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By J. P. Doan, G. Ansel

The important literature concerning zirconium in magnesium-base alloys is predominantly contained in patent references. Sauerwald, Eisenreich, and Holubl-4 discovered the profound grain-refining influence of small amounts of zirconium on cast magnesium and the attendant increases in strength and ductility. They extended their work to reveal that limited amounts of certain other elements, including zinc, could be added for further improvement in strength and hardness. British Patent 5111375 relates to the parent discoveries of Sauerwald, Eisenreich, and Holub. All of these references deal primarily with casting characteristics and properties in the cast state. Minor mention is made of desirable tensile strength, ductility, and toughness of wrought Mg-Zr alloys* modified by one or more additional elements. No extensive reference in the literature5. has been found to the particular characteristics of wrought blg-Zn-Zr alloys, with which the present paper is concerned. The work to be discussed represents essentially an extrusion study of the blg-Zn-Zr alloys and indicates that this system is highly interesting in the wrought state both academically and commercially. Accordingly, an important aim of this paper is to describe the hot-workability, tension and compression properties, metallography, and toughness of these alloys. Compositional variations are limited to the ranges 0 to 7 per cent Zn and 0 to I per cent Zr. Experimental Procedure Alloying and Casting Alloying ingredients were cell magnesium, commercial zinc (intermediate grade), and a chloride salt containing approximately 50 per cent ZrCl² and 50 per cent alkali chlorides. This salt is produced by Titanium Alloy Manufacturing Company. Melting, alloying, and pouring procedure essentially followed the crucible process as described by Nelson.6 The magnesium was melted using Dow No. 310 flux, and the temperature raised to 1350° to 1400°F for the alloying operations. After alloying of the zinc, the zirconium containing salt was added in small portions with vigorous stirring. This is an adaptation of the method described in British Patent 533264.7 The alloying efficiency of zirconium was approximately 30 per cent. During the alloying of zirconium, fluorspar was added in amount required as a flux-inspissating agent. Next the melt was refined with Dow No. 310 flux and held quietly for 15 min. Finally billets were cast in a book-type permanent mold

Jan 1, 1947

By J. W. Hickman, E. A. Gulbransen

One of the important factors that determine the resistance of a metal or alloy to further chemical reaction is the structure of the superficial oxide film. A thorough understanding of the physical and chemical structure as well as the stability of the oxide film formed on the surface as a function of time and temperature of the chemical reaction might furnish clues as to the nature of the reaction process and the protective nature of the film. A comprehensive program has been undertaken to study these phenomena. This paper summarizes the structure of the oxide films formed on the metals iron, cobalt, nickel, chromium and copper at temperatures up to 700°C. Before the introduction of the electron diffraction technique, it was necessary to use either direct chemical analyses or X-rav diffraction analyses to determine the nature of the oxide film formed on the metal or alloy. Chemical analyses yields information on the percentages of the several atomic species present in the film while X-ray diffraction analyses yield information on the atomic geometry. In special cases the information obtained may be identical, but in general both viewpoints are necessary. Much of the early work was carried out on the oxidation of bulk samples where thick films were obtained. The products were identified after cooling to room temperature by X-ray diffraction and chemical analyses. Although much useful information has been obtained in this manner. little could be learned about the character of the protective oxides during the period when the films were actually protective. Evidence concerning the chemical structure of thin oxide films has been made possible by the development of the electron diffraction reflection technique. In this method the most fruitful investigations have been made by carrying out the reaction in situ at the temperature at which the film is actually protective. Literature The oxidation of iron has been extensively investigated by X-ray and electron diffraction. Jackson and Quarrelll found that oxide films formed and examined at the same temperature differed considerably from those allowed to cool to room temperature. The results showed that below 400°C the oxide that was stable in intimate contact with iron was Fe³O4; between 515° and 900°C. the stable film was FeO. Above the upper change point of iron the oxide was found to be Fe³O4. From 400' to 515°C., FeO, Fe³O4 or a mixture of the two oxides was found. Recrystallization of the air-formed film below 400' and above 900°C. led to the formation of Fe3O4. In the range where thicker films consisted of FeO, the air-formed film was converted to a new hexagonal oxide not previously described.

