Anthracite Coal Strike Commission, appointed Oct. 16, 1902, by President Roosevelt. The report of this com-mission, made in March, 1903, was accepted and, with eight modifications made at various dates, has had .almost the force of law, and has kept this great indus-trial region free from strikes for almost a generation. In 1920, President Wilson appointed an Anthracite Coal Commission, and its report, accepted Aug. 30, 1920, governed wage conditions to April 1, 1922. Actually, the agreements have been for terms of two to four years, and lately, in 1916 and 1920, the employ-ees have continued at work pending the negotiation of new agreements which were made retroactive, and which have all been modifications of the original 1903 award. With the expiration, April 1, 1922, of the 1920 award approaching, Mr. Lewis, president, of the United Mine Workers of America, addressed a letter, on Feb. 20, to the operators, suggesting a meeting on March 15; this date was accepted by the latter, with the notation that the time was short. At the meeting, the Mine Workers presented 19 demands, and advised that if a satisfactory agreement was not reached by April 1.a suspension of mining would occur, contrary to the practice since 1916 of continuing work with a retro-active adjustment.

Jan 6, 1922

By John Hall

THE Fremont test for measuring the energy consumed in breaking a notched bar of steel is not so well known in this country as it deserves to be. The test specimen used in this test is about 3/8 by 1/4 by about 1 1/4 in., notched with a hack saw on the lower side to cause the piece to break at a fixed point. A weight of 10 kg. falling 4 m., and provided with a knife or chisel which strikes the specimen, breaks the test piece by impact. The residual force in the falling weight after it has broken the specimen is recorded by a suitable device, and the difference between the total energy and the residual energy of the weight (in kilogrammeters) is the force consumed in breaking the specimen. An experience of several years with the Fremont testing machine has shown its great value in readily detecting brittleness not revealed by tensile testing or slow bending testing. I this paper it is proposed to discuss (1) the supersensitiveness of the test as applied to cast steel and (2) its value in revealing the effect of heat treatment under certain conditions. .

Jan 7, 1913

By W. D. Felix, R. D. Smith, J. A. Campbell

The mechanism most consistent with available information on atmospheric trace element emissions involves the volatilization of a significant fraction of many trace elements during coal combustion, with subsequent condensation on fly ash as the combustion gases cool. The larger surface-td-volume ratio of the smaller particles leads to an enrichment of the volatile trace elements. From an environmental viewpoint, the submicron size particles are of greatest concern. These particles show the highest concentrations of trace elements, are least efficiently collected by pollution control devices, have high atmospheric mobilities, and are deposited preferentially in the pulmonary and bronchial regions of the respiratory system. The mechanisms for trace element enrichment and formation of submicron particles will be described.

Jan 1, 1981

Paper withdrawn from publication September 8,1977, after book was printed. Pages 258.272 are therefore omitted.

Jan 1, 1977

By J. C. Irvine

Meramec Mining Co. has put into operation a crushing and conveying system on its newly established 2475-ft level, 200 ft below the lowest production. To develop this level without interrupting hoisting or mine haulage, a 15.8% decline was driven from the 2275-ft level. A 5-cu-yd LHD diesel loader and a diesel-powered drilling jumbo were put into operation midway down the decline, and were used to develop the remainder of the decline and the entire level. Development of the ore pass system to the crusher required the construction of Swedish-type dumps on the main haulage-ways of all production levels with a minimum disruption of ore haulage. Concrete was handled by both rail-mounted and rubber-tired vehicles. The system features four Swedish-type dumps with control chutes at the lower three dumps, a 42-in. gyratory crusher with attendant feeders, and an 1800-ft long roof suspended conveyor feeding two 5000-ton ore bins. The crushed ore from these bins is conveyed to the lower of the mine's two original loading stations for hoisting. The retention of the original dumping and ore pass system as an alternate route has given mine production a unique flexibility. Operation for 22 months has permitted evaluation of the system from a long-term standpoint.

