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By Frank C. Greene

The wildcatting in northern and northwestern Missouri, which started in 1939, was continued in 1940. Two new gas fields were found and one discovered in 1939 was further extended. The total number of completions was 94, of which 5 were oil wells with about 48 bbl. initial production, 30 were gas wells with an initial open-flow capacity of 37,655,000 cu. ft., and 59 were dry holes. The outstanding discovery was the Polo gas field, T. 55 N., R. 28 and 29 W., in Caldwell County. A sand now believed to be a lens in the Bandera shale at a depth of 400 ft. yielded flows of more than 12,000,-000 cu. ft. In all, I0 wells with 31,490,000 cu. ft. of gas, were drilled. The rock pres-sure is 80 lb. At present no arrangements for an outlet have been made. In Platte County, the Prairie Point gas pool in sec. 7, T. 51 N., R. 33 W., and sec. 12, T. 51 N., R. 34 W., and the Lake-side pool in sees. 5 and 6, T. 50 N., R. 33 W., were further developed, and in the latter both oil and gas have been found, but data are not available for publication at this time. Drilling for gas continued in proven areas in Clay County, and for both oil and gas in proven areas in Jackson and Cass Counties. Table 1 summarizes the results of drilling in Missouri in 1940.

Jan 1, 1941

By J. M. Lovejoy

Tests are described that show that back pressure on flowing wells is a waste rather than a conservation of natural forces. Stop-cocking, however, gives encouraging results. VARIOUS estimates have been made as to the percentage of oil left in a field after the wells have become so small that it is no longer practical to produce them. Engineers have given the matter much study and can substantiate their figures by data taken from fields from the Appalachians to California. The average oil sand has a porosity of about 20 per cent., which gives a capacity per acre-foot of approximately 1500 bbl. The sand thickness in Oklahoma pools averages 20 ft. With 20 per cent. porosity and a 20-ft. sand thickness, the capacity per acre is 30,000 bbl., yet these pools will seldom yield more than 5000 bbl. to the acre. These figures support the theory that at least 50 per cent. of the oil remains in a sand after all known methods to recover it have been used. Certainly we can never recover all the oil, unless in years to come oil becomes so rare and yet so necessary that the price will justify sinking shafts into the abandoned fields and regular mining methods of drifting and stoping. However, with improved methods of production and conservation of the natural agencies of expulsion, we should be able to increase recovery. It is with this in mind that this paper, relating to the effect of back pressure on wells, is presented. Except in the fields where production is caused by hydrostatic pressure, the chief agency for getting, oil out of the sand into the hole is the gas that occurs with the oil. After the pressure has declined, probably gravity also is a factor, but not an important one. With a given amount of oil in a sand and a given amount of gas occurring with the oil, the ratio of gas volume per barrel of oil is the key to the ultimate recovery from that sand. Our efforts should be along lines that will, lower this ratio and make the gas, the agency given us by nature, do its work better and yield more of the oil, of which it is a part.

Jan 1, 1924

By Lachlan Gilchrist

MEASUREMENTS of resistivity by methods involving the use of two current electrodes and two potential electrodes in general collinear with the current electrodes have been made extensively in geophysical investigations. In the method developed by Wenner and made use of by Gish and Rooney, and later in a modified form by Lee, the distance between the current electrodes is divided into three equal parts by the potential electrodes. In one of the methods developed by Schlumberger prospecting methods and by Koenigsberger, one current electrode is placed at considerable distance from the other and potential measurements are made in the immediate neighborhood of one of the current electrodes. The method is described as the single current electrode method, and the effect of the distant current electrode is considered negligible or a correction is made for the effect in the calculation of the resistivity. Usually the correction that is introduced is based on the calculated effect for measurements made in a homogeneous conducting material. The useful application of these methods in prospecting for minerals, of course, is in regions where nonhomogeneous conditions exist. In many of these conditions it is very doubtful whether the effect of the distant current electrode may be neglected, except for measurements in the immediate neighborhood of the "single" current electrode, and corrections based on homogeneity of the medium will necessarily be inadequate. In order to obtain a degree of symmetry that would preclude the necessity for corrections for the distant electrode and that would simplify interpretation, it appeared desirable to use a central current electrode and a set of distant end current electrodes symmetrically placed about the central electrode as shown in Fig. 1 and to provide by means of auxiliary resistances that the currents passing into the earth at the distant end electrodes should be equal. Circumstances did not permit the operation of this plan in complete detail but a degree of symmetry was obtained by using a central current electrode and two distant collinear end current electrodes and by taking measurements along a line passing through