Jan 1, 1947

By J. W. Hickman, E. A. Gulbransen

In a previous paper' the authors have investigated the structure of the oxide films formed on most of the metals that make up the alloys of this study. The metals were studied in order to provide basic information on the structures, both physical and chemical, of the oxide films and to determine how these structures are effected by the temperature, time of oxidation, and surface preparation. It was felt that an understanding of the physical and chemical structure as well as the stability of the oxide film might furnish clues as to the nature of the reaction process and the protective quality of the film. The oxidation of the metals was studied over the temperature range 300' to 7o0°C. except for copper, wherc the range selected was 100' to 500°C. The results of these studies were presented in graphical form as existence diagrams of the oxides on a time-temperature scale. For some of the metals the existence diagrams were simple and showed few chemical transitions, but there were numerous cases where the physical state of the oxide surface was a function of time and temperature. In general the physical state of the oxide surface changed with increasing temperature so as to increase the sharpness of the diffraction patterns and to cause orientation effects to be more pronounced. Deviatiois in lattice Darameters from X-ray values were noted. In general these deviations were of positive nature and may be due to solid solution of the metal in the oxide lattice. This effect might be expected in thin oxide films. In a study of the oxidation of alloys containing two or more metals, there may arise the complicating factor of identification of the oxides formed. A thorough understanding of the oxides formed on the pure metals, therefore, was, essential before investigation of the oxidation of alloys. In this paper it is our purpose to present a study of the following problems: 1. The existence diagrams of various alloys. 2. The effect of the structure of the alloying metal on the existence diagram of iron. 3. The effect of the percentage of chromium on the oxides formed on Fe-Cr alloys. 4. The relationships, if any, between the oxides formed and the protective quality of the oxides. The following alloys are included in this study: alloys of iron with body-centered cubic, face-centered cubic and other metals, 13 Cr-Fe, 18-8 stainless steel, K4²B, Nichrome V, Hipernik, Inconel, Stellite "²I," Refractaloy, Kovar, mild steel, a series of Cr-Fe alloys and a series of Co-Fe alloys. Since many of the commercial alloys in this list contain more than two metals, various complicating factors in the identification of the oxides formed may arise.

Jan 1, 1947

By J. W. Hickman, E. A Gulbransen

The physical and chemical structure of the oxide films formed on metals and alloys is of interest in our understanding of their protective properties. According to Pilling and Bedworth,¹ if the specific volume of the oxide is equal to or greater than that of the metal, a compact or continuous structure results; if the volume of the oxide is less, a cellular or porous structure forms. With the cellular type of coating the surface layer of oxide offers no impedance to oxidation; at a given temperature the rate of oxidation is quite constant. On the other hand, the compact type of coating acts as an effective barrier to oxygen and the rate of oxidation will follow a parabolic law. The recent work of Gulbransen2 and of Leontis and Rhines3 on the oxidation of magnesium indicates that it is not necessary for the volume of the oxide to be greater than that of the metal in order that the oxidation may follow a parabolic rate law. One exception to the rule of Pilling and Bedworth¹ is noted by Scheil;4 namely, tungsten. At 500° and 700°C long-time oxidations indicate a linear rate law with time. However, Dunn's6 0xidation measurements from 700°to 1000°C indicate that a parabolic rate law is followed. The oxide is mainly yellow WO a with a thin layer of the blue oxide. Preliminary results on the oxidation of tungsten6 in the temperature range 400° to 500°C indicate that the oxidation does proceed according to a parabolic rate law. Irrespective of the actual rate law that tungsten may obey, it is of interest to compare the results obtained on the oxidation of tungsten in the thin film region with those found when the metal is scaling. A time-temperature study of the oxides formed on both molybdenum and tungsten may indicate whether there exist any peculiarities in the oxide structures of the thin film region compared with those of the scaling region of oxidation. In a recent paper the authors7 presented an investigation of the structures of the oxide films formed on the metals iron, cobalt, nickel, chromium and copper. The results of these studies are presented in graphical form as existence diagrams of the oxides on a time-temperature scale. The existence diagrams of the oxides occurring on some of the metals are simple and show few chemical transitions, but there are many cases in which the physical state of the oxide surface changes as a function of time and temperature, as evidenced by the appearance or disappearance of orientation effects and sharpness of patterns. In general an increase in temperature results in an increase in

Jan 1, 1947

By Otto H. Henry, Edward L. Badwick

Up to the present time, according to Hansenl and Haughton,² the constitution of the bismuth-indium system has not yet been published. The generally accepted value for the melting point of indium, as listed in most scientific journals and textbooks, is 155°C. Recently, however, H. M. Davis3 has determined a new melting point for indium of 157.3²C O.l°C. Since bismuth has been used in preponderance as an alloying element in the majority of low-melting alloys, and indium has been used with considerable success in lowering the melting points of low-melting alloys, 4,6 an interest has been developed in the application of these two metals, making a complete knowledge of the constitution of its alloys desirable. In this investigation, the melting point of indium reported by H. M. Davis has been found to be substantially correct. A value of 157. ²°C ± O.5°C was determined. The two eutectic compositions have been placed at 34 and 50 pct bismuth with their respective eutectic temperatures as 72.4°C ± 0.5°C and 90°C ± 0.5°C. The bismuth-indium phase diagram has been determined by thermal and microscopic analysis and is shown in Fig I. Thermal Analysis Granulated bismuth and indium shot, having a guaranteed purity of 99.99 and 99.95 pct, respectively, were melted in a carbon crucible by means of a laboratory heater. To minimize oxidation of the alloys, a heavy mineral oil (Nujol) having a high- flash point was used. A platinum-platinum rhodium thermocouple of fine wire encased in a thin-walled Pyrex glass tube, about 1/8 in. in diameter, was connected to a type K potentiometer for temperature measurements. The thermocouple was calibrated against the melting points of tin, bismuth, and the silver-copper eutectic and the boiling point of water. Since the temperature readings could be reproduced to 0.²°Cl and the accuracy of the temperature standards in this range is slightly better than 0.5°C, it scems reasonable to assume that the temperature readings are reliable to approximately 0.5°C. The cooling rate could be controlled by varying the amount of insulation surrounding the crucible. Three or four layers of asbestos paper, 1/16 in. thick, sufficed to give a cooling rate of from I° to ²°C per minute. Undercooling was slightly noticeable. This condition was minimized by vigorous stirring, since the advantage of using slower rates was too small to justify the greater expenditure

