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United Engineering Trustees, Inc. GEORGE D. BARRON ARTHUR S. DWIGHT R. M. ROOSEVELT The Engineering Foundation H. C. BELLINGER E. DEGOLYER J. V. N. DORR

Jan 1, 1932

[Aamot, Clav Crone, (Member '29) Met., Det Norske Aktieselskab for Elektrokemisk, Industri, Inc., Oslo, Norway. Aamot, 0, Crone, (Member '29) c/o Elektrokemisk, Radhusgaten 23, Oslo, Norway. Aase, Glenn D., (Junior Member '40) Jr. Met., American Smelt. & Refin. Co., Selby, Calif. Abadie, Henry G., (Junior Member '43) Div. Petr. Engr., Union Pacific R.R. Co., 422 W. 6th St., Los Angeles 14, Calif. Abbott, Clarence E., (Member '04) Civil Engr., V.P., Tennessee Coal, Iron & R.R. Co., 1542 Brown Marx Bldg., Birmingham, Ala. Abbott, Fred E., Jr., (Member '44) Petr. Engr., c/o Arabian American Oil Co., A.P.O. 816, c/o Postmaster, New York, N. Y. Abel, Raymond L., (Member '28) Chem. Engr., 0. 0., Pittsburgh Chem. Warfare Procurement Dist., American Bank Bldg., Pittsburgh, Pa.]

Jan 1, 1946

By Fred P. Peters

T. D. Yensen.*—As my information is of a negative nature, I think it belongs under this paper. We are particularly interested in magnetic materials and we would like very much on occasions to make use of powder metallurgy. We have tried repeatedly to use powder metallurgy in preparing our nickel alloys but always. with negative results; that is, we cannot get as good magnetic properties by powder metallurgy as we can by starting with a molten material. We have tried by all possible means to make materials' like 50 per cent iron-nickel alloys by powder metallurgy. The compacts can be regularly lorged and rolled but no matter what we do in the way of annealing, the magnetic properties come out very much poorer than if we start with molten material. F. V. Lenel. †—I want to mention one characteristic of articles made from metal powders which distinguishes them from die castings; that is, their wear resistance. Die castings usually are made from zinc or aluminum alloys and a few copper-zinc alloys; all of them are comparatively soft and not very wear resistant. I know of a number of cases where powder metallurgy rather than the die-casting method was used for producing a certain part because higher wear resistance was needed than could be attained in die castings. A, J. LanghammeR.*—The subject of powder metallurgy is somewhat difficult to discuss, and portray, in the time that his been allotted. Most of you would rightly be bored if we went into details. However, I will cite one incident that possibly will help illustrate some of the potentials. Last summer I was in Washington and met Navy officials for the purpose of studying the possibility of making a certain part by powder metallurgy. The part is highly intricate and I happened to remark that the material cost would be high; that is, the cost on one raw material. Promptly a high-ranking Navy officer said: "Mr. Langhammer, if you must pay x dollars a pound for the raw material, but achieve the desired results, the cost of the finished part would still be low."

Jan 1, 1945

Jan 1, 1970

By Orlando E. Romig

As metals and alloys are composed of an aggregate of allotriomorphic crystals or grains, each possessing an individual orientation, the physical characteristics of a metal or an alloy are closely related to the properties of the individual crystals. The preparation and study of single metallic crystals are, therefore, matters of considerable importance. The advent of the X-ray spectrograph as a valuable metallurgical tool has magnified the importance of this subject, because the interpretation of some X-ray spectrographs is difficult unless single crystals are used in these studies. Previous Work The first paper, as far as the writer knows, on the behavior or preparation of single crystals of metals is by Baker.' He describes the behavior of extruded wires of sodium and potassium. These wires, when pulled in tension, instead of showing the usual conical fracture common to most metals, had a chisel-shaped fracture when they were broken. I and 11, Fig. 1, have a similar fracture. Baker checked his results by preparing single crystal wires from molten sodium and potassium and observing their properties. He pre- pared the wires by filling glass tubes, under oil, with the molten metal. The surfaces of the strained wires showed slip bands of remarkable clearness of which photographs are shown in his paper. He concluded that these wires were single crystals and "that the portions of the metal brought into play are cubes. Such cubes, when placed so that a plane through two opposite edges was parallel to the axis of the wire, would allow of lateral contraction by faces gliding over one another in one direction only and not in the direction at right angles."

