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By R. B. G. Yeo

Pronounced isothermal martensite formation at room temperature was measured dilatometrically in a steel containing 0.01 pct C, 24.9 pct Ni, 0.26 pctAl, 2.58 pct Ti and 0.25 pct Cb. It is shown that martensite will form isothermally if stabilization of the austenite-martensite transformation is eliminated by removal of carbon. The decarburization of two iron-nickel alloys allows isothermal transformation to martensite to occur at temperatures above their athermal Ms temperatures. In an Fe-22.4 pct Ni alloy, at the 0.008 pct C level, the Ms temperature during air cooling is 85°F higher than that during- water quenching-. At the 0.15 pct C level this difference is reduced to only 5°F. The introduction of carbon causes stabilization during air cooling which lowers the Ms temperature virtually to the same level as determined during mate?. quenching. Thus in the 0.15 pct C alloy, the Ms temperature is almost independent of cooling rate. It is suggested that rival theories of martensite formation should be reexamined in alloys of sufficiently low carbon and nitrogen content to eliminate the complication of stabilization. The Ms temperature of a steel containing 0.01 pct C, 24.9 pct Ni, 0.26 pct Al, 1.58 pct Ti and 0.15 pct Cb, solution treated at 1500°F and air cooled as 1/8-in. diam specimens, was found to be 57 °F. 1 However, when held for several hours at room temperature the steel hardened slightly and became appreciably ferromagnetic. Isothermal transformation to martensite was first revealed by Kurdjumov and Maksimova2 in an iron-base alloy containing 0.6 pct C, 6.0 pct Mn and 2 pct Cu. Most of the other studies of isothermal martensite have also been confined to highly alloyed steels which transform at subzero temperatures; for instance, DasGupta and Lement, 3 Cech and Hollomon, 4 Machlin and Cohen,5 Shih, Averbach, and Cohen.6 Averbach and cohen7 noted a rapidly decaying volume increase at room temperature in a steel containing 1 pct C, 1.5 pct Cr and 0.2 pct V. cina8 and Marshall, Perry, and Harpster9 have described the isothermal transformation to martensite at room and subzero temperature in stainless steels. Kurdjumov10 has recently reviewed the subject, noting that the isothermal formation of martensite can be observed only in the temperature range somewhat below Ms or below -50°C. The isothermal formation of martensite may be characterized as follows: 1) It occurs in steels of widely different compositions, the main prerequisite being a low transformation temperature. 2) The transformation occurs by the formation of new plates and not by the growth of old ones. 3) The isothermal transformation is suppresed by stabilization during slow cooling or holding at temperatures near room temperature. However, the factors governing this mode of transformation are still not fully understood. The formation of martensite isothermally suggests an activated process. The early theories of martensite formation did, in fact, utilize classical nucleation concepts. Kurdjumov 11 first proposed the presence of thermally activated nuclei of different sizes and compositions which would grow if they reached critical size during cooling. This treatment was enlarged and developed quantitatively by Fisher, Holloman, and Turnbull12,13 and was later reviewed by the latter two authors.14 Fisher15 associates Ms with a nucleation rate of one per cc per sec. At slightly higher temperatures the nucleation rate is so low that isothermal formation of martensite is not observed in reasonable times. At slightly lower temperatures the nucleation rate is so high that it could not be suppressed by rapid cooling. By judicious use of parameters Fisher 16 was able to obtain good agreement between classical nucleation theory and the incubation times of martensite formation.4 However the application of these principles to martensite formation in iron-nickel alloys15 predicts that an alloy containing about 30 pct (31 at. pet) Ni would not transform. The presence of an Ms temperature at -223° C in an alloy containing 34.1 pct (33 at. pct) Ni led Kaufman and cohen17 to reject the hypothesis of homogeneous nucleation in favor of the reaction path theory originally proposed by Cohen, Machlin and Paranjpe.18 This theory conveniently explains the formation of martensite athermally but becomes labored when dealing with isothermal formation. Kaufman and cohen19 did explain the isothermal activation of embryos by assuming it to be a result of the expansion of their boundary dislocation loops but this treatment predicts an upper temperature limit of isothermal martensite formation.