Jan 1, 1947

By B. D. Cullity

Gold and beryllium form an intermediate phase composed of the two metals in equal atomic proportions and having the formula AuBe. According to Winkler,' this phase probably exists in two modifications: beta, stable below about 600°C, and alpha, stable between 600°C and the melting point, about 740°C. Only the low-temperature beta form will be considered in this paper. Experimental Procedure The gold used had a fineness of 999.75 to 999.85, balance mainly silver, and the beryllium purity was better than 99.8 pct. AuBe was prepared by melting the constituents in a beryllia crucible in an evacuated induction furnace. After melting and thorough mixing, the alloy was allowed to solidify in the crucible. No difficulty was encountered in obtaining a homogeneous ingot. Both chemical analysis and microscopic examination of the ingot showed that the alloy was essentially one phase, containing 50 at. pct gold. The alloy was quite brittle and powder samples could easily be prepared by grinding in an agate mortar. The X-ray diffraction patterns were made with CuK-alpha radiation in a Debye-Scherrer powder camera 57.3 mm in diameter. The film was placed unsym-metrically in the camera in order to afford a basis for film-shrinkage corrections. A sample homogenized at 500°C gave the same diffraction pattern as a sample taken from the as-melted ingot. General Results The diffraction pattern of AuBe was readily indexed on the basis of a simple cubic lattice with ao = 4.659 + 0.001kX. If the unit cell is assumed to contain four AuBe "molecules," the calculated X-ray density is 13.46 grams per cc as compared with the measured density of 13.55 gm per cc. The only missing reflections in the diffraction pattern are (100) and (220) (see Table I). Since these missing reflections are not those characteristic of body or face centering, the lattice of AuBe must be simple cubic. To locate the positions of the atoms within the unit cell, two possibilities had to be considered: I. The structure was disordered and there were eight positions to be filled by an LCaverage" gold-beryllium atom. That the structure was disordered seemed unlikely since the lattice parameter did not vary with composition in alloys containing sornewhat more and somewhat less than so at' pet gold, indicating a fixed composition for AuBe.

Jan 1, 1947

By J. R. Long, R. S. Dean, D. C. Root, E. T. Hayes

The U. S. Bureau of Mines has recently reported on the development of a process for preparing pure ductile titanium in substantial quantities1 and on the physical properties that may be attained in the metal, when consolidated by powder metallurgy methods and fabricated by certain hot and cold-working procedures.2 The high physical properties (Table I), combined with excellent corrosion resistance and light weight, will lead no doubt to appropriatc applications of the metal. In any application, methods of joining will be of considerable importance. The relatively high activity of the metal toward the common gases raises the question of weldability and conditions that might be required for successful welding. Since hydrogen, oxygen, and nitrogen embrittle the metal, it should be protected from these gases at elevated temperatures. This was demonstrated by a few preliminary trials of arc, gas, and resistance welding. In these trials only the resistance method proved to be immediately- applicable. While atomic: hydrogen welding of titanium may be successful in some instances, a considerable amount of development work will be required to prove its worth. In addition, it would be suited only to small assemblies that could be heated subsequently in a high vacuum to remove embrittling hydrogen. Heli-are methods likewise would be limited to small assemblies, which could be completely protected by a helium atmosphere. It was quite apparent that titanium required more protection than was afforded by the normal flow of helium gas used for welding magnesium and aluminum. The hot metal is attacked by oxygen and nitrogen, and the rapid diffusion of the oxide into the metal prevents the formation of a protective coating and requires the helium atmosphere to be maintained until the weld has cooled nearly to room temperature. The preliminary work indicated that titanium could be successfully spot-welded without deterioration of the metal and that the microstructures of the welds were normal, exhibiting good bonding, and no oxidation. The high resistivity of titanium (53 microhms per cu. cm.) suggested that it would behave somewhat like stainless steel and allow considerable latitude in the several welding variables. The results reported here are intended to give a general picture of the effects of varying welding current, welding time, and tip pressure on single spot welds made on several different thicknesses of titanium sheet. The work was undertaken to demonstrate the feasibility of welding titanium rather than as an exhaustive study of spot welding. There are, therefore, a number of factors that will require further investigation to establish the specific controls required for actual applications.

