Search Documents

By H. P. Greenwald

THE Committee on Rock-Dusting was formed after the fall meeting of the Coal Division in Chicago in 1938. Its primary task was to study the recommended American practice for rock- dusting coal mines to prevent coal-dust explosions as approved by the American Engineering Standards Committee. After approximately two years' work he committee concluded that although certain portions of the recommended practice could well be revised, information needed for a logical revision was not at hand, and it was inadvisable, therefore, to make revisions

Jan 1, 1943

By N. S. Wagner

The production of lightweight aggregates in Oregon is a new industry, and, like all new enterprises, it is suffering from growing pains characterized by numerous, small operations some of which flourish for a short time and then cease altogether. Normally all industrial mineral products are produced in a highly competitive atmosphere. At the present time this condition does not exist to a very marked degree in the state because as yet producers have not saturated the constantly expanding market. This paper has been prepared with the intention of outlining very briefly the current status of the various products now being used as lightweight aggregates in Oregon. The present picture will surely change, perhaps quite radically within even a short space of time.

Jan 1, 1949

By P. P. Gregory

ESTIMATION of re- serves in prorated sand fields has been discussed by S. A. Judson, H. D. Easton, Jr., and W. A. Schaeffer, Jr., in a paper that appears in Vol. 114 (1935), of the A.I.M.E. TRANSACTIONS. The purpose of this present paper is to extend the investigation to prorated flush limestone fields and to outline a method of procedure in determining the amount of oil originally in place and the amount of oil that can be recovered from such fields. Although it is possible to use the decline curves to estimate the amount of recoverable oil in certain limestone fields that are allowed to produce the oil at or near capacity production, such a method cannot be used in fields under severely restricted production rates. The problem is exceedingly complex due to fluctuation in the allowable rates of oil production over a wide range and at frequent intervals, and especially because of the heterogeneous nature of the reservoir itself. A well completed in a large solution cavity, capable of producing great quantities of oil per day, may be offset by a well of very limited capacity. Also, it is di5cult to arrive at an average figure for porosity in a given limestone reservoir due to abrupt variations in the character of limestone, in many instances even between two ad- joining wells. It is a safe statement that uniformity of porosity and permeability in limestone reservoirs .is nonexistent. It is evident, therefore, that the method of estimation of re- serves on the basis of per-acre content can give only approximate results.

Jan 1, 1935

By H. A. BURK

THE ores of the Tonopah, district are hard, compact and' highly siliceous. They contain from .1 to 2, per cent. of sulfide material, of which argentite is the valuable mineral; occasionally pyrargyrite is found in the richer ore. The sulfide is, chiefly pyrite with small amounts of chalcopyrite,. and sometimes sphalerite. The ore also contains a small amount of gold-about 1 per cent. by weight of the silver present. The major gangue constituent is quartz but frequently considerable rhodonite-called by the miners pink manganese-is present. For primary crushing, jaw and gyratory crushers are used. These crushers are of such capacity that, in most cases, one 8-hr. shift will supply the mill for 24 hr. The Extension Co., at the Victor ore house, passes the ore through a 13 by. 24-in. Blake type McFarland crusher set at 13 in., and at the No. 29 re house, a 14 by 24-in. Blake type Traylor crusher is used. The ore is thus crushed to stamping size in one reduction. The capacity of each crusher is about 40 tons per hr.; the power consumption is 0.6 kw. per ton.

Jan 1, 1921

By Lendall P. Warriner, Blandford C. Burgess

Jasper County lies just north of the geographical center of Georgia, bounded on the west and north by the Ocmulgee River. The county seat, Monticello, is approximately 65 miles east-southeast of Atlanta and 40 miles north of Macon. It is served by the Macon-Athens branch of the Central of Georgia Railway Co. and by five paved highways converging from adjoining county seats. Farming and lumbering are the principal local occupations. About half the county is covered with pine and mixed hardwoods; a large part of the forested land is owned by the Soil Conservation Service of the Department of Agriculture in its Piedmont Land Utilization Project. The topography is one of gently rolling field and forest with occasional hills rising 100 ft or: more above the creek beds. Though annual rainfall is in the neighborhood of 60 in., most of it falls in torrential downpours of short duration which tend rapidly to erode the red soil and convert the country roads to greasy tracks of red mud.