Jan 1, 1931

By I. N. Zavarine

AUSTENITE is often defined as a solid solution of carbon or carbide in a nonmagnetic form of iron. Conversely, magnetic measurements are often used by investigators for the purpose of detecting the degree of austenite decomposition after an iron alloy has been subjected to certain thermal or mechanical treatments. Association of the magnetic state with the gamma-phase decomposition is often extended to the alloys of iron with elements other than carbon. Definition of austenite as a nonmagnetic solid solution cannot be accepted in the light of available information without certain reservations. The relation of magnetic transformations with the gamma-phase decomposition in the complex alloys of iron has never been rigorously proved. The present investigation deals primarily with the magnetic trans-formation that occurs in carbon steels during the quenching process. The work was further limited to a study of magnetic transformation in carbon steels quenched at such rates as are necessary to retain the product of austenite decomposition in a martensitic state.

Jan 1, 1934

By Andrew A. Blair

The increased importance and value of chemical analysis in connection with metallurgical operations is largely, if not entirely, due to the increased accuracy of the analytical methods used for the quantitative determination of the foreign elements always associated with the metal operated upon. This applies especially in the working of iron and steel, and to the determination of the amounts of such elements as phosphorus, carbon, and silicon. The influence of greater or smaller amounts of these elements upon the physical properties of iron and steel will be better understood when the proper experiments shall have been made upon samples whose chemical composition is known with almost absolute certainty. From the present standpoint of analytical chemistry, it is easy to see that at least one reason for the failure of many attempts to solve this problem, is the inaccuracy of the analytical methods used. Even at the present time the frequent want of agreement (over and above the unavoidable error due to manipulation) between chemists working on the same sample, leads one to think that there is still at least a choice in the methods used. It is true that very frequently a faulty method in the hands of a skilful analyst may be made to give corroborative results

By Gunnar Almgren

Hole deviation has great consequences on mining economy, especially for long hole drilling technique. First of all the bore hole datas are concerned but also such factors as development, loss of ore and waste rock dilution are influenced. Hole deviation for sublevel open stoping is illustrated with examples from some mines. The deviations are indicated as mean values but also as standard deviation values, owing to their statistical distribution. The economic influence of the hole deviation is especially studied for steep, small lowgrade orebodies, mined with big hole blasting. Hole deviation can thus influence costs up to US$ 3-4 per ton for operating, development, losses of ore and rock waste dilution. This cost is of the same magnitude as the total operating costs for many sublevel stoping mines. The economic savings in accurate drilling are therefore substantial and are worth all attention.

Jan 1, 1981

By I. R. Kramer

[The final paper in the diffusion symposium was given by I. R. Kramer. The author called attention to the diffusion characteristics of chromium deposited on the surface of steel by treatment with chromium chloride and alloyed with the surface layer of the steel by thermal treatment. As the data cited were previously published in the paper " Chromizing of Steel," by I. R. Kramer and Robert H. Hafner (Metals Technology, October 1942, and in the Transactions, volume 154, 1943, pages 415-420), it is unnecessary to reproduce these data here. The following paragraphs are taken from the author's presentation.— Editor.] Aside from the well-known practical application of the diffusion phenomena to carburizing and calorizing, -diffusion also finds application in adding alloying elements to the surfaces of steel parts. The chromizing of steels is a process by which the surface of a low-alloy steel may be enriched with chromium to form a highly corrosion-resistant case; This chromized case differs from an electroplated coat in that it is a diffused layer integral with the base metal and has all of the properties of a high-chromium steel. Recently a method of chromizing has been developed in Germany by Daeves, Becker and Steinberg in which gaseous chromium chloride and hydrogen are passed over the steel at temperatures of 1650° to 1800°F. The chromium chloride reacts with the iron to give chromium and iron chloride. The chromium atoms are deposited on the surface and diffuse in as the iron atoms diffuse out, forming a layer rich in chromium. The principal role of hydrogen is to remove the carbon from. the surface of the steel. Of the two mechanisms, chemical reaction and diffusion, the one operating at the slower rate will determine the rate of formation of the layer. In this case, diffusion is slower and therefore any factors influencing its rate will affect the process. The rate of diffusion is influenced by the temperature and crystal structure of the parent metal. Depth-concentration studies show that the concentration falls off gradually for a considerable distance and then drops sharply at about 13 per cent chromium, the point coincident with the boundary of the gamma loop. The influence of the composition of the base metal upon diffusion is quite important. The depth of penetration of the chromium decreases as the carbon content increases and, of more importance, the chromized layer becomes brittle and is likely to spa11 if the carbon content is too high. It appears that in order to chromize successfully the carbon must be fixed by strong carbide-forming elements such as chromium or molybdenum, which decrease the diffusion of carbon. If this is not done, the carbon will diffuse from the interior faster than the chromium can diffuse inward, thus forming a carbide barrier. The corrosion resistance of the chromized layer is high, and these steels offer some unique advantages over other corrosion-resisting coating or alloys. While chromizing is not meant to replace stainless steels, it may serve in the saving of alloying elements. The chromizing process uses soft or low alloyed steels that can be easily hot or cold formed and since the chromized layer is soft and firmly adherent, chromized parts can be subjected to cold deformation without spalling or chipping and without loss of corrosion resistance.