Jan 1, 1927

By L. B. Schmitt, N. H. Polakowski

Square bars of cold-dvawn copper, mild steel and a 2024 aluminum alloy were forced through an adjulstable gap between two hardened steel rollers by pulling or pushing. The rollers were either free to rotate or were locked in position so that conditions comparable with drawing, rolling, ad containerless extrusion could be created at will. Push or pull forces as well as roll separatirg forces were measured. Forming efficiency and coefficients of friction were determined. For- slow-rate deformation the values ot µ wrere between 0.09 and 0.14. Possibilities for further investigation are indicated. THIS work was undertaken with the aim of a) determining the principal parameters of cold drawing under simplified conditions directly, without recourse to speculative assumptions and b) comparing drawing with rolling and extrusion from the viewpoint of forces involved and deformation efficiency. Data of type a) relating forces in axially-symmet-rical drawing to die geometry. drafting schedules, material properties and lubrication conditions are abundant. Their intrinsic value is. however. limited as long as the radial die forces are unknown. On the other hand. the difficulties associated with measurement of these forces are serious as witnessed by the extreme paucity of such information."" Comparative investigations of type b) were also remarkably few and they all employed ring-shaped dies through which round bars were either drawn or pushed.2-4 Only in one case were the applied and the die splitting forces measured simultaneously.2 In order to simplify the problem, deformation under approximately biaxial conditions was adopted in the present work;. This enables both the drawing (rolling, extruding) efforts and the separating forces to be measured with reasonable ease by conventional methods. Since drawing, extrusion, and rolling can be carried out under virtually identical conditions only in a roller die. an adjustable tool of this type was constructed. The circular die profile involved a difficulty with interpreting the drawing and extrusion data. This was obviated by arbitrarily defining the angle between a contact chord and the drawing plane as the -.equivalent" die semiangle. The simplification was considered permissible since the effect of die angle was not specifically investigated. An additional conlplication was caused by the square cross section of the processed bars. This shape was selected as a compromise between the desire to have as massive as possible specimens and the capacity of the roller die. The metal was only partially restrained from spreading laterally. the flow conditions being therefore intermediate between plane stress and plane strain. On the Huber-Mises yield criterion the constrained and uni-axial yield strengths differ by up to 16 pct but the actual error due to the ignorance of the constraint factor was presumably much smaller than the maximum. In spite of these reservations it was felt that the method employed and results obtained have some merit. With certain further refinements to be indicated later, this technique can yield data perhaps more useful for checking metal forming theories than other, mostly indirect, methods. EXPERIMENTAL Materials—The metals used together with their principal mechanical properties are listed in Table I.

Jan 1, 1961

By J. Burns Read

IT IS the purpose of this paper to summarize, as far as possible, the metallurgical information and experience gained by the Ordnance Department, during the War, in the manufacture of artillery cartridge cases, to describe the tests to which artillery cartridge cases were put, and to summarize the knowledge and experience gained in this testing. The authors wish to acknowledge the aid given by manufacturers, army officers, and civilian employees of the Ordnance Department in obtaining these data. Artillery cartridge cases are cold drawn from circular disks punched from strips of rolled brass. The manufacture involves from 25 to 30 main operations, which are done almost entirely on a punch press. Descriptions of the operations have appeared in various periodicals and, therefore, will not be given here. After each cupping, or drawing, operation, except the last, the cases are annealed at from 540° to 650° C. (1000° to 1200°F.), to remove all the hardening stresses set up in the metal and to allow complete recrystallization. After each annealing, the cases are pickled in niter cake or sulfuric-acid solution and then washed in water to remove all traces of acid. In some instances, the cases are then immersed in a cyanide-salt solution, and afterwards rinsed in water, to remove the thin layer of copper that forms on the surface of the cases during the acid pickle. The last cold-drawing operation is followed, by the heading operation which, by flattening the head of the case on the outside, causes the metal to flow on the inside to approximately the proper finished dimensions. The mouth, or open end, is then annealed at 430° to 480° C. (800° to 900° F.) by immersion in a salt bath or by gas flames. After being washed, the cases are tapered, when they are ready for machining, inspection, and testing.

