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By Walter Kauzmann

All viscous or plastic flow of incompressible matter is the result of shear strain; the changing shape of any body that is being plastically deformed can be completely described in terms of the shear strain occurring at each point in the body.† Furthermore, the relative amounts of shear strain occurring in different parts of a body under stress depend upon the relative rates of shear strain at those different points, so that if the dependence of the shear rate of any material on the temperature, shear stress, previous history, etc., were understood, the principles of plastic deformation would be known, and we could calculate how a body made of a given material, having a given shape, and subject to a specified system of forces, would change its shape with time. It may be said, then, that the problem of plasticity resolves itself into, first, the problem of the rates of pure shear processes, and second, the application of what is known about pure shear to actual cases. It is the purpose of this work to investigate the former problem —i.e., the dependence of shear rates on temperature, stress, etc.—from the standpoint of .recent developments in the field of chemical-rate theory and with particular reference to the phenomena occurring in the creep of metals and in the plastic flow of crystalline solids in general. It is left for the mechanical engineer, and perhaps the expert in hydrodynamics, to deal with the problem of app1ications.l Resolution of Macroscopic Shear into Microscopic Movements; Resemblance to Chemical Reactions Just as any large body is made up of many small units, or atoms, so macro-scopically observable shear is the result of many microscopic unit shear processes; just as the understanding of the behavior of large bodies demands the understanding of the atoms of which it is made, so the understanding of macroscopic shear demands the understanding of these fundamental unit processes. The study of shear from this "atomistic" point of view has made considerable progress. There has been fairly complete understanding of shear processes in gases for a long time, at least for non-turbulent flow, as a chapter on gaseous viscosity in any text on the kinetic theory of gases will prove' In recent years Andrade2 and Eyring3 have presented important theories for the flow of liquids and amorphous solids. Becker14 Orowan,5 Taylor,6 Burgers,7 and Kanter8 have considered the plastic flow of crystalline solids from this

Jan 1, 1941

By Walter Kauzmann

All viscous or plastic flow of incompressible matter is the result of shear strain; the changing shape of any body that is being plastically deformed can be completely described in terms of the shear strain occurring at each point in the body.† Furthermore, the relative amounts of shear strain occurring in different parts of a body under stress depend upon the relative rates of shear strain at those different points, so that if the dependence of the shear rate of any material on the temperature, shear stress, previous history, etc., were understood, the principles of plastic deformation would be known, and we could calculate how a body made of a given material, having a given shape, and subject to a specified system of forces, would change its shape with time. It may be said, then, that the problem of plasticity resolves itself into, first, the problem of the rates of pure shear processes, and second, the application of what is known about pure shear to actual cases. It is the purpose of this work to investigate the former problem —i.e., the dependence of shear rates on temperature, stress, etc.—from the standpoint of .recent developments in the field of chemical-rate theory and with particular reference to the phenomena occurring in the creep of metals and in the plastic flow of crystalline solids in general. It is left for the mechanical engineer, and perhaps the expert in hydrodynamics, to deal with the problem of app1ications.l Resolution of Macroscopic Shear into Microscopic Movements; Resemblance to Chemical Reactions Just as any large body is made up of many small units, or atoms, so macro-scopically observable shear is the result of many microscopic unit shear processes; just as the understanding of the behavior of large bodies demands the understanding of the atoms of which it is made, so the understanding of macroscopic shear demands the understanding of these fundamental unit processes. The study of shear from this "atomistic" point of view has made considerable progress. There has been fairly complete understanding of shear processes in gases for a long time, at least for non-turbulent flow, as a chapter on gaseous viscosity in any text on the kinetic theory of gases will prove' In recent years Andrade2 and Eyring3 have presented important theories for the flow of liquids and amorphous solids. Becker14 Orowan,5 Taylor,6 Burgers,7 and Kanter8 have considered the plastic flow of crystalline solids from this