Jan 1, 1944

By I. R. Kramer

[The final paper in the diffusion symposium was given by I. R. Kramer. The author called attention to the diffusion characteristics of chromium deposited on the surface of steel by treatment with chromium chloride and alloyed with the surface layer of the steel by thermal treatment. As the data cited were previously published in the paper " Chromizing of Steel," by I. R. Kramer and Robert H. Hafner (Metals Technology, October 1942, and in the Transactions, volume 154, 1943, pages 415-420), it is unnecessary to reproduce these data here. The following paragraphs are taken from the author's presentation.— Editor.] Aside from the well-known practical application of the diffusion phenomena to carburizing and calorizing, -diffusion also finds application in adding alloying elements to the surfaces of steel parts. The chromizing of steels is a process by which the surface of a low-alloy steel may be enriched with chromium to form a highly corrosion-resistant case; This chromized case differs from an electroplated coat in that it is a diffused layer integral with the base metal and has all of the properties of a high-chromium steel. Recently a method of chromizing has been developed in Germany by Daeves, Becker and Steinberg in which gaseous chromium chloride and hydrogen are passed over the steel at temperatures of 1650° to 1800°F. The chromium chloride reacts with the iron to give chromium and iron chloride. The chromium atoms are deposited on the surface and diffuse in as the iron atoms diffuse out, forming a layer rich in chromium. The principal role of hydrogen is to remove the carbon from. the surface of the steel. Of the two mechanisms, chemical reaction and diffusion, the one operating at the slower rate will determine the rate of formation of the layer. In this case, diffusion is slower and therefore any factors influencing its rate will affect the process. The rate of diffusion is influenced by the temperature and crystal structure of the parent metal. Depth-concentration studies show that the concentration falls off gradually for a considerable distance and then drops sharply at about 13 per cent chromium, the point coincident with the boundary of the gamma loop. The influence of the composition of the base metal upon diffusion is quite important. The depth of penetration of the chromium decreases as the carbon content increases and, of more importance, the chromized layer becomes brittle and is likely to spa11 if the carbon content is too high. It appears that in order to chromize successfully the carbon must be fixed by strong carbide-forming elements such as chromium or molybdenum, which decrease the diffusion of carbon. If this is not done, the carbon will diffuse from the interior faster than the chromium can diffuse inward, thus forming a carbide barrier. The corrosion resistance of the chromized layer is high, and these steels offer some unique advantages over other corrosion-resisting coating or alloys. While chromizing is not meant to replace stainless steels, it may serve in the saving of alloying elements. The chromizing process uses soft or low alloyed steels that can be easily hot or cold formed and since the chromized layer is soft and firmly adherent, chromized parts can be subjected to cold deformation without spalling or chipping and without loss of corrosion resistance.

