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By O. W. Simmons, L. W. Eastwood, C. M. Craighead

Binary alloys of titanium with silver, lead, tin, nickel, copper, beryllium, boron, silicon, chromium, molybdenum, manganese, vanadium, iron, and cobalt were studied. One-half-pound ingots of the alloys were prepared in an arc furnace, employing a water-cooled copper crucible, an argon atmosphere, and a water-cooled tungsten electrode. The half-pound ingots were fabricated by forging at 1700°F in air to 1/4-in. slab, followed by hot rolling at 1450°F to 0.060-in. sheet. Tensile properties, minimum bend radii, hardnesses, response to heat treatment and aging treatment, and phase relationships were determined for these alloys. EARLY in 1947, as one phase of the evaluation of materials for Air Force Project RAND, Battelle successfully arc melted Bureau of Mines titanium and obtained a few basic properties of unalloyed titanium and several titanium-base alloys. The low density, excellent resistance to corrosion, and high tensile properties of these materials stimulated a great deal of interest among metallurgists and designers seeking better materials of construction. As a result of this early work, Battelle, under contract with the Air Materiel Command, Wright-Patterson Air Force Base, has continued extensive studies of titanium alloys. The result of the first year's work is described in three papers. The present one deals with binary alloys, the second with ternary alloys, and the third paper with quaternary alloys. Melting Method The arc furnace for melting titanium and other refractory metals was developed at Battelle Institute under Air Force Project RAND. During the present work, considerable improvement has been made in the design and operation of this furnace for making small ingots of titanium and titanium alloys. The improved furnace design is illustrated by fig. 1, which shows a cross-sectional view with the dimensions of various parts and their relationship to one another. The essential features of the furnace are the inert argon atmosphere, the water-cooled copper crucible, and the water-cooled tungsten elec- trode. The melting crucible is formed by spinning 0.064-in. annealed copper sheet. A groove for an O-ring seal is spun into the flange of the crucible. A fiber gasket between the crucible flange and the water-cooled brass cover provides electrical insulation. The brass cover is fitted with a sight glass, an opening for the water-cooled electrode, and a tube through which the material is charged. Direct current is used for melting, with the positive electrical terminal connected to the water jacket and the negative terminal to the electrode. A typical heat is made in the new furnace as follows: Approximately, 0.20 lb of titanium under 2 mesh per in. and the alloy addition, if any is to be used, are placed in the bottom of the crucible. The cover is clamped on the crucible so that the O-rings make a tight seal. The remainder of the charge is placed in a glass bottle, and this is connected by a rubber hose to the charging tube of the furnace. The crucible and the charge are evacuated with a mechanical pump to a pressure below 50 mm of mercury, or less if desired, and held at this reduced pressure for 5 min. Hot water is circulated through the jacket during the evacuation period to assist in outgassing the crucible. Following the evacuation, tank argon of 99.92+ pct purity is flushed through the crucible for 5 min and then adjusted to give a positive pressure of 1 to 2 psi. During subsequent operation, an argon pressure regulator introduces only enough argon to compensate for the small leakage which occurs through a mercury trap. Re-evacuation and reflushing the melting chamber with argon produced a negligible reduction in contamination. Two 550-amp generators, connected in parallel, constitute the power source. Normally, about 800 amp are used for melting alloys which are not extremely refractory. The generators are set for 90 v open circuit and 200 amp. The arc is struck and the electrode is withdrawn to produce an arc of 23 to 26 v. This voltage is maintained while the electrode tip is moved slowly around a circle 1 in. smaller than the diameter of the ingot. The current

