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By M. T. Simnad, C. E. Birchenall, M. H. Davis

The transport mechanisms previously proposed in wustite and hematite have been confirmed by movement of inert markers during the growth of these phases. By similar measurements the mechanism for magnetite has been determined. The rates of growth of multilayer scales on iron, magnetite and hematite on wustite, and hematite on magnetite have been measured. All rates are found to be diffusion controlled under the conditions of the experiments. MANY studies have been made of the rate of oxidation of iron in both the low temperature, film-forming region and the high temperature scaling range. The interpretation of the results has been greatly complicated by the formation of multi-layered scales containing the various phases of iron oxides. In most cases no attempt has been made to determine the composition of the scale and its dependence on time of oxidation in a quantitative manner. However, several recent studies'" have taken this variable into account. It is generally agreed that the growth of thick scales on iron follows a parabolic rate law for the increase of total thickness. In the thin film region agreement has been claimed with parabolic equations of various forms and with logarithmic equations. The discussion here will be concerned only with the formation of scales of considerable thickness, greater than several microns, although some of the conclusions may be applicable to thin films. A brief survey will be given of the solid phases of the iron-oxygen system, the stability of wiistite in bulk and in thin films, the relative densities of iron in the metal and oxides, and the kinetics of forma- tion of oxide scales on iron. New experimental results will be introduced at several points during the discussion, and an attempt will be made to formulate a mechanistic picture consistent with these observations. The experimental techniques are described in an appendix. Iron-Oxygen System Fig. la shows the iron-oxygen phase diagram. Wüstite ("FeO"): The lowest of the oxides has a NaCl type cubic lattice formed by close-packing of the relatively large oxide ions with the smaller iron ions arranged in the interstices. The ionic radius for 0' is about 1.3 A, while Fe++ has a radius of about 0.8A and Fe"' about 0.7A. Its range of existence on the phase diagram is very wide for an ionic material of this type and does not seem to include the stoi-chiometric composition FeO. These deviations appear to be well established as vacancies on iron lattice sites by the comparison of lattice parameters and densities for a series of compositions by Jette and Foote.4 The limits of the field are disputed, but the work which seems most reliable" indicates vacancies in from 5 pct to more than 12 pct of the iron sites. In order for the crystal to be electrically neutral, there must be electron holes which correspond to the formation of trivalent iron ions equal to twice the number of vacancies. Magnetite ("Fe³O4"): Considerable disagreement also exists in the literature about the stable range of the Fe³O4 field. Some diagrams show the Fe³O4 composition to be lower in oxygen than the formula indicates, but Schenck6 gives a diagram from the

Jan 1, 1952

By F. E. Streigert, J. H. Mallery, A. H. Geisler

The existing data on precipitation in Cu-Be alloys have been reconciled with some new data to present a more complete and rational analysis of the atomic rearrangements involved in the process. Two different coherent precipitates were proposed. Each is responsible for a type of diffuse X-ray diffraction effect. THE nature of the atomic rearrangement involved in the precipitation of the compound y-Cu-Be from supersaturated solid solutions of the copper-base alloys has been the subject of two extensive investigations.'-" he precipitate in this alloy system has a rather simple structure; at equilibrium it has a body-centered cubic unit cell with copper atoms on the corner sites and beryllium atoms on the center site. While a simple mechanism would be expected to obtain for the precipitation process, those which have been proposed do not adequately explain all of the reported data. The purpose of the present report is to rationalize some of the previous observations and to contribute new data on the subject obtained by the usual techniques of structure analyses. The Cu-Be system of alloys represents one of the most extensively investigated precipitation systems, so a detailed review of the pertinent literature on structure is in order. Striations: Since one of the important features of the mechanism—the habit plane—is determined by microscopic examination, microstructural features that have been observed should be considered at this time in order to assess their role in the precipitation process in Cu-Be alloys. One of the most prominent features appears as regularly oriented markings or stripings (ripples or striations) across the crystals on a suitably polished and etched sample of the aged alloy. These have been observed and interpreted by many workers. Masing and Dah14 observed striations in both the a and /3 phases of a 2.5 pct Be alloy, and attributed them to the beginning of the precipitation of very fine y crystals along favored planes of the a matrix and to the local decomposition of the £ crystals into a plus y. These markings were apparent in both the a and /3 phases of the micrographs given by Smith5 for a 2.75 pct Be alloy, while Moore" detected them in the a matrix phase using polarized light. Desch7 attributed the markings to fine precipitate particles lined up on a family of matrix planes like Masing and Dahl had done, and he identified the planes as those of the (111) family, the slip planes of the matrix. The striations were presumably the structure which Northcott- eferred to as "martensitic." He found that this structure was present in samples that had been aged under widely different conditions with hardness values ranging from 160 to 400 VHN. Later Guinier and Jacquet' also found striations in both the a matrix and secondary /3 phase. Their analyses showed that the striations were along (110) planes of the matrix phase, apparently in contradiction of the results of Desch. They found that the striations were developed during aging on the surface of a specimen that had been polished prior to aging.' On this basis they concluded that the striations represented mechanical deformation by slip along (110) planes of the matrix resulting from precipitation stresses.'" Similar but fainter striations were observed in the same manner on an A1-Cu alloy sample, in which the change in volume was much less than for Cu-Be alloys and