Jan 1, 1941

By Raymond Wilson

Grinding costs are an important item in cement manufacture, and the cost of power is one of the large items in grinding costs. Even where power is of secondary importance, cost items dependent on mill capacity are influenced by the efficiency with which the mill uses power. Tube mills typify the grinding mills most generally used in cement plants, though other types are in use. Tube mills have been widely criticized as being extremely inefficient, and this feeling regarding them has led to many attempts to design more efficient grinding equipment. Other types may be an improvement over tube mills, but the improvement has certainly not been revolutionatry, at least as applied to clinker grinding. The very fact that there is doubt regarding the relative efficacy of various types of mills is an indication that an adequate basis for an analysis of performance is lacking. The development of methods of analyzing mill performance has been hampered by the lack of a suitable method for measuring the work actually done in pulverizing. There has been no acceptable standard to which mill performance might be compared. As a consequence, it was not known whether the margin of possible improvement in pulverizing operations was large or small. Even direct comparison of different types of mills was seldom possible because most plants had only one type of mill for each type of service. Comparisons between plants were difficult because of differences in the grinding characteristics of various clinkers. Some recent developments complete a chain of circumstances that place the cement industry in a particularly fortunate position for the study of its clinker-pulverizing operations. Modern investigators of grinding phenomena have generally agreed that the best measure of mill performance is the production of new surface. For most materials this measure of performance is largely theoretical and has a rather remote connection with the practical aims of the grinding operation. In clinker grinding, on the other hand, surface area is intimately connected with the properties conferred on the cement by grinding. Morcover, the determination of surface area is rapidly coming into routine use as a tost

Jan 1, 1938

By Raymond Wilson

Grinding costs are an important item in cement manufacture, and the cost of power is one of the large items in grinding costs. Even where power is of secondary importance, cost items dependent on mill capacity are influenced by the efficiency with which the mill uses power. Tube mills typify the grinding mills most generally used in cement plants, though other types are in use. Tube mills have been widely criticized as being extremely inefficient, and this feeling regarding them has led to many attempts to design more efficient grinding equipment. Other types may be an improvement over tube mills, but the improvement has certainly not been revolutionatry, at least as applied to clinker grinding. The very fact that there is doubt regarding the relative efficacy of various types of mills is an indication that an adequate basis for an analysis of performance is lacking. The development of methods of analyzing mill performance has been hampered by the lack of a suitable method for measuring the work actually done in pulverizing. There has been no acceptable standard to which mill performance might be compared. As a consequence, it was not known whether the margin of possible improvement in pulverizing operations was large or small. Even direct comparison of different types of mills was seldom possible because most plants had only one type of mill for each type of service. Comparisons between plants were difficult because of differences in the grinding characteristics of various clinkers. Some recent developments complete a chain of circumstances that place the cement industry in a particularly fortunate position for the study of its clinker-pulverizing operations. Modern investigators of grinding phenomena have generally agreed that the best measure of mill performance is the production of new surface. For most materials this measure of performance is largely theoretical and has a rather remote connection with the practical aims of the grinding operation. In clinker grinding, on the other hand, surface area is intimately connected with the properties conferred on the cement by grinding. Morcover, the determination of surface area is rapidly coming into routine use as a tost

