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By Francisco Cadena

THE construction of Norris Dam, built by the Tennessee Valley Authority on the Clinch River, a tributary of the Tennessee River, involved the production of coarse and fine aggregate for approximately 1,000,000 cu. yd. of concrete. A hammer-mill plant for the manufacture of sand from quarried rock was indicated as the most economical method of providing this material. The abrasive character of the feed as compared to the average hammer-mill feed made it necessary to control operations rather closely, and this resulted in the accumulation of many data bearing on production and maintenance. This paper will deal only with three specific sets of data, accompanied by such general information as may be necessary to explain the conditions under which they were obtained and followed by discussions on the relation of silica content to hammer wear, comparative costs of slugger and stirrup hammers, and comparative costs of tool-steel and manganese-steel grate bars. Coarse Aggregate Aggregate for the concrete poured at Norris Dam came from a dolomite quarry within 2000 ft. of the west abutment of the dam. Geologically this rock is known as a Knox dolomite. A typical chemical analysis is given in Table 1. TABLE 1 .-Typica.1 Chemica1 Analysis [PER CENT H20,1100F ............................................ 0.0'2 Ignitionloss ............................................. 43.56 MgO .................................................. 19.19 CaO .................................................... 29.07 FezO .................................................... 0.39 A1203 .................................................... 1.94 FezO .................................................... 0.39 A1203 .................................................... 1.94 ..................................................... 5.75 SO2.. .................................................. Tr.] Rock was carried by 12-yd. dump trucks to a 42-in. gyratory crusher set at 6 1/2 in. The product of the primary crusher was taken by a belt conveyor to a double-deck vibrating screen followed by a 5 1/2-ft. cone

Jan 1, 1937

By J. H. Palm

Experiments have shown12 that the formula -S = St - (St - Se')e ne [1] expresses very well the relation between the true stress S and the true form monotonic deformation of plastic metals in single tension and compression (Fig 1). St (asymptotic or final stress), Se' (threshold stress) and ne (characteristic or specific strain) are constants, the significance of which immediately follows from Fig 1. Only at the initial stages of deformation the experimental curve runs below the theoretical curve. This may be due, at least partly, to the uneven stress distribution caused by the anisotropy of the crystals. It is now obvious that a similar formula H = Ht- (Ht- He)e ne' [2] might be valid for the relation between the hardness and the strain. The hardness can be only a function of the strain and must therefore be independent on the hydrostatic tension present in the neck during straining. Hence, if Eq 2 is correct it will also represent the relation between hardness and strain in the middle section of the neck, the strain of which is generally assumed to be almost or fully homogeneous. For aluminum, copper, and several copper alloys it is indeed observed that Eq 2 agrees very well with the experimental Vickers hardness-strain relation from zero strain on up to the strain at fracture. Moreover nc' is, for several metals fairly equal to nc- Hence H = C1 + C2S [3] C1 and C2 are constants during uniform uniaxial tension. Eq 3 was also obtained for copper by Voce.3 According to Hencky's theory4 the ratio of the Brinell or Vickers hardness and the yieldstress (expressed in kg per mm2) of a non-strainhardening metal is approximately equal to 2.8. If Eq 1, 2 and 3 are correct the ratio Ht/S, must accordingly be the same for all plastic metals and be equal to 2.8. It is now experimentally established that this ratio varies between 2.7 and 3.1 with a mean value of 2.9. Taking into account that Ht and especially St can be obtained only by extrapolation from the range of rather low strains, the agreement with the theory is very satisfactory. References 1. J. H. Palm: Appl. Sci. Res. Al (1948) 198. 2. E. Voce: Jnl. Inst. of Met. (1948) 74, II, 537. 3. E. Voce: Metal Treatment (1948) 15, 53. 4. H. Hencky: Zlsch. f. angew. Math. and Mech. (1923) 3, 241.