Jan 4, 1922

By H. O. Hofman

At the Lake Superior meeting, September, 1904, Messrs. A. Gibb and R. C. Philp presented a paper entitled " The Constitution of Mattes Produced in Copper-Smelting,"' in which they concluded that ferrous and cuprous sulphides formed the chemical compound, 5 Cu2S, FeS. They arrived at this inference from the observed fact that a matte containing Cu,S, 90.4, and FcS, 9.6 per cent. (or, in round figures, Cu2S, 90, and FeS, 10 per cent.), did not contain any metallic copper, while one with more than 10 per cent. of FeS readily dissolved copper, and with less than this amount retained copper in mechanical suspension. Although they determined the melting-points of five mattes containing from 32.6 to 80.1 per cent. of copper, they did not draw a freezing-point curve, as the necessary apparatus was not available. A microscopical examination of 11 polished samples gave them a grayish-black field of very uniform appearance, except that five of the specimens showed the presence of metallic copper. The object of the present investigation was to supplement the above paper by drawing the freezing-point curve of the ferrous sulphide-cuprous sulphide series, and to see how the constitution could be further revealed by microscopical work. The results obtained lead to conclusions very different from those of Gibb and Philp. While their paper bears the date 1904, it was published only in 1906.2 In the meantime, Bolles3 had presented his paper, " The Concentration of Gold and Silver in Iron-Bottoms." The raw material which formed the basis of the research was a matte containing Fe, 61.68, and Cu, 11.20

Jan 1, 1908

By H. P. Greenwald

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

Jan 1, 1943

By Reginald E. Hore

I. INTRODUCTION. SINCE the discovery of silver at Cobalt, Ontario, in 1903 more than 100,000,000 oz. of silver have been produced b: the mines in the Nipissing district, and there is reason to believe that at least as much more will be produced in the next five years. The estimated value of the aggregate output o ore to the end of 1910 is $48,327,280. The ore yielded 93,977,833, oz. of silver and was mined at a net profit of about $26,000,000. For 1910 the production was 30,558,825 oz. valued at $15,436,894, and yielding a profit of about $9,000',000 The details of the production of the Cobalt district for the years 1904 to 1909, inclusive, are given in Table I. TABLE I.-Silver-Production of the Cobalt District, 1904 to 1909 SMELTING-ORE. Production. Value. Silver-Content. Value Per Ton Ounces. Oz. Per Ton. 1904 206,875 $111,887 1,309 $708 1905.:.... 2,451,356 1,360,503 1,143 634 1906 5,401,766 3,667,551 1,013 687 1907 10,023,311 6,155,391 677 416 1908 18,022,480 8,468,293 736 363 1909 22,436,355 10,809,872 809 389 CONCENTRATES. 1908 1,415,395 $665,085 1,240 585 1909 3,461,470 1,651,704 1,174 559 The shipments from Cobalt are in the form of smelting-ore, concentrates from milling-ore, and bullion. The smelting-or( is largely high grade, averaging about 3,000 oz. per ton- A

