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By W. L. Phillips

Aluminum and copper single crystals were strained in shear, unloaded and rotated 60, 120, and 180 deg. The magnitude of the Bauschinger strain increased rapidly during the easy glide region and became constant as the easy glide limit was reached. An increment in stress was not required to continue slip in any close-packed plane or in the reverse direction during easy glide. A qualitative theory is proposed to explain the present results. FOLLOWING the initial work on tin by Bausch,' there have been several investigatorsB7 who have employed the shear test to study the deformation of aluminum. In all cases the shear technique was employed in an attempt to obtain a more homogeneous shear than in the conventional tension test The direct shear technique has the obvious advantage, relative to the tension test, that a crystal may be stressed in any predetermined plane and direction, including the reversal of strain sense. In the present investigation the shear technique was employed with aluminum and copper single crystals and their behavior was studied with respect to deformation in all close-packed directions in the octahedral plane. In contrast to previous investigations, the shear technique was used in an attempt to obtain a stress-strain curve in shear which is identical with the corresponding tension curve and then to use the additional degree of freedom of the shear test to study the mechanical behavior of crystals in all close-packed directions in the octahedral plane. PREPARATION OF CRYSTALS Single crystals 1/2 in. in diam and 6 to 7 in. long, were prepared from aluminum containing 0.001 pct Si, 0.001 pct Fe, and 0.001 pct Zn, by spectro-graphic ana1ysis and from OFHC copper. Crystals were grown from the melt in graphite at a rate of 1 5 in. per hr. The copper crystals were grown under an argon atmosphere. No lineage structure was observed in Laue patterns, though small angle boundaries were present in the crystals. The aluminum and copper crystals were annealed at 640" and 900°C, respectively, for 24 hr and furnace-

Jan 1, 1962

By William J. Campbell

Expansion measurements of platinum, added as an internal standard, are used for thermal calibration of X-ray cameras and diffractometers. Accuracy of the temperatures derived by this technique depends on the precision of expansion measurements and the reliability of reference expansion data. Temperature measurements to ± 1° C. require ?d or ?a to be determined within ± 0.001 percent. Selected expansion data are concluded to be reliable to 2° C., 5° C., and 25° C., over the temperature ranges 0° C. to 700° C., 700° C. to 1,000° C., and 1,000° C. to 1,700° C., respectively. Tabular expansion values from 25° C. to 1,700° C. in 2° C. intervals were calculated from the following equation; Expansion, percent = [8.91 + 1.28 x 10-3(t-25) + 0.04 x 10-6(t-25) ] [t-25.104 ] These tabular values facilitate future corrections of published temperatures as more reliable expansion-temperature data become available.

Jan 1, 1962

By Mackenzie J. M W

The mechanism of clay slime flocculation in coal washing circuits is considered and it is concluded that polymer flocculants are most suitable. It was found that the addition of sea water with a polymer flocculant improved flocculation and settling, and it was also found that dilution of a flocculated pulp increased floc size and hence settling rate.In predicting plant consumption of reagent it was found that cylinder tests, or even pilot plant tests, could give erroneous results, particularly on flocculated pulps. Different flocculants may, however, be compared in cylinder tests.For filtration, flocculation with Separan plus sea water was much more beneficial than flocculation with Separan alone.INTRODUCTIONDuring the mining of coal, and its subsequent beneficiation by washing, large quantities of minus 10 mesh material are produced. This fine material, which consists of broken down shales and fine coal, causes difficulties in water clarification circuits, in refuse disposal, and in filtration of fine coal.These difficulties can be largely overcome by flocculation, and this paper discusses the mechanism of flocculation, the methods by which a selection of flocculant may be made from the large number available, and the limitation of the prediction of plant performance from laboratory tests. This work applies particularly to the washeries of The Broken Hill Proprietary Co. Ltd. (B.H.P.) and Australian Iron and Steel Ltd. (A.I. & S.) .

