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By N. B. Aughenbaugh, W. C. Patrick

The availability of a thorough, simple-to-use roof fall classification system is desirable for several reasons. First, such a system would expedite the reporting of falls for the purposes of estimating material removal costs, analyzing damage levels, and complying with federal regulations to report falls in certain areas of the mine. Second, the classification system would allow the mining engineer to record falls routinely with little time and effort expended. This would encourage him to make observations concerning what type of roof support would work best in a given situation. Third, and probably most important, an

Jan 3, 1979

By R. Bainbridge

THE Consolidated Mining and Smelting CO. of Canada Ltd. has operated a lead smelter at Trail, B. C., for many years. In order to take advantage of metallurgical advances, as well as to improve materials handling methods, this company, commonly known as "Cominco," commenced planning a program of smelter revision and modernization some years ago. The first stage of this program involved the design and construction of a new blast furnace gas cleaning system. The selection of equipment, the design of facilities, and preliminary operating details of this system will be dealt with in this paper. The essential problem was to clean and collect 100 tons of dust daily from 153,000 cfm* (12,225 lb per min) of lead blast furnace gas which varied in temperature from 350º to 1100°F. Because it was desired to collect the dust dry, either a Cottrell or a baghouse cleaning plant was to be selected. Comin-co's many years of experience with both systems provided a background for choosing the most satisfactory installation. All information pertinent to the two methods of dust recovery was carefully investigated, and it was decided to replace the existing equipment with a baghouse. Very briefly, the reasons for this decision were as follows: 1—A baghouse installation would be practical because the SO2 content of the gas was low and corrosion would not be a problem if the baghouse operating temperatures were held sufficiently above the dew point. 2—Variations in the physical characteristics of fume and dust, which are inherent in this blast furnace operation, should not substantially affect the operating efficiency of a baghouse. 3—For the same capital cost, metal losses (stack and water losses) would be appreciably less in a baghouse. 4—A baghouse would be easier to operate, and would not require the use of highly skilled labor. 5—Operating and maintenance costs of a bag-house would be lower. 6—The only available space for reconstruction was relatively small, and not suited to a Cottrell installation. Once the baghouse system was decided upon, detailed design of the installation was begun. Baghouse Design Gas Cooling: Before the required capacity of the baghouse could be determined, the method of cooling the gas to the temperature necessary for bag-house operation had to be chosen. The problem confronting the design engineers was how best to cool 153,000 cfm of gas from a temperature ranging from 350°F to brief peaks of 1100°F, down to 210°F, the maximum safe baghouse inlet temperature. A survey of existing blast furnace gas temperatures in the outlet flue showed that the normal range was as given in Table I. The obvious choices of cooling method were: 1— cool completely by the addition of tempering air; 2—utilize a heat exchanger; 3—cool by radiation; and 4—cool with water spray in conjunction with the admission of tempering air. The advantages and disadvantages of the various cooling methods were: Air Addition: To cool completely by the admission of tempering air involved tremendous volumes, Fig. 1. For example, to cool 1 lb of blast furnace gas at 450°F requires 1.84 lb of air at 80°F or 1.60 lb at 60°F. As it is necessary to design for peak conditions, it can readily be seen that volumes of tempering air in the order of 1,500,000 cfm would have to be handled. Using the normal design figure of 2.5 cu ft per sq ft of bag area, a baghouse installation comprising some 600,000 sq ft of filter cloth would be necessary. Such design requirements would be prohibitive, not only from a standpoint of capital expenditure, but also because of space limitations. Heat Exchanger: The utilization of a heat exchanger was given serious consideration. A horizontal tube unit using air as the medium to cool the required volume of blast furnace gas from 400" to 250°F was investigated. Cooling above 400°F would be done by water spray, and below 250°F by admission of tempering air. The estimated capital cost of such a unit was found to be prohibitive. From an operating standpoint, there was considerable doubt as to whether the soot blowing equipment provided would effectively keep the dust from building up on the tube surface. The performance of heat exchangers operating on dusty gas in other company operations had not been too favorable. Radiation Cooling: Although somewhat cumbersome, gas cooling by radiation from 'trombone' tubes or other similar equipment (cyclones) is employed in many metallurgical operations. Such an installation was also considered. However, calculations showed that an installation much larger than the space available would be required to handle the gas volume involved. For example, to cool 153,000 cfm of blast furnace gas from, say, 600' to 250°F (i.e., remove in the order of 58,500,000 Btu per hr with heat transfer rates varying from 1.1 Btu per sq ft per hr per OF for the higher temperature ranges to 0.88 Btu per sq ft per hr per OF for the lower ranges) would need a cooling area of some 175,000 sq ft.