Jan 1, 1950

By P. Niessen, S. J. Bercovici

RECENTLY Aust et al.&apos; proposed a model of non-equilibrium grain boundary segregation based on a vacancy gradient induced uphill diffusion process of solute to grain boundaries. According to their proposal, solute atoms which are attracted to vacancies would, during the cooling of a sample, migrate with vacancies toward grain boundaries (vacancy sinks) and thereby enhance the solute concentration in boundary regions. For solute atoms which are not attracted to vacancies no such boundary solute enrichment would be expected. These concepts were given experimental support by boundary and bulk mi-crohardness measurements of various thermally treated dilute zinc and lead alloys and also doped aluminum oxide. The underlying assumption in their work was that solute enrichment in boundary regions is indicated by higher microhardness values. From thermodynamic considerations1&apos;2 it appears that the solid-liquid solute distribution coefficient (K), defined as the concentration of solute in the solid to the concentration of solute in the liquid at equilibrium, indicates whether attractive or repulsive forces exist between vacancies and solute atoms. K < 1 indicates a solute-vacancy attractions, K > 1 indicates no, or a repulsive, vacancy-solute interaction. This note is to report on observations of different grain boundary etching phenomena in high purity zinc alloys. These phenomena appear to depend on whether a K < 1 or K > 1 solute is present. In experiments designed to measure directly the solute enrichment in grain boundary regions, samples of zone refined zinc with 0.1 at. pct solute additions were cooled from 380°C at a rate of 3°C per min. A surface layer of approximately 50 was then removed from the samples by chemical polishing. The samples&apos; surfaces were then protected by a chromating treatment such that in a subsequent etch only grain boundary regions were dissolved. The dissolved regions were approximately semicircular troughs, 10 µ in width. The grain boundaries were usually in the middle, i.e., at the bottom, of this trough. For zinc containing the K < 1 solutes cadmium and aluminum, the grain boundary was always indicated by a ridge as shown in Fig. 1. For pure zinc, and zinc containing the K > 1 solutes copper and gold, a groove at the bottom of the trough indicated the boundary position, Fig. 2., To test if these different grain boundary etching behaviors were possibly connected with the segregation process discussed above, the Zn-Cd alloy was again heated to 380°C and quenched into brine. After surface protection and etching it was found that this specimen no longer exhibited the grain boundary ridges but rather grain boundary grooves as shown in Fig. 2. It would appear, therefore, that the boundary ridge is a consequence of a process occurring during the slow cooling of the samples. From absorption spectrophotometric analysis it was found that for slowly cooled samples containing K < 1 solutes, the solute/zinc ratios of the material from the boundary trough were consistently considerably higher than the solute/zinc ratios of the bulk alloys. This boundary region solute enrichment was not observed in quenched samples. It is concluded therefore, that the boundary ridge shown in Fig. 1 is directly or indirectly connected with nonequilibrium solute segregation.

Jan 1, 1970

By Cyril Stanley Smith

Jan 1, 1949

By Cyril Stanley Smith

Jan 1, 1949

By S. R. B. Cooke, W. Philippoff, Donald E. Cadwell

[THE importance of contact angles in flotation has long been recognized, but little has been done to get quantitative relationships between the surface coverage of the mineral by the reagent, the length of the hydrocarbon chain, and the contact angle. It is well known that for a complete monolayer on the surface of a mineral the contact angle ? is determined only by the reagent&apos; and principally by the chain length of the hydrocarbon radical. Although for flotation the monolayer usually is regarded as being complete, early experiments of Wark and Cox2 showed that at very small concentrations of potassium ethyl xanthate the contact angle on galena changed in a continuous way from 0° to the equilibrium value of 60°. Further, Gaudin and Vincent&apos; showed a similar continuity using heptylic acid and sphalerite. This shows that with probably incomplete monolayers, ? varies with the degree of surface coverage. At the time these experiments were made it was impossible to measure the actual amount of surface coverage, especially since the decrease of the collector concentration in the liquor could be influenced by chemical side reactions. Through the use of the radioactive tracer method for the measurement of the amount of collector adsorbed on the surface of the mineral, Gaudin and Bloecher4 were able to determine accurately the actual surface coverage of dodecylamine acetate on quartz, but they did not measure any contact angles. It is believed that the relationship between the surface coverage and the contact angle is extremely important in flotation, especially as Gaudin and Bloecher showed that a 95 pct recovery is possible with a coverage of only 5 pct. Theoretical Considerations The work of adhesion W is the energy bound (in ergs per sq cm) when an interface is formed. It is determined by, the difference of the free surface energies (surface tensions) of the respective phases ?1 and ? 2 before contact and the interfacial free surface energy ?12 after contact. The definition of the contact angle permits the elimination of the unknown surface energy of the solid and hence the calculation5 of W from the surface tension of the liquid ? and the contact angle ?: [W = y (1 + cos ?)[1]] Consider a surface consisting of two components, identified as 2 and 3, 1 being the liquid. The amount of 2 in the composite surface is x, where 0 < x < 1. The respective contact angles with 1 and air are ? and ?3. The total work of adhesion of such a surface is the sum of the values of the components multiplied by their respective areas. A formal relation can be written: [W,,,=x•W2+ (1-x).WR[2] .] in which Wm is the work of adhesion of the composite surface. Eq 1 can be introduced into W2 and W3 but in the case of Wm some discussion is needed. If the two components are segregated, each component forming an integral part of the composite surface there is no physical meaning for a contact angle ?m, calculated from Wm, by using eq 1. If, on the other hand, the area of each patch of the components is small in comparison with, say, the diameter of the bubble used in measuring, it could be expected that ?m would have aphysical significance, because of the action of the surface tension of the liquid-gas interface tending to smooth out sharp corners. How small these patches would have to be is difficult to predict, but by using composite surfaces with microscopically]