May 1, 1911

By Henry G. Granger

NOTHING in this paper is to be understood as even suggesting a moment's suspension of the splendid work now going forward on the Isthmus of Panama, except so far as it is related to the proposed locks. All the work already done, and all material purchased or ordered, would be available for the plan herein proposed. The situation and the problem concerned may be summarized as. follows : The scheme of a lock-canal through the Isthmus of Panama was adopted, as is well known, on two principal grounds-namely, the greater expense of a sea-level canal, and the longer time required for its construction. Of these, the latter is believed to have been the more influential. But further developments have diminished the weight of both, so that a reconsideration of the question is warranted. It is the purpose of this paper to advocate such a reconsideration-emphasizing the importance of certain objections to the lock-canal not mentioned or not duly appreciated in the report of those members of the International Board of Consulting Engineers who favored this form; showing the nature and bearing of the new facts developed; and, finally, proposing a combination of well-known methods and apparatus, which would, in my judgment, effect the construction of a sea-level canal in less time, and perhaps at no greater cost, than will be required for the remaining work on the lock-canal. I. OBJECTIONS TO A LOCK-CANAL. 1. Earthquakes. Two centuries ago Panama is said to have been destroyed by an earthquake. In 1882 a rather violent earthquake was felt at the southern end of the Isthmus. In 1898 I felt a slight shock near the present border-line of Colombia. In 1900 I felt three shocks at Quibdo, the head of navigation of the

Jan 1, 1909

By H. M. Howe

Page 1. Introduction............................514 2. Definitions.............................517 3. Brevity of the Heating........................517 I. THE HARDENING OF THE BORE..............517 4. The Hardening of the Bore.....................517 5. The Thickness of the Hardened Layer.................517 6. Martensitization..........................518 7. The Hardening Repetitive ......................519 8. The Temperature Cycle.......................519 9. The Hardened Layer is the Merged Layer............... 521 10. The Progressiveness of Merging....................521 11. The Progressive Thickening of the Hardened Layer from Round to Round. 523 12. Merging and Hardening are Cumulative................523 13. Three Additional Causes of the Progressive Thickening of the Hardened Layer 525 14. Progressive Roughening of the Bore..................525 15. Avoidance of an Endothermic Transformation.............525 16. Asymptotic Retardation of the Thickening of the Hardened Layer.....527 17. The Troostitic Layer........................ 529 18. The Usual Lack of Martensitic Markings................529 19. The Thickness of the Hardened Layer Should Increase with the Quantity of Heat Taken up by the Walls of the Bore.................530 20. The Decrease of the Thickness of the Hardened Layer from Breech to Muzsle 531 21. Phstic Deformation as a Contributory aCause of Hardening........531 22. In What Way May Plastic Deformation Hasten Hardening?....... 535 23. Possible Need of Coarsening.....................535 24. Carburization as a Cause of Hardening..........:.....536 25. Does Hardening Increase Erosion?..................-538 11. THE CRACKING OF THE BORE ...............539 26. Appearance of the Bore and Cracks in Elevation............539 27. The Cracks in Elevation in the Rear Ring...............539 28. The Cracks in Elevation in the Forward Ring.............540 29. The Copper Network in the Grooves.................540 30. The Cracking of the Lands......................541