Jan 1, 1949

By A. J. Opinsky

MANY investigators, in their discussions, have reasoned that the ductile-brittle transition in iron could be explained by the intrusion of cleavage into the normal slip process. The purpose of this note is to apply the laws of critical normal stress for cleavage and critical shear stress for slip to explain the orientation and temperature dependence of the ductile-brittle transition in body-centered cubic metals. It will be found that within a certain temperature range, single crystals tested in tension will cleave or slip, depending on their orientation. Some data recently appearing in the literature will be analyzed from this standpoint. For a single crystal with [uvw] parallel to the tensile axis, the resolved shear stress on the slip

Jan 1, 1954

By Lawrence W. Teufel

An anelastic strain recovery technique is presented as a method of determining the directions and ratio of the maximum and minimum horizontal in-situ stresses from oriented cores from deep wells. Predictions of hydraulic fracture azimuth inferred from principal stress directions determined from both elastic and time-dependent (anelastic) strain relaxation measurements of volcanic tuff are consistent with the observed orientations of hydraulic fractures produced in simulation and mineback experiments, underground at the Nevada Test Site. In addition, anelastic strain recovery measurements on oriented cores of shale and sandstone from well depths of about 1680 meters show consistent relaxation directions of the principal horizontal strains and have enabled a prediction of the principal horizontal stress directions and hydraulic fracture azimuth.

Jan 1, 1982

Aamot, Olav Crone, (M'29) Chem. Engr., Elektro¬kcmisk, Raadhusgt. 32, Oslo. Norway. . Aase. Glenn D., (J'40) Jr. Met., American Smelt. & Refin. Co., Selby, Calif. Abadie, Henry G., (J'43) Petr. Engrg., Avenal, Calif. Abadilla, Quirico A., (M'38) Min. Engr., Dir., Bureau of Mines, Manila, P. I. Abbott, Agatin Townsend, (J'40) Jr. Engr., Phelps Dodge Corp., Morenci Branch. Morenci. Ariz. Abbott, Clarence E., (M'04) Civ. Engr. V.P., Tennessee Coal Iron & R.R. Co., 1542. Brown Mars Bldg. Birmingham. Ala. Abel, Raymond L.. (M'23) Chem. Engr., Com¬manding Officer, Pittsburgh Chem. Warfare urement Dist., American Bank Bldg.. Pittsburgh. Pa. Abel, Walter D., (M'32) Min. Engr., Supvr. Engr.. R.F.C., Los Angeles, Calif. Abele, Louis T., (M'31) 423 3rd Ave., Decatur. Ga. Abell, Leo M.: (M'31) Mill Supt. & Met.. Em¬ peror Gold Min. Co., Ltd., Vatukoula. Fiji Islands. Abernathy, G. E., (M'38) Geol., Kansas State Geol. Survey, Pittsburg, Fan. Abernathy, Jack H., (M'40) Cons. Petr. Engr., First National Bldg.. Oklahoma City, Okla.