Jan 1, 1947

By John Wulff, Steinberg Morris, Robert Kamm

In powder metallurgy it has often been observed that shrinkage may occur in one direction and growth in another during sintering. Even in long-time sintering experiments the rate of shrinkage may be different in different parts of the compact. In the fabrication of some parts requiring a constant permeability it is even questionable in some cases whether pressing from one direction should be attempted. These observations require for their interpretation a more detailed study of green or pressed density than has heretofore been available. Usually average density measurements of the whole compact are made and in some cases carefully cut sections are measured. A different approach to the problem was first mentioned by Rakowskil and also used by Balshin.2 Balshin's diagram is reproduced in Fig I and schematically shows the result of pressing three layers of metal powder with fine intervening layers of graphite. The retarding effect of the die walls and a qualitative example of the density distribution is evident. More quantitative information about the distribution of density within a cold-pressed powder compact would be useful in showing the variation in density in as as influenced by the type of poKder, shape of die, lubricatioll during the process, and other variables. Furthermore, information about the cracking of cold-pressed compacts may be obtained from an analysis of the stress distribution within a, powder compact, and some information about the stress distribution can be obtained in turn from the derlsity and strain distributions. A more detailed report on some of the present experiments appears in reference 3. Present Investigation In order to ascertain the density gradients in cold-pressed metal powders, a deformable lead grid within the powder was employed. After pressing in cylindrical di" the ejected compact was radiographed, giving a pattern of the deformed grid. From the radiograph density and deformation from point to point is readily measured. From the radiograph strain distribution and stress trajectories were also determined. The latter also permits the determination of the coefficient of friction at the die wall. This technique indicates that the densest Part of a compact pressed from one side is at the top outer circumference and the least dense region at the bottom circumfercnce near the stationary plunger. For Some heights of compacts the density at the axis is such that the lower density is at the top rather than at the bottom. SO irregular a density distribution is due primarily to die-wall friction. As the ratio - diameter to height of compact is increased the die walls play a correspondingly smaller role. More uniform density

Jan 1, 1947

By Bernard Kopelman

The particle size of tungsten metal powder used to make tungsten wire for use in radio tubes and incandescent lamps must be closely controlled if the highly desirable feature of nonsagging is to be achieved. Our knowledge of factors affecting the particle size of tungsten powder has been limited by lack of any extensive literature on the subject. There are no publications in the English language discussing this problem in any but the most general terms. In this paper the published experimental information on this subject is reviewed. Based on the published data and some experimental data obtained by the author, a general theory of factors affecting the particle size of tungsten metal powder obtained by reduction of the oxides in hydrogen is offered. The various forms of the tungsten oxides and tungsten metal used in the experiments described were those prepared by commercial processes, so that the experimental results obtained on a laboratory scale would be more directly applicable to actual commercial reduction conditions. The effects of time of reduction, temperature. and concentration of water vapor in the hydrogen were observed by counting microscopically the particle distribution obtained. Such a method is very time-consuming, but the data obtained by this method are more reliable and more fundamental than those obtained by any of the several instruments available for measurement of particle size. Review of the Literature Until the year 1912, tungsten powder was prepared commercially by reducing tungstic oxide in the presence of carbon or one of its compounds (such as glycerin or ethylene glycol), usually by firing the mixture in a closed fire-clay crucible. The resultant powder contained about 95 per cent tungsten.' When reduction of tungsten oxides by H² was introduced Commercially,²,³ several investigators became concerned with the equilibria between tungsten metal and its several oxides in an atmosphere of hydrogen and water vapor.4-l3 While these many investigations were in fair agreement on the equilibria WO³ + H2 = WO2 + H2O and WO2 + 2H2 = W + 2H2O there arose considerable controversy as to the chemical composition of the oxide between WO³ and WO², because of very poor agreement on the equilibrium constant of this intermediate oxide reduction reaction. The controversy on this intermediate oxide has been in progress for more than 100 years. Thus Malguti,14 in 1835, decided it was WO2.56 In 1857, Riche15 proposed the formula W³O8. Usler,16 in 1865, confirmed the existence of WsO8 and further proposed W1O1l. In 1897, Desil7 agreed upon W²O8 but also found W5O14.