Jan 1, 1953

By C. Gregory Knight

The Pennsylvania Coal Model is a research activity of the College of Earth and Mineral Sciences of the Pennsylvania State University, in association with the Economic Development Council of Northeastern Pennsylvania, and the Southwestern Pennsylvania Regional Planning Commission. In this project, sponsored by the Appalachian Regional Commission and the Pennsylvania Science and Engineering Foundation, data banks and models have been developed to simulate potential coal production and utilization systems in Pennsylvania. Building from a coal system data base for 1974 and mining simulation models, computer optimization models predict potential coal production and transportation for alternative future demand scenarios. The model allows derivation of costs of various coal supply systems under specific economic, transportation, and environmental constraints. The model also provides insight into such impacts of coal production as employment, land use, and environmental quality.

Jan 1, 1977

By Ernest R. Darby

If the correct balance between fuel and air is maintained in an open-flame furnace,' little chemical action may be expected between the products of combustion and the metal being melted. Physical' changes in the metal are the object of the melting operation, and indirectly, under certain conditions, may be the cause of subsequent chemical actions. If sufficient heat has been introduced into the metal to bring about the change from the solid phase to the liquid phase, and still further from the liquid to the vapor phase, the metal vapor in all probability will be carried from the furnace by the exhaust and rapidly combined with the oxygen of the outside air. The charge being melted in the furnace may contain elements which are chemically inactive at normal temperatures but which will form compounds at the elevated temperatures of the metal bath, or even at a lower degree. Such indirect chemical actions are very confusing and often lead to incorrect conclusions regarding furnace atmospheres. In the open-flame furnaces used in the melting of bronze, the furnace atmosphere is spoken of as being either neutral, oxidizing or reducing in its effect upon the metal. A neutral atmosphere, as mentioned, is generally considered as the atmosphere of the furnace that will produce melted bronze, neither oxidized nor gassed. It is in effect an atmosphere which is not directly the cause of any chemical action. In such an atmosphere absolutely pure metals may be melted and poured without the absorption of gases or the formation of metallic oxide. The metal has undergone a simple, physical change. An oxidizing atmosphere is one in which the air introduced to the furnace is in excess of that required to complete combustion of the fuel used. The oxygen of the excess air may combine with the metal being melted to form metallic oxide, which may or may not be dissolved by the metal. If an absolutely pure metal is melted in a furnace operating with such an atmosphere, a portion of the metal charged may be converted into metallic oxide, the amount depending upon the duration of the

Jan 1, 1930

The October issues* of the Journals of the three AIME Societies carried a brief resume of the historical development of various technical and professional organizations which in some immediate or remote way affect the individual member of AIME. This resume was presented by the Institute Committee on Inter-Engineering Society Cooperation. Recently, several plans have evolved designed as a first step to provide a so-called "unity organization" for the entire engineering profession. Almost all of the plans involve Engineers' Joint Council, Engineers' Council for Professional Development, and National Society for Professional Engineers in some way or other. Hence our committee is presenting to our membership a resume of the recent activities of the two umbrella organizations and of NSPE. More detailed information on any of these organizations may be obtained from annual reports published by the organizations.