Jan 1, 1944

By Leonard D. Jaffe

IN recent years, the advantages of tempered martensite as a microstructure for steel parts have been well established. For parts that must not fracture brittlely when loaded at high rates, at low temperatures, or under conditions of combined stress, tempered martensite is especially desirable. One of the factors that determine whether a steel part will have a martensitic structure after heat treatment is the hardenability of the steel. Despite the large amount of recent research, there are still many unsettled basic questions concerning hardenability and its relation to chemical composition, and, indeed, considerable disagreement among investigators in the field. Much of the uncertainty that beclouds the existing knowledge of hardenability arises from the fact that hardenability is still a wholly empirical concept, and has not been quantitatively related to the more fundamental knowledge of isothermal decomposition of austenite. Hardenability is, essentially, a measure of the time required for small percentages of austenite to decompose, during continuous cooling, to pearlite, bainite, proeutectoid ferrite, or proeutectoid carbide. In the practical heat-treatment of steel, also, the decomposition of austenite is usually not isothermal but rather during cooling, or, in general, is not at a single constant temperature. Thus, both hardenability and practical heat treatment involve anisothermal decomposition of austenite. In a previous publication1 the author and his collaborators outlined the principles that govern the relations between isothermal and anisothermal decomposition of austenite, and reviewed the experimental information available in 1945. To avoid repetition, familiarity with that article (Paper 1) will be assumed, and attention given primarily to work carried out or published since 1945. The method generally employed was explained in Paper 1: anisothermal transformation is studied through investigation of the effect of holding austenite at one temperature upon its subsequent decomposition at another temperature. Both temperatures are below the stability range of the austenite. This paper is confined to studies in which only a small amount of transformation occurred at the first temperature. This is the only case of importance in practical heat treatment when an essentially martensitic structure is sought. MATERIALS AND PROCEDURE It was necessary to use different steels for the studies involving proeutectoid ferrite and for those involving proeutectoid carbide, because the two constituents have not been found to form in the same steel. Several steels were tried and rejected

Jan 1, 1947

By Paul Queneau

Some years from now, perusal of the unfolding saga of the nickel family will show that the year 1968 was the herald of change-both in the geography of its endeavors and in its technology. No one should doubt any longer that oxide ores of nickel have come of lusty age-their heavyweight stature in the Caribbean area and in the Western Pacific can be shrunk only by immersion in the politics of unhappiness. The sulfide branch of the family has been augmented afar off by substantial ore deposits in western Australia-right across the globe from Sudbury-and in southern Africa, 9000 miles from the nickel hub. The Foreword of the 1961 AIME volume, dealing with the extractive metallurgy of copper and nickel, noted that "the dead hands of nitrogen" had been lifted from oxidation reactions utilizing air and that the industry was on the threshold of under- standing this fact. Here, at least, nonferrous industry had led its ferrous counterpart in the commercial use of tonnage oxygen in liquid phase pyrometallurgy-the reference is to oxygen flash smelting. Today large oxygen-producing plants are blossoming everywhere and the fruits which will follow are many and varied. Among them is Inco's forthcoming use of the top-blown oxygen converter for sulfide melts. The bell tolls for those "pyro- metallurgical dinosaurs" which still stalk smelter aisles the world around. Silicate oxide nickel ores will rejoice in the glow of modern elevated temperature chemical metallurgy in its various manifestations, vindicating the bulldog spirit of that ancient of clans, the hot metal men-including the renovator of Le Nickel's Doniambo Works.

Jan 10, 1968

By L. C. Graton

Civilization did not begin until metals became the material of tools, implements and machines. - RICKARD, Man and Metals. HISTORY is no more an end in itself than is a backsight the sum total of a survey. This Institute may view with satisfaction the remarkable development of the mineral industry since its founding three score and fifteen years ago, its own enlarging service to that industry, and the contribution thus made toward the enhanced welfare, opportunity and mutual understanding now in greater or less degree reaching and benefiting all peoples of the globe. But neither this professional society nor the dynamic mining industry as a whole wishes on this anniversary to direct its gaze chiefly toward the past. The foremost purpose of historical review should be to throw into clear perspective the strong points and the defects in the forward march thus far, primarily as the basis for conceiving and designing a still sounder progress henceonward. At various times since the Institute's founding, the theories of ore deposition have been considered from the historical view point.l-7 For the present occasion it seems fitting to lay prime emphasis on the practice and utilization of geology in its varied relations to the problems of the mining industry. It is hoped that the reader will understand and accept the degree to which the whole is sampled by parts familiar to the present writer, and the disproportionate attention to thought and achievement within the United

Jan 1, 1947

By Helmer Hedstrom

THE purpose of this paper is to direct attention to the importance and the usefulness of phase measurements in electrical prospecting for ore, a subject about which virtually nothing has been published. The paper describes a new field method for ore prospecting, the "Turam" method, which makes use of phase measurements, and which has been used with great success for five years. Of the principal geophysical prospecting methods, the gravimetric and magnetic methods determine the direction and strength of the static fields of force of the earth. By seismic and electrical methods, fields of force are applied to the block of ground under investigation. By these methods a third parameter can be measured, besides the direction and strength of the field; namely, the time of arrival of the applied field at the different observation points. This time of arrival has been practically the only parameter measured in seismic work, while in electrical pros-pecting it has generally not been considered, the measurements having been limited to determination of direction and strength of the applied field.