Jan 1, 1953

By W. L. Korbee, P. Hazebroek, M. Prats, E. E. Allen, C. A. 225-000-000-017 Verbraak, H. C. van Elst

In a recent paper,' one of us has presented some experimental evidence on the relationship between twinning and brittle fracture in steel. From metallographic examinations of brittle fracture it could be derived that mechanical twins and microcracks are formed already in front of a running brittle fracture. A tentative explanation based on the evaluation of the statistical distribution of mechanical twins vs various angles to the fracture was given in the above mentioned paper. It was suggested that these twins are caused by stress waves emitted by a running brittle fracture. With the aid of high-speed photography and the use of photo-stress sheet we are now able to study in more detail the propagation of a brittle fracture and the emittance of stress waves connected with fracture. A typical example is given in Fig. 1. In this figure a running brittle fracture in an ordinary Thomas steel is shown. The experiment was performed on a Robertson apparatus and the stress waves caused by the fracture were made visible with photo-stress

Jan 1, 1962

By G. Bhat, J. F. Libsch

A STUDY of the kinetics of embrittlement in engineering alloy steels during tempering has indicated that the presence of alloying elements may define two distinct regions of embrittlement: 1) at 800° to 1000 °F, termed low temperature embrittle-ment, and 2) in the temperature range 1150 ° to 1250°F, termed high temperature embrittlement.13 It has been suggested that embrittlement in each region may be due to a different mechanism. At intermediate temperatures and extended times the course of embrittlement may be influenced by the superposition of the embrittlement occurring in the two regions. Furthermore, low temperature embrittlement has been known to decrease as the temperature is raised slightly above the maximum embrittlement range.' Jaffe and BuffumV ave presented data for a Ni-Cr steel illustrating the removal of the em-brittlement occurring at 932°F by reheating to 1250°F for an hour. Their data further shows that embrittlement proceeds continuously with increased time at 1250°F, becoming pronounced at long times. They interpreted this behavior as a retrogression phenomenon involving the solution of the small nuclei of precipitate formed at 932°F as the temperature was increased, and reprecipitation of larger nuclei stable at 1250°F, with the reoccurrence of embrittlement. It appears desirable to reconsider this explanation in the light of the two regions of embrittlement proposed by the authors1 for some alloy steels. In addition, it appears desirable to determine any influence of a preconditioning treatment in each temperature range upon subsequent development of low and high temperature embrittlement. It is thus the object of this investigation to study the characteristics of the two modes of embrittlement proposed in a commercial Ni-Cr alloy steel (AISI 3140). Experimental Details Material—The material used in this investigation was commercial AISI 3140 steel bar stock, received as % in. hot-rolled rounds. The steel analysis was as follows (in percentages): C, 0.39; Mn, 0.79; Si, 0.30; S, 0.028; P, 0.015; Ni, 1.26; and Cr, 0.77. Material Processing and Heat Treatment—The bar stock was first ground to 0.430 in. squares and cut into specimens 23/4 in. long. These specimens were austenitized at 1650°F for 1 hr and oil