Jan 1, 1962

By L. G. Marshall

This report is one of a series published by the Federal Bureau of Mines, describing mining methods and performance at individual mining operations throughout the United States. The objective of these papers is to promote development and conservation of our mineral resources by disseminating reliable technological information on mining methods, practices, and performance. Limestone deposits in Iowa are extensive and reserves are large. Most of the past production came from the eastern third of the state, although over half of the counties in the state have produced, or are now producing limestone. The stone is used as aggregate, road metal, agricultural lime, riprap, fluxing stone, railroad ballast, and in the manufacture of cement and lime.

Jan 1, 1962

By G. R. St. Pierre, A. J. Wilhelem

In connection with the reduction of hematite or magnetite to metallic iron, it appeared desirable to study the rate of reduction of each oxide to the next lower oxide under conditions which excluded all other condensed phases. For this purpose, pellets of Fe,O,, Fe,O,, and oFeOo were prepared. A gas train for the preparation of Ar-Hz-H20 mixtures was employed to establish a continuous flow of a controlled atmosphere over a pellet suspended on a balance. In this manner the following individual reduction steps could be studied: For example, pellets of hematite were reduced solely to magnetite by adjusting the gas atmosphere such that it was oxidizing to wustite. In other words, the reaction was complete when the hematite pellet had been totally converted to magnetite. The pellets were prepared from Baker Chemical ferric oxide. The ferric oxide powder was moistened and handrolled. Air sintering at 950°C produced Fe,0, pellets with a density of 3.65 g per cm3. The pellets ranged in size from 0.6 to 1.2 cm diam. The magnetite and

Jan 1, 1962

By William R. Wayment

The objective of this investigation was to obtain data on friction-head losses of sand slurries during their transport in pipelines. The data ultimately will be used in designing hydraulic transport systems. Information that was incidental to the primary objective was gathered on degradation, changed percolation characteristics, and critical velocities of the slurries~ Tests were made in a closed-circuit pilot plant, with one type of tailing, through horizontal 2-, 3-, and 4-inch-pipe test sections at various pulp densities and flow velocities. Tests were made in a closed-circuit pilot plant, with one type of tailing, through horizontal 2-, 3-, and 4-inch-pipe test sections at various pulp densities and flow velocities. Approximately 2,000 tests were run in the pilot plant. The ranges of flow velocities used in the experiment were 2.8 to 19 f.p.s. in the 2-inch line, 4 to 14.5 f.p.s. in the 3-inch line, and 4 to 11 f.p.s. in the 4-inch line. Velocities were varied in increments of 0.5 f.p.s. through the entire velocity range in each pipe size. Densities were varied in 3-percent increments from 40 to 70 percent solids by weight except for one series of tests in the 2-inch line; in this series, densities were varied in 5-percent increments from 5 to 65 percent solids by weight.

Jan 1, 1962

By Dogan E. Gücer

In the following note, with the help of a new parameter of strain hardening, the attention is drawn to the close relationship between the relative performances of steels under plastic range cycling and their strain hardening characteristics. If a cantilever beam of rectangular cross section is tested with the arrangement shown in Fig. 1 in reversed bending between constant deflection limits at the lever head, the longitudinal strain-deflection hysteresis shown in Fig. 2 is obtained. There is no lateral strain due to constraint at the rectangular test section.' If the absolute value of strain undergone between a maximum state of tension and maximum state of compression is called A, it will be seen that A decreases with cycling rapidly due to the strain hardening in the test section and the ensuing change in the bent beam profile. It will also be seen that A reaches an approximately stable value around 10th cycle. If we call the first cycle strain range, A,, and that of 10th cycle, A,,, then is an index of the strain hardening capacity at a particular deflection level. A plot of n vs ? is reproduced in Fig. 3 for two ASTM steels: A-302 and A-201. A-302 is a low alloy structural steel, A-201 a low-carbon steel. The specimens were first normalized at 1650°F for 75 min then grooved with a milling cutter; and the notches were ground to 50G finish. The final operation before testing was a stress relief at 1150°F for 75 min. The behavior of the two steels changes around ?1 = 0.8 pct or A,, = A, -n = 0.7. If these curves are compared with the endurance life curves given in Fig. 4, it will be seen that the relative performance of the two steels also change around A,, =. 0.70 pct. The steel with lower strain hardening capacity (7) at a certain strain level shows a longer endurance life, irrespective of their strength levels. Since the exponent governs strain hardening at lower strain levels than the Modulus, the relative values of both parameters also coincide with the change in n values and the relative performances of the two steels at different strain levels. These two observations indicate to the close relationship be-