Jan 1, 1937

Data about production are very meager. In this county from the earliest days until after the Civil War, the amount of coal used locally greatly exceeded that shipped on account of the iron produced; for many years the furnaces used raw coal for melting the ore. In 1846 it was stated that in this county one ton of iron required three tons of iron ore and three tons of local coal used raw.1 In 1864, eleven furnaces in Pennsylvania using 102,230 tons of raw coal produced 44,671 tons of iron, or 2.3 tons raw coal per ton of pig iron .2 This was probably as good a record as was made, as nearly all furnaces changed to coke some years later. Neither of these figures include the coal used for steam and other purposes around an iron plant. The Beaver and Erie Canal was opened in 1845 and the shipments shown from then to 1865, inclusive, are of coal received by the canal at Erie, and do not include any used at local points along the canal. From the completion of the Erie and Pittsburgh Railroad in 1864 the tonnage shipped by canal decreased. rapidly, and, while the canal shipments after 1864 are supposed to be those received at Erie by canal only, they may include some rail tonnages. Tonnages on Erie and Pittsburgh Railroad may, and probably do, include some used locally; those on the Jamestown & Franklin Railroad do not. It is likely that both canal and Erie and Pittsburgh Railroad figures include some coal originating in Lawrence County, and possibly a little from Beaver County. These tonnages are not duplicated in the data for either of the other counties. Not all of the railroad reports can be found now.

Jan 1, 1942

G. H. CLEVENGER, Colorado Springs, Colo.-Mr. Crowe's paper will be of great interest to cyanide operators, as it is a distinct new development in cyanidation. After reading the paper it occurred to me that some of us had done practically the same thing some time ago, but without design and unconsciously. I refer particularly to the operation of some of the earlier types of vacuum filter, used in connection with a dry vacuum pump and a receiver, which is somewhat similar equipment to that employed by Mr. Crowe. However, we did not appreciate the good effects we were getting from such of this solution as was precipitated, and it has remained for Mr. Crowe to bring distinctly to our attention the advantages of removing air from cyanide solutions before precipitation. Full credit is therefore due him for this very clever improvement in the cyanide process.

Jan 11, 1918

By William Ward

ONE often reads of the rich placer gravels in many of the canoe-traveled rivers of South America. The apparent richness of these gold-bearing gravels impresses the traveler, and in fact he may see batea after batea showing enough colors to figure over a dollar per cubic yard. These workings are called "playas" from the Spanish word playa, meaning shore or beach. Many workings have been reported in tropical rivers, but to my knowledge no dredge has made a success in such deposits. Investigation generally shows that the area of richness is limited and especially that the depth of the rich concentration is hardly ever more than a few inches. The Cauca river in Colombia, South America, is noted for its many rich playas.. This river rises near Popayan in the southern part of Colombia, flows north through a narrow valley between parallel mountain ranges and empties into the Magdalena river near Maganque. The airline distance between source and mouth of this river is only about 500 miles. The rainfall is large and the lower Cauca appears to be about the size of the Missouri river in the United States. From its mouth up to Valdivia, in the State of Antioqua, it is navigable. Above Valdivia is a. narrow gorge, above which the river is again navigable for some distance. The part of the Cauca where the playa panning is most noticeable is from Valdivia down to Where the Nechi river enters the Cauca, a distance along the river of about 100 miles. The current in this part is swift, so that the stern-wheel river steamers make the trip with some difficulty. In the course of my work in this section of Colombia I have had the opportunity to make a study of several of these playa workings and will give in detail the conditions observed.