Jan 1, 1951

By A. L. Slaughter

The Homestake mine, located in western South Dakota, was discovered in 1876. The first reported production was in I 878. Total production through 1965 is 6,554,249 troy ounces of silver and 27,961,276 troy ounces of gold, worth $987,000,000 at present prices. Precambrian sedimentary formations at Lead total 20,000 feet. The Poorman Formation, the oldest, is chiefly ankerite carbonate. The Homestake Formation is iron-magnesium carbonate. The younger formations are argillaceous with some quartzites. The Cambrian Deadwood Formation unconformably overlies the Precambrian. All are cut by Tertiary intrusives. Sideroplesite schist of the Homestake Formation was converted to cummingtonite schist in the zones of higher-grade metamorphism. The Precambrian rocks show the effects of extreme isoclinal folding. A second stage of folding ( cross folds) may have been caused by the Tertiary intrusives. All folds plunge to the southeast. The Homestake ore bodies are pipe-like replacements of the Homestake Formation in zones of cross folding. It is believed that dilatation of the schists has increased permeability in these zones. Chloritization of the schists is the most widespread effect of the mineralization which is divided into four stages. Principal minerals of the first stage are quartz, chlorite, and arsenopyrite; in the second stage, quartz, ankerite, and pyrrhotite. In the third stage only pyrrhotite was deposited. The fourth stage followed the intrusions of Tertiary dikes and deposited mostly pyrite and calcite. Gold accompanies all stages and is always the last mineral to be deposited. It is most closely associated with arsenopyrite of the first stage but can be interpreted as having been deposited during the fourth stage and superimposed on the products of the earlier stages.

Jan 1, 1968

By Carleton Ellis

(Presented at a meeting of the New York Local Section of the Institute, Apr. 12, 1912.) I. INTRODUCTION. THE problem of the influence of hot surfaces upon gaseous combustion is one which, from a purely scientific stand-point, has engaged, for many years past, the attention of Prof. William A. Bone, of Leeds University and the Imperial College, London; and as his recent work has been the direct outcome of earlier scientific investigation, it will be appropriate, by way of introduction, to review briefly the present position of science with respect to this important subject, as stated by Professor Bone. One may perhaps best arrive at an understanding of the term " ?flameless " or " surface " combustion by considering certain facts which differentiate it from the more familiar processes of combustion as they occur in ordinary flames. All hot surfaces have an accelerating influence upon chemical changes in gaseous systems. If, at any temperature, a gaseous system, A, tends to pass over into another system, B, contact with a solid at the same temperature will accelerate the process. To take a very simple example, if a mixture of hydrogen and oxygen in their combining proportions (electrolytic gas) were maintained in an inclosure with smooth glass walls at a temperature of, say, 450° C., there would certainly be a tendency to form steam, but the rate of change would be negligibly small. If, however, there were brought into the system some porous solid material at the same temperature, so that a large surface was exposed to the gases, the rate of change would at once be rapidly accelerated in the layer of gas immediately in contact with the hot surface. Steam, the product, would diffuse outward from the surface, and the supplies of hydrogen and oxygen at the surface would be renewed by diffusion inward. Thus combustion would proceed heterogene-

Sep 1, 1912

By H. W. Fox, M. R. Achter

IN a previous study of the effect of atmosphere on creep-rupture properties,' it was shown that the relative strength of nickel in air and in vacuum may be reversed by a change in either stress or temperature, Fig. 1. At low stresses and high temperatures the metal is stronger in air but stronger in vacuum at high stresses and low temperatures. A mechanism to explain this reversal was proposed involving two competing processes; oxidation strengthens the metal while adsorption of gas lowers the surface energy, relative to that in vacuum, and reduces the work required to propagate a crack. The process which controls is determined by stress and temperature. In a number of private communications, however, the objection has been made that even in the vacuum of objection mm of Hg used in this study, the surface of a

Jan 1, 1960

By J. F. Kemp

The use of nickel-steel has directed increasing interest of late towards the deposits of nickel, and at the same time the parallel advance in our knowledge of the basic igneous rocks has rendered these deposits a subject of important geological inquiry. Investigations have led to some views, more or less new, on the igneous origin of certain ores, which, though not universally accepted, have a growing number of adherents. In Europe, the mines in Norway have been especially suggestive subjects of study, and others somewhat less generally known have also added their testimony; while in this country the great economic importance and scientific interest of the developments in the Sudbury district of Canada, have furnished the principal texts for the discourses that have appeared among us. The purpose of the present paper is to set forth these views through the medium of one interesting ore-body, of which but little has been written ; and, by the description of another, to place in contrast two different geological associations in which nickeliferous pyrrhotite occurs, and to indicate a generalization, based upon these different geological characters, and justified by the experience so far gained. To Prof. J. H. L. Vogt, of Christiania, Norway, is due the chief credit for the revival of interest in the geology of nickel. His important contributions* of recent date have made generally available