Jan 1, 1938

By W. F. Kieschnick, Eugene Harrison, W. J. McGuire

W. J. McGuire, et al, are to be commended for their undertaking of a mathematical solution of a very difficult problem. Unfortunately, however, a mathematical approach requires the application of several assumptions. These assumptions appear to be unrealistic and lead to answers which do not describe what actually happens when hydraulically fracturing oil and gas wells. Considering laboratory confirmation of breakdown phenomena, the authors appear to have tested their theories only on cement specimens and on samples of Austin limestone, much too small to provide any fracture system. This work resulted in the formation of vertical fractures. If the authors had tried similar experiments on thick walled cylinders made from almost any sandstone cores, they would have found that, using crude oil as the breakdown fluid, horizontal fractures would almost always occur, and at pressures much lower than any calculated. They would also find that by confining the fluid to within the bore (using oil base mud for example) on similar samples, the pressures required to burst the cylinders would be considerably higher and most of the fractures would be vertical. This breakdown pressure behavior has been duplicated in wells in Texas, Oklahoma, Kansas and in Wyoming. Considering field data the phenomena of different breakdown pressures for different breakdown techniques can be further illustrated. Most production and service personnel will agree that a breakdown can be more easily obtained if injection into a formation can be established prior to the occurrence of the breakdown. This is true whether the formation being treated is completed as open hole or as a perforated interval. This is clearly illustrated by a Lakota well in Wyoming, completed open hole at a total depth of 7,358 ft. An attempt to vertically fracture this well failed when a bottom hole pressure of 10,326 psi was insufficient to break down the formation. A non-penetrating type fluid (oil base mud) was in the well at the time the breakdown was tried." The oil base mud was then cleaned out of the well and replaced by a 30" API gravity crude oil. With this oil in the hole the formation breakdown was easily accomplished at a bottom hole pressure of 3,607 psi. This large difference in fracture pressures would be impossible according to the theories presented by McGuire, et al. The authors have used as an example the breakdown pressures experienced when acidizing Permian Basin wells. During acid treatments of limestone and dolomite the "breakdown" (drop-off in pressure) seldom occurs until some injection of acid has been accomplished. In these cases the breakdown is most likely to result from the chemical reaction of acid and rock in already existing vugs and fractures rather than from making a new fracture by hydraulic pressure. If this is true, then results in the Permian basin should not be used to validate the authors' calculations. *** AUTHORS' REPLY to ROSCOE C. CLARK and HENRY F. COFFER The purpose of our laboratory experiments in which thick-walled rock cylinders were hydraulically fractured was to determine the validity of the "thick pipe" formula for brittle materials, and not to predict nor demonstrate directly the orientation of field fractures. Our conclusions concerning field results resulted from calculations involving the "thick pipe" relationship as well as considerations of overburden stresses, rock strengths, and the geometry and dimensions of the field system. Clark suggests that had the models been more porous or contained weak bedding planes, horizontal fracturing would have occurred. This is undoubtedly true provided external stresses similar to those in the earth's crust are nor imposed. However, if we were going to design experiments to represent directly the field case we would impose the proper stresses on the models. It is generally recognized that the vertical compressive stress in the earth's crust arising from the weight of the overburden is approximately 1 psi/ft of depth. Then, as an example, even though a horizontal bedding plane has zero strength, the formation cannot be separated to form a horizontal fracture unless the hydraulic pressure exceeds the stress due to overburden. And in those cases in which the stress resisting vertical fracturing is significantly less than that resisting horizontal fracturing, vertical fractures should result, notwithstanding horizontal plane weaknesses. We agree that breakdown pressure will be less if the fracturing fluid penetrates the formation. In Appendix HI of our paper it is shown that leak-off reduces the pressure necessary to initiate either a horizontal or vertical fracture. It would be difficult to attempt to

Jan 1, 1955

By L. Mair

A STUDY by J. R. Low, Jr.1 on the effect of quench aging on the Charpy-impact specimens of semikilled 1020 steel disclosed that a decrease in cooling rate from 1275°F raised the transition temperature. This was demonstrated in his investigation by controlling the cooling rate of impact specimens to duplicate that of a heavier plate and com- paring the properties with air-cooled specimens and quenched specimens. The transition temperature of the samples that had been cooled at a rate estimated to be similar to that of an air-cooled 3/4 in. plate was approximately 45ºF higher than the quenched samples. The transition temperature of the air-cooled series was between that of the slow-cooled and the quenched series. On the basis of this work, it appeared that the cooling rate of plates after rolling in a hot mill would have a bearing on the brittle fracture of the

Jan 1, 1955

By Richard McCaffery

WHEN we began the study of blast furnace slags we limited our work at first to a study of those slags containing only lime, alumina and silica. On our paper1 on some of the results of this first work, the solubility of sulfur in slags containing no magnesia was reported and the question of sulfur solubility and slag viscosity discussed. There has been, for a long time, a very great difference of opinion among metallurgists as to he effect of magnesia in blast furnace slags, and the literature is full if expressions of the most contrary opinions on the subject. As a result, our next publication' developed the constitution of slags considered as a four-component system, silica-alumina-lime-magnesia, and advanced an explanation of slag structure which accorded with the facts and with scientific theory. The present paper continues our study of the general subject of slags. As blast furnace slags are included in the silica-alumina-lime-magnesia system, which is a particular case of four-component solutions, we have determined that there are 22 components Table 1), which may enter into the silica-alumina-lime-magnesia system and that 10 or 12 of these components may be present in blast furnace slags which are within the ordinary ranges of composition. To cave a very definite conception of the behavior of these components in a slag, we have developed the theory of the cooling of a four-component solution from the liquid state to the solid and the conclusions that we obtained have been made use of in this paper. On account of the importance of the four oxides and 18 compounds which enter into the silica-alumina-lime-magnesia system, some method of calculating the percentages of the various compounds that are present in the slag when the percentages of the oxides are given, seemed very desirable and we develop L method later herein for doing this, and finally we give illustrations of the composition of a wide series of blast furnace slags and show some applications of these composition data.