Jan 1, 1952

By R. I. Jaffee, J. W. Roberts, D. N. Williams

DISPERSION hardening as an alloying process has aroused increasing interest in the past few years. This alloying procedure, in which an insoluble phase is dispersed randomly through a metal or alloy, is believed to be especially suited for the attainment of creep strength at elevated temperatures since the dispersed phase is metallurgically stable. Another advantage is that the physical properties of the matrix phase, such as electrical conductivity, remain relatively unaffected by alloying. These two characteristics resulted in interest in the applicability of dispersion hardening to copper and copper alloys. A study of copper alloys prepared by powder metallurgy methods has shown some strengthening from oxide dispersions.&apos; However, powder metallurgy processing would not be economical for large scale production of dispersion hardened copper-base alloys. Therefore, the research described in this article was initiated to examine methods of forming dispersion alloys which would not require powder metallurgy processing. If powder metallurgy processing is to be avoided, a method must be found by which the dispersion material can be introduced into and dispersed through the melt before casting. When the dispersed phase is an oxide or similar nonmetallic, it is extremely difficult to form a satisfactory liquid: solid dispersion since successful mixing requires that the melt wet the dispersed phase. It is almost impossible to force a nonwetted particle beneath the melt surface. This difficulty can be avoided, however, if the oxide particles are produced in molten copper by reaction within the melt. The problem would then reduce to maintaining randomness until solidification. Four procedures were considered for producing an oxide particle within molten copper by reaction. In all cases, the intent was to react oxygen (0) with a reactive metal (X) to form an oxide (XO) within the copper melt. These reactions were as follows: 1) (Cu-X), + (O)g (Cu)1 + (XO)S [1] 2) (Cu-X)1 + (Cu2O)s (Cu)x + (XO)S [2] 3) (Cu-OK)1 + (Cu-X)1 (Cu)1+(XO)9 [3] 4) (Cu-OK)1 +(X)s (Cu)1 +(XO)s [4] The reactions were carried out in an 8-lb melt of 99.98 pct Cu maintained in the vicinity of 2200oF by induction heating. Where possible the amount of the reactants was controlled to give 1 to 5 vol pct oxide. Mechanical stirring during the reaction period was used to minimize agglomeration of the reaction product. The presence of a reaction product was determined metallographically by study of an ingot cast from the melt at the end of the reaction period. Reaction [I] was studied by dissolving aluminum in the melt followed by forcing oxygen through the melt. The melts became quite sluggish during the reaction period suggesting that A12O3 was formed. However, the reaction product rose out of the melt rapidly, possibly due to the flushing action of the oxygen stream, and little dispersed phase was formed. Reaction [2] was examined by dissolving aluminum, silicon, or nickel i; the melt and then adding Cu20 (melting point 2250F). This procedure was unsuccessful. Although Cu2O was easily stirred into cop-

Jan 1, 1961

By F. A. J. Fitzgerald

In any kind of furnace the question of preventing the loss of heat is important, for no matter how the heat is obtained it costs something; and consequently, other things equal, that furnace is most desirable which uses the greatest percentage of the total heat generated for the particular object in view. In the furnace which uses electricity for the generation of heat the importance of preventing losses of heat is very much greater than in any other. To generate 1,000 kg-cal. requires an expenditure of 1.16 kw-hr., and consequently the cost per calorie is always expensive when electricity is used for heating. In heating any material in a furnace a general rule is that the generation of heat should be as rapid as possible. In any given furnace the heat-losses may be expressed as so many watts, and, therefore, the longer it takes to heat the furnace-charge the greater the losses will be. Suppose that a furnace contains a charge to be heated to 1,500°C. and that the average loss of heat is at the rate of 100 kw., then if the process of heating the charge takes 1 hr. the losses will amount to 100 kw-hr.; but if by using a more rapid generation of energy the charge can be heated in 30 min. the losses will amount to 50 kv-hr. An example from experiments on a certain process may be given to illustrate this point. The problem was simply to heat a furnace-charge to a certain temperature, and experiments were made to determine the effect of increasing the rate of generation of energy and comparing the kilowatt-hours required to heat a given charge. Here are typical results : Rate of Generation Energy Per Kg. of Energy. of product 88 kw. 1.7 kw-hr. 93 kw. 1.6 kw-hr.