Jan 2, 1961

EDWARD W. PARKER,* Philadelphia, Pa. (written discussion ?).-The two papers on coal-mine costs and pride fixing that Mr. Norris has contributed to the Transactions possess as much general interest and are of as much value to the coal-mining industry as any papers that have been presented in recent years. Until recently one of the troubles with the coal business, and especially the bituminous branch of it, has been that because of the lack of a uniform system of cost accounting (many operators, I regret to say, not having had any system at all), the industry as a whole may be said not to have known where it was at. The system adopted by the Federal Trade Commission may not be absolutely perfect but it has accomplished something in that it has compelled a uniform method of reporting and tabulating costs giving results of these compilations which are comparable. The Institute and the coal-mining industry owe a vote of thanks to, and of confidence in, Mr. Norris and his two associates on the Engineers Committee of the Fuel Administration, Messrs. Garnsey and Allport, for the great work they have done in interpreting the results compiled by the Federal Trade Commission, not to speak of the personal sacrifices made by them in giving their services to the government. Those who have read Mr. Norris' paper will probably join me in wishing he had brought out a little more fully the real meaning of the charts so far as they indicate the difference between the cost of producing a ton of anthracite and the price the operators receive for their product. Mr. Norris could have done this more satisfactorily than anyone else. It seems to me that particular attention should be drawn to the fact that, according to these charts, and the tables accompanying them, not less than 25 per cent. of the total output of anthracite, whether "company" or "individual," during the period covered by Mr. Norris' paper,

Jan 4, 1919

By Dewitt T. Ring

Lack of reliable detailed production figures for earlier years, together with the loose nomenclature in reference to producing horizons and the application of the term "field" without any definite meaning or restriction, has made it impossible to gather statistical data suitable for the Institute's form. In common with all other producing areas in the United States, Ohio has felt severely the economic ills of the entire industry during the past year. With overproduction, not only of crude but also of refined products, going on throughout the country, the price structure as a direct consequence has weakened on Ohio oils. Valuable crude is being sold at a big loss today because producers arc willing to, and do, sell more than the market can absorb. The axe hangs heavy over the heads of Ohio producers, and will until something constructive is done to keep supply in proportion to demand. This not only applies to Ohio but to the entire industry. Production of Pennsylvania grade in Ohio was under 50 per cent proration, which has been in effect since Oct. 1, 1937. Three price cuts since February have lowered the posted price from $1.70 to $1.18, a 30 per cent reduction; other grades were less drastically reduced. Pipeline storage facilities were limited; many producers were faced with the problem of providing their own storage or the risk of ruining their wells. If they wanted to pull and abandon wells, there was no market for junk equipment. Many employees have been cut to half time and in a number of instances their services entirely dispensed with. Summary of Production and Drilling Both oil and gas production in the state during 1938 showed a definite decline over the previous year. (A table showing production by years from 1876 through 1937 was published in Vol. 127 of the Transactions.) The total production of crude oil in the state for 1938 was 3,357,914 bbl., as compared with 3,654,000 bbl. in 1937, a decrease of 7.1 per cent. At

Jan 1, 1939

By Dewitt T. Ring

Lack of reliable detailed production figures for earlier years, together with the loose nomenclature in reference to producing horizons and the application of the term "field" without any definite meaning or restriction, has made it impossible to gather statistical data suitable for the Institute's form. In common with all other producing areas in the United States, Ohio has felt severely the economic ills of the entire industry during the past year. With overproduction, not only of crude but also of refined products, going on throughout the country, the price structure as a direct consequence has weakened on Ohio oils. Valuable crude is being sold at a big loss today because producers arc willing to, and do, sell more than the market can absorb. The axe hangs heavy over the heads of Ohio producers, and will until something constructive is done to keep supply in proportion to demand. This not only applies to Ohio but to the entire industry. Production of Pennsylvania grade in Ohio was under 50 per cent proration, which has been in effect since Oct. 1, 1937. Three price cuts since February have lowered the posted price from $1.70 to $1.18, a 30 per cent reduction; other grades were less drastically reduced. Pipeline storage facilities were limited; many producers were faced with the problem of providing their own storage or the risk of ruining their wells. If they wanted to pull and abandon wells, there was no market for junk equipment. Many employees have been cut to half time and in a number of instances their services entirely dispensed with. Summary of Production and Drilling Both oil and gas production in the state during 1938 showed a definite decline over the previous year. (A table showing production by years from 1876 through 1937 was published in Vol. 127 of the Transactions.) The total production of crude oil in the state for 1938 was 3,357,914 bbl., as compared with 3,654,000 bbl. in 1937, a decrease of 7.1 per cent. At