Jan 1, 1927

W. O. OWEN,* Washington, D. C. (written discussion?). Few people appear to realize that the time to reach the crippled soldier is when he is first hurt. In my own judgment, the best time to reach him is before he is hurt, by showing him what other cripples have themselves clone of their own initiative, without Government-support, rendering themselves self-supporting, able to bear a little bit more than their own weight, so that they may lay aside a little bit for a rainy clay and some for a little fun in

Jan 5, 1918

IT is a pleasure for the translators to record their gratitude to the Seeley W. Mudd Memorial Fund of the American Institute of Mining and Metallurgical Engineers for underwriting the cost of publication of this volume, to the Printing-Office of the Yale University Press for doing an unusually fine printing job, and to the following for granting permission to reproduce the title pages of volumes in their collection: The Bibliothèque Nationale of Paris, for edition A of the Bergbüchlein; the Osler Library of McGill University, Montreal, for editions B and G of the Bergbüchlein and edition D of the Probierbüchlein; Mr. Herbert Hoover, Jr., for editions C and E of the Bergbüchlein and editions E, M, N, and 0 of the Probierbüchlein; the Parsons Collection of the Reference Department of The New York Public Library, for edition D of the Bergbüchlein; the Library of the Bergakademie Freiberg, for edition F of the Bergbüchlein and editions A, H, and L of the Probierbüchlein; the Herzog August-Bibliothek of Wolfenbüttel, for edition C of the Probierbüchlein; the British Museum. Library, London, for edition I of the Probierbüchlein; and the library of the University of California at Berkeley, for edition J of the Probierbüchlein. The cooperation of those who helped with the translation of the Bergbüchlein is acknowledged on p. 64. A. G. S. C. S. S.

Jan 1, 1949

By AIME AIME

FOR the development of a mine, a shaft of small cross-section is usually sunk, of no larger size than is absolutely necessary. After the mine has been developed and put on a production basis it is a common practice to sink a shaft of larger cross-section for hoisting and use the original shaft for the handling of men and material into the mine. While that ar¬rangement is usually expedient, the small size of the supply cages presents a problem in the handling of ma¬terial. Where a cage is, say, 4 by 4 ft., which is not an uncommon size, all lengthy and bulky material must be handled piece by piece several times from the supply department to the underground stations. Thus drill steel and timbers over 4 ft. long will be loaded on cars at the supply department and wheeled to the shaft, where each piece must be unloaded from the cars and stood up in the cage. They are then lowered to the shaft station, unloaded piece by piece and placed in cars, run to the supply station and again unloaded and stored until called for. In such a case handling becomes a major item in the cost of supplies.