Jan 1, 1913

By Walter E. Lewis

Myriad problems face all of us in the next decade. Vietnam, poverty, and pollution are perhaps the most pres- sing. A lesser one but still vital to us as a Nation is the slow hut apparently relentless extinction of the mining, metallurgical. geological and petroleum engineer. Are we doomed to take our place in the crossword puzzle with the moa. to be defined like it as an "extinct bird"? Or can we reverse the trend perhaps, in the next decade? The plain fact is we are an endangered species, and must resign ourselves to virtual extinction in the 1970&apos;s unless the trend is reversed. Probably, many of us have felt the problem will solve itself if left in the in-basket long enough, believing, that the trend will reverse solely on the basis of demand for these disciplines. This approach has not worked up to now, it gives no promise of working in the future, and furthermore, the problem has been in the in-basket much too long. The point is simply this: What can each of us do as an individual, or as part of a company, a State agency, a Federal agency, a university, or an organization such as AIME?

Jan 1, 1970

By AIME AIME

HONORARY COMMITTEE. HON. C. D. WALCOTT (Chairman.), Director U. S. Geological Surrey. HON. FREDERICK I. ALLEN, Commissioner of Patents. DR. FRANK BAKER, Superintendent National Zoological Park. MR. CHARLES A. BELL, President American Security and Trust Co. MAJOR JOHN BIDDLE, Engineer Commissioner of District of Columbia. ADMIRAL C. M. CHESTER, Superintendent U.S. Naval Observatory. GENERAL WILLIAM CROZIER, Chief of Ordnance, U. S. A. ADMIRAL GEORGE DEWEY, Admiral of the Navy. COLONEL CLARENCE R. EDWARDS, Chief Bureau. of Insular Affairs. MR. WILLIAM C. FOX, Director Bureau of American Republics. MR. CHARLES C. GLOVER, President The Riggs National Bank. GENERAL A. W. GREELY, Chief Signal Officer, U. S. A. MR. BERNARD R. GREEN, Superintendent Library Building. GEN. G. H. HARRIES, Vice-President Washington Electric Railway Co. HON. E. A. HITCHCOCK, Secretary of the Interior. COMMANDER H. M. HODGES, Chief Hydrographer, U. S. N. PROF. W. H. HOLMES, Chief Bureau of American. Ethnology. PROF. S. P. LANGLEY, Secretary Smithsonian Institution. GENERAL ALEXANDER MACKENZIE, Chief of Engineers, U. S. A. ADMIRAL N. E. MASON, Chief Bureau of Ordnance, U. S. HON. WM. M. MEREDITH, Director Bureau of Engraving and Printing. HON. V. H. METCALF, Secretary Department of Commerce and Labor. HON. WILLIS L. MOORE, Chief -U. S. Weather Bureau. HON. PAUL MORTON, Secretary of the Navy. MR. F. H. NEWELL, Chief Reclamation Service, U. S. Geological Survey. HON. S. N. D. NORTH, Director Census Office. CAPT. E. C. PENDLETON, Superintendent Naval Gun Factory. MR. GIFFORD PINCHOT, Chief Forester, Department of Agriculture. MR. HERBERT PUTNAM, Librarian of Congress. ADMIRAL CHAS. W. RAE, Chief Bureau of Steam Engineering, U. S. A: MR. RICHARD RATHBUN, Assistant Secretary Smithsonian. Institution. HON. W. T. RICHARDS, Commissioner General Land Office.

Jul 1, 1905

By R. J. Wygal, J. Naar

An equation for three-phase (water, oil, gas) imbibition oil permeability is developed, assuming the water to be the dominant wetting fluid. Oil isoperms are obtained for consolidated sandstones characterized by 1/pc2 = CS*. The evolution of an oil-gas system imbibing water from Swi to(Sw,imb )max is shown to proceed along a line of constant oil saturation with increasing oil permeability and decreasing gas saturation. When the gas satuation cannot be reduced further, the system evolves along a line of constant Sg with decreasing oil saturation and permeability. The initial gas saturation is shown to reduce markedly the effect of complete wetting by either oil or water on flow performance. INTRODUCTION Imbibition oil isoperms are required for performance prediction when a well is producing water, oil and gas. This situation occurs in multiphase displacements such as underground combustion, steam injection and the water flooding of highly depleted reservoirs. In a recent paper,1 a model was presented for the prediction of two-phase imbibition characteristics. This paper extends the imbibition model to the case of three phases by assuming that the water is the dominant wetting fluid. The following results were obtained from the model: (1) an analytical expression of oil isoperms; (2) oil isoperrns as functions of reduced water, oil and gas saturations, valid for all sandstones having a capillary pressure curve which can be approximated by 1/PC = CS*; and (3) evaluation of the three-phase flow performance as dictated by complete wetting by either oil or water. The agreement between predicted and observed oil recovery in the presence of a gas phase, reported in Ref. 1, is a partial support for the present development. However, experimental data are not available at this time to check fully the model predictions. Perhaps this paper will stimulate the collection of such data. The imbibition model of a porous medium has been described previously, and the reader is referred to the paper of Naar and Henderson1 for details. In brief, the model is formed by the random interconnection of straight capillaries, with a provision for the blocking of the non-wetting phase by the invading wetting fluid. The following expressions were derived from the model. 1. The amount of oil blocked by the invading water is

