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By E. P. Jennings

(Read at the Amenia Meeting, October, 1877.) THE abundance and value of the tellurium minerals of Colorado is well known, but, as yet, few analyses have been made of them, and I offer these as a small contribution to the chemistry of these valuable ores. 1. Native Tellurium.-The specimens from which the analyses of this mineral were made are from the "John Jay" Mine, Boulder County, Colorado, where it occurs in quite large masses, though mixed with more or less silica and iron pyrites. It is usually a fine¬grained, tin-white mineral, but sometimes occurs in distorted, hexag¬onal prisms in cavities in the quartz. Before the blowpipe it gives the reactions for tellurium, sulphur and iron; by cupellation, it yields a small amount of gold. An analysis of a coarsely crystallized speci¬men gave the following results

Jan 1, 1878

By J. T. Burwell

The crystal orientation in silicon iron that has been given a particular treatment described by Goss,l has been studied by Goss, by Bozorth2 and by Sixtus,3 but their results do not agree and are almost entirely qualitative. The following pages give a description of the orientation of the crystals in the material as determined by means of X-rays and expressed graphically in a pole figure. The treatment consists of hot-rolling the material into strip and then giving it two cycles of cold reduction followed by recrystallization. This produces remarkably good properties in the rolling direction, the product having a maximum permeability in this direction of more than 25,000 and a permeability at 16,000 Gauss of more than 2200. It is now generally agreed that Goss's original conclusion1 that the crystals in the final product are randomly oriented was incorrect, since Bozorth2 and Sixtus,3 using different methods, have shown that there is a decided preference in orientation. Those writers, however, expressed their results only in terms of one or more ideal orientations with deviations therefrom. X-ray Data A strip of the material containing 3.1 per cent Si, prepared by Goss,† 1.2 by 0.0125 in., was etched rapidly in warm dilute hydrochloric acid until it was 0.005 in. thick, in order to eliminate the effect of the two surface layers. The specimen was then mounted in an integrating camera similar to one described in the literature.4 The purpose of this camera is to translate the specimen during exposure, so that a statistically large number of grains contribute to the pattern photographed. The camera also allows the plane of the specimen to make various angles with the X-ray beam. An area 5 by 1.2 in. was scanned by a beam of unfiltered radiation from a molybdenum target tube operating at 37 kv., and the measurements were made principally on the peak of the white radiation. X-ray photographs were taken at intervals of 15" in a plane

Jan 1, 1940

By J. T. Burwell

The crystal orientation in silicon iron that has been given a particular treatment described by Goss,l has been studied by Goss, by Bozorth2 and by Sixtus,3 but their results do not agree and are almost entirely qualitative. The following pages give a description of the orientation of the crystals in the material as determined by means of X-rays and expressed graphically in a pole figure. The treatment consists of hot-rolling the material into strip and then giving it two cycles of cold reduction followed by recrystallization. This produces remarkably good properties in the rolling direction, the product having a maximum permeability in this direction of more than 25,000 and a permeability at 16,000 Gauss of more than 2200. It is now generally agreed that Goss's original conclusion1 that the crystals in the final product are randomly oriented was incorrect, since Bozorth2 and Sixtus,3 using different methods, have shown that there is a decided preference in orientation. Those writers, however, expressed their results only in terms of one or more ideal orientations with deviations therefrom. X-ray Data A strip of the material containing 3.1 per cent Si, prepared by Goss,† 1.2 by 0.0125 in., was etched rapidly in warm dilute hydrochloric acid until it was 0.005 in. thick, in order to eliminate the effect of the two surface layers. The specimen was then mounted in an integrating camera similar to one described in the literature.4 The purpose of this camera is to translate the specimen during exposure, so that a statistically large number of grains contribute to the pattern photographed. The camera also allows the plane of the specimen to make various angles with the X-ray beam. An area 5 by 1.2 in. was scanned by a beam of unfiltered radiation from a molybdenum target tube operating at 37 kv., and the measurements were made principally on the peak of the white radiation. X-ray photographs were taken at intervals of 15" in a plane

Jan 1, 1940

[MINING AND EXPLORATION DIVISION Established as Mining, Geology and Geophysics Division, Sept. 27, 1949 Name changed February 19, 1958. Lyman H. Hart, Chairman Robert J. Lacy, Assistant Chairman Vice Chairmen: John C. Wangaard, Membership J. M. Ehrhorn, Program John G. Hall, Publications C. E. Nelson, Secretary American, Smelting and Refining Co. 120 Broadway New York 5, New York Editor, Rock-in-the-Box: J. W. Chandler.]