Jan 1, 1962

By Frank A. Peters

This evaluation of the sulfurous acid process for the production of metallurgical-grade alumina is the first of a series concerning various known methods of extracting alumina from low-grade aluminous materials and was undertaken to permit comparison with other processes. In the process with which this Bureau of Mines report is concerned, calcined clay is leached under pressure with 20 percent sulfurous acid and then filtered to remove a siliceous residue. The aluminum sulfite remaining in the filtrate is precipitated as a monobasic sulfite which, together with iron sulfite, is then decomposed under pressure to form a crude alumina hydrate and iron oxide. This intermediate product is purified in a modified Bayer process to yield alumina suitable for electrolytic reduction to aluminum. A study estimate (16)3 is used for these evaluations. The capital cost, not including land, is estimated at $95,701,600 on a Marshall and Stevens index basis of 240.0 for a plant producing 1,000 tons a day of alumina or 350,000 tons a year. The annual operating cost for this size plant is estimated at $22,831,100 or $65.23 per ton of alumina using clay at $1 per ton. Depreciation and local taxes are included in the estimate, but profit and Federal taxes are not considered.

Jan 1, 1962

By Arne Bergholm

Australian rutile was chlorinated in the presence of CO or carbon. The chlorination velocity in CO was found to be strongly influenced by temperature and proportional to the CO concentration, but independent of the Cl, concentration. In the presence of carbon, the reaction velocity is much higher. The reactivity of the carbon and the distance between the carbon and the rutile surfaces are important variables. The reaction velocity is approximately proportional to the Cl, concentration and independent of the CO concentration of the surrounding atmosphere. Experiments with fluidized-bed chlorination of carbon-rutile mixtures indicate that the motion of the bed has little influence on the reaction velocity. At low temperatures, the chlorination velocity of dense tablets is much greater than that of TiO, coke mixtures suitable for fluidization. The reaction mechanism is discussed. In the industrial production of TiCl, rutile is chlorinated in the presence of carbon. Disregarding intermediate steps, the reaction may be expressed by the following equations: The ultimate object of this study was to find out whether the reaction velocity was higher in fluidized bed operation compared with chlorination of pelle-tized carbon-rutile mixtures. From a literature survey and preliminary experiments it was learned that some basic knowledge about the reaction mechanism was needed for a good experimental design. Therefore the following sets of experiments were carried out: 1) Studies on the reaction velocity in the chlorination of rutile with CO as the only reducing agent. 2) Chlorination of separate rutile-carbon tablets. 3) Chlorination of rutile-carbon tablets at different temperatures with various kinds of carbon, various grain sizes, and various tablet-making techniques. This series of experiments was carried out not only with pure chlorine but also with mixtures of chlorine with argon, CO and CO,. 4) Chlorination of rutile-carbon tablets made in a strictly standardized manner. 5) Chlorination of static-bed rutile-carbon mixtures. 6) Fluidized-bed chlorination of the same mixture. The experiments 4 to 6 formed the final and direct test of the main question: Static bed vs fluidized bedo. Although there are many patents and papers dealing with the general aspects of chlorination, only few experiments from which detailed information can be obtained have been reported in the literature. Pamfilov and coworkersl3 have studied chlorination of TiO, with CO or carbon as the reducing agent. They found that the weight decrease per hour at 600o to 800°C amounted to 11 to 14 pct with CO and 45 to 51 pct with carbon. They suggest that phosgene might be an intermediate in the chlorination of TiO,. Takimoto and Hattori have chlorinated reduced titanium oxide (TiO) and found a very high rate of TiC1, -production. They proved that the composition of the gas from the chlorination of rutile-carbon mixtures contained mainly CO. They reported for instance 74.7 pct CO, and 5.6 pct CO at 800°C at which temperature the Boudouard equilibrium composition is 12 pct CO and 88 pct CO. Seligman and Segerchano6 have studied the chlorination of TiO. They proved that Ti0 and chlorine react rather rapidly at temperatures as low as 300°C. Above 400°C, the reaction was complete. At 500°C the velocity of this reaction was much higher than was chlorination of TiO, + C. McTaggart,7 Nishimura, et al. and Wilskam have chlorinated mixtures of carbon and various kinds of rutile or beneficated ilmenite. Nishimura, et al. also report the results from reduction of TiO, with H2, CO, or carbon. At 900°C only 1 pct Ti O is formed in 2 hrs. At 1100°C 23.1 pct Ti, 0, was formed if elementary carbon was present. No carbide formation occurred below 1400°C. McIntosh and Cofferll have observed that the CO, content of the exit gases from chlorination of rutile and calcined petroleum coke is appreciably higher than found in the Boudouard equilibrium. At 900°C the ratio (CO, /CO + CO) is about 80 pct, whereas the equilibrium value is about 2 pct. W. E. Dunn12 has studied the chlorination rates of several TiO,-bearing minerals with CO + Cl, or COCl . Chlorinations were carried out either in a fluidized reactor or a fixed-bed reactor, both having a 30-mm diameter. The results obtained in both reactors were comparable. It was proved that benefi-ciated ilmenite (i.e., ilmenite from which the iron oxide had been removed by chlorination) was chlorinated 10 times faster thanrutile. Sore1 slag showed an intermediate rate. When phosgene is used, the