By G. Gutierrez, D. A. Elgillani, M. C. Fuerstenau

The zero-points-of-charge of apatite, calcite, and fluorite are pH 6.4, 10.8, and 10.0, respectively. Scheelite is negatively charged above at least pH 3. In this article, the flotation responses of these minerals in the presence of potassium oleate and sodium silicate are described and compared with electrokinetic data. Colloidal silica appears to be the species principally responsible for calcite depression, while silicate anion is the species responsible for fluorite depression. Additions as high as 1 x 10-3 mole/liter silicate have no effect on the flotation responses of apatite and scheelite. Selective flotation of nonmetallic minerals is difficult to achieve with fatty acids or soaps by themselves. As a result, specific reagents are added to aid these separations, and one of the reagents commonly employed for this purpose is sodium silicate. Flotation separations of various calcium-bearing minerals such as fluorite from calcite1-3 and scheelite from calcite2,4 and apatite,2,5 for example, almost always involve the use of sodium silicate. The mechanisms by which sodium silicate functions as a depressant are still not understood, probably for a number of reasons. For one thing, the dissolution process of sodium silicate is complex, giving rise to a number of ionic and colloidal species.&apos; Moreover, the type and concentration of these species depend on the ratio of Na2O to SiO2, the concentration of sodium silicate, and the pH of the system.&apos; At the present time, it is not known which species, colloidal silica or silicate anion, is responsible for depression. If colloidal silica is the species that is adsorbing, then adsorption must occur by electrostatic attraction between the colloid and the mineral surface. Silicate anion, on the other hand, may adsorb either physically or chemically. The objective of this paper is to determine first the active species of sodium silicate and then the conditions under which this species will adsorb and function as a depressant. EXPERIMENTAL MATERIALS AND METHODS Pure samples of apatite (Durango), calcite (Iceland-spar), fluorite, and scheelite were used in this investigation. Pure potassium oleate was used as collector, while reagent-grade HC1 and KOH were employed for pH adjustment. The sodium silicates used were samples obtained from the Philadelphia Quartz Co. In one series of experiments, various sodium silicates containing different ratios of SiO2 to Na2O were added to calcite systems. These sodium silicates contained SiO2-to-Na2O ratios of 3.75 to 1, 3.22 to 1, 2.40 to 1, and 1.60 to 1. All other experiments were conducted with the sodium silicate containing the ratio of 3.22 to 1, which is the one that is normally used in industry. Flotation experiments were conducted with 21/2-g charges of 48 x 150-mesh material in conductivity water with an apparatus and technique described previously. Electrokinetic experiments were conducted with both a Zeta Meter and streaming potential apparatus. Particle size was 48 x 65 mesh for the streaming potential experiments. EXPERIMENTAL RESULTS The first series of experiments involved flotation of scheelite in the absence and presence of sodium silicate. As shown in Fig. 1, flotation response was not affected with even the relatively high addition of 1 x 10-3 mole per liter sodium silicate. Interestingly though, no flotation was effected below pH 6 with this collector addition. The responses of apatite to flotation under these same conditions are given in Fig. 2. Similarly, no depression was obtained in basic media under these conditions. Similar experiments were conducted with fluorite, and in this case, depression was noted above about pH 11 with 1 x 10-3 mole per liter sodium silicate (Fig. 3). When calcite was floated with these same levels of addition of sodium silicate, essentially no flotation was possible above pH 7 (Fig. 4). The effect of collector addition with a constant addition of sodium