Jan 1, 1961

By Waldemar Lindgren

Jan 1, 1905

By Oliver Bowles

Dimension stone is a term applied to stone sold in blocks or slabs of specified shapes and usually of specified sizes, contrasted with crushed, broken and pulverized stone covered in another chapter. Dimension stone includes cut stone, rough building stone, ashlar,* rubble, monumental stone, paving blocks, curbing, flagging, and many types of ornaments and novelties carved from stone. Riprap-large, irregular blocks used for shore protection-is classed with crushed and broken stone. Composition, Varieties, and Properties Dimension stones are of many kinds. The principal varieties are granites, trap rock (diabase, basalt, and gabbro), sandstone, limestone, and marble. Slate is covered in a separate chapter. Granite is a visibly granular crystalline rock consisting essentially of feldspar, quartz, and mica or hornblende. The basaltic rocks are darker in color than the granites. They contain little or no quartz and consist largely of plagioclase feldspar, augite, pyroxene, and hornblende. They are classed commercially as black granites. Limestone consists essentially of calcium carbonate. Dolomites and magnesian limestones used as dimension stone are classed with the high-calcium limestones. Marble is a crystalline form of limestone, but in the trade, any carbonate rock which will take a polish is called a marble. Many limestones which are fossiliferous but which will take a polish are sold as a decorative stone for lobbies of hotels and office buildings. Sandstone consists essentially of silica in the form of sand grains cemented into a coherent mass. Although rock occurrences are numerous and widespread, the exacting requirements of use condemn all but a small fraction of them for commercial use as dimension stone. No deposit that has closely spaced joints or planes of weakness can be used because sound blocks of moderate to large size are demanded. Uniform texture and grain size, constant and attractive colors or color pattern, and freedom from impurities that may cause stains or deterioration usually are demanded. Hardness is a variable property. Granites and diabases are as hard as or harder than steel, while limestones and marbles may be scratched with a knife. The hardness of sandstone depends upon the degree of cohesion of the grains. Workability depends to a considerable extent on hardness, but the degree of hardness has little influence on use except where stones are subjected to abrasion as on steps or floors. "Texture" as applied to stone relates to the arrangement, uniformity, and size of the constituent grains. Stones are of many colors and thus can satisfy a variety of tastes. For monumental stone, a marked contrast between polished and tooled surfaces is preferred in order that inscriptions may be read easily. Strength requirements usually may be disregarded because any sound structural stone suitable in other respects is almost invariably many times as strong as would be required for any ordinary use. The pressure on the base course of the Washington Monument, Washington, D. C., is less than 700 psi, and highgrade granites, limestones, sandstones, and marbles will sustain a crushing load of 10,000 to 25,000 psi. A structure made of stone with a crushing strength of 15,000 psi would have to be nearly 21h miles high before crushing of the lower courses would occur. However, stone disintegrates more readily under severe

Jan 1, 1960

NEW MEMBERS The following list comprises the names of those persons who became .members during the period of Jan. 10, 1918, to Feb. 10, 1918. ANTISELL, TONER, Min. Engr.; Supt., Great Falls Mine of Maryland, Chevy Chase, R: F. D. No. 4, Washington, D. C. BAKER, RAYMOND FRANK, Geol:, The Texas Co., Producing Dept., Box 362, Tulsa, Okla. BERTON, ADRIEN, Chief Engr., Corocoro United Copper Mines, Ltd., Corocoro, Bolivia. Buck, WILMER EARLE, Met., Curtis & Co. Mfg. Co., Hamberger & Kienlein Aves., St. Louis, Mo. BUELL, WILLIAM H., Asst. Director, Experimental Station, E. I. duPont de Nemours & Co., Wilmington, Del. CARDENAS, FEDERICO F., Mgr., Cia. Minera Nazareno y Alicante, S. A., Allende, No. 112, Saltillo, Coah., Mexico. CHEVALIER, JEROME A., Pet. Geol., The Carter Oil Co.; Exchange National Bank Bldg., Tulsa, Okla. CLEAVES, DANIEL LUNT Supt., St. Joseph Lead Co., Herculaneum, Mo. CLOTHIER, GEORGE A., Resident Min. Engr., Province of British Columbia,