Jan 1, 1939

By J. H. Bechtold, R. Kossowsky

1 HE superplastic behavior of the eutectoid A1-78 wt pct Zn alloy has been thoroughly investigated by Back-ofen et al.' The superplastic elongations and the marked resistance to necking were rationalized in terms of high strain rate sensitivity. In a subsequent paper2 superplastic behavior was formulated to show Nabarro-Herring diffusional creep as rate controlling at low strain rates, giving way to a dislocation climb process at higher strain rates. In a paper devoted to an interpretation of superplasticity in two-phase alloys, Packer and sherby3 have included the results of an examination of the structure of an Al-Zn eutectoid specimen before and after superplastic deformation. No significant change in grain size or directionality was observed in the deformed microstructures. This one observation led the authors3 to suggest that con- tinuous recrystallization or grain boundary migration was responsible for superplasticity. The purpose of this note is to report our observations on the superplastic behavior of the Al-Zn eutectoid alloy which differ in certain respects from works previously reported. Following Hayden et al., the results are discussed in terms of dislocation climb as the important factor during superplastic deformation. A heat of nominally high (99.995) purity 22 wt pct A1-78 wt pct Zn was induction-melted and cast into a 0.5 by 6 by 12 in. slab. The slab was heated to 350°C and rolled to 1/8-in.-thick plate. The plate was then cold-rolled to 0.040-in. thickness, annealed at 35OaC, and rolled to the final thickness of 0.020 in.* Speci-

Jan 1, 1969

By Harold Margalin, Elmars Ence

M. H. Mueller, M. V. Nevitt, and H. W. Knott (Argonne National Laboratory)—We have reported1 the crystal structure of Ti2CU as body centered tetragonal with a. = 2.944A and co = 10.786A, six atoms per unit cell, and space groupl4/mmm(MoSi2 type). This cell is larger but definitely related to the unit cell reported by the authors. It permits definite positions for the titanium and copper atoms in the cell located as follows: 2 Cu (a) 0 0 0; 1/2 1/2 1/2 4 Ti (e) 0 0 z; 1/2 1/2 1/2 + z; 0 0z; 1/2 1/2 1/2- z where z = 0.341 The face centered tetragonal cell reported by the authors can be transformed to a small body centered tetragonal cell with flo (small bet) = ao(fct)v2 Both unit cells have the same CO. Neither the face centered tetragonal cell with four atoms per unit cell nor the small body centered tetragonal cell with its two atoms per unit cell lend themselves conveniently to an orderly arrangment of the 2 to 1 ratio of titanium to copper atoms. When the co of this small body centered cell is tripled, however, a large body centered tetragonal cell results with six atoms per unit cell as described above. We had also noted that the X-ray patterns of Ti2Cu indicated that the structure could be approximately described by the face centered tetragonal cell as reported by the authors; how- ever, there was evidence for a few additional very weak lines whose positions indicated a larger unit cell. Since the X-ray scattering amplitudes of titanium and copper are nearly equal, it is evident that it is difficult to distinguish their positions especially from X-ray powder patterns. It was therefore decided to look at a powder pattern obtained by neutron diffraction since the scattering amplitudes of the two elements are considerably different in magnitude and opposite in sign. The sample used for neutron diffraction was selected from a group of three alloys prepared by arc melting using crystal bar titanium of 99.92 pet nominal purity and 99.999 pet pure Cu. The alloys designated as A, B, and C had the following respective compositions: Ti-32.8 at. pet Cu, Ti-33.3 at. pet Cu, and Ti-33.8 at. pet Cu. On the basis of the melting losses incurred, it was established that the actual concentration of either component in any of the alloys probably did not deviate from the intended value by as much as 0.1 at. pet. The alloys were annealed for 5 days at 700°C in evacuated Vycor capsules and quenched in tap water. The metallographic structures of these alloys are shown in Fig. 1. None of the alloys contained sufficient second phase to permit its positive identification. Since alloy B contained the least amount of second phase and since its composition placed it closest to the ideal stoichiometry, it was chosen for the neutron diffraction study. The oxygen content of alloy B was found by chemical analysis to be 0.06 at. pet. This particular intermetallic compound is especially suitable for investigation with neutron diffraction since if the titanium and copper atoms have a random statistical distribution, a near null-matrix would result in which there would be practically no coherent scattering of neutrons, and hence no Bragg diffraction peaks. Such a condition could come