Jan 1, 1962

By E. G. King

The literature contains little thermodynamic information regarding inter-oxidic compounds of the ferroalloy elements and, as a result, thermodynamic considerations of extractive and utilization processes involving these elements have been hampered. As part of a Bureau of Mines program to improve this situation, this paper reports the heats of formation of three calcium vanadates and two magnesium vanadates. There were no previous similar data for any of these compounds. The experimental method was hydrochloric acid solution calorimetry, using calorimetric reaction schemes involving the vanadates and their component oxides. The results were expressed as heats of formation from the component oxides and from the elements. Corresponding free energy of formation values were calculated. The data show that the calcium and magnesium vanadates are stable with respect to all possible decompositions in which vanadium remains pentavalent. This conclusion is similar to the one drawn by Koehler6 for three sodium vanadates.

Jan 1, 1962

By George J. Carter

Data obtained from field and laboratory examinations were used by the Bureau of Mines to evaluate 82 silica deposits in the Pacific Northwest. A total of 94 field samples was taken from 64 deposits, and an additional 18 deposits were investigated that did not warrant sampling. Of the 37 deposits found to be of high quality, only 16 were large enough to be classified as industrial silica resources. Another 27 deposits did not meet quality requirements. Methods of simple low-cost beneficiation and rapid classification of a large number of samples were investigated in the laboratory. These tests indicated that high-intensity electromagnetic separation was equal or superior to either high-or low-intensity electrostatic separation. In general, the electromagnetic method gave higher recoveries and produced equal or better grade concentrates. A glass button method developed for estimating iron oxide content of silica samples proved to be highly satisfactory as a means of classifying field samples and evaluating beneficiation tests.

Jan 1, 1962

By Howard P. Hamlin

This Bureau of Mines report is concerned with the testing procedures for evaluating clays, shales, and slates for lightweight aggregates using the rotary-kiln method of production. To meet the increasing demand for light-weight concrete, rapid, accurate methods for appraising raw materials for light-weight aggregate are needed. Preliminary tests were made on samples of clay, shale, and slate, using laboratory equipment, and the data were used to establish operating conditions for pilot-plant-size rotary-kiln tests. Lightweight concrete was made from the processed aggregates and the properties determined. The results show that the laboratory data can be used to guide rotary-kiln testing, and, with the exception of sampling, a complete appraisal of a raw material for lightweight aggregate concrete can be made in 3 days by the methods described in this report.