Jan 1, 1958

By J. E. Dorn, S. K. Mitra

The low -temperature tensile and creep behaviors of single crystals of copper were evaluated and analyzed in such a manner as to provide an estimate of the separate contributions of short-and long-range stress fields to strain-hardening. Furthermore, the average force-displacement diagram for thermally activated intep-section of two dislocations was estublished. This diagram plus a knowledge of the variation of dislocation spacing and the long-range back stresses with strain permits on accurate prediction of creep rates. The calculated activation energy for intersection under conditions of a constant strain rate increases linearly with the absolute tempevatus-e as required by theory. AN understanding of the detailed mechanisms for strain hardening constitutes one of the principal unsolved problems in dislocation theory. Two major models for strain hardening have been advanced in the past. The one that has received greatest attention assumes that strain hardening arises exclusively from long range interaction stresses between moving dislocations and piled-up arrays of blocked dislocations on the slip planes. This type of interaction was first announced by Taylor' who revealed that the back stress fields due to a simple uniform array of positive and negative dislocations entrapped in the deformed crystal would result in parabolic hardening. Shortly thereafter Andrade and Henderson" demonstrated that the strain hardening of fcc single crystals was not parabolic, as previously thought, and finally it was recognized that a typical stress-strain curve consisted of three successive stages of deformation, niz., the easy glide, Stage I, linear hardening, Stage 11, and the parabolic hardening, Stage 111, ranges. The objections to Taylor's somewhat na'ive model, which were presented so forcefully by cottrell; were largely removed by the more realistic details incorporated in Mott's analysis.5 But because Mott's theory for hardening via long range stress fields gave somewhat analogous results to that of Taylor's (inasmuch as it also predicted a parabolic rate of strain hardening whereas the observed rate of strain hardening in Stages I and I1 were linear), it was not widely accepted. Major consideration was therefore given to models, such as those which were advanced by Friedel and seegere that were formulated for the ad hoc purpose of yielding linear rates of strain hardening. The second major thought regarding strain hardening is based on the concept that it arises principally from short-range stress fields due to the interactions between intersecting dislocations. Cottrell and stokes7 showed, several years ago, that the constancy of the flow stress ratio at two temperatures regardless of the strain was inconsistent with the concept that strain hardening arose exclusively from long-range back stresses. The argument that strain hardening was primarily due to local interactions of intersecting dislocations was presented in considerable detail by asinski.' Extending Basinski's method of analysis of the intersection process, Mitra, Os-borne, and dorn recently demonstrated that indeed the strain hardening in aluminum single crystals arises principally from local effects coincident with intersection; however, these conclusions, too, must be modified, as will be shown later in this report. The present investigation, devoted principally to the low-temperature deformation of copper single crystals, was initiated in an attempt to ascertain whether or not the same conclusions arrived at for aluminum also apply to metals, such as copper, which have much wider stacking faults. It was soon observed that the strain hardening in copper could not be attributed exclusively to local effects between intersecting dislocations. Previously no analytical method for arriving at the possible simultaneous contributions of long-range stress fields and localized forces on intersecting dislocations was available; consequently, the separation of these two factors could not be readily accomplished. In the present report a method of estimating the separate contributions of each of these two factors to strain-hardening will be presented. The authors will show that both long-range stress fields of the type contemplated by Seeger and Friedel as well as short-range forces of the type considered by Basinski are responsible for strain hardening in fcc metals at low temperatures. This method of analysis also accounts for, in a satisfactory way, the effect of stress, temperature, and strain on the creep rate under constant stress. Furthermore, in the course of presenting their methods of analysis the authors will also reveal the rather complete agreement of their experimental data with the concepts of the theory for thermally activated intersection of dislocations. INTERSECTION MODEL As shown by seegerl0 the strain rate arising from thermally activated intersection of dislocations is given by