Jan 1, 1895

By T. F. Witherbee

It is proposed to give, first, a description of the works; second, a report of the first six months of the present blast; and third, such improvements as have been suggested by the practical working. The site selected for this furnace was, at the time of commencing work, October, 1872, entirely covered by the navigable waters of Lake Champlain. A coffer-dam was first built of cribs of round timber filled with stone, forming three sides, while the shore answered for the fourth. Considerable excavating was done with a steam-dredge, a hole being left for it to pass out. The opening was then built up, and the cribbing banked up with blue clay from the bottom of the lake, to render it water-tight and the dam pumped out; the remainder of the excavating being done by hand. All of the foundations, with the exception of the elevator-tower, and fifteen feet of the east side of hot blast, rest on the Potsdam sandstone, which forms the shore line, dipping into the lake at an angle of fifteen degrees. Owing to jogs in the formation, a much greater depth was found necessary than was at first anticipated, the foundation under the stack

By T. F. Witherbee

IT is proposed to give, first, a description of the works ; second, a report of the first six months of the present blast; and third, such improvements as have been suggested by the practical working. The site selected for this furnace was, at the time of commencing work, October, 1872, entirely covered by the navigable waters of Lake Champlain. A coffer-dam was first built of cribs of round timber filled with stone, forming three sides, while the shore answered for the fourth. Considerable excavating was done with a steam-dredge, a hole being left for it to pass out. The opening was then built up, and the cribbing banked up with blue clay from the bottom of the lake, to render it water-tight and the dam pumped out; the remainder of the excavating being done by hand. All of the foundations, with the exception of the elevator-tower, and fifteen feet of the east side of hot blast, rest on the Potsdam sandstone, which forms the shore line, dipping into the lake at an angle of fifteen degrees. Owing to jogs in the formation, a much greater depth was found necessary than was at first anticipated, the foundation under the stack

Jan 1, 1876

By J. P. Hirth, C. S. Hartley

A simple graphical technique is presented for rapidly determining the ratio of resolved shear stress on slip systems in single crystals to the applied stress (Schmid factor) for various simple states of stress. Master plots are presented which, when used in conjunction with an appropriate stereo-graphic projection, allow one to determine the Schmid factor for all slip systems in a crystal of given orientation. It is shown that one such plot suffices for simple tension or compression, flex-ural bending, and biaxial compression, while a combination of two different plots must be used for torsion and simple shear. STUDIES of the deformation behavior of single crystals are most valuable when the applied stresses are resolved onto the various slip systems of the crystal. A careful study of the available slip systems and proper selection of the state of stress used and the specimen orientation can then yield quantitative information about the probability of specific dislocation reactions, the strength of barriers to plastic flow, and the mechanisms of yielding and flow in general. It is the purpose of this work to analyze some common states of stress used in deformation studies and to present a simplified way of determining for these cases the ratio of the resolved shear stress on the slip systems to the applied stress (Schmid factor). I) CALCULATIONS We first define two orthogonal coordinate systems: one based on the specimen geometry (a right circular cylinder of radius, R, is considered here) and one based on the particular slip system of interest. The unit vectors and angles specifying the two coordinate systems and the relationship between them are listed in Table I. The relationships among the various angles and unit vectors are shown on a stereographic projection in Fig. 1. The transformation matrix between the (XI X2 X3) and (x'1 x'2 x'3) system is x1 x2 x3 X'1 a11 al2 a13 x'2 a21 a22 a23 x'9 a31 a32 a33 where in this case the direction cosines aij are given by a11 a12 a13 aij = a21 a22 a23 a31 a32 a33 sin 0 cos F cos 0 sin F cos 9 = -cos 0 cos F sin 0 sin F sin 6 [1] 0 -sin F cos (p In terms of Eq. [I.], the stresses sij, referred to the slip system, are determined from oij, referred to the specimen axes, by1,2