Jan 1, 1962

By A. G. Loomis

METHODS for measuring relative permeability as a valid function of saturation were compared by the. Bureau of Mines, using core samples from representative oil-productive California formations, from the Bartlesville sand in Oklahoma, and from synthetic samples. Measurements for gas-oil systems were made by steady-state dynamic, unsteady-state displacement and two stationary-phase methods. Measurements for water-oil systems were made by the unsteady-state displacement method. As the ratio rather than individual relative permeabilities is measured by the last method, three methods for calculating individual relative permeabilites from their measured ratio were compared for gas-oil systems and two methods for water-oil systems. Errors arising from capillary discontinuities, such as the end effect and stabilized-zone flow, are discussed and evaluated; possible errors rocs arising from turbulant flow are also examined. The inapplicability of non-steady-state methods for water-oil systems that are not definitely oil-wet is discussed in detail. Measurements of relative permeability to both gas and oil can be made quickly and accurately by the steady-state dynamic method when rates of flow of the two phases are sufficient to minimize the capillary discontinuity at the outflow end of the sample. At such rates relative permeability-saturation measurements are essentially independent of the rate of flow. The steady-state method wits modified by a dispersion section at the inflow end of the sample acid designated tie dispersed-feed method.

Jan 1, 1962

By Heinz W. Sternberg

The literature on electrochemical treatment of coal is reviewed, and possible avenues of further research in this field are discussed in this report. Electrolytic reduction of finely distributed coal resulted in the addition of as many as 9 atoms of hydrogen to 100 atoms of carbon. Reduction of coal extracts at controlled potentials indicated the presence of condensed aromatic hydrocarbons and reducible quinones in coal. As much as 65 percent of low-rank coal can be made alkali soluble by electrochemical treatment. Higher rank coals gave smaller yields of alkali-soluble products. However, the nature of this reaction is not clear. The difficulty of reducing coal electrolytically is probably due to the insolubility of coal and not to any structural peculiarity. Reduction of coal by electrolytically generated radical anions appears to be a promising approach for further research.

Jan 1, 1962

By L. M. Irwin

This Bureau of Mines investigation relates the physical properties of copper reverberatory furnace slags to changes in composition, The smelting of upper Michigan copper ore presents some problems that probably differ from those of other copper smelting areas. The study of these problems has, however, provided important data regarding slags in general and therefore will be of value to other operations as well. Conclusions reached from this study were: (1) Slag fluidity and refractive indices varied directly with the iron content and inversely with silica, lime, and alumina, and (2) there was no apparent correlation between slag fluidity and its copper content.

Jan 1, 1962

By R. Ward Stahl

The underground junction or intersection is analogous to the doorway or window in a building in that the continuous wall or support for the overhead structure has been weakened by making the opening. Some type of bridge or support seems necessary to prevent roof sag and possibly eventual failure at this point, although frequently it appears that little is done until a fatal accident induces action. The intersection generally represents less than 15 percent of the exposed roof area. As a result of recent multiple fatalities, some of which occurred at or near intersections, the Bureau of Mines was asked to examine the junction-support problem more thoroughly and to report its findings. A national survey of the junction-support systems in use has been made by correspondence, and the local area has been canvassed rather thoroughly to determine just what and how much is being done.

Jan 1, 1962

By W. Kunda, J P. Warner

SHERRITT GORDON Mines Limited annually produce 300,-000 pounds of pure cobalt by processing a nickel-cobalt-copper-iron sulphide ore which is mined at Lynn Lake, Manitoba. The ore (containing 0.04 per cent Co) is •concentrated to give a concentrate containing l 1-12 per cent nickel, about 2.0 per cent .copper, and 0.25-0.35 per cent cobalt, which is treated at the Refinery in Fort Saskatchewan, Alberta. The concentrate is leached in an ammoniacal solution of ammonium sulphate using compressed air as the oxidant. After filtration the leach solution contains, besides nickel and cobalt, copper ammines, sulpharnates and salts of various thionic acids. The copper is removed by precipitation as sulphide and the sulphur compounds converted to ammonium sulphate by a combined oxidation and hydrolysis treatment. The purified solution •Containing about 45 gpl of nickel and 1 gpl of cobalt is treated with gaseous hydrogen under pressure at 350°F to precipitate metallic nickel powder, the precipitation 'being terminated when the nickel content of the solution is about 0.8-1 gpl. Only about