Jan 1, 1947

By Alexander Squire

A brief study of the effects of material and processing variations upon the tensile properties of steel formed from mixtures of iron and carbon was made in order to provide information regarding the properties obtainable in iron-carbon compacts as influenced by forming pressure, sintering temperature, and graphite particle size. Sintered steels formed from mixtures of iron and graphite have been studied by Stern,' who investigated the effect of various percentages of graphite on compacts formed from electrolytic iron that were repressed and heat-treated after sintering. A further study, by Stern and Greenberg,l is concerned with the heat-treatment of steels formed by the car-burization of iron compacts, and Margolies3 has reported work on the simultaneous sintering and carburization of iron-powder parts. Glauch4 investigated the effect of various types of graphite on the properties of iron-carbon powder alloys but did not determine the effect of different particle sizes of the same graphite alloyed with different types of powder. In the investigation reported in this paper, powders typical of those produced by electrolytic deposition and the decar-burization of shotted steel scrap were used. The powders were mixed by tumbling in a jar mill with graphite powder ground to an average particle diameter of 2, 4, 6, and 16 microns (as determined by microscopic measurement). The properties of the iron and graphite powders are presented in tabular form as Table I. In order to obtain the maximum information from a minimum number of test specimens, the study was divided into two sections with one set of specimens treated identically in each section as a basis for comparison. In the first section, iron powder produced by the shotting and subsequent decarburization of scrap steel was mixed with 2-micron graphite powder, pressed at 50,000, 100,-000, and 200,000 psi, and sintered in hydrogen at 1200°C for the periods of time ranging from 15 to 120 minutes. In the second section of the investigation, electrolytic iron powder was mixed with graphite of an average particle diameter of 2, 4, 6, and 16 microns, pressed at 100,000 psi, and sintered at temperatures ranging from 1000° to r200°C'. for periods of time of 30 to 180 minutes. By following this procedure an indication of the effect of the following variables upon the density and tensile properties of iron-carbon powder compacts was obtained: (I) forming pressure, (2) sintering time, (3) particle size of graphite powder, (4) sintering temperature, (4) type of iron powder.

Jan 1, 1947

By Alexander Squire

One of the principal factors that have contributed to the hesitancy of design engineers to use metal-powder parts is the difficulty experienced in the determination of the mechanical properties of compacted components. Because standard test methods cannot usually be applied in the inspection of such parts, and because adequate special test methods have not been developed, it has been considered desirable to investigate the methods that are applicable. These may then be included in specifications for metal-powder materials and components in order that the design engineer may be assured that the subject parts possess the desired mechanical properties for satisfactory performance. It is known that direct relationships exist between usually nonmeasurable properties as tensile strength and elongation and shear strength and the angle through which compacts may be plastically deformed before fracturing. These correlations are valuable in the inspection of specific parts, but it is necessary to set up standards before they may be satisfactorily employed. Apart from the use of correlations, the number and character of the inspection methods that are applicable to almost all powder parts is limited to three—chemical analysis, density, and hardness. The last of these may or may not be a pertinent characteristic, since the indentation hardness of many powdeied-metal materials is so low as to have little significance. It is, however, occasionally desirable to use hardness measurements as an indication of the uniformity of the structure of pieces of a given type. Chemical analysis reveals very little about the physical properties of metal-powder compacts, since the unpressed powder is usually of a composition almost identical with that of the finished pieces. Density determinations are simple to perform and have the advantage of being nondestructive in character. If the dimensions of a machine part are known (and usually they are), the average density may be determined by weighing a given number of pieces and dividing by the calculated volume of the parts. More accurate measurements may be made by the water-displacement method. It is recognized that mechanical properties of metal-powder materials are related to their density, but usually these relations are determined for only one type of powder, processed under a given set of conditions. Comparisons of the pioperties of compacts formed from different types of powders are made on the basis of compacting pressures instead of density, and for this reason the results obtained by using powders of different types appear widely variant.

Jan 1, 1947

By Richard Paul Seelig

The following review covers published information on pressing of metal powders at room temperature. Only those operations are considered which occur between the time the powder is filled into the cavity and the compact is ejected from the die. Thus, this review does not concern hot pressing, coining or sizing feed or flow problems, commercial presses nor designs. It was also necessary to disregard to a large extent the effect of pressing on subsequent operations and on properties after sintering. 'The pressing operation is considered independently in its function to compact loose metal powder into useful shapes which can subsequently be handled. There are some comments by the writer in connection with a few of the findings quoted in the literature in order to stimulate thought and discussion. The selection of references quoted in the text is in some cases arbitrary although an attempt was made to favor papers containing novel ideas, techniques or results which mag stimulate future research. In order to enable the reader to check further into the subjects mentioned, the original, rather extensive, bibliography is appended even though not all the references are touched on in the printed version of this review. The equipment used by various workers, for example a die design created by Bridgman,22 is very interesting. 'The die insert has a conical external surface. The vertical pressure exerted on the punch transmits itself to the die which in turn is pushed harder into its tapered retainer. Thus, the higher the pressure exerted on the punch, the higher also the pressure exerted inwards on the die inserts. Inasmuch as this pressure counteracts the internal pressure from the compact the two stresses balance each other so that it is possible to obtain tremendous pressures without breaking the die. The die collar was made from an oil hardening tool steel, heat treated to a tensile strength of some 300,000 psi. The die was closed at the bottom by a plug made from special tool steels. Bridgman found that there is no steel which will withstand a com-pressive stress of 700,000 psi without continuous slow flow or immediate fracture. Therefore, the only material suitable for use in the pressing punch was sintered carbide. In view of the ingenious design it was possible to use special tool steel as die material. Jones22 raises the question whether this method of pressing has practical application in powder metallurgy. Although these tremendous pressures cannot readily be utilized without many special precautions, the tapered die and retainer idea is believed to be useful even for lower pressures. Bridgman, himself," alls attention to the fact that the properties