Jan 1, 1918

Aamot, Olav Crone, Chem. Engr., Elektrokemisk Raadhusgt..23, Oslo. Norway. '29 Abadilla, Quirico A., Dir., Bureau of Mines Manila, P. I. '3S Abbott, Clarence E., V.P., Charge of Raw Materials, Tennessee Coal, Iron & R.R. Co., 1242 Brown-Marx Bldg., Birmingham, Ala. '04 Abel, Raymond L.. Prof., Dept. of Pet. Refin., Univ. of Pittsburgh Pittsburgh, Pa. '2S Abel, Walter D., Div. of Corporations Los Angeles, Calif. '32 Abele, Louis T., U. S. Corps of Engrs 7211 Glen Oak Ave., Baltimore. Md. '31 Abel], Leo M., Research Met., Mount Morgan Ltd Mount Morgan, Queens.. Australia. '31 Abenius, Hakan V c/o Falu Gruva, Falun, Sweden. '37 Abernathy, G. E., Geol., Kansas State Geol. Survey Pittsburg, Kan. 3S Aborn. Robert H., Asst. Met., Research Lab., U. S. Steel Corp., Lincoln Highway, Kearny, N. J. '19 Abrams, Charles Jackson 1624 17th St., Denver, Colo. '3 t. Abstein. Henry T., Engr. & Mgr., Profile-Tamarack Mines CoYellow Pine, Idaho. '27 Acker, E. O'C., Met L28 East Washington Lane, Germantown, Philadelphia, Pa. '86 Ackerman, D. E., Met., Assoc. Prof. of Met., Purdue Univ Lafayette, Ind. '35 Ackerman, E. Dumont, Sub-Surface Geol., Temblador Camp, Standard Oil Co. of Venezuela, Caripito, Venezuela. '3S Ackerman, George F.,. Div. Foreman. The Fresnillo Co Fresnillo, Zac., Mexico. '36 Adami, A. F., V.P. & Prof. of Min. Engrg., Montana School of Mines Butte, Mont. '19 Adami, Charles J., Min. Engr 99 S. Downing St., Denver. Colo. '12 Adams, Army, Cons. Engr 714 W. Main St., Grass Valley, Calif. .'37 Adams, Clyde B.. Geol.. Socony-Vacuum Oil Co., Inc 26 Broadway, New York, N. Y. '39 Adams, Ernest C., 6th Engrs Fort MacIntosh, Laredo, Tex. '35 Adams, F. J., Gen'l Agent, Gulf Production & Pipe Line Cos Fort Worth, 'lox. '29 Adams, F. S., Supt., Power Dept., Anaconda Copper Min. CoAnaconda, Mont. '37 ADAMS. FRANK DAWSON, Hon. Mbr., 1913; Logan Prof. of Geology and Dean, Faculty of Applied Science. McGill Univ., Montreal, Que., Canada. '13 Adams, Gale L., Supervisor, Process & Dev. Lab., General Pet. Corp. of California, Higgins Bldg., Los Angeles, Calif. '18

Jan 1, 1939

By A. J. Opinsky

THE purpose of this note is to indicate the locations and sizes of various interstitial holes in the orthorhombic uranium lattice based on a hard-sphere model. First, plane configurations of three and four atoms will be examined, and then the true interstices surrounded by four atoms in space and by five atoms in space will be obtained. The data and notation contained in a report by Tucker' will be used. Plane Configurations Fig. 1 presents the orthorhombic uranium lattice made of spheres touching at the closest interatomic distance. The three light-colored spheres in the ab plane are illustrative of the first type of configuration to be examined. If one edge of the unit cell is taken as the origin, the three atoms can be represented by the vectors [Oi + Oj + Ok], [ai + Oj + Ok] and [(a/2)i + (b/2)j + Ok] where i, j, and k are respectively parallel to a, b, and c. In the future, this notation will be shortened to [000], [a00] and [a/2 b/2 0], respectively. A vector R = [r s t] de-scribes the position of the hole surrounded by the atoms. Since the center of the hole must be equidistant from the three atoms R2 = r2 + s2 + t2 = (r-a)2 + s2 + t2 = (r-a/2)2 + (s-b/2)2 + t2. R = [a/2 (b/4) - (a2/4b) 0] is the solution of these