Jan 1, 1962

By Michael G. Zabetakis

The spillage of liquid diethyl ether in rooms at floor level and 3 feet above the floor resulted in flammable vapor-air mixtures in the immediate vicinity of the exposed liquido The liquid temperature was found to decrease by as much as 35° C., with a resultant decrease in vaporization rate. A search of the literature yielded numerous references to unstable peroxide (residue) formed by the autoxidation of ether. Such residues appear to constitute an explosion hazard in the condensed state.

Jan 1, 1962

By Walter C. Lorenz

In connection with its renewed study seeking solutions to problems created by release of acid water from bituminous coal mines, the Bureau of Mines recently surveyed reports already written on the subject. This publication is based on that search. The Problem Poor distribution of water is evident on an ordinary geographic map of the United States. The more abundant supplies of surface water appear to be centered in the northeast, the southeast, and the central humid areas of the country. It is in the midst of this abundant surface water, in the Ohio River Valley, that most of the bituminous coal is mined. Varied industry has located in the valley to use the coal and the river. The coal is a source of power and o raw material. The river provides transportation for raw and finished materials; equally important, it provides the water that is used for cooling and processing in manufacturing. It also serves as a vehicle for the disposal of waste.

Jan 1, 1962

By M. E. Fine, A. A. Hendrickson

The critical resolved shear stress and the strain rate dependence of the .flow stress are reported for Ag base A1 single crystals up to 6 at. pct A1 over a temperature ralzge of 4.1° to 470°K. At room temperature the solid solution strengthening is attributed brinciballv to an increase in the dislocation density on alloying. At 42°K the alloys are relatively stronger because the dislocations widen on alloying and are more difficult to cut. In a previous paper, the authors reported the characteristics of strain aging in Ag base A1 alloys.' The variation of the magnitude of the strain-aging yield drops on aging time, aluminum content, and testing temperature strongly indicated that the phenomenon is due to the Suzuki mechanism. In the present paper, the critical resolved shear stress (CRSS) and the strain rate dependence of the flow stress are reported for Ag base A1 single crystals as functions of testing temperature (4.2" to 470") and A1 content (0 to 6 at. pct). Observations on the substructure and measurements of the effect of crystal growth rate are also given. The experimental re- sults appear explainable considering that aluminum additions increase the dislocation density and dislocation width. EXPERIMENTAL METHOD The methods of specimen preparation and tensile testing were described previously.' Briefly, single crystals were grown from the melt in a vacuum (1 x lom5 mm Hg), shaped into tensile samples by a combination of abrading and acid etching, annealed at 850°C in a vacuum (1 x 10" mm &Z) for several days, and furnace cooled to 200'. The testing was done on a model TM Instron using friction grips and a strain rate of about 5 x 106 per sec unless otherwise noted. The various testing temperatures were obtained by immersing the specimens in the following media: 1) 4.2': liquid helium using the apparatus of G. Byrne;' 2) 77°K: liquid nitrogen; 3) 200"K: dry ice and acetone; 4) 415' K: ethylene glycol; 5) 460' \ to 480' : molten Stanalax. In the determination of the CRSS above 296' K, a ratio method was used; the crystals were strained initially at the higher temperature, 0.1 pct shear strain, and then tested at 296' . The ratio of the flow stress between the two temperatures was then multiplied by the average CRSS at 296' K to obtain the value of the CRSS at the high temperature. (The test at 296' showed a yield point resulting from strain aging; the flow stress at 296' K was taken as the lower yield stress.) The ratio method, we believe, is more accurate than using different crystals since