Jan 1, 1962

By J. R. Nettle

The development of a process for upgrading offgrade titanium metal by electrorefining in molten salt led to an investigation of the electrotransfer characteristics of selected metals when alloyed with the titanium to be refined. Previous tests on seven binary titanium alloys showed that the degree of transfer of the alloying constituent depends on the constituent and on the operating procedurese.5 This report describes tests on electrorefining ternary mixtures of titanium with selected metallic elements. Ten alloys were prepared from high purity titanium and 2-1/2 percent of each of the metal pairs selected from the same elements used in the binary study; manganese, vanadium, chromium, zirconium, tin, molybdenum, aluminum. Operating variables were similar to those investigated in the binary alloy study that gave minimum alloy metal transfer. The data presented indicate the transfer characteristics of the various metals and combinations tested relative to each other.

Jan 1, 1962

Titanium and Zirconium Industries Pty. Ltd. separates rutile and zircon from heavy mineral concentrate recovered from sand dunes on the east coast of North Stradbroke Island, Queensland. Separation plant feed is delivered to Dunwich, on the west coast, by a seven mile aerial ropeway traversing the island. Mining and concentration is effected by two floating dredge-concentrators now operating on the beach 31; miles from the aerial ropeway terminal. Heavy mineral concentrate is transported hydraulically from the dredges to the ropeway through a 6 in. pipeline. Six pumps in series deliver 24 ton/hr of dry solids in a pulp containing 13 per cent solids. For maximum economy the transfer pumping system is controlled deliberately to cause transportation in the zone of incipient settlement of solids, ieat velocities below the limit deposit velocity for the particular pipe diameter, pulp density, and specific gravity of solids. Automatic density control, based on a combination of power consumption and pipeline pressure, eliminates the danger of plugging the line but periodic flushing is necessary to remove gradual accumulation of solids in the bottom of the pipe. After 15 months operation the pipeline was descaled with hydrochloric acid to remove severe blistering with rust nodules, regrowth of which is now prevented by continuous injection of inhibitors. After transporting 100,000 tons of heavy mineral the average wear on the steel portion of the pipeline was 0·01 in. and indications are that wear on the asbestos cement portion is less.DESCRIPTION OF OPERATIONSGeographyTitanium & Zirconium Industries Pty. Ltd. (T.A.Z.I.) operates on North Stradbroke Island, some 30 miles southeast of Brisbane, Queensland. The island is approximately 25 miles long and eight miles wide, and is bounded on the east by the Pacific Ocean and on the west by Moreton Bay (Fig. 1). With the exception of a small outcrop of volcanic 1. Manuscript received at The Institute. 8th May. 1962. This paper was presented at the Annual Conference of The Institute. 5th-11th August. 1962.

Jan 1, 1962

The conclusions reached by den Tex after a study of the fabric of some rocks from Broken Hill have been used to support the epigenetic hypothesis for the origin of the ore, first by Edwards (1959, p. 70) and then by Stillwell (1962, p. 131) in his criticism of Segnit's (1961) views. Den Tex claimed that the petrofabric study provided "independent evidence that the ore, at least in its present form, post-dates all events of a diastrophic nature in the area concerned".Repetition of this claim by Edwards and by Stillwell and the lack of any criticism of den Tex's work for more than three years implies its general acceptance by geologists in Australia. Therefore it appears necessary to examine parts of den Tex's paper in detail to show that his, conclusions are unwarranted. The major weaknesses in his study are that1. the petrofabric study was inadequate to warrant any major conclusions, and2. the petrofabric data allow alternative conclusions.Den Tex made a single visit to the field, collected six carefully selected specimens and presented quartz and· biotitepetrofabric diagrams for two specimens, quartz-diagrams alone for three more and included three diagrams of the orientation of c-axes and fractures in one specimen. It is not reasonable to come to firm conclusions about the origin of such a complex area as Broken Hill on such inadequate data, despite den Tex's claim (p. 87, lines 22 and 23) that "a thorough investigation of the quartz-fabric of the wall rock was undertaken".Den Tex's interpretation of each diagram is open to criticism, and alternative (and to my mind, preferable) interpretations may be made. It is impossible to evaluate den...