Jan 1, 1969

By John J. McKetta. Jr., Louis B. Lesem, George H. Fancher

The proration of oil produced in the field frequently is based partially or entirely upon the gas-oil ratio of wells. The measurement of the gas-oil ratio is one of the more important field tests in regulatory and pro-ration work, and the test always should be conducted according to standardized methods and procedure. Obviously, the gas-oil ratio and the volume of gas produced by a well depend upon many factors but should be independent of the method of measurement and of the devices used to measure gas and oil. Consequently, the volume of gas accompanying a barrel of oil produced by a well may be measured by any reliable and accurate device or instrument. Frequently either a critical flow prover or an orifice well tester is used for this purpose, and for a particular well the same rate of flow of gas should be obtained regardless of whether a critical flow prover or an orifice well tester is employed in the test. In Texas, when using either instrument, either Capacity Table 1 or 5&apos; is employed in making the necessary computations. If the tables are used, a discrepancy always is found whenever the two instruments are compared by extrapolation to the same conditions of flow. Clearly, Tables 1 and 5 must be at fault in some respects. The orifice well tester and the Bureau of Mines type of critical flow prover are essentially the same instrument; both devices utilize a square-edged orifice 1/8 in. in di-ameter as the primary element, and both freely discharge gas to the atmosphere. Tables for the orifice well tester&apos; have been published in the ranges of 0 to 15 in, of water and 0 to 40 in. of mercury (Hg) differential in pressure. Coefficients for the critical flow prover have been published for differentials in pressure greater than 75 psia. An extrapolation of either differs from the other set of data as much as 18 per cent at some points. No immediately obvious reasons for the discrepancy was found, and data available from the literature were insufficient to effect reconciliation. Consequently, a series of experiments was performed to check the available data and to determine discharge coefficients for the two devices in an overlapping range of differential pressure. The correlating equation used in preparation of tables such as Tables 1 and 5&apos; is the so-called hydraulic equation, Q = C1 vh .....(1) The tables cover orifice sizes from 1/8 through 1 1/4 in. A second set of tables, for use with greater differentials in pressure, apply only to the 3/4, 1, and 1 1/4-in. orifice plates over a pressure range of 0 to 40 in. of Hg. The correlating equation used in preparation of the tables is Q = C2 vH(29.32 + 0.3H)/G . (2) Each of these equations is valid only for the range to which it has been applied, and neither equation is valid for extrapolation. Theoretical equations for flow through an orifice are based upon assumptions of fractionless flow and an emergent jet the size of the orifice. A multiplier, C,, called the discharge coefficient, is inserted into the theoretical expression to compensate for both frictional losses and the contraction of the jet experienced in the plane of the orifice. Buckingham3 shows that C, should vary with the ratio of upstream to downstream pressure for flow of a compressible fluid at any average linear velocity through the orifice less than the velocity of sound. Work published by the National Advisory Committee for Aeronautics4 indicates that the variation continues into the so-called critical flow region until the vena contracta coincides with the plane of the orifice. The NACA work, however, does not indicate a leveling off of the coefficient. The work of the Bureau of Mines5 for the critical flow prover was based on differential pressures greater than 75 psi and indicates that the discharge coefficient, Cd, is constant in this region at a value of about 0.86.

Jan 1, 1958

By W. W. Gerberich

SINCE the original formulation of fracture mechanics concepts,&apos;y2 relatively little work has related the fracture mechanics description of metal behavior on a gross, structural component scale to the behavior of its microstructural constituents. The purpose of this note is to suggest the utilization of fracture mechanics to describe material behavior on a microscopic scale. A Fracture Concept for Two-Phase Structures. A critical displacement concept considering the tough unidirectional phase in a relatively brittle matrix is first examined. It is assumed that a flaw exists at position 1 as depicted in Fig. 1. As the crack moves from position 1 to 2 the plastic zone could be of the shape described with the size approximated by the Dugdale3 model: where c is the half-crack length, OO is the applied stress, and oyS is the yield strength. Hahn and Rosen-field4 have presented a simple fracture criterion for homogeneous materials based upon the displacement at the crack tip. They also have shown the equivalence of the critical displacement, v*, to fracture toughness by Kc = (2v*oysE)1/2 [2] The displacement at the crack tip is given by and the displacement at any distance in front of the crack tip may be determined knowing the plastic zone size and utilizing the development of Goodier and Field.5 Recalling Fig. 1, the value of v* for fracture in material M1 may be calculated from Eq. [2] providing the critical stress intensity factor is known. As the material is loaded, when vc > vM1 the crack moves from position 1 to position 2 where it encounters the tough second phase. If vc2 < vm2, then the crack will be arrested providing the width of the M2 phase is sufficiently large. This condition is necessary since the displacement at position 2 has increased due to the longer crack length. Thus, the displacement at the distance X (representing the dimension of the second phase) in front of the crack may be larger than the critical displacement for failure in the brittle material. If v, > vm, then failure will proceed in the brittle material. The value of v, may be calculated as indicated above. This latter consideration is the same as predicting fracture of a brittle second phase at some distance in front of a crack located in a ductile matrix. Experimental Evidence. On a macrostructural scale, tungsten wires in a ductile Be-Cu matrix are seen to fracture well ahead of the main crack front in Fig. 2. Utilizing a Kc value of 14.2 ksi-in.1/2 obtained by Schroder et al.6 for as-received tungsten, the critical displacement 2v*, for fracture is calculated from Eq. [2] to be about 6.5 X 10-5 in. The crack tip displacement, 2vc, is calculated from Eq. [3] to be 0.0028 in. indicating that fracture would occur at a considerable distance in front of the crack tip. From the ratio of v*/vc and the plastic zone estimate of Eq. [I], the distance in front of the crack tip at which a tungsten wire should fracture is calculated to be about 0.195 in. As shown in Fig. 2, a fractured wire occurs at a distance of 0.140 in. (fractured in three places), not at 0.250