Jan 1, 1962

By ir. H. Eraly

At the Zolder mine a S/7 computer is used for two purposes : - to monitor production at the coal face - to monitor the distribution of mine cars. By using sensors attached to equipment at the coal face and at the loading points, the computer provides realtime information and also summarized reports, which help management to control production better. The computer will display this information to the control room, where two operators monitor all production events and the availability of the right numbers of mine cars at every production face. All benefits obtained from the system are described.

Jan 1, 1977

By M. J. Shulman

An algorithm used by the US Coast Guard to find lost objects is utilized to optimally allocate exploration efforts during initial stages of an exploration program. Based on classical search theory, the algorithm assumes a target probability distribution function, a detection function, and a cost function. The three functions are analogous to delineating areas of possible mineralization, choice of exploration methods, and exploration budget. Application of the algorithm is shown for a hypothetical target distribution. Using the maximum number of field day available as the cost function, the optimal allocation of effort is shown for different exploration methods, e.g. electromagnetic survey and induced polarization. The adaption of the algorithm for the exploration process is discussed.

Jan 1, 1984

Wabush Mines is the largest single supplier of iron ore to the Canadian steel industry, with 42% of its 6 million tpy of iron ore production going to the company's two Canadian owners-The Steel Co. of Canada and Dominion Foundries and Steel Ltd. Six other companies hold interests in Wabush Iron Co. Ltd. These are Lykes-Youngstown, Inland Steel Co., Intrerlake Steel Corp., Wheeling-Pittsburgh Steel Co., Finsider of Italy and Pickands Mather & Co. Field work on Wabush began in mid-1957 when a long-range program of economic, geologic, and metallurgical investigations started. This work was followed in 1959 by the construction of a temporary camp and a 700-tpd pilot plant. At the same time, work was also started on a 38-mi railway connection to Ross Bay, Newfoundland.

Jan 1, 1970

By C. K. Rose, J. H. East

Proved oil shale reserves in the Green River formation in Colorado, Utah, and Wyoming dwarf present U. S. petroleum resources. Indications are that the appetite for petroleum products will continue to grow and that this potential source of liquid fuels and related byproducts cannot be disregarded. As a part of its synthetic fuels program, the U. S. Bureau of Mines has opened a mine in the richer beds on the naval oil shale reserves. In addition to supplying material for retorting and refining studies, the development of methods, procedures, and equipment for mining oil shale on a large-scale commercial basis is of the greatest importance.

Oct 1, 1955

By W. A. Boyer

HOISTS for metal mines are seldom designed for H one particular depth. They are intended for an ultimate load and depth with a given speed but are first used to hoist from a shallower depth, gradually working to the ultimate as development progresses. Sometimes the mine is not worked on the upper levels because of the kind and grade of ore, the mining of which depends on market conditions. In this case the hoist may be used in the same working shift to lift ore, for example, from the 1200 and the 4400-ft level. This means that the safety factor of the rope should be considered not only when it hoists from the greatest depth, but also when it hoists from the upper levels. According to present safety factor standards, a hoisting rope can have ample safety margin when hoisting from the lower or lowest level and still be shy of sufficient safety margin when hoisting from the upper levels. This will be shown by curves presented in this paper.