Jan 1, 1962

By Sandip K. Mitra, John E. Dorn

The Basinki-modified Seeger equation for deformation of metals by means of thermally activated intersection of dislocations was used to ascertain the various factors responsible for the strain hardening of poly crystalline aluminum and a series of a solid solutions of magnesium in aluminum. The analyses were based principally on the rate of change of strain rate with stress and the Cottrell-Stokes ratio. From measurements of these quantities on a series of strain-hardened states, the force displacement diagram for intersection, the density of dislocations in the entanglements, and the contributions of the athermal local stress and long-range stress interactions were deduced. Poly crystalline aluminum was observed to have the same force-displacement diagram for intersection as single aluminum crystals, and the corresponding diagram for the magnesium alloys differed in a manner that suggested that small amounts of magnesium may decrease slightly the stacking fault energy of aluminum. Although poly crystalline aluminum had about the same initial density of dislocations as the single crystals, the density of dislocations increased much more rapidly with strain in the polycrystals. This factor and the higher back stresses generated in the poly crystalline aluminum were the major factors responsible for the higher strength of the poly crystalline aluminum, As the magnesium content of the alloys was increased, the initial density of the dislocations also increased. Most of the alloy strengthening arose from this factor; alloying effects due to short-range order strengthening, Suzuki locking, Cottrell pinning, and so forth, were estimated to be quite small. The gveater rate of strain hardening in the alloys was deduced to be due primarily to the greater increase in the density of the dislocations with strain as the magnesium content was increased. It is the purpose of the present investigation to shed additional light on the average plastic behavior of a grain in a polycrystalline aggregate, by analyses, based on dislocation theory, of appropriate experimental test results. These deductions when compared with those from single-crystal data will then serve to illustrate the major items of difference between the plastic behavior of single crystals and the average behavior of a grain in a

Jan 1, 1963

By D. Kramer

HASEN1 has published a phase diagram for the zirconium-nickel system. This phase diagram has been redetermined by Hayes, Roberson, and paasche2 in the range 0 to 50 at. pct Ni. Recently, Smith and Guard3 have published a tentative diagram for the