Jan 1, 1973

By J. H. Henderson, H. J. Ledbetter, N. B. Gove, J. D. Griffith

INTRODUCTION The results of a series of laboratory flood tests using liquid Iso-butane to displace refined oils from test cores are pre- ented and interpreted on an empirical bask. The study Revealed the similarity of the miscible liquid displacement to that of the immiscible-fluid displacement mechanism. The efficiency of the iso-butane flood decreased markedly as the oil Viscosity increased. but the effect of injection rate on the effectiveness of the primary production stage was negligible over the range investigated. The presence of free-gas saturation prior. to iso-butane breakthrough increased the volume of iso- Butane required to recover a given percentage of the oil present. Injection of liquid i.e.-butane prior to water follicle sculpted in a marked improvement in oil recovery by the water flood. INTRODUCTION The production of petroleum is often enhanced by the injec-1i1)n of extraneous fluids into the reservoir. It has been suggeited that the injection or cycling of a wet gas or a liquefied petroleum gas would he instrumental in increasing the effic.ienr!; of oil recover! to a greater degree than the commonly injected fluids. dry pas and water. Although instances of injection of light liquid hydrocarbons are not unknown, a systrmatic recording of the result is unavailable and superfi- cially, the practice gives the impression of being economicaIIy unsound. For specific types of displacement, analytic: solutions have been advanced which aid in understanding the physical mechanisms involved. However, there is no generalized theoretical concept which permits adequate prediction of displacement efficiency from a knowledge of readily measured reservoir rock and fluid properties. The Buckley-Leverett approach to oil displacement by an immiscible phase is an admirable analysiy of that type of mechanism. Dykstra and Parsons have introduced a useful concept in their evaluation of the role of the mobility ratio and its merit in rationalizing displacement phenomena. Everett, Gooch and Calhoun3 in their report on the effect of viscosity ratio and miscibility have pointed out the lack of a comprehensive theoretical approach and the desirability of investigating the mechanism of miscible-miscible displacement. In lieu of a well-developed theory concerning miscible-111isci1)le displacement and in view of the scarcity of engineering information on actual LPG injection trials, the limited program of laboratory experimentation described below was undertaken. OBJECTIVES The original broad objectives of the program, to study the oil recovery process using LPG as the displacing phase, defined the direction and scope of the laboratory tests. The specific objective. of the experimentation were to evaluate

Jan 1, 1953

By Robert B. Fulton

Staurolite, an iron aluminum silicate mineral, is used industrially as a high value-in-use sand-blasting agent, as a premium grade foundry sand, and as the source of aluminum in portland cement manufacture in areas where the aluminum constituent is not economically available from shale or argillaceous limestone. It is produced by E. I. du Pont de Nemours & Co. as a coproduct in titanium mineral production in Florida where it was first recovered on a commercial scale in June 1952 from the Pleistocene sand deposit known as Trail Ridge. In the Trail Ridge deposit it comprises about one-fifth of the heavy minerals, the principal other heavy mineral constituents being ilmenite, leucoxene, rutile, zircon, kyanite, sillimanite, and tourmaline. Staurolite and the other silicate nonconductive heavy minerals are separated from the conductive titanium minerals on high-tension separators. The silicates are then separated from one another magnetically, the staurolite being relatively magnetic. In the total processing, 200 tons of raw sand yield 7 tons of heavy mineral concentrate from which about one ton of staurolite is recovered. This process yields staurolite concentrates of the characteristics given in Table 1. These concentrates are sold as three products with the size distribution of subrounded particles shown in Table 2. All three grades are used in sand-blasting for cleaning metal, for paint removal, and for cleaning buildings. Staurolite compares favorably with lower unit cost abrasives, such as boiler slags and mineral aggregates, in applications where the abrasive is used only one time and is not recovered. Because it is hard, fine, clean, and dense it can reduce blasting time, with less material reportedly being required [ ]