Jan 1, 1962

By R. Barany

In this paper, closed expressions have been obtained for the frequency spectrum of a Born-Karman square lattice in terms of elliptic and hyperelliptic integrals. This work is part of continuing research by the Bureau of Mines with the thermodynamic properties of metals and minerals. Although other workers have obtained various types of approximations for the general case of the frequency spectrum of a square lattice, no one previously has obtained closed analytic expressions for this spectrum. To understand the optical and thermodynamic properties of crystals, several investigators have studied the distribution of frequencies of normal modes of vibration of the crystal lattice. Born and Karman3 laid the foundation for the theory of lattice dynamics and obtained detailed results for the case of a one-dimensional lattice. Blackman4 used numerical techniques to estimate the frequency distribution of a two-dimensional square lattice. Mbntroll5 analytically determined the frequency distribution of a square lattice for a particular value of the force constants. He also studied the more general problem and obtained some analytic approximations, using the method of moments. However, the calculations by this method were so difficult that it was not always practicable to carry them out. Van Hove6 and Montroll7 studied the nature of the singularities in the frequency spectrum of both a two and

Jan 1, 1962

By R. L. Lincoln

The effects of adding from 1 to 50 atomic percent (a/o) to vanadium were investigated by the Bureau of Mines. Properties studied included as-cast and annealed hardness, microstructure, fabricability at room temperature and elevated temperature, tensile strength, electrical resistivity, and oxidation resistance at 625° and 800° 2. Additions of small amounts of hafnium resulted in lessened as-cast hardness, decreased electrical resistivity, impaired roll- ability, increased oxidation resistance, and greater tensile strength. Larger amount of hafnium caused greater as-cast hardness, increased electrical resistivity, further impaired rollability, continued increase in oxidation resistance, and lessened tensile strength. INTRODUCTION The purpose of this study was to determine the effect of hafnium additions on the properties of vanadium and to learn if this binary alloy had any special or unusual properties. This investigation is a part of a larger research project in which new and expanded uses of vanadium are being sought. Domes tic vanadium is found frequently in combination with uranium, and because of the demand for uranium as a nuclear fuel, there now exists a surplus of vanadium-bearing minerals and vanadium pentoxide as a byproduct of uranium production. Primary principles of conservation demand that greater use be made of this readily available surplus; finding suitable metals to alloy with vanadium to enhance its properties is one way to increase its utilization. This report is the result of an investigation of the effects on the properties of vanadium when hafnium is added in amounts from 1 to 50 a/o.

Jan 1, 1962

By Alla D. Mah

The need for more and better basic thermodynamic data for the oxides of many of the rare metals is evident to anyone who attempts thermodynamic calculations involving these substances. In continuation of a Bureau of Mines program to meet this need, this paper reports new experimental values of the heats of formation at 298.15° K. of the hexagonal crystalline variety of germanium dioxide and germanium dioxide glass. The values were obtained by means of combustion calorimetry and sodium hydroxide-solution calorimetry. The calorimetric results also made possible the derivation of values for the heat and entropy of fusion of hexagonal germanium dioxide at its melting point. The newly measured data were combined with previously known entropy and high-temperature heat content values to obtain heats and free energies of formation of germanium dioxide (in the hexagonal crystalline, glassy, and liquid states) over the temperature range from 298.15° to 2,000° K.