Jan 3, 1918

By Parke A. Dickey

POTENTIAL differences between strata of shale and sandstone have been recognized for about 15 years, and they form the basis of the electrical logging of oil wells. Hitherto these potentials have been ascribed solely to electrochemical reactions caused by the disturbing effects of the water in the drill hole through which they are generally measured. Observations by the author in wells empty of water and in a mine shaft suggest that potential differences between sandstones and shales are natural and specific properties of the rocks, although they are modified to measurement by the disturbing effects of the water in the drill hole. The cause of these potentials probably is to be sought in the relative polar adsorptive capacities of quartz and clay particles.

Jan 1, 1944

By H. R. Aldrich

This paper is not a treatise on the theory and practice of magnetic surveying. It presents a diagram upon which have been plotted observations taken with the simplest form of magnetic instrument, the lowly dip needle, over a large area astride the Lake Superior syncline of northern wisconsin. The exposures of the underlying formations are not sufficiently great in number nor fortunate in distribution to have provided the fuller understanding of the geology which has been secured by the use of the magnetic observations as an auxiliary tool or accessory in the hands of the geologist. The diagram (Fig. 2) in large part speaks for itself if studied in connection with the geological map (Fig. 1) for which it is the main control. It is presented to demonstrate the extent to which the use of such methods may aid in the solution of geological problems in a covered country. The diagram is probably unique in assembling the expression of such a wide range of formations, affected by so wide a range of secondary processes, and deformed by so many different structures in terms of magnetic variation. Few geologists outside of the Lake Superior country have had any first-hand experience in the taking of magnetic observations and the interpretation of the results in terms of geological conditions; nor have the Lake Superior men gone with the methods far afield from the mere tracing of iron formations. In more recent years the oil companies have gone heavily into investments in magnetometers, balances, and dip needles in the quest of concealed structural anomalies which are the favorable loci of petroleum accumulation. But these geophysicists come back from the fields with their collections of observations facing the question of interpreting the geological meaning of their magnetic anomalies. It is considered probable therefore, and certainly it is the hope of the writer, that the appended charts, or magnographs, which show how character of the country rock and its changes, structural strike and dip and their changes, depth of burial and its variation, contact metamorphic

Jan 1, 1929

Jan 1, 1967

By C. V. Corless

We are living at a period of the world's history in which social phenomena are on so vast a scale, are of so profoundly soul-searching a nature, and are occurring in such rapid succession in the great world drama in which we are both actors and spectators, that, in our efforts to obtain a rational point of view in relation to them, our minds may fail to discern the simple in the complex and our understanding is liable to become confused or even overwhelmed. To the social student whose: scientific training has convinced him of the truth of the evolutionary law, Natura non facit salium, it is neither the vast scale of the events, their deeply soul-stirring nature, nor their rapid succession that matters so much, as the discovery of the underlying principle or law in accordance with which the disintegration and reintegration, which are the two aspects of social evolution, or indeed of evolution everywhere, are occurring. He is most deeply concerned in seeking an answer to the question: Have we in the present great and perplexing upheavals in human society, whether regarded in Central Europe, in Russia, in Great Britain, or in America, a really new cause at work, or, have we, though on a very large scale, merely new manifestations of the working out of an old principle? When we think of the appalling struggle in Europe, into which the world's greatest exemplar of democracy was finally drawn, no one has any hesitation in admitting that the great conflict was fundamentally a life-and-death struggle for self-preservation and self-propagation on the part of autocracy. The variations we meet with in the statement of the cause of the war arise mainly from differing distances of perspective; but in the last analysis all agree that the autocratic system of political gov ernment, which found its very soul and center in Prussian despotism, was consciously arrayed in a final "world-power-or-downf all" struggle against a love of freedom which was steadily widening and deepening throughout the world, and particularly throughout those parts of the world where this love of freedom and justice hasfound expressionin democratic institutions. It is not irrelevant to our discussion to recall in passing that this most imposing structure ever conceived by the human mind as an instrument of tyranny is lying today an irretrievable mass of ruins, completely over-