Jan 1, 1983

Jan 1, 1879

By Kichizo Niwa, Toshio Yokokawa, Mitsuo Shimoji, Yoshihiko Watanabe, Satoshi Kado

A LTHOUGH a systematic research on diffusion in liquid metals has not been carried out, partial studies have been developed by various workers in several systems. A few recent papers among them have shown that this line of approach is quite useful for understanding the structure of the liquid state. Furthermore, it has been found in kinetic

Jan 1, 1958

By J. A. Heskett

NEW ZEALAND is dependent on the outside world for its ferro goods, yet it can boast of at least two well-defined iron-ore deposits; namely, Para Para limonite, 3 Fe203 + 21120 also found as lower hydrated oxides, and Taranaki iron-sand, a combined magnetite and ilmenite, 2FeO + 2Fe203 + FeO + Ti02. The former is of massive variety and the FIG. 1.-VIEW OF WORKS SHOWING IRON-SAND DEPOSITS, ALSO WHARF AND BREAK¬WATER IN THE DISTANCE. latter granular and mixed with various proportions of fine shell and siliceous sand well water-worn. This latter deposit forms the greater portion of the beach sands of the west coast of the North Island of New Zealand. It is so fine that the whole of a sample passed through a sieve of 40 meshes to the inch. The ilmenite cannot be detected by the microscope, as in the titaniferous ores of the Adirondacks, nor can it be magnetically separated, as in the titaniferous ore of Natashkwan, Canada. To all appearances it is a chemical compound of the double oxides of iron and titanium and not a mechanical mixture, as is the ore of the Adirondack deposits.

Jan 8, 1920

By Franklin Moeller

Considering the really short time that has elapsed since hydro-metallurgical processes of extracting copper from ores have been extensively developed, and the large scale on which this method is practised at Ajo, the successful operation of the plant must excite the admiration of every visitor. The application of the mechanical unloader to the purpose for which it is employed at Ajo is but an extension of the use for which it was originally designed, some 20 years ago, for unloading iron-ore vessels at the lower lake ports. At a time when the maximum output of a single machine, with men shoveling the ore into buckets, did not exceed 40 tons per hour, G. H. Hulett invented and constructed a mechanical unloader with a bucket of 10-ton capacity. This machine was of the steam hydrauIic type, and it is still in operation after nearly 20 years of service. Several more machines of the same type were built, but the difficulties of power transmission, and the rapid development of electrical machinery, soon led to the adoption of electrically operated machines, and practically all of the later installations have been thus equipped. This electrically operated unloader has proved so well fitted for the work that the design of the lake boats has been practically revolutionized, with special view to the ease and rapidity of unloading. It is now possible to unload a 12,000-ton vessel with four machines in a little over 2 hr. This has necessitated an increase in the capacity of the machine, and the largest yet built handles an average load of 17 tons, with a possible maximum of 20 to 21 tons. The Ajo excavator is somewhat simpler in design than the iron-ore unloader, in that it is not provided with a larry. In the unloader, the iron ore, picked up by the bucket, is delivered to a larry or transfer car which runs in the lower chord of the bridge; the larry then delivers the ore either into railroad cars, standing on several parallel tracks, or into the stock pile, thereby saving the time that would be required for the bucket to make the trip. At Ajo, the bucket delivers the tailing

Jan 1, 1920

By Ross W. Smith, Nikhil Trivedi

The variation of point of zero charge (PZC) of both simple and complex oxide minerals was studied as a function of aging time in water. In most cases the PZC's of the simple oxides moved toward more basic pH values with aging time. Evidence to date suggests that this phenomenon relates to dissolution of disturbed layers on the mineral's surface accompanied by later readsorption of metal hydroxy species back onto these surfaces. The readsorption takes place after the solution becomes supersaturated with respect to some crystalline phase. The variation of PZC's of complex oxides as a function of aging time in water is apparently related to several different mechanisms. In a few cases PZC shifted toward more basic values with time. This shift could be attributed to much the same mechanism as for simple oxides. In most cases, however, PZC of complex oxides shifted toward more acid values with aging time, probably because of loss to solution of soluble cations whose oxides possess basic PZC's.