Jan 1, 1960

By M. E. Nicholson

IN order to understand how alloying elements influence hardenability through their effect on the rate of pearlite nucleation, it is advantageous to use a model to describe the mechanism of pearlite nucleation. The model which currently is most widely accepted has been described, among others, by Mehl et a1.1-3 and by Hultgren.4 Pearlite nucleation involves both the nucleation of ferrite and cementite.4,5 Cementite nucleates first, followed rapidly by the formation of ferrite at the cementite-austenite interface. The conclusion that cementite is the first phase to form during the process of pearlite nucleation is based, in part, on the observation that proeutectoid cementite is continuous with pearlitic cementite and that the orientation relationship between proeutectoid ferrite and austenite is not the same as that between pearlitic: ferrite and austenite.6,7 Recently, Smith" has suggested that the dissimilarity in orientation relations, instead of indicating the pearlite nucleation sequence, may be evidence that pearlite is nucleated in a grain adjacent to the one in which it is growing. Also, Modin9 as shown that ferrite in pearlite may be continuous with proeutectoid ferrite, and he has also shown that proeutectoid cementite is not always continuous with pearlitic cementite. Thus, it appears that the conclusion that cementite always initiates the pearlite nucleation process is open to serious question. The author believes that important evidence on the question of how pearlite is nucleated exists in the rates of pearlite nucleation of different steels. The following is a review and analysis of this evidence. If the nucleation of pearlite is considered as requiring the nucleation of both cementite and ferrite, then the time to nucleate pearlite consists of the time to nucleate the first phase to form, plus the time to nucleate the second phase at the advancing interface of the first. In the absence of a visible proeutectoid constituent, the second phase must be nucleated very soon after the first. If cementite is the first phase to form, the time to nucleate pearlite will be approximately equal to the time to nucleate cementite. Since the nucleation rate of a phase precipitating from solid solution increases with the degree of supersaturation, it would be expected that the rate of pearlite nucleation should increase with increasing carbon content. Digges10 has shown that the reverse is true. He determined the quenching velocity necessary to suppress pearlite formation in plain carbon steels as a function of carbon content. His results showed that pearlite formation could be suppressed with lower quenching velocities as the carbon content of the steel increased, at least up to 1.25 pct C, the highest carbon content he studied. Thus, it would appear that in plain carbon steels, in which pearlite is formed at the nose of the C-curve, the hypothesis that cementite nucleates first does not predict the observed change in nucleation rate. The validity of the current model of pearlite nucleation may be tested also by determining whether or not it predicts the relative influence of alloying elements on the nucleation of ferrite and pearlite. This can be done best by a consideration of the changes in a TTT diagram produced by a change in alloy content. Hultgren4 suggests that the general shape of a TTT diagram, as well as what constituents will form from austenite, can be predicted from the relative nucleation rates of ferrite and cementite. This is illustrated in the schematic diagram for a hypoeutectoid low alloy or plain carbon steel shown in Fig. 1. The C-curves for ferrite nucleation and for cementite nucleation are represented by AA' and CC', respectively, and the start of ferrite formation and pearlite formation are represented by AX and BC respectively. Adopting the current theory, Hultgren suggests that between X and C pearlite forms directly from austenite, since cementite nucleates more rapidly than ferrite in this temperature range. Conversely, at temperatures above Tx, ferrite is the first to nucleate and proeutectoid ferrite is formed. As proeutectoid ferrite grows, austenite becomes enriched in carbon, so that the cementite nucleation rate is increased. As a result, pearlite nucleation above temperature Tx is accelerated, beginning along BX and not along C'X. Temperature T, represents the temperature at which the nucleation rate of ferrite equals that of cementite. By extending this type of reasoning, using the principle that the nucleation rates of ferrite and cementite increase with increasing supersaturation of austenite with respect to these phases, it should be possible to predict the influence of carbon content on the shape of the isothermal transformation diagram. For a slightly higher carbon content than that of Fig. 1, the curve A A' representing the beginning of ferrite formation should be moved to the right, whereas the curve CC' representing the beginning of cementite formation should be moved to the left. For hypoeutectoid plain carbon and low alloy steels, this prediction does not agree with existing data. Instead, as the carbon content is increased, the pearlite curve moves to the right along with the ferrite curve and always appears to join it tangen-tially. This behavior is demonstrated by the TTT-curves of a series of manganese steels" shown in Fig. 2. In this figure, TTT-curves for four alloys containing 0.20, 0.40, 0.60, and 1.20 pct C are superimposed. The curves are identified in the figure legend. The letters F, P, and C are used to indicate the start of ferrite, pearlite, and cementite formation, respectively. In these steels, it appears that the nucleation of ferrite and of pearlite are related processes. As a result of the foregoing evidence, it is proposed that the formation of pearlite be considered as follows: Either ferrite or cementite may nucleate from austenite, then grow until the remaining phase is nucleated at the interface between the growing phase and austenite. (The growth of the first phase to form is assumed to be accompanied by a composition change in the adjoining austenite.) According to this model there are two modes of nucleating pearlite: 1—where cementite initiates the succession