Jan 10, 1954

By N. H. Cone

It is somewhat surprising that among the many mechanical devices that were brought into the State of Colorado, that the Brückner cylinders alone have stood the test for roasting ores. The brick walls of the Arey and Stetefeld furnaces have been remodelled into reverberatories and compound reverberatories, their binding and anchor irons have been forged into hoes and shovels, while the Crosby and Thompson cylinders have been rent by the ruthless hand of the foundryman searching for a tough piece of boiler plate. Two only of these furnaces remain in operation, of the large stock that came into Colorado by car-loads several years ago, and they occupy only a subordinate position to some reverberatories on the North Boulder Creek. But to-day there are in Colorado, in active operation, ten Brückner cylinders, and two or three more running part of the time. Dur-

By N. E. Cone

IT is somewhat surprising that among the many mechanical devices that were brought into the State of Colorado, that the Brückner cylinders alone have stood the test for roasting ores. The brick walls of the Arey and Stetefeld furnaces have been remodelled into reverberatories and compound reverberatories, their binding and anchor irons have been forged into hoes and shovels, while the Crosby and Thompson cylinders have been rent by the ruthless hand of the foundryman searching for a tough piece of boiler plate. Two only of these furnaces remain in operation, of the large stock that came into Colorado by car-loads several years ago, and they occupy only a subordinate position to some reverberatories on the North Boulder Creek. But to-day there are in Colorado, in active operation, ten Brückner cylinders, and two or three more running part of the time. Dur-

Jan 1, 1876

By Harvey T. Kennedy, Charles R. Olson

In many investigations of the performance of petroleum reservoirs the assumption is made that the liquid, if below its bubble-point pressure, is at all times in equilibrium with gas. On the other hand, observations by numerous investigators have indicated that gas-liquid systems including hydrocarbon systems, may exhibit supersaturation to the extent of many hundred psi in the laboratory. Up to the present, there has been no reliable data on which ti judge the actual extent of supersaturation under conditions approaching those existing in petroleum reservoirs. The work reported here deals with observations and measurements on mixtures of methane and kerosene in the presence of silica and calcite crystals. Bubbles were observed to form on crystal-hydrocarbon surfaces in preference to the glass-hydrocarbon interface or to the body of the liquid. Statistically, it was found that the number of bubbles formed per second per square centimeter of crystal surface was a function of the supersaturation only. and the function was evaluated graphically. Supersaturations were observed up to 770 psi, under which condition bubbles formed quickly and with considerable violence. With decreasing degrees of supersaturation, the frequency of bubble formation became less, until at 30 psi supersaturation and lower, no bubbles were observed to form, even though the observation at 30 psi was continued for 138 hours. It was found that silica and calcite crystals had identical effects, within experimental error, in accelerating the formation of bubbles, and that small amounts of water and crude oil had no effect on the results. It is shown that the maximum supersaturation that can exist in a reservoir may be calculated from the data presented and from the area of the rock surface. It is also shown that the number of bubbles formed in the reservoir, in order of magni- tude, may be calculated for any rate of pressure decline imposed on the reservoir by production. The bearing of the number and distribution of bubbles on reservoir performance is discussed. INTRODUCTION A liquid system is supersaturated with gas when the amount of gas dissolved exceeds that corresponding to equilibrium at the existing pressure and temperature. The degree of super-saturation may be conveniently expressed as the difference between the bubble-point of the mixture and the prevailing pressure. Thus, if a mixture having a bubble-point of 1,000 psi at a given temperature exists in single liquid phase at 700 psi at the same temperature. it is supersaturated to the extent of 300 psi. There are many examples of high supersaturations, mostly in aqueous solutions, reported in the literature. Thus, Kenrick, Wismer and Wyatt1 showed that water may be saturated with oxygen, nitrogen or carbon dioxide at 100 atmospheres, and the pressure reduced to one atmosphere without producing bubbles immediately. When liquids are in a state of tension, they may be considered as supersaturated at least to the extent of the tension. The tensile strength of water has been reported as 30 atmospheres by Meyer,1 60 atmospheres bv Budgett. 30 to 50 atmospheres by Temperley and Chambers,4,5 200 atmospheres by Dixon6. and 223 atmospheres by Briggs.7 Vincent8,9 determined the tensile strength of a mineral oil as 45 psi. Gardescu1 maintained pressures for short times in a model reservoir at 115 psi below the bubble-point. It should be noted that the high supersaturations observed were obtained on systems carefully purified to remove particles or surfaces which might promote the formation of bubble; These "nuclei" were considered as contaminants which interfered with the determination of a property of the liquid. In

Jan 1, 1952

Electrical requirements in surface mining can be divided into three categories: main substation, plant power, and pit distribution. A main substation may vary from a 500-kva transformer supplying 480-v power to motor-driven pumps and conveyors, to a 50,000-kva substation serving a large beneficiation plant or a large strip mining operation. Regard- less of size, it should be designed with the realization that a failure of the main substation will totally shut down the operation. Location of a main substation usually is a compromise between expense of running the incoming high-voltage transmission lines and the voltage drop of long secondary runs. Based on a geological survey for immediate and future areas of excavation, the main substation should be located as near to the center of load as possible.

