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By D. M. Boulin, E. S. Greiner

Single crystals of vanadium were bent at 293" and 77°K to a maximum fiber strain of about 1 pct. Analysis of slip line and etch markings of- crystals deformed at either temperature show the slip planes are {112}. The slip directions at 298° and 77°K, deterwined from the asterism axes of rotation of crystals compressed in a {110} direclion, were (111). Etch pits, associated with dislocations, were observed in the plastically deformed vanadium. There was no evidence of mechanical twinning. THIS paper presents results on single crystals of vanadium plastically deformed by bending and compressing at 298° and 77°K. Bcc metals have been observed to slip on {110}, (1121, and (123) planes while the slip direction has invariably been found to be ( 111) 1 Lindley and smallman2 have studied the deformation intension of polycrystalline vanadium between 298° and 20°K and reported that at and above 77°K the deformation is predominantly by slip, but at 20°K the deformation is associated with twinning. Later, Edington and smallman3 found that single crystals of vanadium compressed in a (111) direction at 77°K deformed by twinning on { 112}( 111) systems. Clough and pavlovic4 have reported that mechanical twins were observed in vanadium loaded by impact at 77°, 173°, and 195°K, respectively. PREPARATION OF SINGLE CRYSTALS The vanadium single crystals were made from commercial vanadium reported to contain 0.03 pct C, 0.03 pct 0, 0.02 pct N, 0.0X* pct Ca, 0.0X pct Si, proximately 0.8 cm diam, 4 cm long and were grown in (100) and (110) directions. A crystal for studies of etch pits was gound to have a face parallel to a {l00} plane by the Bond crystal-orienting technique.7 In order to avoid straining, the crystals were placed on the steel mount with a low-melting organic compound (glycol phthalate) before grinding. Crystals for the bending experiments were ground to have the four side faces parallel to ( 100) planes. The crystals were electropolished8 in 10 pct H2So4 using a current density of about 3 amp per sq cm to remove the strained surface material. The crystals were bent slowly by three-point loading in a stainless-steel jig designed by Sylwestrowicz.9 The end rollers of the jig were 3.8 cm apart. DEFORMATION AT 298°K The bent vanadium crystal, after removal from the jig, had a radius of curvature of 20.4 cm over the 2-cm length close to the center loading roller, where the maximum bending moment occurred. This radius of curvature corresponded to a maximum fiber strain of 0.9 pet. The side faces contained slip bands as shown in Fig. 1. These bands are straight where the strain is high, top and bottom of micrograph, but are curved on either side of the neutral axis in the center. This curvature of the slip bands in the low-stress area may be due to cross slip. The plastically deformed crystal was subsequently electropolished and then electroetched in 10 pct H2SO4 solution, using a current density of 0.25 amp per sq cm. The structure is shown in Fig. 2. The directions of the traces on two adjoining faces were plotted stereo graphically, Fig. 3.* Since there were two sets of

Jan 1, 1968

ALABAMA Altoona -Cain, J Anniston-Cowie, L K Hermrod, A A White, H E Bessemer -Abbott, C E Ball, E M Mitchell, F R Thompson, N E Birmingham -Adler, J E Aldrich, T H Aldrich, T H, Jr Blackburn, A R Bush, M W Clark, G H Cowrn, P G Crane, W R Crawford, G G Crockard. F H

Jan 1, 1923

By B. Wilshire, W. J. Evans

W. J. Evans and 8. Wilshire SEVERAL recent investigations1-6 have shown that the strain, c, during transient and steady-state creep is well-represented by the expression: € = e0 + et(l - e-mt) + Esl [l] where Eo is the instantaneous strain on loading, ET the total transient strain, C, the steady creep rate! and m a constant relating to the rate of exhaustion of transient creep. However, it has been noted6 that deviations from this equation occur over the first 10 to 15 pct of the transient stage, when the creep rate, (. decreases more rapidly than is predicted by this equation. This rapid decrease has been attributed to a large change in work-hardening coefficient. It 1s widely accepted that steady-state creep results from a balance between the rate of strain hardcning h and the rate of recovery r (=-s(st) as: dE/dt = Es = r/h [2] Comparison of values obtained for h at the end of the initial extension and during steady creep suggests that h increases several fold during the transient stage. which has the effect of reducing the creep rate proportionally.7 To examine the dependence, on r and h, of the deformation behavior during transient and steady-state creep. a series of constant-stress creep tests was carried out at 413°C at 6000 psi using 70-30 a brass. Prelinlinary investigation showed that. with this material. the transient stage constituted a significant portion of the total creep life (-0.4tf. where tf is the time to fracture). The alloy. obtained from Metals Research Limited. was made from high-purity copper, 99.999 pct. and zinc. 99.99 pct. Heat treatment at 675°C for 4 1/2 gave a uniform grain size of 5 mm-1. Details of specimen preparation and creep testing procedures have been given previously.6 Values of h (?s/?E) were determined by measuring the instantaneous strain. ?E. which occurred on increasing the stress during creep by a small amount. ?s. Similarly. v (= -?s/ ?t) was derived from the incubation period. At, after a small decrease in stress.' Several values of v and h were obtained throughout duplicate creep tests. using different stress increments in the range 300 to 800 psi. The accuracy with which Eq. [I] represents the present creep curves was established by determining the best value of the constants Es, Et, m , and 6, using a digital computer program based essentially on the graphical solution for this equation devised by Conway and Mullikan.9 About 40 strain/time readings were taken during transient and steady-state creep. Over most of the creep curve, the average difference between the measured reading and the calculated strain at the appropriate time was less than 0.0001. However.