Jan 1, 1930

By H. H. Kaveler, W. R. Evans, Jack Tarner

The geological features, development history and engineering detail of the Shuler Field and the results of approximately two years of unitized operation of the Shuler Jones Sand Pool, were discussed in a prior publication.' The purpose of this paper is to present the results of pressure maintenance in the Shuler Jones Sand Pool after nine years of unit operation. GENERAL INFORMATION The Shuler Jones Sand Pool is located in and about Section 18, Township 18 South, Range 17 West, Union County, Ark. The pool was discovered .in September, 1937, unitized in February, 1941, and subjected to gas injection operations in July, 1941. Water was first returned to the reservoir in July, 1944. The reservoir is an anticlinal trap covering about 4,000 acres. The 154,000 acre-ft of sandstone initially consisted of approximately 150,000 acre-ft of productive oil zone and 4,000 acre-ft of gas-cap. The average depth of production is 7,400 ft. Maximum closure of the reservoir is 135 ft and the oil column lies between a gas-oil contact at -7,270 ft and a water-oil contact at -7,370 to -7,380 ft. The field is approximately four miles long. east and .west, and one and one-half miles wide. The sand grains are angular and vary from fine to medium size. The porosity of the sandstone averages 20.2 per cent. The specific permeability averages 400 md. Some zones have as high as 30 per cent porosity and specific permeability of 4,000 md. The reservoir rock is not uniform in character but consists of sandstone zones interspersed with shale. The variation in rock characteristics is evident in the electric log and core analyses presented in the original publication. Asphalt present in the pore space of the sandstone limited the reservoir to the southeast and apparently blocked any encroachment of water from that direction. The initial reservoir pressure at a subsea depth of 7,300 ft was 3,520 psi. The reservoir temperature was 198ºF. Initially, the solution gas volume was 765 cu ft per bbl and the reservoir volume factor was 1.45. The gas solubility and formation-volume-factors of the reservoir liquid are related with reservoir pressures above 300 psi as follows: Solution gas, cu ft per cu ft, S = 0.0334 P + 18.65 Formation volume factor of reservoir oil, FVF = 8.0 x 10 -5 P + 1.168 Gas volume factor, standard cu ft of gas equivalent to one cu ft of gas at reservoir conditions of temperature and pressure, F = .062 P - 4 Pressure (P) measured in psia. The equation for the gas volume factor presented above is based on a direct measurement of a sample of the gas and is a correction of that used in the original paper. The gravity of the oil produced is from 32 to 34" API. CALCULATION OF INITIAL OIL IN PLACE The Jones Sand production history is interesting because it lends itself to analysis by material balance. Production statistics from discovery of the Jones Sand through 1949 and material balance calculations of the initial stock tank oil in place are shown in Table I. The usual procedure in testing the application of material balance calculations is to compute the apparent initial volume of oil in place, using production and pressure information obtained at different time periods. If the apparent oil in place volumes computed increase with successive time periods, water encroachment is indicated and approximations must be mads to correct for its influence. The first requirement in utilizing such calculations is reliable reservoir pressure, accumulated gas, oil and water production, and PVT data. Calculations of apparent oil in place in the Jones Pool, based on field data

Jan 1, 1951

By W. R. Evans, H. H. Kaveler, Jack Tarner

The geological features, development history and engineering detail of the Shuler Field and the results of approximately two years of unitized operation of the Shuler Jones Sand Pool, were discussed in a prior publication.' The purpose of this paper is to present the results of pressure maintenance in the Shuler Jones Sand Pool after nine years of unit operation. GENERAL INFORMATION The Shuler Jones Sand Pool is located in and about Section 18, Township 18 South, Range 17 West, Union County, Ark. The pool was discovered .in September, 1937, unitized in February, 1941, and subjected to gas injection operations in July, 1941. Water was first returned to the reservoir in July, 1944. The reservoir is an anticlinal trap covering about 4,000 acres. The 154,000 acre-ft of sandstone initially consisted of approximately 150,000 acre-ft of productive oil zone and 4,000 acre-ft of gas-cap. The average depth of production is 7,400 ft. Maximum closure of the reservoir is 135 ft and the oil column lies between a gas-oil contact at -7,270 ft and a water-oil contact at -7,370 to -7,380 ft. The field is approximately four miles long. east and .west, and one and one-half miles wide. The sand grains are angular and vary from fine to medium size. The porosity of the sandstone averages 20.2 per cent. The specific permeability averages 400 md. Some zones have as high as 30 per cent porosity and specific permeability of 4,000 md. The reservoir rock is not uniform in character but consists of sandstone zones interspersed with shale. The variation in rock characteristics is evident in the electric log and core analyses presented in the original publication. Asphalt present in the pore space of the sandstone limited the reservoir to the southeast and apparently blocked any encroachment of water from that direction. The initial reservoir pressure at a subsea depth of 7,300 ft was 3,520 psi. The reservoir temperature was 198ºF. Initially, the solution gas volume was 765 cu ft per bbl and the reservoir volume factor was 1.45. The gas solubility and formation-volume-factors of the reservoir liquid are related with reservoir pressures above 300 psi as follows: Solution gas, cu ft per cu ft, S = 0.0334 P + 18.65 Formation volume factor of reservoir oil, FVF = 8.0 x 10 -5 P + 1.168 Gas volume factor, standard cu ft of gas equivalent to one cu ft of gas at reservoir conditions of temperature and pressure, F = .062 P - 4 Pressure (P) measured in psia. The equation for the gas volume factor presented above is based on a direct measurement of a sample of the gas and is a correction of that used in the original paper. The gravity of the oil produced is from 32 to 34" API. CALCULATION OF INITIAL OIL IN PLACE The Jones Sand production history is interesting because it lends itself to analysis by material balance. Production statistics from discovery of the Jones Sand through 1949 and material balance calculations of the initial stock tank oil in place are shown in Table I. The usual procedure in testing the application of material balance calculations is to compute the apparent initial volume of oil in place, using production and pressure information obtained at different time periods. If the apparent oil in place volumes computed increase with successive time periods, water encroachment is indicated and approximations must be mads to correct for its influence. The first requirement in utilizing such calculations is reliable reservoir pressure, accumulated gas, oil and water production, and PVT data. Calculations of apparent oil in place in the Jones Pool, based on field data