Jan 1, 1943

By Mark J. Klein

The creep of 043 was studied over the temperature range 1650" to 3200°F and over the stress range 3000 to 44,000 psi. The steady-state creep rate over this range of stress and temperature can be expressed by the equation where A is a constant, is the stress, and is -0.8 x 103 psi-'. Over a narrow range of stress variations c0 a and for this proportionality n varies from 3 to 30 in accordance with the relation n = aB. Above about 2400° F, H, the apparent activation energy for creep, is 110,000 cal per mole, a value about equal to that estimated for self-diffusion in this alloy. Below 2400°F, H increases with decreasing temperature reaching a value of -125,000 cal per mole at 1700° F. In this temperature region, H appears to be a function of the interstitial concentration of the alloy. MOST of the detailed creep studies of dispersion strengthened metals have been concerned with metals having fcc structures. However, there are a number of important refractory alloys with bcc structures that derive part of their high temperature strength from an interstitial phase and whose creep behavior has not been well defined. This paper describes the creep behavior of the bcc alloy, D43, over the temperature range 1650" to 3200°F (0.4 to 0.7 Thm) and over the stress range 3000 to 44,000 psi. In addition to colum-bium, this alloy contains 10 pct W. 1 pct Zr, and sufficient carbon (-0.1 pct) to form a carbide dispersion throughout the matrix of the alloy. The effects of variations in temperature and stress on the steady-state creep rate of this alloy are presented in this paper. EXPERIMENTAL PROCEDURES Creep tests were made in a vacuum of 106 torr under constant tensile stress conditions using a Full-man-type lever arm.' Creep specimens were machined from 0.020-in. D43 sheet (grain size -5 x l0-4 in.) processed in a duplex condition (solution annealed -2900°F, 40 pct reduction in area, aged 2600°F). The specimens were tested in this condition without further heat treatment. Specimen extensions over 1-in. gage lengths were continuously recorded using a high temperature strain gage extensometer. Differential temperature and stress measurements were used to determine temperature and stress dependencies of the creep rate. Activation energies were calculated from the changes in strain rate induced by abrupt shifts in the temperature during constant stress creep tests. The 100°F temperature shifts used in most of the activation energy determinations required 15 to 90 sec depending upon the temperature at which the shift was made. The dependence of strain rate on stress was determined by measuring the change in strain rate for incremental stress reductions during constant temperature tests. It has been shown that columbium-base alloys such as D43 are susceptible to contamination by gaseous interstitial elements during vacuum heat treatments.' In this regard, it is unlikely that these alloys can be heat treated without some loss or gain of interstitial elements despite the precautions taken to control the heat treating environment. However, several factors suggest that changes in interstitial concentrations of the specimens during testing did not affect the results presented in this paper. First, the dependence of the creep rate on the stress or temperature determined during the course of a single creep test showed no variations with the duration of the test. A variation would be expected if a loss or gain in interstitial concentration during the course of the test affected results. In addition, precautions taken during this investigation to minimize interstitial contamination by wrapping the gage lengths of the specimens with various foils2 (Mo, Ta, W) did not produce a detectable change in the stress and temperature dependencies relative to the unwrapped specimens. The averages of duplicate analyses for carbon and oxygen in several specimens determined before and after creep testing are listed in Table I. The combined nitrogen and hydrogen concentrations which were ordinarily less than 50 ppm did not change in a detectable way with creep testing. The analyses show that only minor changes in carbon concentration occurred during creep testing except for specimen 4. This specimen which was tested at 3100°F lost a significant amount of its carbon concentration to the vacuum environment. Specimen 1 gained 100 ppm of O, while specimens 2, 3, and 4, which were tested at progressively higher temperatures, lost increasing portions of their initial oxygen concentrations during testing. RESULTS AND DISCUSSION The Temperature Dependence of the Creep Rate. The apparent activation energy for creep, H, was de-rived from creep curves similar to that shown in Fig. 1. Steady-state creep was rapidly attained at the beginning of the test and with each change in temperature. This behavior suggests that the alloy rapidly attains a stable structure with each shift in temperature or that the structure is constant throughout the test. Since the dispersion will tend to stabilize the structure, the latter is probably the case. The activation energy was found to be independent of the direction of the temperature shift and the magnitude of the shift (50" or 100°F). Although H was approximately independent of the strain, there was a tendency for it

Jan 1, 1970

By Leslie C. Richards

The competitive position of producers of industrial minerals depends upon the delivered price of their product. Freight charges are a major factor in the sales to consumers. A comparison of freight rates on movements of limestone and silica rock in the Pacific Northwest shows a wide variance in mills per ton mile for like hauls, thereby favoring some localities over others.