Jan 1, 1969

By D. Turnbull, J. C. Fisher

ACCORDING to the "reaction-path" modell,2 of martensite nucleation, the shear angle of the embryonic martensite plate must be treated as a variable, and included in any calculation of nucleus critical size. Also, as can be deduced from this model, the interfacial free energy between austenite and martensite does not reach its final value until the shear is completed. It is zero for zero shear angle. However, in order to account for the kinetics of the martensite transformation, some sort of interfacial energy barrier appears to be necessary even with the reaction-path model, for otherwise the volume and the energy of formation of the critical size nucleus both collapse to zero.3 Cohen independently suggested that surface energy could be incorporated into the reaction-path model, with the overall free energy of a martensite embryo being a function of its volume and shear angle.' It is possible to estimate the energy associated with the formation of a critical-size martensite nucleus starting with the reaction-path model and including a surface free-energy barrier. As the dependence of interfacial free energy upon shear angle is unknown, a simple type of dependence will be assumed, with the belief that the true dependence would not lead to appreciably different results. Consider the work required to form a lenticular martensite plate with radius r, thickness t, and shear angle 8. There are three contributions; one being the interfacial free energy, one being the free energy change in the martensite plate, and one being the free energy increase in the surrounding austenite. The interfacial free energy u is assumed to depend upon the shear angle 0 according to the relationship s=s0(?/?0)n [1] where 8, is the equilibrium shear angle and n is an exponent that may lie in the range 0 n 2. The work required to form the interfaces of a martensite plate then is W. = 2pr² s0(?/?0)n [2] The free energy change per unit volume of martensite is composed of two parts, one the ordinary volume free energy ?f1. which is negative, and the other the elastic strain energy G?m²/2, where G is the shear modulus and 7, the shear strain relative to the martensite structure. This expression for the strain energy is valid only when the shear strain ym, is sufficiently small that the martensite is within its linear elastic range. There is no doubt that ym, lies beyond the linear elastic range for embryos that are considerably subcritical. However, for critical nuclei it will be shown that ym, is 1.5 pct or less, within the linear elastic range of martensite. For embryos of nearly critical size, then, the strain energy of the martensite is correctly given by G?m²/2. The shear strain in the martensite is ym, = 8, — 8, and the work required to form the strained martensite is Wm --= (pr²t/2) [?fv + G(?O - ?)²/2] [3] The free energy change in the austenite is entirely that due to elastic distortion. The elastic strain is not uniformly distributed in the austenite, being large near the martensite plate and small elsewhere. Approximately, however, the energy corresponds to a uniform shear strain ya= (?t/2)/r [4] throughout the volume 4pr³/3 surrounding the plate. The work required to strain the surrounding austenite then is Wa = (4pr³/3) (G?a²/2) = (G?²/6) prt² [51 For simplicity, the same shear modulus G is assumed for each structure. The total free energy for forming a plate then is W = W3 + Wm + Wa. = 2pr² s0 (?/p?0)n + (pr²t/2) [?fr+G(?0-?)²/2] + (G?²6) prt2 [6] This expression is correct for nuclei and for embryos of nearly critical size, where, as will be shown, the strain energy in the martensite is correctly given by the expression G (? — ?)². Having W as a function of r, t, and 8, as in Eq. 6, there is a saddle-point where W has a stationary value, W subsequently decreasing indefinitely as the nucleus volume increases along the reaction path. The stationary value of W is the energy of the critical nucleus. The critical nucleus has radius, thickness, and shear angle such that ?W/?r - awlat: = ?W/?p? = 0. Performing these differentiations and calculating the critical nucleus energy, W* = [8192p(G?/6)²;s/27 ?fv4] [7] where a= (?/?0)3n+1[l +G(8"-8)'/2af.]' [7a] and where 8 is to be determined from the equation (1 + 3n/4) + G8(6O - (9)/[Af. +G(6>o-6>)72] = 0 [8] For ?f, near —200 cal per mol or —10" ergs per cc, and 8, near 1/6, as for iron-base alloys, Eq. 8 gives ?0 - ? ~ - (4 + 3n) ?f1./4G0O [9] as the difference between the equilibrium shear angle and the actual shear angle for a critical nu-

Jan 1, 1954

By AIME AIME

SCRIPTURE, statistics and imagination all were drawn upon by the speakers who acclaimed Daniel C. Jackling as recipient of the William Lawrence Saunders Gold Medal for 1930. The award was made at a special dinner at the Ritz-Carlton, in New York, on Oct. 31. Lafayette Hanchett, old friend and associate, said that if it were his task to compress the life story of Daniel Jackling into a single sentence, he could find noth¬ing so appropriate as these words from the 22nd Chapter of Proverbs, "See'st thou a man diligent in his business, he shall stand before Kings." Mr. Jackling's diligence, according to the speaker, his love for his task, have been outstanding in his career. W. S. Boyd, now ranking official in the Jackling organization, cited amazing statistics as to the quantity of copper supplied to industry by the four "porphyry". coppers that are under Mr. Jackling's immediate direc¬tion, as well as by those that, in a sense, owe their existence to the pioneer work at Utah Copper. In the aggregate- 16,000,000,000 lb. of copper having an approximate value of $2,700,000,000 have been produced from disseminated ores since 1905; and of this total 42 per cent came from Utah and the Nevada group. Newcomb Carlton, president of the Western Union Telegraph Co., long an admirer of Mr. Jackling, adroitly drew a picture of a similar occasion in some 'foreign country. He imagined Mr. Jackling being raised to the peerage and whimsically addressed him as Sir Daniel, the Right Honorable Earl of Bingham!