Jan 1, 1962

By R. M. Waterstrat

X-ray diffraction and metallographic examination of binary Mn-rich alloys with Ti revealed the presence of intermediate phases in this system. A binary R phase has been identified and also a phase having an a-Mn type structure. The X-ray pattern of the phase TiMn3 is presented and a tentative phase diagram for the Mn-rich portion of this binary system has been constndcted. MANGANESE-rich alloys with titanium have been subjected to thermal analysis at temperatures down to 1100°C by Hellawell and Hume-Rothery.1 Their results indicate the existence of an intermediate phase TiMn3 in this binary system. This phase appears to coexist with the Laves phase TiMn2, and with terminal solid solutions based on the allotropes of manganese, at least down to 1100°C. The above investigators did not attempt to determine the crystal structure of this phase, however. Since, by analogy to the binary systems Mn-V and Mn-Cr3 one might expect to find a phase in this region of the diagram, it seemed desirable to obtain X-ray diffraction patterns of alloys in the concentration range in question, in order to ascertain whether the sigma phase or related structures occur. EXPERIMENTAL PROCEDURES Alloys were prepared by arc-melting electrolytic manganese and iodide titanium in a water-cooled copper crucible under a helium atmosphere. Excess manganese was added to each melt in order to allow for losses incurred during melting. The alloys were then wrapped in molybdenum foil and sealed in evacuated quartz tubes for annealing at various temperatures, as shown in Table I, followed by quenching in cold water. Although the inside of the tubes showed evidence for some loss of manganese from the specimen during annealing, there was no evidence of any reaction between the specimen and either the molybdenum foil or the quartz tube at these temperatures. It was later found that the manganese loss was considerably reduced by annealing these alloys in sealed quartz tubes containing one atmosphere of purified argon. As an added precaution the surface of each specimen was ground off before crushing the alloys to -270 mesh powder, using a hardened steel mortar and pestle. X-ray powder patterns were obtained using either FeKa or CrKa radiation in an asymmetrical focusing camera, which gave excellent dispersion of the closely spaced lines. Pictures were also obtained using a Debye camera of 5-cm radius which provided data in the angular region not covered by the focusing camera. The alloy specimens were polished and examined metallographically, using an etchant consisting of 60 pct glycerine, 20 pct nitric acid, and 20 pct hydrofluoric acid. The 10-g buttons were in each case broken in half and found to be well-melted and free of any gross segregation. One half of certain alloy buttons was submitted to chemical analysis in the "as-cast" condition. No appreciable change in composition seemed to occur during annealing . RESULTS The X-ray pattern of alloy Ti1.17Mn0.83 was found to agree well with that of the ternary R phase which was first found in the Mo-Cr-Co system,' and re-

Jan 1, 1962

By R. A. Bell, R. Schultz, P. G. Hallof

The Ballyvergin area is located in County Clare on the southwest coast of Ireland. It is one of six areas in County Clare in which mining operations were carried out during the last century. The ores mined were high grade Cu-Pb-Ag deposits in the form of small fracture fillings and gash veins in the lower Carboniferous limestones. The zone of primary economic interest is situated on the north limb of a geosyncline which plunges moderately to the southwest. The zones of mineralization previously mined were associated with local structures and folds, and the initial geophysical investigations took the form of reconnaissance induced polarization measurements around, and between, the old mines. This work located an anomaly which, on drilling, resulted in a small extension of the Pb-Cu ore at the Ballyvergin mine. However, a potentially more important zone of mineralization resulted from the drilling of another IP anomaly near Ballyvergin. This wide anomaly was found to be a domal shaped deposit of disseminated chalcopyrite located at a depth of more than 100 ft. The deposit is controlled by local folding in the sediments and is of a type previously unknown in the area. More IP investigations are under way to locate other deposits of the same type. The Ballyvergin area is located in County Clare, about 35 miles northeast of Shannon Airport, near the Atlantic west coast of Southern Ireland (Fig. 1). Interest in the area stems from a number of occurrences of small, but high grade, Pb-Ag deposits. From the summer of 1960 to the spring of 1961, Irish Base Metals carried out a comprehensive exploration program on a 38-sq mile concession in east-central County Clare in an attempt to locate additional deposits of this type. Field operations consisted of geologic mapping, geochemical soil and stream sampling, geophysical surveying and diamond drilling. The geophysical program consisted primarily of detailed induced polarization (IP) surveys in the general vicinity of old mine workings, supplemented by electromagnetic and self-potential investigations. Subsequent diamond drilling of a well defined IP anomaly close to the old Ballyvergin mine disclosed a sizeable deposit of low grade disseminated copper, a type of deposit previously unknown in this area. REGIONAL GEOLOGY Topography: The topography is of the Karst type with low regional relief. The northern parts of the area are covered almost completely with glacial deposits including a large number of drumlins. Elsewhere the overburden is patchy and only moderately deep. A close network of roads makes every part of the area readily accessible, and rail and harbor facilities are available nearby — Fig. 2. Stratigraphy: The area was mapped on a reconnaissance basis by the Geological Survey of Ireland during the latter part of the 19th century at scales of 1 and 6 in. to the mile. Mapping is complicated in