Jan 1, 1962

By D. Kuhlmann-Wilsdorf

A new theory of work hardening is developed which rests on only a few simple principles and is applicable to a wide variety of materials and dislocation structures. It explains, qualitatively, the general characteristics of the three-stage shear stress-shear strain curve of fcc metals, as well as the most important features connected with easy glide. The value of, the work-hardening coefficient in stage 11, is derived quantitatively, from first principles, and is shown to be insensitive to many changes in detailed dislocation behavior. The low rate at which energy is stored during mechanical working in stage 11, the dependence of slip line length on stress, and the so-called Cottrell-Stokes law are explained. Although the theory is primarily developed for fcc metals and alloys, it is largely applicable also to some other materiuls, and in particular apparently to poly crystalline simple steels in theh linear range of hardening. FOR pure fcc metals and alloys, after many different pretreatments and under a great variety of testing conditions, the well-known three-stage work-hardening curve is commonly observed. Moreover, the work-hardening coefficient in stage 11, 011, bears an almost constant relationship to G, the modulus of rigidity, such that K = G/Brr" = 300, within a factor of about 2 either way. The very fact that the three-stage curve and the value of K are so very persistent, can hardly be understood except on the assumption that some quite simple phenomena are responsible. In this light all available theories of work hardening must be judged unsatisfactory: Each of them is based on some quite specific dislocation model, while it is known that metals with similar values of K may have widely different dislocation structures, for example, dislocation tangles in the case of pure fcc metals, and piled-up groups of dislocations in a-brasstype alloys. Thus, while a particular theory might conceivably represent a special case with a reasonable degree of accuracy, it cannot possibly have illuminated the underlying principle. Another severe criticism applying to the presently most widely discussed theories is that they employ empirical or even quite unexplained parameters in order to arrive at a numerical value of K. This indicates that some vital aspect of the work-hardening process has remained unexplained. In the present paper, a new theory of work-hardening is developed which does not suffer from the above shortcomings. It is derived from first principles, and is founded on the realization that the underlying causes for the three-stage work-harden- ing curve and for the persistence of the numerical value of O,, must be few and simple. As a first step it is shown herein that the experimental oklservations on "easy glide" can be explained on the assumption that in this stage dislocations multiply, beginning in a number of restricted area:;, and from there penetrate into crystal regions still substantially free of glide dislocations until a quasi-uniform dislocation distribution has been established. During "easy glide", the resistance to the movement of the foremost dislocations, advancing into still largely a dislocation-free regions, is believed to control the flow stress. This resistance is determined by various factors, among them the reaction of the dislocations against bowing-out into loops, which is due to their line tension. Without such bowing-out no dislocation multiplication would occur, but the corresponding contribution to the flow stress stays practically constant all through stage I. According to the present theory, stage TI begins as soon as there are no more areas left into which newly formed dislocations have not yet penetrated, i.e., as soon :is a quasi-uniform dislocation density has been attaned. Regardless of how, in detail, the dislocations should happen to be arranged at the end of "easy glide", whether in pileups or tangles, on one glide system or on several, the stress necessary to overcome the line tension of the segments must now increase, because the dislocation density increiises while the average free dislocation length decreases. It is argued that all other contributions to the flow stress stay at about the same level as in stage I, and that the said increase in the stress necessary to bow out dislocation segments into loops is responsible for the major part of work hardening in stage 11. Stage TII of the stress-strain curve is explained by largely follouing the ideas of Seeger and his co-workers; however, it is pointed out that the start of stage m may on occasion indicate the onset of "conservative climb" instead of cross slip. Indirect evidence indicates that linear work hardening persists even under the profuse action of cross slip, but at a lower rate. Only when, in addition to cross slip, climb operates extensively, does the work-hardening rat,. drop sharply, ultimately down to zero. BRIEF SURVEY OF EXPERIMENTAL EVIDENCE The stress-strain curve of crystals of many different substances are qualitatively similar. No significant permanent plastic deformation takes place below the so-called "critical resolved shear stress". As the applied stress is raised beyond this level. yielding occurs with little or no work hardening and