Jan 1, 1930

By Prince Gelasio Caetani

PRESIDENT DWIGHT'S invitation to be a guest of the American Institute of Mining and Metal-lurgical Engineers was the first of the subsequently very numerous invitations to dinner I have received from my American friends. When I received his telegram I had not yet been even formally appointed Ambassador. I cannot tell you how deeply I appreciated it. It was a hearty welcome in returning to your country which has been for me a second home and it came from the American mining brotherhood which has been my second family.There are two distinct periods of learning in life. The first one are the years spent in school where we learn many things we after-wards forget; the second one are the years of prac-tical apprenticeship which engrave indelible signs in a man's character and shape his life. These latter years I spent in the United States and they have influenced the whole course of my life. I owe very much to my American friends who trained me. The earliest was Prof. Robert Peele, of Columbia University. At the Daly West mine, in Park City, Utah, he curbed my futuristic English spell-ing and had a hard time at it. Prof. James F. Kemp taught me that geology is a guess work just as unre-liable as the prediction of international events; he taught me also that a frank, honest and loyal character will lead a man equally straight through a mining report and through public life.

Jan 3, 1923

By Larry Kaufman, Martin Schatz

The effect of pressure on the extension of the ? loop in the FeSi system has been determined by means of metallogvaphic studies and hardness measurements performed on a series of high-purity Fe-Si alloys containing 7.5, 11.0, and 13.9 at. pct Si, respectively. These mensurements, performed at 42 kbar and temperatures up to 1200oC, indicate that the ? loop is expanded to about 10 at. pct Si at 42 kbar as opposed to a maximum extension of 4 at. pct Si at 1 atm. Comparison of the experimental results with thermodynamic predictions of the pressure shifts yields satisfnctory results. DURING the past few years, several studies have been performed in our laboratory1-' in order to determine the effect of high pressure on phase equilibrium in pure iron and iron-base alloys. The purpose of these studies has been to elucidate the effects of high pressure experimentally and to compare the observed results with predicted pressure effects derived on the basis of known thermody-namic and volumetric data at 1 atm. These studies have included work on pure iron2,5,7 as well as Fe-Ni,1,5 Fe-cr,l,5 and Fe-c4-6 alloys. In addition, Tanner and Kulin3 have reported results of pressure studies on two Fe-Si alloys containing 2.0 and 6.25 at. pct Si. At the time of this latter study, no detailed information was available concerning the difference in volume between the a (bcc) and ? (fcc) phases in the Fe-Si system as a function of silicon content. In order to compare their observations with calculated pressure shifts, Tanner and Kulin were forced to assume that silicon had no effect on the difference in volume between a and ? iron. The resulting discrepancy between their calculation of the a/? phase boundary at 42 kbar and the observed results led them to the conclusion that silicon additions probably decrease the difference in volume between a and ? iron. Recently: Cockett and Davis8,9 have reported de- tailed studies of the lattice parameters of a series of Fe-Si alloys at temperatures ranging from 20" to 1150°C. These measurements, performed on alloys in the bcc and fcc range, show that silicon does indeed decrease the difference in volume between a and ? iron. By correcting the calculations of Tanner and Kulin in line with the observed effect of silicon they were able to show improved agreement between computed and observed pressure shifts.' The present measurements were undertaken to provide additional corroboration of this effect, by extending the range of composition, in addition to exploring a situation where large extensions of a ? loop could result in impingement of the ? field with an ordered bcc phase (based on Feo.75Sio.25). I) EXPERIMENTAL PROCEDURES AND RESULTS The alloys investigated were obtained from Dr. F. Kayser of M.I.T. They were prepared at the Ford Scientific Laboratory by vacuum melting electrolytic iron and high-purity silicon. The melts were poured under an argon atmosphere into hot-topped steel molds. Subsequently the ingots were hot-worked down to 1/2-in.-diam rods. Three alloys containing 7.5, 11.0, and 13.9 pct Si were studied. Carbon, regarded as the principal impurity, analyzed at, or below, 0.001 wt pct for all of the alloys. Prior to pressure-temperature treatment, the rod was annealed for 24 hr in vacuum at 1000°C, water-quenched, and subsequently machined into 0.100-in.-diam by 0.100-in.-long specimens. Subsequent to machining, the specimens were again annealed and then examined metallographically. They were found to exhibit a clear coarse-grained ferrite similar to Figs. 10 and 110 of Ref. 1 and Fig. 2 of Ref. 3. Subsequently, specimens of each alloy were equilibrated at 42 kbar at various temperatures in supported piston apparatus.1,3,4,6 Three specimens, one of each alloy, were wrapped in platinum and exposed simultaneously. The pressure-temperature cycle consisted of increasing the pressure from ambient to 42 kbar at 25oC, heating rapidly to the desired temperature, holding for 15 min, and quenching to 100°C, followed by slower cooling to 25°C and pressure release. The temperature was measured with a Pt/Pt-13 pct Rh thermocouple which was not corrected for pressure effects. Subsequently, specimens were examined metallographically and by