Jan 1, 1955

By Richard L. Ashbrook, John F. Wallace

Several high-temperature eutectics of cobalt and nickel alloys were modified by small additions of selected elements. Thes-e alloys were compared to unmodified melts for microstructural variations. A few modified compositions were selected on the basis of structure and their tensile and stress-rupture behavior determined. The results of stress-rupture tests in air at 1800 F and room-temperature tensile tests of four high-temperature eutectics showed modification capable of producing substantial improvements in properties. The microstructures were altered and mechanical properties improved by: a.) dispersing a subordinate phase more uniformly throughout the matrix; b) replacing large continuous -network or platelike constituents with small equiaxed discontinuous phases; and c) by forming new, finely divided phases. tHE term "modification" is most commonly used to describe the refinement in microstructure of the Al-Si eutectic that occurs as a result of rapid cooling from the melt or on slow cooling after treatment with small amounts of sodium.1 "Modification" has also been used to describe the change from flake to spheroidal graphite in the austenite-graphite eutectic of cast iron.2 This change of graphite shape is accomplished by small additions of cerium or magnesium.3 Other systems have also been shown to be capable of modification, for example: Pb-Sn by copper;4 Al-Cu by sodium;5 Al-Mn by sodium;5 and Pb-Sb by aluminum.5 Although modification of Al-Si alloys and cast irons is usually accompanied by improved mechanical properties, a general definition of modification has been suggested to include the effect of small quantities of impurity elements on the microstructures of all eutectic alloys, regardless of the effect on the mechanical properties.6 In this paper, the term "modification" is employed in a broad sense to include the formation of third phases or even the supplanting of one of the binary eutectic phases by a third phase. The mechanism of modification, as for any solidification phenomenon, must be considered primarily in terms of nucleation and growth. Although both nuclea-tion and growth mechanisms are required to explain all the phenomena observed in connection with the solidification of modified eutectics, various investigators have usually favored one or the other.7"16 It has been shown that modification of a binary eutectic can be effected by addition of a solute element that has greatly different distribution coefficients or k values in the two phases of the eutectic. Under these conditions, differences in the temperatures at the solid-liquid interfaces of the two phases retard the growth of one phase with respect to the other.4 It has also been shown that increased undercooling favors a transition from a rodlike eutectic to a globular eutectic.17 A mechanism proposed for the transition from lamellar to rodlike eutectics depends on the concept of constitutional super cooling.18 The modification of eutectic alloys may be of interest for high-temperature service as well as at room temperature. Although "high-temperature eutectic alloys" may appear to be a contradiction in terms, many eutectic systems, including those studied in this work, have melting points in excess of 2400°F. One of the mechanisms by which high-temperature alloys are strengthened is dispersion of a relatively brittle phase such as an oxide, carbide, or an inter-metallic compound throughout a ductile matrix. For a given volume fraction of dispersed phase, strength is increased by decreasing the size and spacing of the dispersed particles.19'20 Furthermore, room-temperature ductility may also be increased by changing the shape of a brittle dispersed phase from platelike to equiaxed or spheroidal.8 Overaging and redissolving of the secondary phase limit the maximum temperature to which precipitation-hardened alloys can be used. However, in a binary eutectic system, both phases coexist up to the melting point. Although all eutectic structures are not completely stable,21 a dispersion-hardened cast high-temperature alloy might result if a fine distribution of one of the eutectic phases could be obtained during solidification. An additional reason for interest in eutectic alloys is their excellent castability.22 Since eutectic alloys, like pure metals, freeze at a single temperature rather than over a range of temperatures, their castability is superior to solid-solution alloys with long liquidus to solidus ranges. The purpose of this research was to study the effects of small solute additions on the microstructure and mechanical properties of a number of high-melting-point eutectic compositions.

Jan 1, 1967

By W. L. Remick

The hydrotator coal-cleaning process was developed as an economic necessity to meet the ever-increasing demand for an inexpensive method of cleaning coal down to the sizes ordinarily referred to as "dust." As the most urgent demand seemed to be in the anthracite field, all experimental work has been conducted in that territory during the past two years, with the exception of a few months during the strike of 1925-26, when some experiments were performed in the Alabama bituminous fields. The first commercial plant was constructed at the Middle Creek Colliery of the Philadelphia & Reading Coal & Iron Co.,. Pottsville, Pa. This plant is now operating. Application The field of application of the process is: 1. Cleaning anthracite fines, ordinarily described as "slush" or "silt." Slush contains all sizes from 3/32 in. down to and including I(dust." (Anthracite passing a 3/32-in. mesh is also referred to as No. 2 Barley and No. 4 Buckwheat.) 2. Cleaning sizes too fine for recovery by other methods. 3. Removal of coal from sand circulated in the Chance sand-flotation process. 4. Cleaning of bituminous sizes from % in. down to "dust." 5. As equipment for the performance of the froth flotation process. 6. Other separating, extraction and washing processes which may be considered outside the realm of coal cleaning. Principle of Operation Fig. 1 shows the method of classification practiced under the Hydrotator patent.' In coal cleaning the machines are operated as "hindered settling" classifiers, the flow of solids and liquids being so controlled that the units may be combined in series.