Jan 1, 1950

By G. B. Gould, F. M. Gibson

IN DECEMBER, 1934, the joint Committee on Fuel Values, of the American Institute of Minim and Metallurgical Engineers and the American Society of Mechanical Engineers, submitted a preliminary report, which briefly stated its conclusion that it was not possible to devise any formula for the valuation of coal, based upon the various physical and chemical properties, that would be generally applicable. That report also listed those chemical and physical properties of coal that are generally recognized to have some effect on its use in steam plants, and those physical characteristics of steam plants which affect, in one way or another the relative importance of the properties of coal used in them. Since then, the Committee has considered and discussed in greater detail the interrelationship of the properties of coal and plant characteristics. The conclusions of the Committee are summarized below, with certain recommendations regarding engineering procedure, which will promote the collection of more easily correlated observations with respect to this subject, and thus advance more rapidly the accumulation of data capable of general application.

Jan 1, 1936

By Arnold Hoffman

A RESPONSIBLE steel executive recently declared that scrap shortages, despite fantastic prices reaching up to $50 per ton, are responsible for the loss of 140,000 tons of steel a month and that in March 1947 alone 25 more steel furnaces could have been operating were it not for scrap scarcities. His answer to this serious situation was to ask for a speedier flow of scrap and also abolition of Government control over pig iron distribution. It would be more logical, perhaps, if an answer to this growing problem of scrap deficiency were sought within the steel industry itself. As long ago as 1933, L. B. Lindemuth, a consulting steel metallurgist, warned the steel industry that a shortage of scrap was inevitable and that beyond 1938, adequate supplies for open-hearth furnaces could not be expected. The outbreak of war, with consequent phenomenal demands on the industry, accelerated production of steel and further worsened the scrap situation. Today we are suffering from a condition which could have been prevented had the industry been more far-seeing and provided for an inevitable contingency. However, better late than never, and measures can now be taken to alleviate permanently scrap shortages in the future. This can be done by greater utilization of heavy sinter which experience proved is an excellent substitute for scrao and lump ore.

Jan 1, 1947

By D. M. Schuster, E. Scala

The elastic effects occurring in the matrix of a composite reinforced by discontinuous fibers were studied by means of photoelastic techniques. A hirefringent plastic was employed as the matrix material with high-strength a Al2O3 whiskers as the reinforcing fibers. It was found that for whiskers aligned parallel to the tensile load direction: (I) Matrix reinforcement occurred along the length of the whisker to within about 5 diameters of the whisker tip for a length to diameter ratio, L/D, of 40. (2) Significant stress concentrations were created in regions immediately surrounding the tips; the fine as-formed tapered ends exhibited the minimum stress concentration whereas the square-ended whisker produced relatively high values, K r 2.5 for L/D = 40. (3) The axial and radial stress distributions could he determined quantitatively; the stress distribution at the whisker-matrix interface was in general agreement with theoretical calculations. (4) The highest source of stress concentration occurred at points of fracture in whiskers which had ruptured after incorporation into the composite. Whiskers aligned perpendicular to the load direction neither reinforced nor caused appreciahle stress concentrations in the matrix. ThE properties of composites have generally been formulated empirically on the basis of macroscopic tests. There are still many questions concerning the mechanical and chemical interactions occurring at the interface between the reinforcing fiber and its matrix. Continuously reinforced plastics and dispersion-hardened metals represent the two extremes of composite reinforcement. Whether artificially produced or formed in situ, the whisker composite falls between these two extremes and is an example of discontinuous fiber reinforcement. The effect of fiber shape, size, surface condition, and end configuration on the stress distribution in the matrix is important since the presence of stress concentrations, especially in any high-strength, thin-wall structure, could become the cause of catastrophic failure. DOW,' in his theoretical discussion of discontinuous fiber reinforcement, has pointed out that appreciable stress concentrations occur at the tips or ends of the reinforcing fibers. It is the purpose of this study to examine directly, by means of the photoelastic technique, the stresses which occur in the vicinity of a discontinuity or whisker tip and to measure qualitatively and quantitatively the effects of whisker geometry when embedded in a birefringent matrix material. The use of sapphire (a A1,O3) whiskers was decided upon as the reinforcing agent because of their high elastic modulus (E- 60 X 106 psi) and in some cases strengths in excess of one and a half million psi. Sapphire whiskers are of further practical interest since they retain large fractions of their strength up to temperatures approaching the melting point (3720oF).2 The whiskers were grown, by the vapor-phase reaction commonly employed,3 as part of this study to insure a physically uniform supply. Tensile and bend tests were performed to verify that the whiskers were of the expected ultra-high strength. The high-strength whiskers can be identified and selected from the combustion boats by surface perfection, shape, and size; otherwise, strength values can vary by a factor of ten or more. Macroscopic defects are quite common on the surface of large bladed whiskers and the principal experiments were conducted with hexagonal whiskers of about 0.002 in. diameter and lengths ranging from 0.1 to 0.4 in. Upon completion of these two phases of the experiment, several birefringent resins were evaluated. A plastic, developed by Zandman,4 which is supplied by the Budd Co., was found most suitable and was used as the matrix material for the whisker composite throughout the study. It has a sensitivity of 60.5 lb per in. order, calibrated in tension and cures without introducing residual stresses. Young's modulus for this matrix material is 430,000 psi in the fully cured condition. Since good wetting and bonding between the sapphire and the matrix material is essential to the interpretation of the results, a wettability test was performed. The contact angle was measured to be 168 deg where perfect wetting is defined as 180 deg; therefore, the Budd Plastic wets the sapphire