Jan 10, 1967

By E. F. Poncelet

Forty years ago A. A. Griffith developed a theory explaining why brittle materials displayed such low tensile strengths.' He based his views on two points. First, he found himself compelled to assume that all brittle materials are replete with flaws, cracks, and other defects that act, although quite invisible, as large stress raisers. Second, he applied the "theorem of minimum potential energy," which says that the total potential energy of a system must pass from the unbroken to the broken condition by a process involving a continuous decrease in potential energy. By this means he satisfactorily accounted for the noted low strength of such solids and also for the wide spread obtained in experimental measurement of these strengths. So successful has the theory been that it is favored by some to this day. Unfortunately this theory is of limited use beyond the explanation of these two noted phenomena and it is keenly felt that a better theoretical insight into the physics of the fracturing process is needed as the volume of experimental evidence accumulates. The author proposes in the following to build on the fundamentally sound concepts of Griffith and, with the help of increased theoretical knowledge over that available to Griffith, develop a mechanism for frac-ture which will provide far greater understanding of the experimental evidence accumulated to date than is possible from the original Griffith idea. THE GRlFFlTH THEORY Very little progress indeed can be made without accepting the first postulate of Griffith which supposes all brittle solids to be full of microcracks. It would be difficult indeed to find a better mechanism for the small strength of such brittle materials, in conjunction with the fact that the energy that must be expended for comminution is by no means small. The postulate of the existence of the microcracks permits the breakup of the various bonds a few at a time by concentrating the stress at the tip of the progressing crack, while the total energy expended is the same as if they all had been ruptured simultaneously. The only flaw in the argument is that no reasonable explanation has been proposed to account for the genesis of such cracks. Indeed their very presence is in violation of the Griffith second postulate, the potential energy theorem. This theorem is straightforward for isothermal processes, and, in spite of Griffith, there is some doubt that treating the problem isothermally is legitimate. The surface energy of bodies is a free energy, not a potential energy as stated by Griffith, and the production of new surface free energies is not necessarily an isothermal process. There is ample evidence to the contrary. Generally speaking, if heating a body increases its surface area, then, by virtue of Le Chatelier's principle, any increase of that area by other means will tend to lower its surface temperature. Lord Kelvin calculated the actual cooling that resulted in drawing out a film of liquid.2 R. A. Houston calculated the surface cooling that resulted in stretching a metal wire.3 These calculations were made by applying the Carnot cycle to the process and evaluating the thermodynamics thereof. IRREVERSIBILITY OF THE FRACTURING PROCESS While Griffith was very careful not to say so, the impression gained from studying his papers is that he considered the fracturing process as reversible, that is, a succession of quasi-equilibrium states. There is ample evidence that it is not. The indication that the new surfaces produced by the propagation of a crack are cooler than the original body points to an irreversible heat flow from the interior to the new surfaces to equalize the temperatures. If the process be reversible, any crack accidentally formed should immediately close up as, in the absence of any strain energy, the potential energy would thereby be lowered. The fact that they do not, constitutes a paradox. Such paradoxes are nothing new where certain phenomena that propagate from minuscule nuclei are assumed to be reversible. Such is, for instance, the condensation of a pure saturated vapor that is suddenly chilled by adiabatic expansion. At the beginning the tiny droplets that are formed should be only a few angstroms in size, but the vapor pressure at such droplets is so high that they should evaporate at once. A similar situation arises if a saturated pure solution becomes super-saturated upon cooling; the first tiny crystal nuclei should dissolve as fast as

Jan 1, 1964