Jan 1, 1951

By Robert Mehl

THE purpose of this investigation was to prepare high-purity iron-carbon alloys, to determine as precisely as possible the A3(GOS), the Acm(SE), and the A1(PSK) transformation temperatures in the meta-stable iron-iron carbide system (up to 1.4 per cent C), and to study the influence of carefully controlled and constant rates of heating and cooling (1/8 to 2° C. per minute) upon the transformation temperature and upon the resulting microstructure. Apart from the general metallurgical importance attending the completion of such a task, it will be noted that highly precise transformation temperatures are of interest and importance in the thermodynamic study of this system1. Several determinations of the iron-iron carbide diagram have been made. These suffer generally from the low purity of the alloys used, and from the application of methods of investigation of low sensitivity. Attempts to compare and weight the many data available in an effort to construct as accurate a diagram as possible have, in the main, been unsuccessful. In general, the wide differences in the results of different workers, the lack of complete analytical data, the omission of important details relating to the heat-treatment of the alloys, and the meager description of the methods of investigation applied, render such a process of averaging nearly meaningless. It may be seen from the summaries by Epstein2 and Körber and Oelsen1 that variations as great as 30° C. exist in the reported data on the A3 temperatures in iron-carbon alloys. For-tunately, the A3 temperature in pure iron is now known to be 910° C. ± 1° C.3 The best recent work on iron-carbon alloys is that of Esser4 on hypoeutectoid steels and that of Sato' on both hypoeutectoid and hyper-eutectoid steels.

Jan 1, 1937

By Thomas M. Drown

Remarkable as have been the direct results of Danks's puddler, there are some indirect and incidental results, which are well worthy of study for their intrinsic value and suggestiveness. The success of Danks's machine is due mainly to the nature of the lining and the manner in which it is attached to the walls of the revolving chamber. Herein lies Danks's merit and good fortune. Given such a lining, and the success of the machine, as far as puddling iron is concerned, could easily be predicted. Other important results have, however, been obtained with this machine, which, though clearly explicable, were, nevertheless, unanticipated. These are the increased yield of bar-iron over the pig-iron charged, and the elimination of phosphorus, which, though not absolutely complete, is yet more decided than in the case of hand-puddling. As regards the increased yield, this is merely what we have a right to expect if we consider the puddling process to consist in the oxida tion of the carbon and silicon of the pig by the oxygen of the oxide of iron. That this result is attained, nearly to the extent that the theory requires, in Danks's puddler, and has never been more than partially attained by the most careful experiments in band-puddling, points clearly to the fact that the contact of the molten pig-iron with the oxide of iron is much more intimate and complete in the one instance than in the other. The action of puddling in Danks's machine may be considered to be twofold: first, the removal of the carbon, silicon, and phospho rus of the pig, which is the primary object, and, second, the produc tion of wrought iron direct from the ore, which is entirely an inci dental result. Intelligent metallurgists were not long in recognizing in this latter result a fact of deeper import and greater value than the attainment of a perfect puddling process. A new method

The American Mining Congress, 841 Munsey bldg., Washington, D. C. J. F. Callbreath, Secretary. The American Mining Congress is a trade association rather than a technical society and as such does not issue scientific papers. Aside from the articles appearing in the monthly Mining Congress Journal, and the Proceedings of the Annual Meetings, only two works have been issued. They are: The standard handbook on mining methods, practice and equipment. $3.