Jan 1, 1947

By John H. Hollomon

In a recent paper,' a very early suggestion by Ludwik2 concerning the nature of the mechanical behavior of metals has becn reexamined and extended. In essence it was suggested that there exists, at least under certain conditions, a mechanical equation of state; that the stress required for flow depends upon the instantaneous values of the strain, strain rate, and temperature, and not upon their past values. It is proposed that under these circumstances thc stress does not depend upon past history of these variables, but is like the temperature of a gas that depends only upon the instantaneous values of the pressure and volume. This notion has not been applied to present-day studies of metals, though it is especially applicable to the study of creep. It is the purpose of this paper to analyze the significance and possible range of applicability of this idea and to determine how it influences the accepted ideas concerning creep. Stress-strain Relations It is wcll known that the stress-strain curves of metals are influenced by both train rate and temperature. For a fixed strain rate and temperature there is associated with each metal a stress-strain curve. If either the strain rate or temperature is changed a new stress-strain curve will be characteristic (Fig. I). A much more genera1 relation between the effects of these variables is possible, however. Consider the stress-strain curves of Fig. I determined at

Jan 1, 1947

By J. C. Fisher, J. H. Hollomon

The fundamental problem concerning the fracture of both crystalline and noncrystalline solids is the divergence between the actua1 and the theorcticallY computed fracture stresses; the stress required for fracture, computed from the forces between atoms, is many times that actually observed with commcrcinlly available materials. Computatiolls have been made,,2 indicating that the theoretical fracture stress should be from 100 to 1000 times that actually observed. There are other incidental problems that have arisen, perhaps the most importallt of which is the problem of size effect often observed in the measurement of the fracture stress of non-metallic solids, such as glass. Another effect conccrns the relation between deformation and the stress required for fracture, Experiments recently made with pearlitic steels indicate that the tensile fracture stress increases with increasing tensile deformation and decreases with increasing prior com-pressive deformation, This marked ani-sotropy of the effect of deformation on the fracture stress is in contrast with the essential isotropy of the flow stress. Early experiments on rock salt crystals by Joffe, et al.3 have illustrated the effect of tensile strain in increasing the tensile stress required for fracture. A consistent theory must be constructed that will explain not only the divergence, of the measured fracture stress from the theoretical value, the size effect, and the ergence of deformation; but will also explain and predict the effects of combined stress, of temperature, of strain rate, and of metallurgical structure. With respect to this last variable, it has now been relatively well established that the carbide particle is the clement of structure controlling the fracture of steels. In steels carbide particles vary in shape from plates to spheroids. It has been found that not only docs the magnitude Of the Fracture stress depend upon the size and shape of these particles. but also its dcpendencc upon strain is affected by changes in 'hap' an' size Or the particles. The precipitate resulting from the age hardening Of duralumin also modifies the fracture stress of this alloy. Nonmetallic inclusions greatly lower the fracture stress of all metals. The magnitude of the lowering depends 0' the size and shape of the included particles. In glass, the major source of the low fracture stress has been fairly conclusively demonstrate' by Griffith4 '0 arise from real flaws or cracks present in the material. He showed that the stress concentration at the end of a defect was of suficient magnitude to raise the stress at this location to a value comparable with the theoretical strength Of the material. If the cracks were reduced in size, Griffith showed that the observed fracture slrength the by virtue Of the decrease in stress concentration. He also pointed out that cracks disposed perpendicularly to the applied tensile stress would be more effective in lowering the fracture