Jan 1, 1964

CONTENTS PAGE ZAPFFE, CARL.-Manganiferous Iron Ores of the Cuyuna District, Minnesota. Discussed by A. K. Knickerbocker 1 MCCORMACK, C. P.-Economics of the Cuyuna Manganiferous Iron Ores. Dis-cussed by T. L. Joseph, J. Wilbur Van Evera, C. P. Perin, T. T. Read, L. E. Ives 4 READ, T. T.-Probable Error in Blast-furnace Records and Calculations Therefrom. Discussed by C. H. Herty, Jr., T. T. Read, T. L. Joseph, Ralph H. Sweetser 8 SCHWARTZ, H. A. and HIRD, (Mrs.) ANNA NICHOLSON.-Chemical Equilibria During Solidification and Cooling of White Cast Iron. Discussed by N. B. Pilling, Ralph H. Sweetser, H. M. Boylston, Albert Sauveur 10 HERTY, C. H., JR., BELYEA, A. R., BURKHART, E. H., and MILLER, C. C.-Some Factors Affecting the Elimination of Sulfur in the Basic Open-hearth Process. Discussed by Henry D. Hibbard, L. F. Reinartz,. C. H. Herty, Jr., Ancel St. John, A. L. Feild, C. R. Hayward, Ralph H. Sweetser, C. D. King, Haakon Styri, George A. Orrok 12 HIBBARD, HENRY D.-Finishing Melting Temperatures of Simple Ingot Steels. Discussed by Haakon Styri, George V. Luerssen, A. G. Zimermann, A. L. Feild, George A. Orrok, Albert Sauveur, R. F. Harrington, Henry D. Hibbard, I. A. Billiar, William J. Priestley, H. W. Gillett, W. P. Barba, Jerome Strauss, Harry H. Smith, H. LeChatelier, L. F. Reinartz 19 HERTY, C. H., JR., and TRUE, O. S.-The Reaction between Manganese and Iron Sulfide. Discussed by A. L. Field, H. S. Rawdon, C. H. Herty, Jr., T. L. Joseph, Haakon Styri 37 KAMURA, HEIHACHi.-Reduction of Iron Ores by Carbon Monoxide. Discussed by T. L. Joseph, R. Franchot, Ralph H. Sweetser, C. H. Herty, Jr 43 JOSEPH, T. L.-Effect of Sulfur on Blast-furnace Process. Discussed by R. Franchot, C. A. Meissner, T. L. Joseph, C. H. Herty, Jr., Ralph H. Sweetser, I. E. Waechter, F. N. Speller, T. T. Read 45 GOOSTRAY, JOB, HARRINGTON, R. F., and HOSMER, M. A.-Brief History of Metallurgical Practice in Cannon-making with Particular Reference to the Cast-iron Gun. Discussed by A. G. Zimermann, Geo. A. Orrok, Chas. Me-Knight, Jr., F. Brauer 51 Manganiferous Iron Ores of the Cuyuna District, Minnesota Discussion of the paper of CARL ZAPFFE, presented at the New York Meeting, February, 1925, and issued, as Paper No. 1390-I, with MINING AND METALLURGY, December, 1924. A. K. KNICKERBOCKER,* Virginia, Minn. (written discussion).¬The author makes a broad distinction between the "black" ores (the

Jan 6, 1925

By William Marsh Baldwin

TWO of the most useful and important equations available to the metallurgist for the study of plastic deformation of metals are the Huber-von Mises-Henckyl-~ and the St. Venant7-10 equations. Huber-von Mises-Hengky Equation The Huber-von Mises-Hencky equation answers the question: When does plastic flow occur in metal that is subjected to a multi-axial stress? It occurs, according to this equation, when the three principal stresses,t UI, u2, and u3 satisfy the equation: (<ri - <r2)2 + (<r2 - <rsY + (ff! - <r3)* = 2Ki [i] Here K is the yield strength of the material as determined in an ordinary tensile test. If the quantities ul, 52, andas are assigned to the coordinates of a Cartesian three-dimensional system, this expression describes a cylinder whose axis of symmetry is inclined at equal angles to the three coordinate axes4s6 (Fig. I). The radius of this cylinder is .\/%K. For the purpose of simplicity, it is sometimes advantageous to ascribe the values al/K = sl, az/K = s2, UD/K = SJ to the three coordinate axes instead of the principal stress alone. In this case, Eq. I becomes (*i - s*)1 + (s2 - S3)2 + (si - SiY = 2 [2] and the radius of the cylinder becomes \/%. In the latter method of representation, a point lying inside the cylinder indicates that the metal will react elasti-cally, whereas a point lying on the cylindrical surface indicates that the metal will behave plastically. Some of the geometric features of this cylinder are worthy of study. Let us inquire first as to what interpretation may be placed upon what we will choose to call the "circles of latitude" of the cylinder (L in Fig. I) and the "meridians" of the cylinder (M in Fig. I). Circles of Latitude Circles of latitude are formed by allowing a plane, passing perpendicular to the cylinder axis, to intersect with the cylinder. Any point, P, on this circle is presumed to have the coordinates sl, SZ, and s3. The coordinates of the point resulting from the intersection of the plane and the cylinder axis will be a, a, and a (since the cylinder axis is equally inclined to the three coordinate axes). L?t US now pass a line through the point on the circle and the point on the axis.

Jan 1, 1946

By William Marsh Baldwin

TWO of the most useful and important equations available to the metallurgist for the study of plastic deformation of metals are the Huber-von Mises-Henckyl-~ and the St. Venant7-10 equations. Huber-von Mises-Hengky Equation The Huber-von Mises-Hencky equation answers the question: When does plastic flow occur in metal that is subjected to a multi-axial stress? It occurs, according to this equation, when the three principal stresses,t UI, u2, and u3 satisfy the equation: (<ri - <r2)2 + (<r2 - <rsY + (ff! - <r3)* = 2Ki [i] Here K is the yield strength of the material as determined in an ordinary tensile test. If the quantities ul, 52, andas are assigned to the coordinates of a Cartesian three-dimensional system, this expression describes a cylinder whose axis of symmetry is inclined at equal angles to the three coordinate axes4s6 (Fig. I). The radius of this cylinder is .\/%K. For the purpose of simplicity, it is sometimes advantageous to ascribe the values al/K = sl, az/K = s2, UD/K = SJ to the three coordinate axes instead of the principal stress alone. In this case, Eq. I becomes (*i - s*)1 + (s2 - S3)2 + (si - SiY = 2 [2] and the radius of the cylinder becomes \/%. In the latter method of representation, a point lying inside the cylinder indicates that the metal will react elasti-cally, whereas a point lying on the cylindrical surface indicates that the metal will behave plastically. Some of the geometric features of this cylinder are worthy of study. Let us inquire first as to what interpretation may be placed upon what we will choose to call the "circles of latitude" of the cylinder (L in Fig. I) and the "meridians" of the cylinder (M in Fig. I). Circles of Latitude Circles of latitude are formed by allowing a plane, passing perpendicular to the cylinder axis, to intersect with the cylinder. Any point, P, on this circle is presumed to have the coordinates sl, SZ, and s3. The coordinates of the point resulting from the intersection of the plane and the cylinder axis will be a, a, and a (since the cylinder axis is equally inclined to the three coordinate axes). L?t US now pass a line through the point on the circle and the point on the axis.