Jan 1, 1920

By C. H. Mahoney, A. L. Tarr, P. E. Le Grand

Magnesium, it is now generally realized, differs in some important aspects from most other structural metals, not excepting even its close neighbors, the aluminum-base alloys. This is particularly true with respect to the effects of elevated temperatures on the two light metals when in the molten state. Aluminum, 0' the one hand, should not be raised above its melting point any higher than is absolutely necessary if one is to avoid danger of gas absorption and a tendency toward grain growth in the resultant casting.' Magnesium alloys, in sharp contrast, actually benefit by being heated to temperatures considerably above their melting point, It is a commonly accepted practice to establish the desired fine grain in the industrial magnesium alloys of the aluminum-hearing group by raising the temperature of the melt after the refining treatment to some 250°C (482°F.) above the melting range. To recall briefly the typical practice for magnesium alloys, the molten metal is refined by fluxing at about 730°C. (I350°F.), and after the melt has been covered with a suitable flux, the temperature is raised to between 870°C. (I600°F.) and 930°C. (1700°F.). It is then cooled as quickly as possible to the casting temperature. This superheating, as it is called, results in a fine-grained cast metal structure which has superior mechanical properties, enhanced amenability to 'solution heat-treatment, and better machinability than cast metal that has not been superheated. The minimum temperature of superheating varies to some extent with the composition of the alloys to be treated and usually increases with the percentage of magnesium in alloys containing the same constituent metals.' It should be noted that the grain-refining effect of superheating is markedly apparent only in connection with the alloys containing aluminum as an alloying Constituent—the binary alloy containing 1.5 per cent manganese, for example, is not refined in grain to any noticeable extent by a superheating effort. While the phenomenon of superheating is well known in the magnesium industry, the mechanism of the process has remained a mystery During the superheating cycle something occurs that forces a fine grain upon the solidifying metal. The process has been controlled in an empirical manner, and occasionally, especially on large-scale melts, and for no apparent cause, no grain refinement is obtained from a superheating treatment. Only a few papers of importance have been published on the subject. Of these, one of the most helpful is the paper by Achenbach, Nipper and Piwowarski,3 which gives considerable data concerning the effect of superheating on various properties such as fluidity, shrinkage and hot crack

Jan 1, 1945

By M. Gensamer

THE PURPOSE OF THIS PAPER is to lay a foundation of elementary theory that might be useful in the discussions which it is hoped will be evoked during this Symposium. It is not my purpose to try to expound the details of the most complete theories as that would be impossible in the time at our disposal and, even if time were available, would probably be of less usefulness than a discussion of the principles underlying the advanced theoretical treatment. I shall try to discuss the fundamental bases for these advanced theories. There exists at the present time very much less need for a detailed description of complete theory than existed when this Symposium was being organized. The reason for this is that a series of papers by L. R. Underwood has been appearing in the magazine Sheet Metal Industries. It is understood that this series will he published soon in the form of a book. Dr. Underwood's articles are complete, critical and well written and it would be hopeless to try to do better in less space. The need, then, is for a brief treatment of basic theory. The objective of any theory of plastic forming- is to enable one to calculate the force and power requirements for the process, and where the deformation is not uniform, to calculate the distribution of strains- In the formed object. We need as the basis for the calculation the relationship between stress and strain in the metal, particularly for the combination of stresses imposed by the forming process. We need to know the stress-strain curve for some simple state of stress, and we need in addition some theory