Jan 1, 1947

By W. T. Lankford, Edward Saibel

During the course of an investigation of the plastic flow of aluminum aircraft sheet under combined loads, several problems arose in which analyses of the conditions leading to unstable plastic flow were needed. In order to provide these analyses, and in the hope of attaining a better understanding of the general problem of unstable plastic flow, the present study was undertaken. It is well known that unstable plastic flow is associated with a form of mechanical instabi!ity frequently observed during the plastic deformation of ductile metals. This instability is characterized by the fact that, at its onset, plastic straining mill proceed at a constant magnitude of the externally applied forces. It is further typical that the resulting unstable flow is generally accompanied by the formation of a neck, a local bulging, or some other form of heterogcneous deformation. Perhaps the most familiar example of unstable plastic flow to the metallurgist is the formation of the neck in the ordinary tension test. It is well known that in this test most metals exhibit a maximum in the externally applied load, followed by the process commonly referred to as "necking down." Instability in the simple tension test has been frequently discussed and numerous investigators1'2'3'12 have derived the criterion for instability in terms of a critical rate of strain hardening. It is the purpose of the present study to extend the criterion for unstable flow to the more general case where the body undergoing flow is subjected to combined loads. It is hoped that the problems considered will provide a more consistent picture of the general features of this important form of mechanical instability. The most practical implications of instability in plastic flow arise in connection with sheet metal forming operations. In the formation of a great many sheet metal parts, the deformations are produced primarily by stretching. If the conditions which lead to unstable flow are fulfilled in such a formation, and if the resultant instability leads to a pronounced localization of flow, then the useful limit of ductility of the material will have been reached. It i; also essential that the effects of instability be taken into consideration in any study of the plastic flow and rupture of metals under combined stresses. In general, when unstable plastic flow is initiated, straining becomes localized, the geometry of the test splecimen changes, and the state of stress in that portion of the specimen undergoing plastic flow is no longer under external control. In many past studies of the effects of combinetl Metals On flow and rupture) account has not been taken of the fact that, although a given test may be started under constant

Jan 1, 1947

By W. T. Lankford, Low J. R., Gensamer M.

The problem of sheet metal formability is one which has received a vast amount of attention during recent years. In spite of the great amount of study and experimental work which has been devoted to this problem, many of its fundamental aspects are still not well understood. No generally satisfactory test has been developed which is capable of providing a reasonably adequate evaluation of sheet metal formability, particularly in borderline cases. Anomalies persistently arise in which a lot of supposedly satisfactory material exhibits excessive breakage when formed. This lack of suitable technological tests greatly hinders the design of new parts and the substitution of new materials in parts of existing design, frequently necessitating considerable costly trial and error experimentation on an actual production basis. When, at the beginning of World War 11, it became apparent that mass production methods of forming would bc required in the aircraft industry if the large numbers of military aircraft needed were to be supplied, renewed attention was focussed on the problem of sheet metal formability. It was widely recognized that the formability requirements placed on sheet metals had been steadily increasing in severity through the years, especially as greater and greater emphasis was placed on streamlined designs with the resultant freer application of doubly curved surfaces. The recent advent of several new high strength aluminum alloys of more limited formability than some of the older alloys also served to emphasize the need for new approaches to the problem. It seemed evident that progress in the technology of sheet metal forming would depend to a great extent on the development of more reliable criteria for the evaluation of formability. Although the problem is admittedly very complex, the most logical approach appeared to be through studies of the fundamental material properties of sheet metals, especially under complex stress conditions simulating those prevailing in actual forming operations. Most previous investigations have failed to make full use of existing knowledge of fundamental material properties, and in many instances have attempted correlations with properties which are now recognized as being ambiguous in nature. This investigation was undertaken, therefore, with the aim of developing methods for the study of the flow and fracture of sheet meta1s under combined stresses, and of making use of such methods as might be developed in

Jan 1, 1947

By G. Sachs, Jr. Brown W. F., Ebert L. J.

It is a generally recognized fact that a steel quenched from the austenitic range and tempered to yield a structure composed of tempered martensite becomes increasingly more ductile with increasing tempering temperature. However, the conventional tensile test fails to yield any value that is sensitive to differences in behavior on tempering among the various low-alloy steels or among different heats of a particular steel. The notched impact bending test, on the other hand, has been recognized for a considerable length of time as capable of revealing differences in impact properties among various steels tempered to 'the same strength level (i.e., the same tensile strength in a conventional tensile test). However, this test is very complex and its significance has not been clarified up to the present time. Of its three characteristic features—the high speed, the notch, and the bending—the notch has been found by Davidenkov2 to be the most potent embrittling factor. Recent investigations on low-alloy steels have shown static notch-bar tensile tests to be more lucid and to evaluate the metal properties in much the same manner as impact tests. In an attempt to analyze the fundamental nature of this test, it was found possible to separate the effects of the two basic characteristics of the stress pattern introduced by the presence of a circumferential notch, the stress state and the high initial stress concentration at the notch bottom. The major conclusions drawn from these previous investigations were as follows: I. The magnitude of the triaxiality at fracture depends primarily on the initial notch depth. Its effect is a great reduction in the average ductility (contraction in area at fracture in the notched section) as compared with that observed in uniaxial tension. This triaxial stress state occurs at a point in the interior of the notch specimen. It determines the notch ductility if the notch is mild and/or the metal possesses a considerable ductility. On the contrary, brittle specimens probably fracture on the metal surface (at the notch bottom) at which point biaxial stress state is present. This biaxiality also considerably reduces the ductility of the metal. For small notch ductilities the notch strength and the notch ductility become very sensitive to embrittling factors. This is contrary to the behavior. of the ductility values derived from a conventional tensile test, which are comparatively insensitive.