Jan 7, 1914

By Shiou-Chuan Sun

DISCUSSION shiou-chuan sun (author's correction) - Too late for revision, the author realized that the data on stability of froth presented in this paper were not based on the same height of froth column. It is recommended herein that the stability of froth is better calculated by dividing the time elapsed until the froth disappeared by the volume (in cu cm per sq cm) or height of the froth column, and is expressed in sec per cm. The stability data in Tables I, II, and III of this paper were recalculated, in accordance with this recommendation, and the results are shown respectively in the accompanying Tables VII, VIII, and IX. Compared with Tables I, II, and III of the paper, the stability data of Tables VII, VIII, and IX are more reliable in disclosing the persistence of froth of various frothers having different frothabilities. For example, the conclusion given in the paper that the stability of froth is generally proportional to the volume of froth becomes invalid when the stability of froth is expressed in sec per cm, as shown in Tables VII, VIII, and IX. Table VII shows that both the stability and volume of froth increase with the addition of small amounts of n-hexyl alcohol, and that further additions of n-hexyl alcohol decrease the stability but increase the volume of froth. Table VIII indicates that the stability of different types of frothers is governed by their chemical composition and is difficult to predict from their frothability. Table IX shows that the stability of different frothers with similar nonpolar groups tends to increase with a decrease of the hydro- philic property of their polar groups, and consequently with the decrease of their solubilities. This is further substantiated by the fact that the stability of frothers, as listed in Table IX, is generally lowered by the solvent effect of absolute ethyl alcohol. Table IX shows also that the stability of froth tends to increase with the decrease of the volume of froth* provided the frothers used have similar nonpolar groups and dissimilar polar groups.

Jan 1, 1953

By Shiou-Chuan Sun

DISCUSSION shiou-chuan sun (author's correction) - Too late for revision, the author realized that the data on stability of froth presented in this paper were not based on the same height of froth column. It is recommended herein that the stability of froth is better calculated by dividing the time elapsed until the froth disappeared by the volume (in cu cm per sq cm) or height of the froth column, and is expressed in sec per cm. The stability data in Tables I, II, and III of this paper were recalculated, in accordance with this recommendation, and the results are shown respectively in the accompanying Tables VII, VIII, and IX. Compared with Tables I, II, and III of the paper, the stability data of Tables VII, VIII, and IX are more reliable in disclosing the persistence of froth of various frothers having different frothabilities. For example, the conclusion given in the paper that the stability of froth is generally proportional to the volume of froth becomes invalid when the stability of froth is expressed in sec per cm, as shown in Tables VII, VIII, and IX. Table VII shows that both the stability and volume of froth increase with the addition of small amounts of n-hexyl alcohol, and that further additions of n-hexyl alcohol decrease the stability but increase the volume of froth. Table VIII indicates that the stability of different types of frothers is governed by their chemical composition and is difficult to predict from their frothability. Table IX shows that the stability of different frothers with similar nonpolar groups tends to increase with a decrease of the hydro- philic property of their polar groups, and consequently with the decrease of their solubilities. This is further substantiated by the fact that the stability of frothers, as listed in Table IX, is generally lowered by the solvent effect of absolute ethyl alcohol. Table IX shows also that the stability of froth tends to increase with the decrease of the volume of froth* provided the frothers used have similar nonpolar groups and dissimilar polar groups.

Jan 1, 1953

By Guy Crane

I. INTRODUCTION THE geology of the Tintic mining district, fully treated, would occupy an elaborate monograph. This less comprehensive paper is devoted primarily to the occurrence and origin of the orebodies of the district, while space is given to those phases of the general geology only which seem necessary to a proper setting of such a discussion. The first geological report on the Tintic district to be issued was that by Tower and Smith, published in 1899, in the form of a paper in Part III of the Nineteenth Annual Report of the U. S. Geological Survey, and also as Folio No. 65, Geologic Atlas of the United States. About four years ago a second investigation was begun by Waldemar Lindgren and G. F. Loughlin, of the U. S. Geological Survey. With the exception of a paper on the oxidized zinc ores of the Tintic district by Mr. Loughlin, the results of their work are still unpublished. The writer's acquaintance with the district began in the fall, of 1913, and has extended over a period of about two years.