Jan 1, 1946

By A. B. Parsons

AN often repeated criticism of the profession of engineering is that it is as a whole it lacks solidarity. organization, co-ordination, and leadership. Significantly, the critic, are all engineers. Other members of the body politic either do not know about the absence of organization or they do not care. If engineers have no organization they have a plethora of organizations. There exist in the United State, today some 350 societies. institutes. clubs, associations, and councils of engineers and engineering technologists and this number excludes several hundred local chapters of national societies. trade associations, and local engineers&apos; clubs of purely social character- Successful engineers must be proficient in analyzing, planning, and co-ordinating. but it is generally admitted that for their profession as a whole their success in this respect has been indifferent.

Jan 1, 1943

For the first time, the attendance at the meetings of the Institute passed the thousand mark; as is shown by the following table: REGIS- AT BANQUET DID TOTAL TERED NOT REGISTER Men :..:... 703 76 806 Women 195 61 256 1062 The names of the members and guests who registered or attended the banquet but did not register are: A A. D. Beers C. A. Adams Hans Behr Thos. J. Adams Edgar G. Bell Lawrence Addicks Donald A. S. Bell H. T. Abrams W. de LeBenedict G. Aertsen G. B. Bertelli M. M. Albertson Charles P. Berkey James Aldrich Clinton Bernard D. C. Alexander, Jr. W. N. Best W. H. Alexander Robert M. Betts A. W. Allen Christopher H. Bierbaum F. D. Aller Paul Billingsley R. H. Allport R. A. Bingham F. C. Alsdorf R. M. Bird Capt. M. Altmayer John L. W. Birkinbine A.&apos; W. Ambrose G. S. Bisey Henry M. Ami Charles W. Boise F. L. Antisell J. J. Blackmore R. S. Archer A. E. Blackwood Paul&apos; Armitage Capt. C. K. Blatchly Andrew B. Armstrong E. L. Blossom Clifton T. Armstrong C. A. Bohn Ralph Arnold James M. Bonsall R. M. Atwater, Jr. E. E. Boon Joseph E. Aue Gail Borden A. M. Austin R. S. Botsford W. S. Ayres John M. Boutwell

Jan 4, 1919

By M. Prats

This paper presents a method for obtaining the correct values of the breakthrough sweep efficiency of the staggered line drive, taking into account the proper shape of the breakthrough streamline. Results obtained were different from those previously published, which were obtained by using an inexact shape of the breakrhrough streamline. INTRODUCTION In Section 9.31 of Muskat&apos;s&apos; The Flow of Hotnogeticous Fluids Through Porous Media, it is stated that in a staggered line drive flood "the streamline of highest average velocity [is] the line of centers between input and output wells" (see Fig. I). Muskat used this concept to determine the relationship between the breakthrough sweep efficiency and the geometry of the staggered line drive pattern. Although it is clear from symmetry considerations that the breakthrough streamline passes through the midpoint between input and output wells, it is equally clear, as shown in Fig. 239 of Ref. 1, that the breakthrough streamline is not represented very well by the straight line joining the input and output wells. Therefore, it is desirable to determine the proper relationship between the breakthrough sweep efficiency and the pattern geometry by using the proper shape of the breakthrough streamline. METHOD OF SOLUTION It was found that the effect of the geometry of the staggered line drive on the breakthrough sweep efficiency can be investigated easily by making use of the method developed in Ref. 2. With this method, it can be shown that the general complex potential for the staggered line drive, which can be considered as a rectangular five-spot, is given in the coordinate system of Fig. 1, by O(z) = In cn(z\m) = +(x,y) + i $(x, y) . (1) where z = x + iy, +(x, y) is the potential distribution and $(x, y) is the stream function. The function cn (zm) is a Jacobian elliptic function of parameter m and has simple zeros at z,. = (2n + 1) K + 21iK and simple poles at z, = 2nK + (21 + 1)iK. Thus, the complex potential behaves like a(z) = ln(z - zr.) in the neighborhood of the production wells and behaves like a(z) = - ln(z - Z,) in the neighborhood of the injection wells. Since (z - z1.v) = rll.ei, we note that the potential + has the proper logarithmic behavior near the two wells, while the stream function $ varies with the angle, decreasing clockwise around the production well and increasing clockwise around the injection well. The functions K(m) and K&apos;(tn), related by K(m) = K&apos;(m,), where m + m, = 1, are known as the complete elliptic integrals of the first kind. By use of other properties of the Jacobian elliptic functions, the general stream function distribution for the staggered line drive can be obtained from Eq. 1: From the Jacobian elliptic function values, sn(0lm) = 0 dn(O(m) = cn(0jm) = 1, and f[K&apos;(m)Iml = 03, it follows that the stream function given by Eq. 2 satisfies the proper symmetry conditions near a production well P located at [K(m), 01 and an injection well I located at [0, K&apos; (m)]. That is, the line IOP in Fig. 1 is a streamline with value G (0. 0) = -0. and the straight lines connecting I and P to the point [K(m), K&apos; (m)] is a streamline of value $[K(m), K&apos; (m)] = -7/2. Similar symmetry conditions are obtained near other wells. It should be nuled that for m = m1, = 0.5, Eq. 2 reduces to the stream function distribution of the regular five-spot given in Ref. 7. SHAPE OF THE BREAKTHROUGH STREAMLINE It is apparent, from symmetry considerations, that the breakthrough streamline ($,) passes through the point [K(m)/2, K&apos; (m)/2]. Its value there is so that the shape of the breakthrough streamline $,, is given by