Jan 1, 1933

By Edward Saibel

THE various theories that have been advanced to explain or predict the conditions under which a metal fractures may be divided into two categories: First, there are the macroscopic theories generally used in engineering practice. These are empirical in nature and limited in application. For example, the maximum normal stress criterion, which is quite satisfactory for a mild steel in simple tension at atmospheric pressure, no longer suffices when this steel is pulled under hydrostatic pressure.2 In all of these empirical theories, the critical condition characteristic of the material and of the loading conditions must be obtained experimentally. Secondly, there are the theories based on interatomic forces,3,4 or on the energy required to form new surface.5,6 These have all dealt with the theoretical evaluation of the tensile stress necessary to bring about rupture in a purely brittle manner; that is, without plastic flow preceding fracture. All of these attempts have led to values of the tensile strength of crystals or of polycrystalline bodies that are 100 to 1000 times higher than observed values. On this account, it has been thought necessary by some investigators to conceive of a microcrack structure or distribution of flaws throughout the specimen such that the resulting stress concentrations provide the factor necessary to bring about agreement between calculation and experiment. It has been pointed out by several observers7 that this point of view is highly unrealistic, in that the weakening effect of these flaws or microstructures must be very uniform from specimen to specimen, since the fracture stresses found for various specimens of the same material tested under similar conditions are so - nearly constant. Furthermore, since calculations based on atomic forces or atomic energy are for purely brittle fracture, a condition probably never satisfied in tests, agreement is hardly to be expected. Thermodynamic Theory Of Fürth In order to resolve this apparent discrepancy between the theoretical cohesive strengths and the observed fracture strengths, Fürth8 advanced a thermo- dynamic theory of the tensile strength of isotropic bodies based on work of Born9 relating to the melting of crystals. Assuming an isotropic material free from imperfections and flaws, behaving elastically up to the breaking point, and assuming a connection between rupture and the melt- ing phenomenon, Fürth obtains an expression for the rupture stress u, in the form [ ] where Q is the melting energy per unit mass, ? is the density, and µ is Poissons’ ratio. Fürth compares fracture stresses computed from Eq I with the fracture stresses of metals as given in the Landolt-Bernstein Tables (1927) and in the Hand-

Jan 1, 1947

By Paul C. Merritt

Chrysotile asbestos producers in Quebec may soon experience a unique situation-i.e., strong competition from American ore sources for the short fiber market west of the Mississippi River. This com- petition will be forthcoming from Copperopolis and Coalinga, two deposits now being developed on opposite flanks of the San Joaquin Valley in central California. The combined output now planned from both deposits is 100,000 tons annually, equivalent to about 50% of the annual market demand in the western, central and Gulf States, and more than twice the tonnage sold in 1960 by all other American asbestos producers combined. The principal companies involved in these new undertakings are Jefferson Lake Asbestos Corp. (subsidiary of Jefferson Lake Sulphur Co.), Hidden Splendor Mining Co., Coalinga Asbestos Co. (Johns- Manville Corp. in conjunction with Kern County Land Co.), Union Carbide Corp., and Asbestos Corp. Ltd. Jefferson Lake's principal interest is at Copperopolis where the company's new 70,000-ton per yr mill recently went on stream. The company also holds some claims at Coalinga, but this latter area is better known as the site where Hidden Splendor, Coalinga Asbestos Co. and Todd Industries (a local company) have established operating mines and mills capable of turning out 30,000 tons of fiber each year. Coalinga is also the site of exploration by Union Carbide Nuclear and Asbestos Corp. Ltd.

Jan 9, 1962

By D. W. Fuerstenau

The United States is rapidly approaching an acute shortage of minerals. According to some observers, this situation may even be more severe than the energy crisis because the US consumes nearly 30% of the world's mineral production. With the mounting competition for world mineral supplies, we can no longer take for granted that foreign mineral products will be available to the US as abundantly as in the past. In 1973, US consumption of mineral raw materials was $35 billion. Of this, $7 billion consisted of imports. Without a drastic reorientation towards the mining of domestic mineral resources, the 1973 $7 billion deficit might mushroom to $100 billion by the year 2000. Thus, a return to domestic sources of raw materials will become absolutely necessary-and will be bucking the trend of the past 25 years, characterized by capital investment for growth in multinational overseas mining operations.