Jan 1, 1965

By Lloyd R. Jackson

IN the past 15 years there has been a great deal of interest in the fundamentals of plastic flow and rupture in metals and a number of papers have presented substantial advances toward a fundamental insight into the mechanism of these two processes. This paper is an appraisal of the present position with respect to the following: I. The relative importance of shear and hydrostatic stresses in controlling the plastic flow of metals. 2. The relative importance of shear and hydrostatic stresses in determining the amount of flow before rupture in metals. 3. The use of generalid strains in determining the effect of plastic flow on the work-hardening of metals. FUNDAMENTALS INVOLVED IN PLASTIC FLOW In attempting to devise a quantitative description of plastic flow in metals, it has been customary to assume that metals are homogeneous and isotropic. The fact that neither of these assumptions is correct complicates the experimental appraisal of relations developed. Never- the less, as will be shown, metals are close enough to being isotropic and homogeneous so that considerable insight into the mechanism of plastic flow can be obtained. The assumptions of .isotropy and homogeneity allow both the elastic and plastic behavior of metals to be described in terms of 12 variables-six being stress variables, and six being strain variables. ) From this viewpoint, it should be possible to represent the stress-strain relations in the plastic range for metals by a surface in 12 dimensions. One boundary of this surface would be the surface of transition from elastic to plastic behavior; the other would be the surface of rupture. These two surfaces would be joined by the surface of plastic flow. The shape of this composite surface would depend on the test temperature and speed of straining. This paper is concerned only with results obtained at constant temperature and constant speed of straining. While such a representation is conceivable, the demonstration of such a surface would present almost insurmountable obstacles. The most fruitful simplification of this concept has been the recognition that the behavior of metals in the plastic region is primarily a result of shear stresses and strains. Based on this viewpoint, it is possible to utilize stress and strain invariants that are independent of hydrostatic components to define an effective stress and strain. In effect, this amounts to reducing the task of representing stresses and strains in 12 dimensions to one of representation in two dimensions. The two invariants (one for stresses . and one for strains) that have received most attention are the following: [ ]

Jan 1, 1946

By J. D. Mote, A. Rosen, J. E. Dorn

The effect of strain rate and temperature on the critical resolved shear stress for (1100) [1120] prismatic slip was determined for the intermediate hexagonal phase containing about 67 at. pct Ag and 33 at. pct Al. Whereas the flow stress increased only slightly as the test temperature was first decreased below room temperature, a rapid increase inflow stress was obtained with yet greater decreases in temperature from about 240" to 4°K. The effect of both temperature and strain rate on the flow stress over the low-temperature range could be completely rationalized in terms of the Peierls mechanism when the deformation is controlled by the rate of nucleation of pairs of kinks. A few years ago Mote, Tanaka, and Dorn1 observed that the critical resolved shear stress for prismatic slip of a 67 at. pct Ag plus 33 at. pct A1 hexagonal intermediate phase by the (1100)[1120] mode decreased precipitously as the test temperature was increased from 4" to about 160°K. Their results for both basal and prismatic slip are given in Fig. 1. It is obvious that only the flow stress for prismatic slip is strongly temperature-dependent, whereas the flow stress for basal slip is independent of temperature. If the temperature dependence of the flow stress were primarily due to interstitial impurities, it might be expected that they would influence the flow stress for basal slip as well. Since the activation volume at 115°K for prismatic slip was determined to be about 15b3, where b is the Burgers' vector, this thermally activated deformation process was tentatively ascribed as being due to the Peierls mechanism. But the various analyses of the Peierls mechanism then available as formulated by Seeger2 and also by Lothe and Hirth3 did not agree well with the experimental data. Since that time a more realistic theory for the operation of the Peierls mechanism under conditions where the strain rate is determined by the rate of nucleation of pairs of kinks has been presented by Dorn and Rajnak.4 The present investigation was, therefore, undertaken in order to provide the essential data for a careful check on the agreement between this theory and the low-temperature deformation by prismatid slip of the above-mentioned Ag2A1 intermediate phase. EXPERIMENTAL TECHNIQUE Single-crystal specimens so oriented that the [1120] direction and the normal to the (1100) plane were at 45 * 2 deg to the tensile axis were grown from the congruent melting composition of about Ag2Al for the intermediate hexagonal phase by the