Jan 1, 1962

By R. C. Bates

Uranium mine workers? daily exposure to radon daughters was estimated by two methods of sampling, detailed and spot-check. Both methods involve time- weighting measured exposure levels to arrive at an average exposure figure. Random sampling, or sampling without regard for the duration of exposure, has proved inadequate for estimating average exposure levels. During the first phase of the study, the breathing zones of eight workmen in three underground uranium mines were sampled for an entire shift; 20 to 36 radon-daughter samples were collected per man-shift, Analysis of these data indicated that a suitably accurate estimate of the full-shift exposure could be made by time weighting a considerable lesser number of representative radon-daughter samples. This analysis led to the spot-check method of estimating full-shift exposures to radon daughters. Additional detailed studies were made in seven mines to Learn more about the full-shift radon-daughter exposures and to test the spot-check method, In all, 617 radon-daughter samples were taken in 10 underground uranium mines during 26 man-shifts, and the spot-check method was tested 35 times.

Jan 1, 1962

By C. J. Chindgren

Upgrading of commercial red cake and recovery of vanadium oxide from uranium-vanadium mill solutions were investigated by the Bureau of Mines. Alternative procedures potentially useful for manufacture of high-quality vanadium oxide at the mill site were explored and developed. The simplest and best procedure for converting commercial red cake containing about 10 percent combined sodium and potassium oxides (Na20) (K20) into a 98- to 99-percent vanadium pentoxide (V205 product appeared to be a metathesis in an ammoniacal solution of ammonium sulfate. Molybdenum, as well as the alkali metal oxides, was removed from the red cake by this procedure at a modest expenditure of labor and reagents. When preparing vanadium oxide of higher grade, it was necessary to dissolve the red cake and reprecipitate the vanadium as ammonium metavanadate. Calcination at 450° C, decomposed the metavanadate and yielded oxide of about 99.5 percent V205. By recyrstallizing the metavanadate before decomposition, an oxide product approaching 99.9-percent purity was obtained.

Jan 1, 1962

resident Schloss called the meeting to order at 9:30 a.m. Bob Dean, manager of the Hotel Colorado, gave a brief explanation of hotel policies governing the swimming pool, and also extended an invitation to the Institute to return in 1963, and stated that the dates June 30 through July 3 were available for next year. He also stated that June 28 through July 1 were available for 1964. He felt that holding the convention during the 4th was not good policy, and that dates prior to or following the 4th would make for better attendance. John A. Reeves, chairman of the Resolutions Committee presented the following resolutions: RESOLVED: That the members of the Rocky Mountain Coal Mining Institute in convention assembled, hereby ratify and confirm all official actions of the officers, the Executive Committee and other committees of the Institute between June 28, 1961, and the present time.

Jan 1, 1962

By William F. Butler

I propose to do three things today. First, take a broad look at the role of mining in the Latin American economy; then, review briefly the current situation in four principal metallic mineral exporting nations -- Chile, Mexico, Peru and Venezuela; and. finally, raise some, policy questions that seem to me to be important. The Role Of Latin America In World Mining First, let's consider Latin America's position in world mining markets. Latin America provides more than 5% of world output in 16 metals or ores, ranging from antimony and barite to Tungsten and Zinc. Latin America supplies a fifth or more of the world's antimony, beryl, bismuth, copper, fluorspar, silver and Tellurium.