Jan 1, 1957

By Raymond Mancha

When calculating the pressure-volume characteristics of projected mine-ventilating circuits by orthodox methods, certain basic assumptions are required in order to employ the various available empirical data. It is assumed, for example, that the mine air is an incompressible fluid subjected to isothermal flow, an assumption sufficiently accurate for practical purposes since pressure and temperature differentials are small throughout the average circuit. A more erroneous assumption, however, is that all air is accounted for as it travels throughout the mine. No attempt is usually made to evaluate stopping leakage as it occurs; instead, the air volume required at the last crosscuts is assumed to enter the mine, travel the various intake air courses intact, sweep the workings and travel out by the return air courses to the point or points of exit from the mine. Actually, there is a leakage of air from intake to return at every stopping, the quantity of this leakage depending upon the tightness of the stopping and the pressure difference across the stopping. Unfortunately, a lack of empirical data and knowledge of the condition of individual stoppings makes an exact analysis of underground stopping leakage impossible. Generally, leakage is most severe through the old stoppings outbye the circuit. These are also subjected to higher pressure differences than the newer inbye stoppings. Therefore the circuit air volume diminishes at a decreasing rate progressing from outbye to inbye the circuit. Consider a simple mine circuit consisting of one intake and one return air course, each of equal and uniform section area and interconnected at regular intervals with crosscuts equipped with stoppings. At any point X inbye the circuit the air volume q on the intake air course equals that on the return air course and decreases with diminishing rate from outbye to inbye the circuit between the limits of Q1 completely outbye and Q completely inbye. Such a volume change is represented by curve a, Fig. I, which is computed with the aid of the equation q = Q1- (Q1- Q)(X + L)N. This equation results from the general algebraic equation of form q = k, — kXN after solving for kl and k with the knowledge that completely outbye X = o and q = QL, also completely inbye X = L and q = Q. Curves a, b and c, Fig. I, show values of q as ordinates versus values of X as abscissas, for values of N equal to 0.50, 1.00 and 2.00, respectively. Distribution of underground stopping 1eakage directly affects the air-volume distribution along the circuit, which in turn determines the circuit pressure gradient. To deliver any required air volume inbye a circuit or portion thereof requires a higher circuit-pressure differential if stoppings leak than is necessary with tight stoppings. Every mining engineer engaged in the analysis of projected mine-ventilation circuits is therefore confronted with the problem of making proper allowance for the effects of leaking stoppings. The purpose of this paper is to present evidence in support of the author&apos;s suggestion that circuit pressure increase (per cent)

Jan 1, 1942

By Raymond Mancha

When calculating the pressure-volume characteristics of projected mine-ventilating circuits by orthodox methods, certain basic assumptions are required in order to employ the various available empirical data. It is assumed, for example, that the mine air is an incompressible fluid subjected to isothermal flow, an assumption sufficiently accurate for practical purposes since pressure and temperature differentials are small throughout the average circuit. A more erroneous assumption, however, is that all air is accounted for as it travels throughout the mine. No attempt is usually made to evaluate stopping leakage as it occurs; instead, the air volume required at the last crosscuts is assumed to enter the mine, travel the various intake air courses intact, sweep the workings and travel out by the return air courses to the point or points of exit from the mine. Actually, there is a leakage of air from intake to return at every stopping, the quantity of this leakage depending upon the tightness of the stopping and the pressure difference across the stopping. Unfortunately, a lack of empirical data and knowledge of the condition of individual stoppings makes an exact analysis of underground stopping leakage impossible. Generally, leakage is most severe through the old stoppings outbye the circuit. These are also subjected to higher pressure differences than the newer inbye stoppings. Therefore the circuit air volume diminishes at a decreasing rate progressing from outbye to inbye the circuit. Consider a simple mine circuit consisting of one intake and one return air course, each of equal and uniform section area and interconnected at regular intervals with crosscuts equipped with stoppings. At any point X inbye the circuit the air volume q on the intake air course equals that on the return air course and decreases with diminishing rate from outbye to inbye the circuit between the limits of Q1 completely outbye and Q completely inbye. Such a volume change is represented by curve a, Fig. I, which is computed with the aid of the equation q = Q1- (Q1- Q)(X + L)N. This equation results from the general algebraic equation of form q = k, — kXN after solving for kl and k with the knowledge that completely outbye X = o and q = QL, also completely inbye X = L and q = Q. Curves a, b and c, Fig. I, show values of q as ordinates versus values of X as abscissas, for values of N equal to 0.50, 1.00 and 2.00, respectively. Distribution of underground stopping 1eakage directly affects the air-volume distribution along the circuit, which in turn determines the circuit pressure gradient. To deliver any required air volume inbye a circuit or portion thereof requires a higher circuit-pressure differential if stoppings leak than is necessary with tight stoppings. Every mining engineer engaged in the analysis of projected mine-ventilation circuits is therefore confronted with the problem of making proper allowance for the effects of leaking stoppings. The purpose of this paper is to present evidence in support of the author&apos;s suggestion that circuit pressure increase (per cent)

Jan 1, 1942

C. M. Kay, Chairman L. W. Moore, Post Chairman C. W. Conn, Vice-Chairman R. W. Shearman, Secretary-Treasurer BLAST FURNACE, COKE OVEN, AND RAW MATERIALS COMMITTEE F. C. Anderko, Chairman James Chisholm, Past Chairman W. F. Huntley, Senior Vice-Chairman W. O. Bishop, Vice-Chairman R. W. Shearman, Treasurer D. C. Brown, Secretary IRON AND STEEL DIVISION Gerhard Derge, Chairman J. J. Golden, Past Chairman B. M. Larsen, Chairman-Elect R. W. Shearman, Secretary-Treasurer THE METALLURGICAL SOCIEN OF AIME J. S. Smart, Jr., President C. C. Long, Past President K. L. Fetters, Vice-President T. D. Jones, Treasurer R. W. Shearman, Secretary