Jan 1, 1964

By L. F. Bishop

The ore bodies of the Butte district1 are found in many different vein systems having many different structural characteristics; some are narrow with self-supporting ore but with weak walls; some are wide with weak or strong ore and weak walls; some of the veins dip steeply and others do not; some have well defined walls, and others, in the "horsetail" area, are mined to sample limits. Consequently, many types of stoping methods are used in mining these ores. The stoping methods used in the Anaconda Copper Mining Company's properties are the square-set and cut-and-fill. The square-set method is the principal stoping method used because, generally speaking, the ore and walls are weak, the ore is high grade, and good extraction is required. These square-set stopes may be classified as conventional, vertical slice, slot, timber rill, and Mitchell slice types. The conventional type square sets are those of various shapes and sizes, mined by horizontal slicing to the boundaries of the stopes. The rock is slid to the chute and the filling is moved by gravity. The ore and waste may be handled with a scraper when local conditions require it. The vertical-slice square-set system is the type used in narrow veins that are mined in vertical panels. The slot stopes are stopes in wide veins that employ a slot across the vein instead of a con- ventional chute to handle the ore. The timber rill is a type of square set in which the ore is mined as in inclined cut and fill but the square-set timber is used. The Mitchell slice is the type used for some broken or heavy ore blocks, or for pillar extraction between two converging slot stopes. The cut-and-fill method is used where the ore will stand without much support although the walls may be weak. The principal type of this method is the horizontal cut-and-fill, with mechanical scraping. The inclined cut-and-fill, or rill, stopes are used in some veins too narrow for scraping. The production from the various methods in use for the second six months of 1944 are shown in Table I. This paper deals mainly with the vertical slice and slot types of square-set stoping, because of their effect on production locally and their potential possibilities here and in other districts, with sufficient reference to conventional square-setting for comparison.

Jan 1, 1946

By W. E. Wrather

DURING the war the mineral industry, and metal mining in particular, extended itself more than any other to attain the limit of its productive capacity. Likewise, probably no other industry went quite so far toward jeop¬ardizing its own economic future through depletion of material reserves. Once we looked to Europe for most of the manufactured goods we needed. Our own limited mineral requirements were easily supplied from mines near the Eastern seaboard. With expansion and industrialization, our mineral needs increased in proportion, and the centers of mining activity moved westward to Michigan, Wisconsin, Minnesota, and the Tri-State district, where seemingly inexhaustible high-grade deposits of iron, copper, lead, and zinc ores were opened and rapidly developed.

Jan 1, 1946

By Joe B. Alford

Jan 1, 1971

Iron Ore Resources of the World (Die Eisenersvorrate der Welt)_ By G. Einicke. Verlag Stahleisen, Dusseldorf, 1950. 418 p., with 192 tables and an atlas volume containing 100 p. of reaps. 66 German Marks.-A notable work in which the latest available information on iron ore deposits has been compiled by diligent work, continent by continent, country by country. The author reveals the effect of geological formations, iron content of ore, accessability, cost of transportation, political and economic considerations. Ore beds of importance to the German iron and steel industry are given more space than others. The bibliography contains almost 250 references. A tragic comic feature is the author's complaint that as soon as a map of iron ore resources of a country has been completed, the country's boundaries are changed. Reviewed by W. Trinks, Carnegie Institute of Technology. Industrial Research Laboratories of the United States. National Research Council, Washington, D. C. Ninth Edition. 1950. 445 p. $5.-Contains information on the research laboratories of 2845 industrial and commercial organizations, including names of research executives, location of labs, types of activity, whether any consulting services are offered. There are two appendices, one of which lists data on government labo ratories which cooperate with industry, and the :)ibex naming universities and colleges offering research services to industry.