Jan 1, 1968

By P. M. Kelly

TWO analytical methods for calculating the positions of matrix and twin reflections on electron-diffraction patterns of a twinned cubic crystal have recently been published.1,2 Meieran and Richman1 considered the case of twinning on (1 12) in a bcc structure, while a more general treatment, capable of analyzing twinning on any plane in a cubic crystal, was developed by Johari and Thomas.2 The latter authors applied their general rotation matrix to both (111) twinning in face-centered crystals and {112} twinning in body-centered crystals and they derived separate expressions for these two cases. This separate treatment masks the fact that in a holosymmetric cubic crystal a (111) twin is crys-tallographically equivalent to a {112} twin.3 This is analogous to the crystallographic equivalence of rotation and reflection twins in centrosymmetric crys tals. A particularly simple example of this equivalence occurs when the two twin planes are perpendicular to each other—for example (111) and (112). Then, if twinning on (111) moves a point P to a new position P1, and twinning on (112) moves P to P2, P1 and P2 will be related to each other by a 180-deg rotation about [110]— the direction normal to both (111) and (112). Since there are diad axis axis along (110) direction in a holosymmetric cubic crys tal the two positions P1 and P2 must be crystallo-graphically equivalent. In other words if a particular pole (hk l) is in a position P1 after twinning on (Ill), then after twinning on (112) a pole of the type {hkl}—but not the particular pole (hk1)—will also be in the position P1. As a result, when only the general (as opposed to the particular) indices of poles after twinning are required, twinning on (111) gives the same results as twinning on (112). To convert the results for a (111) twin to those applicable to a (112) twin, when the particular (as opposed to the general) indices of poles after twinning are required, all that is necessary is to multiply the indices of the twin poles by the matrix for 180-deg rotation about [lie], i.e., The analytical methods suffer the disadvantage that a new set of calculations must be performed for each different diffraction pattern or, as is done in the Meieran and Richman treatment,1 a lengthy list of the location of the twin spots in reciprocal space must be prepared. All the tedious computation involved in these analytical approaches can be avoided by simply plotting, on tracing paper, a stereographic projection of a crystal twinned on say (112). By superimposing this twin stereogram on a standard (001) projection (preferably with the points and indices in a different color from those on the twin stereogram) the relative positions of both matrix and twin reflections can be determined by inspection. Alternatively, a composite projection can be

Jan 1, 1965

By G. W. Bain

The Canadian magnesite deposits are situated in Grenville township, about 8 miles from Calumet station, on the Canadian Pacific Railway, but the poor transportation facilities have hindered their development. Magnesite was discovered in the boulders near White Rock Lake by Rev. W. P. Boshart in 1900. Observing that the material of these boulders was more glistening and whiter in color than Grenville limestone, he sent a specimen to the Department of Mines, Ottawa. An analysis showed this to be almost pure carbonate of magnesia and of commercial value if present in sufficient quantities. That summer, Boshart and McAllister found numerous outcrops, both of boulders and of bed rock, that gave promise of being magnesite of a commercial grade, and decided that this mineral deposit, if developed, would rival that at Veitsch, Austria. So they procured options on most of the land on which they knew the magnesite occurred. But the transportation difficulties were too great for the deposits to be mined at the prices offered for the product. In 1907, T. J. Waters organized the Canadian Magnesite Co. and opened a quarry on the north half of lot 18, range IX, and later on lot 15, range IX, of the same township. A lirnestone kiln was erected and the calcined rock was hauled to Calumet. In 1914, the North American Magensite Co, took over the quarries and shipped both crude and calcined magnesite until January, 1923. During 1915, S. Melkman organized the Scottish Canadian Magnesite Co. and opened a quarry on lot 15, ranges X and XI, Grenville township. A light, narrow-gage railway connects this quarry with the C. P. R. at Magnesite station. but shipments are made only during the summer months. Numerous other quarries have contributed to the output of the district but the greater part has come from the open pits of the