Jan 1, 1955

By A. E. Dwight, A. F. Berndt

Binary and ternary alloys of uranium with transition metals were prepared with U2X stoichiometry. The compounds U2Tc, U2Rh, U2Os, and U2lr were formed by peritectic or peritectoid transformations, and were shown to be isostructural with U2Ru. The lattice constants are presented. Miscibility relationships obtained from the study of ternary alloys are graphically summarized in terms of an area-of-stability plot. The compound U2Re is not isostructural with either U2Ru or U2Mo. A series of compounds with stoichiometry U2X has been prepared in which X is technetium, rhodium, rhenium, osmium, or iridium. The only other U2X compounds, for which X is related to the above transition metals by proximity in the periodic table, are U2Mo and U2Ru. The structure of U2Mo is the tetragonal C11b type (MoSi2 type)1 and U2Ru is monoclinic, with a new structure type.' This investigation was undertaken to determine if any of the above compounds are isostructural with either U2Ru or U2Mo and to find the range of occurrence of these phases. EXPERIMENTAL Alloys were prepared from stoichiometric amounts of electrolytic uranium (99.99 pet pure) and transition metals of 99.5 pet purity (98+ pet pure Tc), by arc melting on a water-cooled copper hearth under an Ar-He atmosphere. Weight losses were negligible. The buttons were homogenized at temperatures between 700o and 800°C (900°C for U2Tc) in evacuated capsules and air-cooled. The X-ray powder specimens were annealed briefly at the temperature of homogenization. Except in the case of the technetium alloy, metallographic examination was used to determine the number of phases present. The radiation hazard involved in handling technetium precluded the use of metallography to examine U2Tc. The temperature and mode of formation of the U2X phases were determined by heating the metallographic specimens to successively higher temperatures, until examination indicated the presence of chilled liquid or a peritectoid transformation. RESULTS The U2X compounds investigated were found to be formed under the following conditions: UzTc unknown U2Ru peritectic 897o ± 3°C U2Rh peritectoid 755o ± 5°C U2Re peritectoid3 below 750°C Uas peritectic4 920°C U2Ir peritectoid 775o ± 5oC Debye-Scherrer patterns for the above U2X phases were made with CuKa radiation (nickel filter). The similarities in the positions and intensities of the strongest lines in the front-reflection region strongly suggested that U2Tc, U2Ru, U2Rh, U2Os, and U21r are isostructural with only minor differences in the unit-cell dimensions. The known lattice constants and intensities of the Debye-Scherrer rings for U2RU2 were used as a guide in order to index the low-angle X-ray reflections of the U2TC, U2Rh, U2Os, and U2Ir powder patterns. Approximate lattice constants for these compounds were thus obtained and were used along with the intensities observed for U2Ru to index the strongest lines in the back-reflection regions. A sin2 2? correction term was included and the lattice constants were refined and standard deviations estimated by least squares. Comparison of observed and calculated values of Q(= 4 sin2?/?2) used in these calculations are given in Table I. In each case when the positions of lines could not be resolved on the films they were not measured. The final lattice constants, with their standard deviations, are given in Table 11, along with the unit-cell volume and X-ray density. The values of the atomic volume5 of the transition ele-