Jan 2, 1951

By Paul Beck

IT is well known that the hardness of metallic single crystals, like that of polycrystalline metals, increases during deformation (hardening by cold-work). It is also known that, as a consequence of deformation, the metallic material acquires an evident thermodynamic instability, revealed, for example, by the fact that the increased hardness gradually decreases with time, especially at elevated temperatures (softening by annealing). The temperature at which the stabilizing process begins is different for various metals, and for any metal it depends on the amount of deformation. Such stabilization of deformed metals may proceed in two different ways: through recovery, and through recrystallization. The former process allows the unstable deformed metal body to approach stability gradually and without visible change in the grain structure; the latter process, like an allotropic transformation, yields directly the undeformed stable "phase" in the form of new undeformed crystals, which, starting out of a certain number of nuclei, grow into and' consume' the deformed hard material. The extent of stability attainable through recovery is limited, espe-cially if the deformation of the metal crystal or crystals involves not only the gliding along slip planes, but also the bending of the slip lamellae, or at any rate the bending of comparatively large parts of the crystal lattice. In such cases, for instance in bent single crystals or poly-crystalline metals subjected to any deformation, recovery will not as a rule be able to restore the "straight" undeformed lattice, and stability can be attained only by recrystallization; that is, by the consumption of the bent crystal lattice parts by new, undeformed crystals-a much more drastic process. It is evident that the part of the surplus free energy stored in deformed crystals, which is present in the form of the elastic energy of the bent lamellae, is in these instances not considerably involved

Jan 1, 1937

By H. R. Wuthrich

The Metallgesellschaft AG decided in late 1965 to build an Electrolytic Zinc Plant at Datteln (W. Germany). Lurgi-Chemie was entrusted with the engineering and erection of the entire plant. Ground was broken in February 1967 and the operation was started on August 1st, 1968. The new Electrolytic Zinc Plant was designed to produce a minimum of 100,000 metric tons of special high grade zinc and 200,000 metric tons of sulphuric acid. Concentrates from Meggen (W. Germany) and mainly Timmins (Canada) are roasted in two turbulent layer roasters. The sulfur dioxide containing gases are converted in a "Bayer double catalysis unit" to sulfuric acid. The calcine is leached batch wise, the leach residue separated from the pregnant solution by counter-current thickeners and drum filters. For maintaining the sulfate balance a modified jarosite leach is being used. After a two step purification the neutral solution is mixed with spent electrolyte and cooled in unpacked atmospheric cooling towers. Three electrical circuits are supplying the power to the tankhouse, each rated at 30,000 amperes. With a maximum current density of 750 amperes per square meter and a stripping cycle of 24 hours, an average current efficiency of 90 percent is obtained. Cathodes are melted in one induction furnace and cast into shapes, or alloyed with aluminum and copper for die-cast metal.

Jan 1, 1970

By Eifu Moriyama

In 1953, Akita Plant, having a capacity of 560 tons per month, was built at Akita city by Mitsubishi Metal Mining Co., Ltd. for the purpose of treatment of the Ikuno and Akenobe Mines's zinc concentrates. Akita city, in whose neighborhood the black ore has been discovered, is located about 500 Km north of Tokyo and faced with the Japan Sea. This plant has been continuously expanded to have the capacity of 7,500 tons per month by the end of 1969. Efforts have been made to mechanize installations and to achieve continuous process. One of the characteristics of Akita Plant is the recent establishment of the residue treatment process. Many processes had been investigated, and finally commercial sulphate roasting of the residue has been carried out since 1965. At Akita Plant, special high grade electrolytic zinc, zinc alloy for die-casting (MAK brand), cadmium, cement copper and sulphur dioxide gas are produced. Sulphur dioxide gas is sent to the next door fertilizer plant to make acid. Table 1 shows production and the average assay of the electrolytic zinc and cadmium in 1969. This plant is divided into four main sections, two subsections, and residue treatment sections: Main sections are: (M-1) roasting section, (M-2) leaching and purification section, (M-3) electrolysis section, (M-4) melting and casting section,

Jan 1, 1970

By AIME AIME

ADDRESSING the Ohio Section at a recent meeting in Columbus, Ohio, R. C. Allen, executive vice-president for Oglebay, Norton & Co., Cleveland, spoke on "The Iron-Ore Industry of the Lake Superior Region in Prosperity and Depression." The speaker considered this region in connection with the problem of national security. This is the age of minerals; progress depends on them; and next to agriculture, the mineral industry is of prime importance. The United States has no shortage of minerals rather an over-supply; but many mines have been and are being exhausted. The shifting of the sources of supplies of minerals so important as copper, petroleum, and iron to other countries would create internal strains and affect international relations. There will be no early decline of ore mining in the Lake Superior region unless it is forced by unwise public policies. Iron ore is industrial strength and self-sufficiency. A study of economic geography is important for statesmen and mining men, because the minerals essential for peace and war are haphazardly or irregularly distributed throughout the world. Of these minerals, 75 per cent are owned by 10 per cent of the population, mainly peoples of Anglo-Saxon origin.