Jan 1, 1964

By J. Paone, S. Tandanand

This paper studies the behavior of rock at the initial state of crater formation resulting from stresses created under a drill bit. The purpose of this study is to determine which mechanical properties of rock are important in rock fragmentation by drilling. Although a definite relation between the drilling strength and relevant mechanical properties has not been established, maximum yield strength or hardness of rock is apparently a parameter of drillability of rock. The strengths of rock were considered from the Mohr-Coulomb criterion from which the surface of failure was constructed. The results from previous triaxial tests on Solenhofen limestone were adopted in establishing a limit of failure. Inelastic behavior of Solenhofen limestone was observed under a low velocity impact of a hemispherical bit and under static indentation with a similar bit. Permanent set at low applied loads in the indented area was measured with an interferometric technique. A quantitative determination of strengths of the rock was made under static indentation. The maximum yield strength estimated from the average stress over the contact area for plastic deformation was used as the crushing strength of rock under a drill bit. Much research has been done on energy requirements and mechanisms of energy dissipation to perfect rock fragmentation by a drilling process. But more needs to be done. More needs to be known about the mechanisms of energy dissipation or failure criteria of rocks in the drilling process in order to evaluate the efficiency of energy requirements in specific rock fragmentation. This paper examines some published studies on rock failure and energy dissipation and presents some findings in that phase of research concerned with rock fragmentation by drilling. This work is specifically concerned with rock behavior at an early stage of failure induced by a concentrated load. Consideration is limited to the primary phase of the crater formation under drill bit, i.e., before chipping takes place. Failure Phenomena of Rocks: Failure of rocks can be classified into two types, fracture and plastic flow. Both involve separation of material to form new surfaces with complete or partial loss of cohesion. Fracture is further classified as extension (or cleavage) fracture and shear fracture. Extension fracture involves separation in a plane without shear stress component, while shear fracture involves slippage along a plane as a result of combined stresses. Then, shear fracture inclines to the axes of the principal stresses. Plastic flow occurs under combined stresses, especially at high confining pressure and temperature, and denotes macroscopically irrecoverable deformation of rocks. Flow mechanisms have been classified as in-tergranular failure, intragranular gliding, and re-crystallization of mineral constituents.6 Failure phenomena in rocks are complicated because they include fractures and plastic flow as well as a friction process developed intrinsically as the internal stresses increase. All can occur in one rupture process, depending on the varying stress conditions. Both fracture and plastic flow are encountered in rock drilling. Rock failure under a drill bit as observed in drop tests simulating a single blow of a percussion drill, consists of two types, crushing and chipping. Crushing is considered as a separation of material particles by many fractures resulting from the application of high compressive stresses exceeding the strength of rock at the contact area. Chipping results from subsurface fractures extended to the face surface; this phase is preceded by crushing or surface deformation. The state of stress under the drill bit and the strength of rock create and control these two types of failure. The state of stress under the bit and in the vicinity of the contact area depend on the bit configuration and the magnitude of applied force. The strength of rock, characterized by its ability to resist penetration, depends on its composition and structure. However, the term "strength" quantitatively defined, is still ambiguous and may or may not correspond to the tensile, compressive and shear strength obtained from simple tests. Rock Failure Criterion: Rocks are weak in tension, their tensile strength being many times less than their compressive strength. This characteristic excludes