Jan 1, 1975

By E. W. Schilling

THE-separation of hematite by hysteretic repulsion was first brought to the attention of the public in 1922, by W. M. Mordey1. Three-years later another paper2 was published and after another four years a third paper3 appeared in the South African publications. Certain data were lacking in these papers. In order to continue the work intelligently a knowledge of the shapes of the hysteresis curves for certain minerals was very necessary. This information was not available until the present year4. It was known that reduction of certain ores rendered them amenable to this process of separation but definite data in. the form of curves showing exactly the effect of such treatment were lacking. Prob-ably our best source of information on the separation of minerals by the use of alternating-current magnetic fields today is the reports from the U. S. Bureau of Mines 5-7. It is not the purpose of this paper to tell the reader in detail how to make a commercial separator. Experimental models have recently been made7 and the results obtained have been so good that it is the opinion of the authors that the public will soon take an active interest in the subject and its development. The writers have constructed a separator that is considerably different in construction and operation from the two types described by Mr. Davis. This will be described; but the real purpose of this paper is to outline certain experiments and give curves showing data that have a fundamental bearing upon the practical construction of a separator of this type.

Jan 1, 1936

By John Boardman

THE Anaconda company has never indulged in any employee activities at Butte which might be termed paternalistic, but it has exerted a vast amount of effort in care of its employees during working hours. The reason for this policy is not lack of interest or that the company does not feel the effect of employees' activities while they are "off the job"; it is that the company and the city of Butte have grown up together and, each has been adequate in its own sphere, the company in providing employment at the highest possible wage and the city in providing housing, sanitation, commercial services, medical services, schools, churches, amusements and entertainments. The one exception to this independence between the company and the community is the Butte Water Co., which is a wholly owned sub-sidiary of the Anaconda Copper Mining Co. Mention of this relationship is made here because the water supply of such a city as Butte is one of the principal factors in determining the health of the people. Very early in the development of the Anaconda company an adequate and dependable water supply for the operations became necessary, therefore the company took over this important community function. So well has this activity worked out that during the whole period of time covered, in which the company has expanded to become practically the sole mine operator and the community has grown from a small mining camp to the status of a modern city, there has been no shortage of water or any outbreak of water-borne, epidemic disease.

Jan 1, 1938

By J. J. Gilvarry

Recently, Gilvarry1,2 has given a rigorous derivation of the proper distribution function for fragment size in single fracture, based on a closely defined physical model and deduced strictly by the laws of probability. The physical point of departure is Griffith's theory of brittle strength, identifying sub-microscopic flaws as the cause of the low strength of a solid in comparison with values implied by cohesive energies. Gilvarry and Bergstrom,4-7 and Gilvarry8 have compared the predictions of the theory with experiment, and have found excellent agreement, in general. The purpose of this communication is to sketch the extension of the theory to the case of comminution, and to indicate the applications to some examples in nature. The present treatment represents an amplification of a brief discussion appearing elsewhere. 9 Although the basic ideas of the Griffith theory are perfectly general for rupture of brittle solids, it was originally formulated with very brittle materials such as glass in mind. Moreover, Griffith's original experimental work was carried out on glass specimens. Recently, however, the theory has been extended by race" to apply directly to rocks. This extension makes the theory immediately applicable to the materials generally of interest from the standpoint of comminution. GENERAL CASE To obtain the distribution function for fragment size in single fracture, three assumptions are made, that: 1) Fracture proceeds by activation of preex-istent Griffith flaws in the volume, faces, and edges of a fragment; 2) the distributions of flaws of these three types are independent of each other; and 3) activated flaws of a particular type are distributed at random, individually and collectively, in the sense of Fry.11 The last assumption implies that each distribution is separately of Poisson type.

Jan 1, 1964