Jan 1, 1934

By Rudolph G. Wuerker

Charles T. Holland (Head, Dept. of Mining Engineeri*, Virginia Polytechnical Inst., Blacksburg, Va.) Mr. Wuerker has presented a very interesting discussion of the use of triaxial test methods for investigating the strength properties of rocks. Such methods, no doubt, eventually will develop considerable information of interest to those concerned with the design of mine layouts, particularly in the field of pillar design. From his discussion of my recent article, "Cause and Occurrence of Coal Mine Bumps" (Holland Mining Engineering 1958, p. 933-1002), it is evident that in one place at least I did not make my meaning clear to him and perhaps others. To clear the matter up I think it best to quote from the article, somewhat more fully than did Mr. Wuerker, as follows: "4) In actual operations — because rocksare not perfectly elastic, homogeneous, nor isotropic and because local yield does occur — the maximum stress as demonstrated by Phillips (Ref. 22, pp. 64, 65) and indicated by much experience in mining, does not occur at the walls of the opening but at a short distance inside the pillar. Furthermore, the maximum stress does not reach as great a value as theoretical considerations and laboratory experimental methods indicate.* Actual distance inside the pillar, measured from the wall, at which the maximum stress exists, has not been determined. Observations in many mines, however, indicate that this distance could have a mini-value of one to six or eight times the bed thickness and that it is probably affected by width and height of the opening, depth of cover, and relative values of the elasticity and plasticity of materials comprising the roof, floor, and coal seam. The actual value of the stress produced probably lies between the theoretical maximum and the average stress concentration that would be produced if the weight of the strata above the unsupported opening were evenly distributed over the pillars for a distance equal to the opening width." The footnote reference in the above quotation referred to the following: "*For example, the Pocahontas No. 4 coal bed in southern West Virginia is mined under cover up to 1800 ft thick. Development openings are driven 18 to 20 ft wide, and the bed is about 6 ft thick. According to the work of Panek, the tangential wall stress at mid-bed height under these conditions would reach values between 4000 and 5000 psi. Actual tests of 3-in. cubes of this coal show its compressive strength would be much less than this, perhaps as low as 400 psi. Yet the pillars usually show no evidence of failure in these headings. In this same bed at a depth of 800 ft, the author has seen an opening 225 ft between supports lying between two old groves approximately 1100 ft apart. According to the theoretical considerations, the stress in the pillar walls would have been about 18,000 psi, yet the pillar showed little or no evidence of weight. In view of these observations, it is clear that the wall stress does not attain the maximum values indicated by theory." (Underlining added to original wording.) By referring to Fig. 2A of my paper it will be noted that theoretically the maximum pillar stress would occur at the pillar wall, i.e., at the passageway surface of the pillar. Obviously this cannot be correct in the cases of stress ranging from 4000 to 18000 psi since the coal at the surface of the pillar is under no constraint and cannot have a strength much greater than 400 or 500 psi. Hence, my conclusion that the maximum stress does not occur at the wall but back in the pillar some distance from the wall. Since these stresses are pushed back in the pillar from the wall, it is also obvious that the loads transferred to the pillar from the opening will be spread over a greater area and hence Pillar stresses will not rise to the values postulated by theory and photoelastic experiment. Further since to visual inspection the coal along the pillar wall did not appear to be failed the conclusion was reached that the stress shift was caused by local elastic or plastic yield and by difference in the elastic modulus of the rocks composing the mine floor, mine roof, and coal bed. Later on under the heading "Strength of Mine Pillars" (pages 1000-1002) the effects of constraint is briefly described. Also a formula taking into account constraint is developed relating pillar strength to the uniaxial strength of coal and the L/T ratio of the pillar. Since my paper was written, reports of experiments conducted in South Africa (Denkhaus, et. al., 1959), in Sweden (Hast 19581, and in Canada (McInnes, et.al., 1959) reveal that the conclusion expressed relative to the existence of a low stress area existing around the edges of pillars and solid faces as described above is generally correct. But it seems possible that where the wall stress developed is less than the unconfined strength of the rock composing the pillar and where the roof, floor, and pillar