Jan 1, 1927

By AIME AIME

T HE Institute of Metals Division and the Iron and Steel Division will meet jointly at the Stevens Hotel, Chicago, during the week of the American Metals Congress, Sept. 22-26. The Iron and Steel Di- vision of the American Society of Mechanical Engineers, the American Society for Steel Treating and the American Welding Society meet at the same time. but the sessions have been arranged to conflict as little as possible. A rich program of papers and plant visits has been arranged for the members and guests of the two Institute Divisions. The annual dinner and a pro- gram of entertainment are being arranged by the Woman's Auxiliary of the Chicago Section. Members are urged to register immediately up011 arrival and to make dinner and plant visit reservations at the same time.

Jan 1, 1930

Jan 1, 1948

Jan 1, 1948

P. W. BRIDGMAN.-Owing to a misunderstanding, I did not see Dr. McAdam's and Dr. MacGregor's remarks on my paper on Flow and Fracture (Metals Technology, December 1944, Pp. 32-38), until after their publication. Both Dr. McAdam and Dr. MacGregor speak of my analysis for the stress distribution at the neck of a tension specimen as containing several assumptions; in particular, that the strain is uniform across the section of the neck, that there is no hoop tension at the periphery, and that the plasticity conditions of von Mises hold. As far as the mathematics goes, the situation is no different in this problem of plastic flow than in a conventional problem of elasticity. That solution is unique which satisfies the boundary conditions on the stresses, the stress equations of equilibrium, and in addition the constitutive equations connecting stress and strain in the elastic case, or a corresponding set of equations, of which the von Mises relations are a special form, in the plastic case. In the particular case of the necked tension specimen I have found that there is a solution satisfying the boundary conditions, the stress equations of equilibrium, and the von Mises plasticity conditions in which the strain is uniform across the section, and there is no hoop tension at the periphery. This is therefore the solution, and the uniformity of strain and vanishing of hoop tension at the periphery are to be described as discoveries, over which the operator has no control, rather than as assumptions. The only part of the solution that can properly be described as an assumption is the von Mises plasticity condition. With regard to this it is to be noted that the condition is needed only in a much weakened form, for the analysis uses the condition only at the neck, where the strain is approximately constant. Thus, in the extreme case referred to in a footnote of my paper (p. 37, Met. Tech. Dec. 1944) the actually measured strain across the section varies from 2.4 to 2.6. Obviously it is a much weaker assumption to postulate that the von Mises condition holds in the strain range 2.4 to 2.6 than to assume it to hold for the entire range of strain from o up to 2.6, which would be necessary if the solution applied to the entire tension specimen rather than to the immediate region of the neck only. Furthermore, it is to be commented that under the special conditions of this problem the von Mises condition becomes identical with the maximum shearing-stress criterion of plastic flow; this amounts also to a weakening of the restrictions imposed by the von Mises condition. Dr. MacGregor refers to actual experiments of his own in which the strain was found not to be uniform across the neck. It is to be emphasized, however, that these were experiments on bars of rectangular section, and that the nonuniformity established was a nonuniformity around the perimeter, not a nonuniformity from the surface toward the axis. My method of solution applies only to a circular cross section. It can be said that the solution that satisfies the boundary conditions, etc., would definitely not be expected to demand a uniform strain for noncircular sections. In discussing my results, Dr. McAdam uses a definition of "flow stress" different from mine, so that the immediate applica-

Jan 1, 1945