Jan 1, 1961

By F. Seitz

STAFF: Editor, Gerhard Derge Carnegie Institute of Technology Schenley Park Pittsburgh 13, Pa. Editorial Assistant, M. A. Redmerski Managing Editor, James J. Burke THE METALLURGICAL SOCIETY: John Chipman, President; W. R. Hibbard, Jr., Post-President; C. C. Long, Vice-President; T. D. Jones, Treasurer; R. W. Shearman, Secretary. PUBLICATIONS COMMITTEE OF THE METALLURGICAL SOCIETY: R. Maddin, Chairman; Dennis Carney, J. C. Fulton, J. H. Hollomon, T. B. King, C. C. Long, W. 0. Philbrook, J. D. Sullivan, David Swan, and F.L. Vogel. Review and selection of manuscripts is under the supervisian of the following Publications Committees: Extractive Metallurgy D ivis ion: T. 0. King, Chairman; S. J. Dick inson, R. P. Hermsdorf, R. Schuhmann, Jr., and H. H. Kel logg. Institute of Metals Division: F. L. Vogel, Choirmon; R. L. Smith, Vice Chairman; R.W. Balluffi, J. H. Bachtold, A Servi, C.D.Graham, Jr., C. G. Goetzel, F. E. Joumot, Jr., G. E. Pellissier, Paul Gordon, Jock Washburn, Harold Margol in, A. U. Seybolt, I. R. Kromer, R. A. Meussner, R. W. Guard, M. Harmon, J. N. Hobstetter, Dean Starr, P. Shewmon, R. Gordon, J. 0. Betterton, and E. Morgan. Iron and Steel Division: W. 0. Philbrook, Chairman; F. C. Langenberg, C. W. Sherman, J. Wagstaff, and E. J. Whittenberger. Published bimonthly by the American lnstitute of Mining, Metallurgical, and Petroleum Engineers, Inc., 29 West 39th Street, New York 18, N. Y. Telephone: PEnnsylvania 6-9220. Subscription $20 per year for non-AIME members in United States and North, South, and Central America; $25, foreign; $5 for AlME members. Single copies, $4.00, single copies foreign, $5.00. The AlME is not responsible for any statement made or opinion expressed in its publications . . . Copyright 1959 by the Americon Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. . . . Registered cable address, AlME New York ... Indexed in Engineering Index, Industrial Arts Index, and Chemical Abstracts . . .Second class postage paid at New York, N. Y. , ond Ann Arbor, Mich. Volume 215, Number 3

Jan 1, 1960

By Nelson P. Hulst

COMMITTEES. DULUTH.-Nelson P. Hulst, Chairman; J. B. Adams, W. C. Agnew, M. H. Alworth, C. W. Andrews, R. Angst, William R. Appleby, C. E. Bailey, G. G. Barnum, E. F. Bradt, Mylie Bunnell, George L. Cheesebrough, Peter Christen¬sen, F. A. Cokefair, T. F. Cole, C. A. Congdon, N. Cowling, George H. Crosby, M. D. Cullum, C. d&apos;Autremont, Jr., H. L. Dresser, C. T. Fairbairn. Walter Fitch, F. L. Gilbert, J. T. Hale, G. G. Hartley, E. B. Hawkins, M. S. Hawkins, J. H. Hearding, Louis Hill, L. J. Hopkins, F. E. House, J. C. Hunter, 0. D. Kinney, J. W. Kreitter, E. J. Longyear, Alexander McDougal, W. A. McGonagle, A. M. Marshall, W. N. Merriam, T. D. Merrill, John Millan, P. Mitchell, Clarence Moore, Hon. Page Morris, C. H. Munger, Henry Nolte, W. J. Olcott, A. L. Ordean, Thomas Owens, F. A. Patrick, H. M. Peyton; D. M. Philbin, Capt. Charles Potter (U. S. A.), L. W. Powell, Harry Roberts, Louis Rouchleau, George A. St. Clair, J. U. Sebenius, Joseph Sellwood, Amos Shepherd, W. B. Silvey, George Spencer, George C. Stone, H. B. Sturtevant, George D. Swift, Kirby Thomas, C. D. Thompson, A. D. Thomson, G. A. Tomlinson, Charles Trezona, R. R. Trezona, Maj. J. H. Upham, Charles Van Barneveld, W. W. Walker, J. L. Washburn, A. C. Weirs, H. J. Wessinger, A. B. Wolvin, Dwight E. Woodbridge. HOUGHTON.-W. E. Parnall, Chairman; W. D. Calverley, Secretary; W. B. Anderson, L. S. Austin, Jacob Baer, William Bath, F. J. Bawden., Simon Beahan, John Been, C. H. Benedict, Walter Bloomfield, S. H. Brady, Samuel Brady, Henry Brett, A. L. Burgan, F. I. Cairns, W. H. Cake, Arthur L. Carnahan, William Carpenter, Phillip Carroll, John J. Case, T. L. Chadbourne, W. A. Childs, B. F. Chynoweth, Captain James Chynoweth, H. P. Clausen, F. G. Coggin, H. D. Conant, J. B. Cooper, J. R. Cooper, John Cuddihy, Thomas Cummings, Robert Davidson, J. B. Dee, J. R. Dee, T. S. Dee, Theodore Dengler, M. M. Dennis, Captain Thomas Dennis,. F. W. Denton, A. D. Edwards, R. M. Edwards, C. S. Fales, Daniel Fisher, Henry Fisher, James Fisher, A. L. Floeter, Frank H. Getchell, M. C. Getchell, W. M. Gibson, W. M. Gilliland, James G. Glanville, George Goodale, H. S. Goodell, A. R. Gray, Edward Grierson, Homer Guck, H. D. Haddock, Captain Josiah Hall, John L. Harris, Captain S. B. Har¬ris, Enos Harrold, F. William Hartmann, George L. Heath, C. M. Hoar, Thomas Hoatson, 0. P. Hood, Captain Thomas Hooper, Captain Joshua D. Husking, Dr. L. L. Hubbard, Arno Jaelinig, E. D. Johnson, G. A. Koenig, Edward Koepel, C. H. Krause, R. H. Leach, A. W. Leonard, James MacNaughton, Edward McCormick, Thomas McDonald, R. T. McKeever, F. W. McNair, James McRae, John Mackey, John C. Mann, Major G. A. Marr, Captain Thomas Maslin, Harry Mercer, James Merton, Michael Messner, William F. Miller, Captain J. Milligan, Dr. J. W. Moore, Charles H. Moss, H. F. Nickerson, Charles L. Noetzel, P. H. Paine, John Penrose, Captain John Pentecost, Graham Pope, R. C. Pryor, James Ramsay, J. T. Reeder, Allen F. Rees, J. H. Rice, W. G. Rice, James