Jan 1, 1967

By H. O. Hofman

(Canal Zone Meeting, November, 19]0.) THE sudden decease, April 1, 1910, in Chicago, of Dr. Franklin R. Carpenter was a shock to his- many friends. He died in his sixty-second year, of heart paralysis. To most fellow-members of the Institute who have followed the progress of the. last twenty-five years in the mining and treatment of non-ferrous ores, the work of Dr. Carpenter in that line is familiar ; but very few, even of those who knew him well in the later years, are acquainted with his earlier struggles to satisfy an inborn hunger for knowledge. The story of his life resembles that of the pioneer who opens up new country; overcoming hardships with indomitable courage, meeting doubts and difficulties with an alert and open mind, and exercising in the face of reverses an unconquerable perseverance. It seems appropriate to place on record in the Transactions a brief outline of the life and work of this eminent engineer. During the past 15 years of his life Dr. Carpenter was much interested in genealogy. In the pursuit of this study as an avocation, he traced his own ancestry to the time when ?Hugh," called "le Charpentier" on account of the dexterity with which he had swung his battle-axe as a crusader, settled in Sussex on lands received from William the Conqueror. The Carpenters came to this country with William Penn. A prominent member of the family was Joshua Carpenter, the founder of Christ Church, Philadelphia. Dr. Carpenter's branch of -the family moved from Pennsylvania into that part of Virginia which is now West Virginia, where his grandfather settled in Harrison county, while the grand-uncle went further west, and built the first iron-furnace at Hanging Rock, Lawrence county, Ohio. In fact, since early times, the Carpenters appear to have been iron-masters. Franklin R.. Carpenter was born, Nov. 5, 1848, in Parkers-

Aug 1, 1910

By William B. Millar

IN ONTARIO development of the gold mines is being rapidly pushed, while the intensity of the search for new mines has probably not been equaled at any time in the past. Even to outline the results of recent prospecting activity in Ontario would be a big undertaking, but it would be timely and, I hope, interesting to Institute members to review some generalities regarding the work of the prospector and then to discuss in some detail the growth of Ontario's most promising prospect area, the Swayze district, where serious mining operations are already under way. Probably no one writing about prospectors and pros¬pecting can resist hoping that his article will not reach the eyes of a certain portion of the uninformed general public and cause a further influx of "prospective prospectors" into any given area. It is somewhat mystifying how so many people reach the conclusion that prospecting is in

Jan 1, 1933

By Leo Wolrnan

IN the relations that exist between capital and labor in this country, there is a bright as well as a dark side. After many years of distressing conditions of labor and a plentiful supply of propaganda, it is doubtful that the doctrine of the class struggle, however defined and stated, has been embraced by any influential and numerous elements of our population. Extreme and uncivilized methods of conflict, whether they be the labor spy as used by the employer or the sit-down strike by organized, labor, have come to be abandoned as the result of the pressure of sober and distinterested public opinion. Unwise terms of our law of trade unions and the unbridled zeal of its administrators show some slight signs of being revised in the light of 'experience and the protests of the law's own beneficiaries. At the point where labor policy touches economic conditions, the two powerful factions in the American labor movement appear to look with a less friendly eye on the bewildering succession of economic experiments and to have a deep nostalgia for a simpler and more prosperous economy.

Jan 1, 1938

By J. P. Smith

Permian salt measures carry extensive lenses of soluble potash salts in north central Germany. Potash deposits of Oligocene age are found in the Upper Rhine Graben of Alsace (France), and in the Catalonian Basin of Spain. These deposits are found in a wide range of structural settings. Reserves are large, and the production of potash salts is an important phase in the economy of each of these countries.