Jan 1, 1923

By G. W. Bain

The Canadian magnesite deposits are situated in Grenville township, about 8 miles from Calumet station, on the Canadian Pacific Railway, but the poor transportation facilities have hindered their development. Magnesite was discovered in the boulders near White Rock Lake by Rev. W. P. Boshart in 1900. Observing that the material of these boulders was more glistening and whiter in color than Grenville limestone, he sent a specimen to the Department of Mines, Ottawa. An analysis showed this to be almost pure carbonate of magnesia and of commercial value if present in sufficient quantities. That summer, Boshart and McAllister found numerous outcrops, both of boulders and of bed rock, that gave promise of being magnesite of a commercial grade, and decided that this mineral deposit, if developed, would rival that at Veitsch, Austria. So they procured options on most of the land on which they knew the magnesite occurred. But the transportation difficulties were too great for the deposits to be mined at the prices offered for the product. In 1907, T. J. Waters organized the Canadian Magnesite Co. and opened a quarry on the north half of lot 18, range IX, and later on lot 15, range IX, of the same township. A lirnestone kiln was erected and the calcined rock was hauled to Calumet. In 1914, the North American Magensite Co, took over the quarries and shipped both crude and calcined magnesite until January, 1923. During 1915, S. Melkman organized the Scottish Canadian Magnesite Co. and opened a quarry on lot 15, ranges X and XI, Grenville township. A light, narrow-gage railway connects this quarry with the C. P. R. at Magnesite station. but shipments are made only during the summer months. Numerous other quarries have contributed to the output of the district but the greater part has come from the open pits of the

Jan 1, 1923

By C. W. Crispell

The four nomograms presented in this article were designed to simplify and make more rapid the calculations connected with the compression and transmission of air. The formulae involved are rather complicated, but the graphic solutions are simple; their use requires an ability to follow explicit directions and to interpolate values on a logarithmic sca1e. † For the sake of convenience, the nomograms will be divided into two classes, and the purpose and accuracy of each will be discussed. Power foR CompREssion It is frequently desirable to determine the horsepower necessary to compress a given amount of free air from atmospheric pressure to a certain final pressure. The nomograms in Fig. 1 and 2 present a rapid method of calculating the horsepower required to compress 1 cu. ft. of free air per minute by single or two-stage compression. The general formula for the horsepower required to compress air adiabatically is: S X 144 PVn [(P&apos;)n-1/sn -1 (1) where: P = absolute atmospheric pressure at compressor, in pounds per square inch. P&apos; = final absolute pressure of compressed air, -in pounds per square inch. V = volume of free air compressed per minute, in cubic feet. S = number of stages. n = exponent of the compression curve.

Jan 1, 1918

Jan 1, 1955

By P. D. Southgate

VIBRATION, both ultrasonic and sonic, can affect the course of a variety of metallurgical processes. Reports of work on this subject have appeared at intervals over the last twenty years and a thorough review has been made by Hiedemann,&apos; who gives a full list of references. It has been established that both refinement of structure and outgassing of the melt can be produced in most metals with sufficiently intense vibration. Many of the experiments in this field have been carried out using alloys of direct commercial interest in production- type casting equipment. Here a different approach is adopted, and simple binary alloys which exhibit different types of structure are used to facilitate examination of the effects produced under well-controlled conditions. Results from this kind of experiment should enable the basis of larger scale experiments with similar types of materials to be better substantiated. The alloys selected for this work are: 1) aluminum of 99.2 pct purity, the principal impurity being iron, near 0.4 pct; 2) A1-1.8 pct Fe, which is near eutectic composition; 3) A1-4 pct Fe—the second phase, of composition FeAl3, forms distinct acicular crystals; and 4) A1-12 pct Si—although this is of eutectic composition, the silicon normally appears in the form of large plates. Experimental Method There are three practicable methods by which acoustic vibration can be transferred to liquid metals: a) vibration of the whole of the container; b) electromagnetic induction; and c) insertion of a vibrating probe into the liquid. Method c is chosen here, and a frequency of 8 kc per sec is used. The end of the probe is electrically heated so that the metal near it will be the last to solidify. This ensures that vibration is transmitted directly to the liquid metal without passing through any solidifying and pasty intermediate region, which would attenuate acoustic waves severely. In addition, the heating prevents solid metal adhering to the probe, with consequent detuning. The transducer assembly is shown in Fig. 1. A stack of Permendur laminations 30 cm long acts as a half-wave vibrator and a winding along its length carries polarizing and energizing currents. It is joined by a half-wave coupling bar to a mild steel exponential horn, which tapers from 3.8 to 1.1 cm diam. A stainless steel stub 3 cm in length is welded on the free end. The assembly is supported by a plate located at the node of the coupling bar. Acoustic radiation losses are minimized by allowing the free end of the transducer to protrude above the surface of the cooling water. The exponential horn serves the function of matching the acoustic output impedance of the transducer to the radiation resistance of the probe into the melt. Electrical drive is provided by a 1 kw generator. Measurements of probe vibration amplitude during melt treatment are obtained from a gramophone pick-up with the needle attached to the wide end of the horn. This device is calibrated with a microscope before use. Liquid aluminum is very actively erosive and solution of materials with which the molten metal comes into contactcauses difficulties. Erosion of the probes in particular can be severe since it is greatly accelerated by the vibration. Tests of various acous-

Jan 1, 1958