Jan 1, 1962

By John S. Newton

Modern high capacity underground mining machinery is a complex of mechanical, electrical and hydraulic components which have greatly increased capability over similar components of mining machinery of ten and. even five years ago. Looking into the future I feel certain in stating that there will be changes equally great in the coming five and ten year periods. With this premise in mind, I should like to bring to your attention some of the things that do and will have a continued major impact on the industry, particularly as they relate to the maintenance and operation of these machines of increasing capability. In underground mining today, nearly every individual plays a key role. A machine operator's importance in his work is comparable with that of the pilot of an airplane, a railroad engineman, a bus driver, a skilled machinist, a bulldozer operator and many others whose assignment is one of doing, by himself, with his hands and his brains all that the specially designed machine has been created to do. These machine operators are supported by a staff of skilled engineers, maintenance personnel, supervision, etc., but objectives are realized only when the operator maintains his schedule. What is being done and what can be done to make it easier for the operator to maintain his schedule which, as with the airplane, is constantly being improved? This question can be answered best, perhaps, by dividing the subject into four general categories - (A) Power Supply. (B) Control and Protective Devices. (C) Hydraulic Component Design. (D) Mechanical Design.

Jan 1, 1962

By Robert K. Koch

Laboratory-scale studies on defluorination of natural and synthetic fluorspars by pyrohydrolysis at 1,500° C. were made to determine the feasibility of developing a process for producing hydrogen fluoride from siliceous fluorspars. It was found that the reaction (at 1,500° C.) is not promising for process development, even though a silica-free offgas can be generated. The primary difficulty is the low hydrogen fluoride content of the offgases; an HF content of 6 percent was the best achieved. Previous research by the Bureau of Mines has demonstrated that offgases averaging 27 percent hydrogen fluoride can be produced under carefully controlled conditions at 1,280° C. The lower temperature process is a better method for production of HF. However, charges in which the CaF to Si02 mole ratio varied from 0.4 to 2 could be processed with similar results. Also, combined alumina and ferric oxide contents up to 25 mole-percent did not noticeably alter the rate of defluorination. Therefore, virtually any natural siliceous fluorspar would respond in essentially the same manner when exposed to water vapor at 1,500° C.

Jan 1, 1962

By S. J. Aresco

The Bureau of Mines has been active in promoting the purchase of coal for Government use under specifications that define the requirements in terms of heating value of the coal, expressed in British thermal units, and the composition as shown by proximate analyses. To these, when required, are added the ash-softening temperature, the free-swelling index, and the Hardgrove grindability index. Under most of these specification contracts the bidders guarantee the quality of the coal, and that guaranteed by the successful bidder becomes the standard of his contract. The deliveries are sampled in accordance with instructions 5/ issued by the Bureau of Mines; the samples are analyzed in the Bureau laboratory to determine whether the coal is of the quality guaranteed by the contractor and, if it is not, a price adjustment is made. Analyses of the delivered coal and tipple samples (samples collected at mine tipples as coal is being loaded into railroad cars or trucks) provide valuable data for use in evaluating future bids. In addition, the continuous sampling of coal as delivered is a check on the practical results obtained in burning the coal.

Jan 1, 1962

By Clark F. Grain

These investigations were undertaken as part of the Bureau of Mines program for the development and evaluation of high temperature nonmetallic materials. This report consists of thermal expansion and phase inversion measurements by high-temperature X-ray diffractometry on the principal oxides of beryllium (BeO), calcium (CaO), titanium (TiO2 ), zirconium (ZrO2 ), hafnium (HfO2), and thorium (ThO2); all were high-purity commercially available oxides. Thermal expansion values were calculated from unit cell dimensions measured at selected temperatures. Expansion was determined parallel to each major crystallographic axis for the anisotropic oxides: BeO, TOi2, ZrC2, and HfO2. Combined random and systematic errors in the thermal expansion values are considered to be less than 3 percent of the total expansion at 500° C. and approximately 2 percent at 1,000° C. No hysteresis in the expansion curves was noted between heating and cooling cycles. The Bureau's values were compared with published expansion measurements obtained by X-ray diffraction, dilatometric, interferometric, and telemicroscopic techniques. For anisotropic oxides, average linear expansion values were calculated from the volume expansion.