Jan 1, 1948

By John Gross

The study of the energy used in crushing operations has advanced from a period of perplexing confusion to one of greater clarity. Only within the last few years has any true conception of the work in crushing been possible, owing to the chaotic state of theoretical knowledge. For some 20 years a controversy existed between those advocating the Rittinger law and those advocating the Kick law. The Kick law now appears to be definitely out of the picture, and crushing efficiency may be based confidently on the Rittinger theory. There also seems to be a generally crystallized conception as to the meaning and nature of sub-sieve material. There is needed a simple, direct method for determining surface on a crushed ore product, and also a simple and accepted method for size determination on minus 400-mesh material. The Crushing Law The Rittinger(l)‡ theory of crushing was advanced in 1867 and the Kick(3) theory in 1885. While the Rittinger theory might have been accepted without much question and actually had been accepted by many investigators, a serious doubt as to its validity was raised by Stadler(10) who upon purely theoretical grounds proclaimed the Kick "law" as the true law of crushing. According to Rittinger the energy required in successive steps in reduction increases geometrically, while according to Kick the energy increases arithmetically. These "laws" therefore are at variance, and the establishment of the true law was recognized as of first importance. Many simple experiments have been made to demonstrate the application of the Rittinger theory to crushing, and it would seem that its simplicity should favor its acceptance. Experimental evidence, however, was not convincing, as no reliable data could be obtained on the finer material from a crushing or grinding operation. Gates,(13) Bell,(19)

Jan 1, 1935

By B. A. Rogers, K. O. Stamm

BECAUSE it is the basis of the economically important operation of hardening steel by quenching, the A3 transformation in iron has been the subject of numerous investigations. Although the contributions to this subject are interesting, no general review will be given here. Readers who care to follow the matter further are referred to the comprehensive summary by Cleaves and Thompson,1 which covers the literature to about 1935. Their references to 53 papers on the subject suggest that further investigation is hardly justifiable. However, considerable interest has developed recently concerning the reversibility of the transformation. From thermodynamic considerations, the transition ought to occur at the same point on heating or cooling, if the change of temperature is sufficiently slow. Yet all of the earlier investigators found a difference of several degrees. Burgess and Crowe,2 who used thermal methods, obtained average temperatures of 912° for Ac3 and 900°C. for Ar3 on electrolytic iron. Their data indicate a considerable range of temperature over which the change occurs, both on heating and on cooling. Terry3 measured the susceptibility in the critical range and estimated from the steepest parts of his curves that Ac3 came at 9180 and Ar3 at 903°C. Ishiwara4 was one of the first investigators to report a shorter interval between the temperature of the change in the two directions. He measured the change of susceptibility of kaolin-coated samples of steel, in a hydrogen atmosphere, at rates of heating and cooling so low that about 3 or 4 hr. were required for the transformation to complete itself. His results show some variability between samples, but indicate that the difference between Ac3 and Ar3 is in the vicinity of 6°C. Roberts and Davey5 measured the space lattice in pure iron in the vicinity of 900°°C. and concluded that a change occurs reversibly between 907° ± 3° and 9100 ± 3°C., probably between 907° and 910°C. Wells, Ackley, and Mehl6 made dilatometric determinations of the Ac3 and Ar3 points in samples of hydrogen-treated carbonyl iron maintained under a vacuum. They used three rates of heating and cooling: 2°, '1/2°, and 1/8°C. per min. and found the spread between the two points decreased with low rates. At the slowest rate, the Ac3 transition occurred at 909° to 909.5°C. and the Ar3 change at 907°C. in three of the samples believed to contain the lowest percentages of alien elements. They concluded that if the rate of temperature change and the content of alien elements were low enough, the A3 transformation would be completely reversible at 909.5° ± I°C. The question of reversibility is an interesting one and when some iron with especially small percentages of alien elements became available the opportunity to conduct an investigation was welcomed. This iron was prepared by the Division of