Jan 1, 1950

By A. B. Parsons

LAST YEAR (1934) saw the completion of a ten-year program of reconstruction and modernization of the world's largest lead- smelting plant, that of the ' Broken Hill Associated Smelters Proprietary, at Port Pirie, South Australia, which has a capacity for smelting and refining 220,000 (short) tons of lead per year. It deals with the entire output of lead concentrates from the famous Broken Hill district in Australia, being owned .jointly by the three leading companies: North Broken Hill, Broken Hill South, and the Zinc Corporation. These companies, together with the Sulphide Corporation, are credited with a production of 198,000 tons of lead in 1934. When one says regarding any metallurgical plant that modernization is "completed" he should add "for the moment." Development in the art of metallurgy and in the equipment used never ceases; that which seems close to the last word today is likely to be obsolete in a few years even in a process so well standardized as smelting and refining lead. However, the reconstruction at Port Pirie has altered the procedure materially. More im-

Jan 1, 1935

By W. F. Hosford

A series of aluminum single crystals was subjected to axially symmetric flow by drawing through dies. The orientation dependence of the drawing stress, which indicates the resistance to this type of flow, compares reasonably with predictions of Taylor and of Bishop and Hill. Measured lattice rotations likewise are generally consistent with theory. The most successful analyses of the plastic behavior of polycrystalline metal and its relationship to single crystal behavior are those of Taylor1-3 and of Bishop and Hill.4-6 The purpose of this paper is to provide a critical test of some of the basic assumptions involved in these theories. Both treatments apply to fcc metals and assume the shape change of each grain in a polycrystal to be the same as that of the polycrystal as a whole. Thus for a randomly oriented polycrystal extended under uni-axial tension each grain is assumed to undergo axially symmetric flow. dey = dez = -1/2dex, deyZ = dezx = dexy = 0 [l] where x, y, and z are a set of orthogonal axes, x being the tensile axis. Although [011.] oriented grains in bcc and fcc metals may depart markedly from this ideal behavior,7,8 the assumption is probably quite reasonable for most grains. Under a uniaxial tensile stress, ox, the work dW per unit volume expended in producing an increment of axial strain dex is, dW=oxdex [21 Since this work is expended in slip, dw =STi dyi 131 where Ti and yi are the shear stress and shear strain on the active slip systems. In both analyses Ti is taken to be the same on all slip systems, and dependent only on the total prior shear strain on all systems, so dw = Tdy [41 where t is the shear stress required for slip and y is the sum of the shear strain yi on all slip systems. Combining 121 and [4] and defining M = oX/T The ratio M is a generalized Schmid factor. It relates the tensile stress required for axially symmetric flow, ox, to the basic shear stress, 7, and it also expresses the ratio of crystallographic strain, y, to the tensile strain, Ex It depends only on the orientation of the crystal. Taylor evaluated M for various orientations by finding the least value of dy/dEx which could satisfy the shape change. Bishop and Hill, on the other hand, found M by considering the relative work (1/T)dW/dEx expended by stress states which could activate enough slip systems to produce the shape changes. The results of both methods appear to be equivalent, although certain omissions were made in Taylor's original work. The orientation dependence of M, calculated by the second method,9 is shown in Fig. 1. Taylor used the average 2= 3.06 for all possible orientations to predict the tensile stress-strain curve (oxvs Ex) for a random polycrystal from the shear stress-strain curve (t vs y) of a single crystal. Changes in M from lattice rotation were neglected so points on the ox vs ex curve were simply taken at ox = 3.06t and e = y/3.06 from corresponding points on the t vs y curve. Recent extension of the analyses of Taylor and of Bishop and Hill to crystallographically textured metals has been used to relate plastic anisotropy to textures, and to predict the potential texture hardening that could result from texture control.9 Unfortunately there have been relatively few experimental tests of the underlying theory. Taylor found that the tensile stress-strain curve of polycrystalline aluminum did agree reasonably well with that predicted from a single-crystal T-y curve. Had the single crystal undergone easy glide, how-

Jan 1, 1965