Jan 1, 1962

By J. E. Dorn, S. K. Mitra

The low -temperature tensile and creep behaviors of single crystals of copper were evaluated and analyzed in such a manner as to provide an estimate of the separate contributions of short-and long-range stress fields to strain-hardening. Furthermore, the average force-displacement diagram for thermally activated intep-section of two dislocations was estublished. This diagram plus a knowledge of the variation of dislocation spacing and the long-range back stresses with strain permits on accurate prediction of creep rates. The calculated activation energy for intersection under conditions of a constant strain rate increases linearly with the absolute tempevatus-e as required by theory. AN understanding of the detailed mechanisms for strain hardening constitutes one of the principal unsolved problems in dislocation theory. Two major models for strain hardening have been advanced in the past. The one that has received greatest attention assumes that strain hardening arises exclusively from long range interaction stresses between moving dislocations and piled-up arrays of blocked dislocations on the slip planes. This type of interaction was first announced by Taylor' who revealed that the back stress fields due to a simple uniform array of positive and negative dislocations entrapped in the deformed crystal would result in parabolic hardening. Shortly thereafter Andrade and Henderson" demonstrated that the strain hardening of fcc single crystals was not parabolic, as previously thought, and finally it was recognized that a typical stress-strain curve consisted of three successive stages of deformation, niz., the easy glide, Stage I, linear hardening, Stage 11, and the parabolic hardening, Stage 111, ranges. The objections to Taylor's somewhat na'ive model, which were presented so forcefully by cottrell; were largely removed by the more realistic details incorporated in Mott's analysis.5 But because Mott's theory for hardening via long range stress fields gave somewhat analogous results to that of Taylor's (inasmuch as it also predicted a parabolic rate of strain hardening whereas the observed rate of strain hardening in Stages I and I1 were linear), it was not widely accepted. Major consideration was therefore given to models, such as those which were advanced by Friedel and seegere that were formulated for the ad hoc purpose of yielding linear rates of strain hardening. The second major thought regarding strain hardening is based on the concept that it arises principally from short-range stress fields due to the interactions between intersecting dislocations. Cottrell and stokes7 showed, several years ago, that the constancy of the flow stress ratio at two temperatures regardless of the strain was inconsistent with the concept that strain hardening arose exclusively from long-range back stresses. The argument that strain hardening was primarily due to local interactions of intersecting dislocations was presented in considerable detail by asinski.' Extending Basinski's method of analysis of the intersection process, Mitra, Os-borne, and dorn recently demonstrated that indeed the strain hardening in aluminum single crystals arises principally from local effects coincident with intersection; however, these conclusions, too, must be modified, as will be shown later in this report. The present investigation, devoted principally to the low-temperature deformation of copper single crystals, was initiated in an attempt to ascertain whether or not the same conclusions arrived at for aluminum also apply to metals, such as copper, which have much wider stacking faults. It was soon observed that the strain hardening in copper could not be attributed exclusively to local effects between intersecting dislocations. Previously no analytical method for arriving at the possible simultaneous contributions of long-range stress fields and localized forces on intersecting dislocations was available; consequently, the separation of these two factors could not be readily accomplished. In the present report a method of estimating the separate contributions of each of these two factors to strain-hardening will be presented. The authors will show that both long-range stress fields of the type contemplated by Seeger and Friedel as well as short-range forces of the type considered by Basinski are responsible for strain hardening in fcc metals at low temperatures. This method of analysis also accounts for, in a satisfactory way, the effect of stress, temperature, and strain on the creep rate under constant stress. Furthermore, in the course of presenting their methods of analysis the authors will also reveal the rather complete agreement of their experimental data with the concepts of the theory for thermally activated intersection of dislocations. INTERSECTION MODEL As shown by seegerl0 the strain rate arising from thermally activated intersection of dislocations is given by

Jan 1, 1962