Jan 1, 1962

By Harry A. Lipsitt, Douglas Y. Wang

A fatigue study in completely reversed axial tension-compression has been perforried on high-purity titanium and on three high-purity alloys of titanium. The alloys each contain approxi7nately 0.75 at. pct of a single interstitial element; carbon, nitrogen, and oxygen, respectivley. The results corroborate a previously published theory which proposed that strain aging under alternating stress was responsible for the fatigue limit behavior of certain alloys. The present data indicate that in these alloys an increasing strain-talline aging effect under alternating stress is provided by oxygen, carbon, and nitrogen, respectively. CURRENT research on the nature of the fatigue limit in metals suggests that the presence of a fatigue limit in metallic materials is a manifestation of strain aging that occurs under alternating stress.lm5 A comprehensive theoretical model based on the above hypothesis has been developed to explain the existence of a fatigue limit.' This model also provides increased insight into several other fatigue phenomena as under stressing, overstressing, and coaxing effects. The theory, as well, provides equal understanding for those cases where no real fatigue limit is observed. Briefly, this theory assumes that the S-N curve for a pure metal is a smooth function of the applied stress, and the effect of adding an element that is soluble (or forms a precipitate) in the pure metal is simply to shift the S-N curve to the right. If the added element confers the power to strain age, the result is a further shift of the S-N curve, this time upward and to the right. Since strain aging is not expected to be a strong function of stress, and since damage per cycle is known to be quite stress dependent, it is to be expected that there will be some limiting lower stress at which the strengthening due to strain aging will balance the damage due to crack propagation. This stress is the fatigue limit. The position of the fatigue-limit knee was thought to be a function of the magnitude of the strain-aging effect on both the finite and infinite life portions of the S-N curve. Although the strain aging hypothesis seems to be reasonably valid for bcc materials,2'6 it needed to be tested for both fcc and cph metals. This report is the first of a series concerning the fatigue-limit behavior of titanium with varying amounts of the interstitial solutes (C, N,, and 4) that are known to cause static strain aging in titanium. Yield-point effects have been reported for polycrys-talline high-purity titanium alloys containing either carbon, nitrogen, or oxygen.7'9 These effects were observed at testing temperatures in the range 100 to 300'. In addition yield-point and strain-aging effects have been reported for single crystals of titanium containing 0.1 wt pct C plus N.' These yield points were observed over a wide temperature range, but no room-temperature aging occurred. Aging at 180' was required to cause the return of the yield point. The magnitude of the yield phenomena in titanium containing interstitials is not expected to be as large as is observed in bcc metals because of several factors. Titanium has a very high chemical affinity for oxygen and nitrogen. The thermodynamic stability of solutions of oxygen or nitrogen in titanium is recognized. Lattice parameter measurements of titanium containing arbon, oxygen,1° or nitrogen" show that the "c" parameter is expanded more than the "a" parameter, but that up to about 2 wt pct this results in an insignificant change of the axial ratio 'c/a." Ehrlich" has shown that the sites occupied by interstitial atoms in titanium are spherically symmetrical and therefore a lattice expansion, at a constant c/a ratio, results in a simple dilation of the interstitial site. Such a dilation involving no shear has been shown to react only with edge components of dislocations.13 This causes only a weak pinning action. Shear stresses would be anticipated locally when only one of the two interstitial positions was occupied. The carbon atom will cause a symmetrical distortion of the lattice whereas the oxygen and nitrogen atoms have, in addition, the previously mentioned chemical affinity of titanium for these elements. These factors will result in a considerably smaller reduction of free energy upon the association of interstitial atoms with dislocations, and therefore a much weaker pinning than has been observed for the bcc metals. These considerations would lead to the hypothesis that of the interstitial elements considered here carbon would cause the strongest pinning effect in titanium where the amount of interstitial in solution is constant. This hypothesis will be borne out in the analysis of the present results.

Jan 1, 1962