Jan 1, 1947

By Lloyd R. Jackson

In the past 15 years there has been a great deal of interest in the fundamentals of plastic flow and rupture in metals and a number of papers have presented substantial advances toward a fundamental insight into the mechanism of these two processes. This paper is an appraisal of the present position with respect to the following: 1. The relative importance of shear and hydrostatic stresses in controlling the plastic flow of metals. 2. The relative importance of shear and hydrostatic stresses in determining the amount of flow before rupture in metals. 3. The use of generalized strains in determining the effect of plastic flow on the work-hardening of metals. FundamentalS Involved in Plastic Flow In attempting to devise a quantitative description of plastic flow in metals, it has been customary to assume that metals are homogeneous and isotropic. The fact that neither of these assumptions is correct complicates the experimental appraisal of relations developed. Nevertheless, as will be shown, metals are close enough '0 being isotropic and homogeneous so that considerable insight into the mechanism of plastic flow can be obtained. The assumptions of isotropy and homogeneity allow both the elastic and plastic behavior of metals to be described in terms of 12 variables—six being stress variables, and six being strain variables. From this viewpoint, it should be possible to represent the stress-strain relations in the plastic range for metals by a surface in 12 dimensions. One boundary of this surface would be the surface of transition from elastic to plastic behavior; the other would be the surface of rupture. These two surfaces would be joined by the surface of plastic flow. The shape of this composite surface would depend on the test temperature and speed of straining This paper is concerned only with results obtained at constant temperature and constant speed of straining. While such a representation is conceivable, the demonstration of such a surface would present almost insurmountable obstacles. The most fruitful simplification of this concept has been the recognition that the behavior of metals in the plastic region is primarily a result of shear stresses and strains. Based on this viewpoint, it is possible to utilize stress and strain invariants that are independent of hydrostatic components to define an effective stress and strain. In effect, this amounts to reducing the task of representing stresses and strains in 12 dimensions to one of representation in two dimensions. The two invariants (one for stresses and one for strains) that have received most attention are the following: q2 = ½[(Txx= - Tyy)2 + (Tyy - Tzz)2 + (Tzz - Txx)2 + 3(Txy2 + Tyz2 + 7xx2) [1]

Jan 1, 1947

By Edward Saibel

The various theories that have been advanced to explain or predict the conditions under which a metal fractures may be divided into two categories: First, there are the macroscopic theories generally used in engineering practice. These are empirical in nature and limited in application. For example, the maximum normal stress criterion, which is quite satisfactory for a mild steel in simple tension at atmospheric pressure,' no longer suffices when this steel is pulled under hydrostatic pressure.2 In all of these empirical theories, the critical condition characteristic of the material and of the loading conditions must be obtained experimentally. Secondly, there are the theories based on interatomic forces,3'4 or on the energy required to form new surfaces.5,6 These have all dealt with the theoretical evaluation of the tensile stress necessary to bring about rupture in a purely brittle manner; that is, without plastic flow preceding fracture. All of these attempts have led to values of the tensile strength of crystals or of polycrystalline bodies that are 100 to 1000 times higher than observed values. On this account, it has been thought necessary by some investigators to conceive of a microcrack structure or distribution of flaws throughout the specimen such that the resulting stress concentrations provide the factor necessary to bring about agree- ment between calculation and experiment. It has been pointed out by several observers' that this point of view is highly unrealistic, in that the weakening effect of these flaws or microstructures must be very uniform from specimen to specimen, since the fracture stresses found for various specimens of the same material tested under similar conditions are so nearly constant. Furthermore, since calculations based on atomic forces or atomic energy are for purely brittle fracture, a condition probably never satisfied in tests, agreement is hardly to be expected. Thermodynamic Theory of Fürth In order to resolve this apparent discrepancy between the theoretical cohesive strengths and the observed fracture strengths, Fürth8 advanced a thermodynamic theory of the tensile strength of isotropic bodies based on work of Born relating to the melting of crystals. Assuming an isotropic material free from imperfections and flaws, behaving elastically up to the breaking point, and assuming a connection between rupture and the melting phenomenon, Fürth obtains an expression for the rupture stress a, in the form where Q is the melting energy per unit mass, p is the density, and is Poisson's ratio. Furth compares fracture stresses computed from Eq I with the fracture stresses of metals as given in the Landolt-Bernstein Tables (1927) and in the Hand-

Jan 1, 1947

Jan 1, 1947