Jan 1, 1941

By Zay Jeffries

This paper will include a brief discussion of Prof. Howe's paper on The Supposed Reversal of Inheritance of Ferrite Grain Size from that of Austenite.l The general subject of grain refining in steel and iron will also be treated. The conclusions reached are stated in the following hypotheses which are discussed more in detail below. 1. The ferrite grain size in pure iron, the ferrite and pearlite grain size in hypoeutectoid steel, the pearlite grain size in eutectoid steel and the cementite and pearlite grain size of hypereutectoid steel are not inherited from the grain size of the mother austenite. 2. The only structural feature that is generally inherited from the austenite of hypo- and hypereutectoid steels on cooling through their transformation ranges is the position of the excess ferrite or cementite at the austenite grain boundaries, sometimes causing complete and sometimes incomplete networks which outline the old austenite grain boundaries. Rapid cooling through the transformation range will cause the non-inheritance of this structural (network) feature. 3. The austenite grain boundaries themselves are nearly always effaced in all steels and also in pure iron during the At transformations. 4. The grain-size refining of steel and iron is brought about by the combined effect of non-inheritance of the transformation products on either heating or cooling, i.e., the austenite transformation products do cst inherit their grain size from the austenite on cooling through the transformation range nor does austenite inherit its grain size from the products which form austenite on heating. 5. In general, in both iron and carbon steel the larger the austenite grain size, the larger will be the grain size of the transformation products on cooling. This, of course, assumes all other conditions constant except the austenite grain size. An exception is found to this general rule in very pure iron such as electrolytic iron. In this instance small austenite grains may form very large ferrite grains on cooling through Arg.

Jan 1, 1918

By H. A. Kuhn

The Pittsburgh coal field in Western Pennsylvania is conceded to be the most important in the world.

Jan 1, 1915

By J. S. Hardison

In the fall of 1912, the appearance of water in the oil of the Nevada Petroleum Co., Coalinga, Cal., made necessary the installation of a dehydrating plant to reduce the water below the 3 per cent. limit prescribed by the agency. Unlike the mining industry, technical literature of the oil industry is limited and extremely unsatisfactory. Until the recent efforts of the Petroleum and Gas Committee of the American Institute of Mining Engineers, no concerted movement has been instituted to secure publication of papers dealing with the problems of the oil business, and because of the additional fact that dehydrating of oil has not been practiced in California to any extent up to comparatively recent time, it was found necessary to experiment in order to determine the most satisfactory plan for this purpose. It is easy to write regarding successful enterprises, but, while not SO pleasant, it is equally desirable to write of failures so that others may be saved the loss incident to such investments. The water in this oil occurs both free and as an emulsion. Free water easily settles out, but the emulsion requires treatment. So far as can be determined, the emulsion consists of globules of water surrounded and enveloped by a film of oil. Starting with this hypothesis the theory has been evolved that in order to break up this emulsion the water must be heated at least to boiling point, when an explosion takes place destroying the globule. Unfortunately, this condition was not recognized in the installation of the first plant, which was planned on the following lines: A heater was arranged so that all the oil from the wells could be heated before reaching the shipping tanks, these being already fitted with coils for steam heating. Tanks were filled with about 4 ft. of water, live steam was turned into the coils and the water brought nearly to the boiling point, when the heated oil was run in. This for a time was partly successful, but the length of time necessary to apply this heat was too great for practical operating.

Jan 1, 1915

By J. Morgan Clements

The manufacture of coke in Peru, as practiced at the coalmines of the Quishuarcancha and Goyllarisquisca districts, is intermediate between the primitive coke-heap and the bee-hive oven. The method of coking is quite simple. In constructing the coal-heap, preparatory to burning, the ground is first leveled, and a simple stack of stone and clay is built, giving the bottom, to a height of 6 ft., approximately 6 ft. of external diameter. The size of the stack varies in different districts, but is generally 9 ft. high, and slightly smaller at the top than at the bottom. The walls of the heap are from 12 to 14 in. thick, which allows an inside diameter of from 3.75 to 4 ft. These walls are pierced at intervals by three or more tiers of openings or flues, connected with the central flue. The radial flues have a diameter of about 5 in. and are built with a gentle upward slope. The stack (shown in Fig. 1) is permanent; and in this respect the practice in Peru differs from other primitive practices in which nothing is permanent except the yard. Above the permanent 6-ft. portion of the stack there is added a cap of clay, about 3 ft. high, which contracts toward the top, where it has an inside diameter of about 2 ft. This clay cap is temporary, and frequently has to be renewed after each burning. Before charging the coal, there are first built, from the lowest tier of flues upon the ground, a number of temporary flues, leading from the central stack out to the edge of the coal-heap, and constructed of blocks of coal for the greater part of the distauce, the outer edge alone being of rough stoue. The coal is then piled up over these flues and around the stack to a height of about 6 ft. The bottom flues are the only ones that

Jan 1, 1905

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