Jan 10, 1915

By B. H. Bergstram, C. L. Sollenberger

When glass spheres are crushed by slow compression loading, the outer lune-shaped fragments resulting from the fracture consistently fly outward at high velocity. About 45 pct of the strain energy fed into the sphere-platen system reappears in the form of the kinetic energy possessed by these fragments. These measurements were obtained from high-speed photographs. This kinetic energy can be utilized for addtional comminution if the fragments are allowed to impact against a suitable structure. Comminution theory has advanced considerably in recent years by the study of this unit operation under laboratory conditions. Some of the parameters have been isolated, but the experimental measurements of the pertinent quantities, such as energy, particle size, etc., are still only made prior to and after the conclusion of a fracture sequence. The catastrophic fracture process itself has not been adequately studied from a comminution point of view. It has recently been suggested by Gilvarry that the fragments which result from the free crushing of a single glass sphere by slow compression contain a considerable amount of kinetic energy after fracture. This kinetic energy, if properly directed, possibly can be partially utilized to cause additional fracture. In this paper a hypothesis will be presented which suggests that this kinetic energy is necessarily present and that its dissipation is the process by which a large part of the thermal energy imparted to the crushed product is generated. Evidence supporting the existence of kinetic energy and its utilization for secondary fracture will also be presented. THEORETICAL A previous paper4 has shown that the load-deformation curve of a system composed of an elastic sphere gripped by a pair of parallel platens, can be predicted by a consideration of the theories of Hertz as summarized by Timoshenko.' The deformation A, of one half of the system is given by which states that the deformation is a function of the mutually applied load, P, the radius of the sphere, R; and the respective physical properties of Poisson's ratio, v, and Young's modulus of elasticity, Y. The shape of experimental load-deformation curves conform to this relationship. The energy input to the sphere-platen system, can be predicted from the integral of the load acting through the appropriate distance, dA. Since dA can be evaluated in terms of P from the derivative of Eq. 1, this integral can be integrated between limits of 0 and P. The test sphere, however, is loaded at not one but at two points of contact, i.e., at both ends of a diameter, and hence the total energy input, E, is twice the energy input at each end, or The energy input to the system calculated from this equation corresponds to the energy computed from the measured area under the load-deformation curve. Timoshenko, considering the impact of two perfectly elastic spheres, has shown that the inter-penetration distance A is given by - m f (D (^ * ^t w as modified for the special case where one sphere is of infinite radius, i.e., its surface is a plane; where M is the mass of the finite sphere of radius R, and V is the velocity of approach at the start of an impact and also equals the final velocity of separation for perfectly elastic bodies. Because A is also a function of the load and the elastic properties, as shown in Eq. 1, the velocity, V, can also be calculated in terms of the elastic properties and maximum load, P, or

Jan 1, 1961

By A. Goldberg, T. E. Tietz, J. E. Dorn

INTRODUCTION THE concept that the flow stress for plastic deformation of metals in the work hardening range is a function of the instantaneous values of the strain, strain rate and test temperature was promulgated by Ludwick1 many years ago. This thought has been more or less a guiding principle throughout the immediate period of development and growth of mechanical metallurgy. It has been tacitly assumed or knowingly applied to many investigations on the plastic behavior of metals. Spurred by the theoretical interest and practical importance of the plastic behavior of metals, many investigators have attempted to determine empirical, semi-empirical, and theoretical equations2-18 relating the flow stress with the strain, strain rate, and temperature. Although the applications of such equations have been extensive, the experimental verification of the existence of a mechanical equation of state is weak. Furthermore, some of the available evidence on plastic flow appears to suggest that no simple functional relation between stress, strain-rate, strain and temperature can exist. The mechanical equation of state demands that [a = a(e, E, T)[I]] Where o = true stress = load/instantaneous area e = true strain = In Instantaneous gauge lengths initial gauge length e = true strain rate T = temperature] This formulation implies that [da] is an exact differential. Therefore the flow stress (o) is a function of the instantaneous values of the strain (e) the strain rate (e) and the temperature (T), independent of the previous mechanical or thermal history. Having reached a certain strain, strain rate, and temperature, by any path whatsoever, a definite and fixed value of the flow stress should be obtained. One check on the validity of the mechanical equation of state is easily obtained. Consider the following three tests on the stress-strain curve at constant temperature: [A. Strain at rate [ei] B. Strain at rate i2 C. Strain at rate [Ei] to [ei] and continue test at i2] A graphical representation of possible results of such tests are shown in Fig I. If, for strains greater than [el], test (C) data coincide exactly with the data from test (B), as shown in Fig Ia, a limited verification of the mechanical equation of state is obtained for the range of strain rates from [ii] to [e2]. But if the data from test (C) differ from those of (B) beyond strain [el] where the strain rate is changed from [e,] to [€2i] the mechanical equation of state is not

Jan 1, 1948