Jan 1, 1905

By S. Nenno, T. Saburi, Y. Mizutani, M. Yomarnoto, K. Komatsu

In the equilibrium phase diagram of the Ni-Mo sys-tem1,2 available at present, intermetallic compounds (or ordered phases)ß(Ni4Mo) and ?(Ni3Mo) are known to exist to the nickel rich side. In our recent investigations on Ni-Mo alloys, however, it has been found that the quenched alloys from the high temperature region containing more molybdenum than the Ni4Mo do not decompose directly into 0 and when annealed isothermally below the peritectoid temperature, i.e., 865°C. This note is to report the existence of Pt2Mo type superlattice (possibly ordered Ni2Mo) as a metastable phase in the early stage of decomposition. Alloys containing 20.1, 22.7, and 24.4 at. pct Mo were prepared by vacuum-melting electrolytic nickel of 99.9 pct purity and molybdenum powder of 99.9 pct purity in an alumina crucible. From the resulting ingots, sheets 0.3 mm thick were obtained by forging, hot-, and cold-rolling. The sheet specimens were water-quenched from ! region and subsequently annealed for various periods of time at temperatures below the peritectoid temperature. On these specimens were made optical-microscopic and transmis-sion-electron-microscopic observations. Fig. 1- Optical micrograph of the 22.7 at. pct Mo specimen annealed for 100 hr at 700°C after quenching. (ß + ?) region, B, nucleated along a grain boundaries are invading the preexisting (ß + Ni2Mo) region, A. Details of A are observable only by electron microscopy. Etchant: 60 pct HNO3-40 pct CH3COOH.

Jan 1, 1970

By F. D. Richardson

STAFF: Editor, Gerhard Derge Carnegie lnstitute of Technology Schenley Park Pittsburgh, Pa. 15213 Editorial Assistant, M. A. Redmerski Production Editor, Otto T. Johnson THE METALLURGICAL SOCIETY: Jack H. Scoff, President; Richard C. Cole, Past-President; Harold 0. Emerick, President-Elect; Ralph L. Hennebach, Treasurer; Robert W. Shearman, Secretary; Donald A. Parks, Assistant Secretary; Leslie S. Wilcoxson, Assistant Secretary. PUBLICATIONS COMMITTEE OF THE METALLURGICAL SOCIETY: R. E. Lund, Chairman; T. E. Dancy, H. O. Emerick, P. R. Gouwens, R. E. Grace, J. H. Jackson, H. H. Johnson, A. E. Lee, Jr., R. R. Nosh, R. D. Pehlke, and Paul Queneau. Review and selection of manuscripts is under the supervision of the following Publications Committees: Extroctive Metallurgy Division: R. E. Grace, Choirmon; G. M. Bell, D. W. Bridges, J. M. Cigon, G. W. Heoly, T. A. Henrie, R. D. (Holli-doy, C. E. O&apos;Neill, C. S. Somis, A. W. Schlech-ten, and Charles Shull. Iron and Steel Division: R. D. Pehlke, Choirmon; T. P. Floridis, Arnulf Muon, G. R. St. Pierre, E. T. Turkdogan, L. H.Von Vlock, and J. M. Uys. lnstitute of Metals Division: H. H. Johnson, Jr., Chairman; J. B. Clark, Vice Choirmon; M. R. Achter, G. F. Bolling. J. O. Brittoin, G. P. Conard, II, R. S. Davis, L. A. Girifolco, G. T. Hohn, J. P. Hirth, L. Himmel, G.T.horn, George Krauss, J. D. Livingston, R. D. Manning, H. M. Otte, S. V. Rodcliffe, R. E. Reed-Hill, H. C. Rogers, E. ScaIa, O. Sherby, M. T. Simnad, G. R. Speich, E. A. Steigerwald, R. A. Swolin, W. A. Tiller, W. R. Upthegrove, J. B. Wagner, Jr., Derek Wolton, H. W. Weart, W. W. Webb, and D. Published seven times yearly in February, March, April, June, August, October, and December by the American lnstitute of Mining, Metallurgical, and Petroleum Engineers, Inc., 345 East 47th Street New York, N. Y. 10017. Telephone PLAZA 2 -6800. Subscription $30 per year for non-AtME members m United States and North, South, and Central America; $32, foreign; $7.50 for AlME members Single copies, $6.00, single copier foreign, $6.50. The AiME is not responsible for any statement made or opinion expressed in its publications . . . Copyright 1964 by the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. . . . Registered cable address, AiME New York Indexed in Engineering Index, Industrial Arts Index, and Chemical Abstracts. Second dost postaas poid ot New York, N. Y.,ond Ann Arbor, Mich. Volume 230, Number 6.

Jan 1, 1964