Jan 11, 1975

By Howard N. Eavenbon

The low-volatile, or smokeless, coal field of southern West Virginia is in Fayette, Raleigh, Wyoming, Mercer, Summers and McDowell counties, in the extreme southern portion of the state, and extends into the adjacent counties of Tazewell and Buchanan in Virginia. McDowell County is the largest producer, with Fayette and Raleigh counties next. The total area of the field (Fig. 1) is approximately 1600 square miles, or 1,024,000 acres. The percentage of volatile matter in the various seams ranges from 15 to 26 per cent, The upper limit of true low-volatile coal is usually considered to be 23 per cent volatile matter; above this point, the coal usually is classed as medium volatile. This limit will be used in this paper. Geological Position of Seams The smokeless seams are among the oldest coal seams in the country, as the Pocahontas group of rocks is the lowest member of the coal-bearing series and rests on top of the Mauch Chunk red shale, in or below which no coal seams of any importance occur. The Pocahontas group, or Lower Pottsville measures, has a thickness of 750 ft. in southern McDowell County, which decreases to about 350 ft. at Prince, on the New River, in Fayette County, 50 miles to the northeast. In this group, at various points, 12 coal beds have been found, of which 4 have been found in workable thickness and are now being mined. The New River group, or Middle Pottsville measures, is just above the Pocahontas group and varies in thickness from 1300 ft. in southern McDowell County to about 700 ft. along New River. At various places, 16 beds of smokeless coal have been identified in this group, of which 5 have been found in workable thickness and are now being mined. A general columnar section of these strata is shown on Fig. 2. The workable seams in these strata, arranged in geological sequence, are as shown on page 77.

Jan 1, 1932

By C. E. Mills

The Verde mining district is in Yavapai County, in north-central Arizona. Jerome, the principal town, has a population of 6000 and the two important mines of the district—the United Verde and the United Verde Extension—lie almost within its limits. Perched high on the southwest side of the Verde valley, at elevations of 4800 and 5500 ft. (1463 and 1676 m.) respectively, both mines have long tunnels from their lower levels through which the ore is hauled to the smelters. Clarkdale, the smelter town for the United Verde mines, lies in the Verde valley 4.1 miles (6.5 km.) distant in an air line from Jerome and at an elevation of 3560 ft. The two towns are connected by the standard-gage railroad of the Verde Tunnel and Smelter R. R., a subsidiary of the United Verde Copper Co. This road is 11 miles long and has a compensated grade of 4 per cent. At Clarkdale it connects with the Verde valley branch of the Santa Fe railroad. Clemenceau, the smelter town for the United Verde Extension mine, lies 3.5 miles (5.8 km.) in a southeasterly direction from Clarkdale, at an elevation of 3420 ft. It is connected to the Verde Valley branch of the Santa Fe railroad at Clarkdale by the Arizona Extension R. R., a subsidiary of the United Verde Extension Mining Co. The portal of the haulage tunnel, at an elevation of 3757.5 ft., is also connected with the smelter town by 4 miles of standard-gage track belonging to the same company. In the vicinity of Jerome, the great southern escarpment of the Arizona plateau forms the northeast side of the Verde valley. The general level of this escarpment, or "rim" as it is called, is about 4000 ft. above the Verde River. A corresponding elevation is reached only by the highest peaks of the Black Hills, which bound the valley to the southwest. Two lava-capped mesas, known as "Mingus" and "Woodchute mountains," form the culmination of the Black Hills. That part of the Old Black Hills mining district which lies between their crests and the Verde River is now known as the Jerome, or Verde, mining district. If the smelter towns are not included, a strip about 7 miles long by 3 miles (11 by 5 km.) wide, embraces practically all of the properties belonging to the Jerome district. T-bis strip lies parallel to and along the side of the Verde valley from First View, 2 miles northwest from Jerome, to the

Jan 1, 1925