Jan 1, 1961

By George R. Cowan

A number of studies hare been reported of the effects produced in metals subjected to deformation by shock waves with maximum pressures ranging from tens to hundreds of kilobars. On the basis of the equations for the flow of mass, momentum, and energy through a stationary shock front, the macroscopic stress-strain curve for the resulting shock deformation can be calculated within narrow limits from the experimentally determined Hugoniol curve. In relatively weak shocks which are preceded by an elastic wave, the stress rises above the clastic limit only as plastic deformation proceeds cold thus the shock has a long toe. In strong shocks that override the elastic wave a high stress is applied without prior plastic deformation. A more important effect of increasing the shock pressure is the generation of shear stresses, called supercrilical shear stresses, that exceed the strength of the perfect lattice. A change in the mechanism of deformation is expected to result from the onset of supercritical shear. The shock disordering of ordered Cu3Au in strong shocks appears to be an example of such a change. It is suggested that the formation of fine twins in copper and nickel and the formation of structures which enable visible twins to be formed in the rarefaction ware, observed in copper and presumably in disordered Cu3 Au, are related to the occurrence of supercritical shear in shock dcformation. In recent years several studies1,2 have been made of the changes in structural and mechanical properties of metals produced by the passage through the metals of strong shock-compression waves ranging from about 50 to 800 kbar pressure. Recent work involving dynamic measurements of the shock compression "Hugoniot" curves 3-8 of many metals has developed techniques and provided data required to obtain the shock pressure and the (transient! plastic deformation produced in the shock-conlpression experirnents.9 Shock deformation has been found to be much more effective than slow deformation in changing the mechanical properties of metals, when the two are compared on the basis of equal plasti strain, Holtzman and Cowan9 made quantitative estimates of the shearing stress occurring in a shock front in a metal by assuming that the shearing stress is similar to that occurring in a shock front in a viscous, heat-conducting fluid, with the addition of a yield stress. Taylor's solution9 for a weak shock was used to estimate pairs of values of shearing stress and thickness of the shock front obtained by assumed choices of the ratio of effective kinetic viscosity to thermal diffusivity. It was noted from these values that. unless the shock front is extremely thin. heat conduction has slight effect, and the shearing stress is nearly independent of the mechanism of deformation. This mechanism does, however, determine the thickness of the shock front and the rate of strain. Furthermore, since the maximum possible shearing stress occurring in shocks of moderate strength does not greatly exceed the shear stress occurring in conventional slow deformation, the mechanism of deformation is not expected to be qualitatively different. The greater effectiveness of shock deformation in changing the mechanical properties of metals can be attributed partly to the fact that dislocations, when driven by near-conventional stresses, cannot keep up with the shock front, thus necessitating a higher dislocation density than required for an equivalent slow strain. The fast uni-axial strain occurring in the thin shock front would also be expected to cause a larger number of dislocation intersections to occur. In the upper range of shock pressures that have been studied the estimated values of the shearing stress exceeded the estimated shear strength of a perfect crystal. Under these circumstances it is reasonable to expect that the mechanism of deformation might be considerably different from that involved in slow deformation. Except for the observation by smith1 of twins in shocked copper, the effects of shock waves on metals did not show any obvious or large changes in properties that would indicate the onset of a change in the mechanism of deformation. The recent investigation of the effect of shock waves on ordered and disordered specimens of Cu3Au by Beardmore, Holtzman, and ever" showed a spectacular decrease in the amount of long-range order retained by initially ordered Cu3Au when the shock pressure was raised from 290 to 370 kbar. Since Dr. Holtzman and I suspected that this behavior probably was due to the onset of a shearing stress in the shock front in Cu3Au which exceeded the limiting shear strength of the perfect crystal. it was considered appropriate to examine directly the shock-front equations for a solid. and to obtain a sound estimate of the shearing stress occurring in the front using equation of state data obtained from shock studies. In this paper an estimate is made of the

Jan 1, 1965