Jan 1, 1965

By F. N. Rhines, A. S. Nemy

The mode of high-temperature tertiary creep of 523-0 aluminum alloy was found to be strongly stress dependent. The occurrence of necking and/or fissures during tertiary creep exhibited a sequence with varying stress, wherein fissures with no necking occur at a minimum stress and necking with no fissures occur at a maximum stress. At an intermediate stress, tertiary creep begins without necking but with fissures in a region just beneath the external surface, followed by necking and the development of fissures along the axis of the specimen. The results are interpreted in terms of grain boundary gliding and the hydrostatic stresses produced by restraints to grain boundary gliding. THERE appear to be two possible reasons for the existence of a period of accelerating elongation prior to rupture during high-temperature creep in metals; namely, 1) a change in the structure of the metal itself, leading to a change in its response to loading, and 2) a reduction in the cross section of the metal resulting in a higher unit loading. Howe,' by annealing and retesting broken low-temperature creep specimens, found that irreparable damage is done once a metal is subjected to creep. Andrade2 first pointed out the association between the reduction in cross section and the increase in creep rate. The present research was designed to investigate both of these factors by retesting specimens machined from material which had been subjected to high-temperature creep testing short of rupture. EXPERIMENTAL METHOD An aluminum alloy, 52s-0, was selected for these studies because it is constitutionally simple, is strong enough to be relatively insensitive to mechanical damage during machining,3 and undergoes accelerating creep in a convenient temperature range. This alloy is hardened by 2.6 wt pct Mg in solid solution and is not subject to overaging effects; it has a very small quantity of an insoluble impurity phase, Mg2Si, finely dispersed throughout its micro-structure. Creep specimens, similar in design to ASTM 0.252-in. tensile specimens, were machined from 3/4-in. round stock and the surfaces were electro-polished. A 24-hr anneal at 500°C was then applied to stabilize the grain size to an average diameier of 0.27 mm. Subsequent heating for as long as 700 hr at the intended test temperatures produced no change in the tensile properties, indicating a well-stabilized state of the material. Corresponding to each of the typical testing conditions listed in Table I, one creep specimen was tested to destruction and this test was employed as a guide in the selection of times for subsequent tests. Duplicate creep tests were then run to various points along the creep curve to produce specimens which were used to determine changes in mechanical properties and microstructures. The latter were examined at the midsections of the specimens. Other specimens were tested to various stages of tertiary creep, after which they were remachined to new cylindrical test specimens, electropolished and re-tested in creep. RESULTS The major findings of this investigation may be illustrated by a comparison of the results of three sets of creep tests. These were run at 400°C at three stress levels, namely 750, 1000, and 1500 psi. In presenting these results in Figs. 1, 5, and 8, the creep curves are given in pairs: That curve of each pair which is drawn through filled circles corresponds to the initial test, and the curve drawn through open circles (and designated by - R) represents the result of retesting the same specimen after machining to a new cylindrical surface. The load was readjusted to the original unit stress at the beginning of each retest.

Jan 1, 1960

By H. I. Aaronson

THE TTT-curve for the beginning of transformation in hypoeutectoid steels containing appreciable amounts of relatively strong carbide-forming alloying elements often exhibits a "bay" at intermediate temperatures. In many of these steels, proeutectoid ferrite is the initial product of the decomposition of austenite not only at temperatures above the bay but also in an appreciable temperature range below the region of the bay. Hultgren has postulated that ferrite formed above the bay, termed "orthoferrite", contains the equilibrium concentration of alloying element at temperatures above the eutectoid range, and the extrapolated metastable equilibrium concentration at lower temperatures. The ferrite formed below the bay, on the other hand, termed "paraferrite", was assumed to inherit completely the bulk alloy content of the austenite without regard for the compositional requirements of equilibrium. As shown schematically in Fig. 1, the two types of ferrite were taken to have different Ae3 temperatures and different C-curves on a TTT-diagram. Their different kinetic behaviors were thus considered responsible for the bay in the TTT-curve for the proeutectoid ferrite reaction in this type of alloy steel.

Jan 1, 1962

By T. Federighi, S. Ceresara, C. Panseri

The results of an exploratory investigation by means of resistivity measurements at -195ºC, on the aging characteristics of a set of Al-Mg alloys with a maximum content of 7 pct Mg, are reported. Whereas for dilute alloys (Mg < 1.5 pct) only a decrease in resistivity is observed at about 100°C (due to the elimination of quenched-in vacancies), for more concentrated alloys such a decrease is preceded by an increase in resistivity in the range between -60ºand +40°C. Following some previous suggestions, this increase is considered as good evidence for clustering of solute atoms @reprecipi-tation process). From the analysis of the results it appears that, although the process is substantially similar to that observed in other Al-rich alloys, it is characterized by a strong interaction between vacancies and zones. THE process of formation of Guinier-Preston zones, i.e., preprecipitation,1&apos;2 which occurs during the aging at about room temperature in many supersaturated aluminum-rich alloys, has been extensively investigated in the past few years by several workers.2,3 owever, a very interesting question arises when the case of Al-Mg alloys is considered: although it is very easy to supersaturate Al-Mg alloys, just in the same way as for many other aluminum alloys showing preprecipitation, only very little experimental evidence was available until a short time ago in the literature supporting the existence of "natural" aging in supersaturated Al-Mg alloys (see, for example, Refs. 4 to 6). On the other hand, as is well known, the X-ray method is not useful in this case because the X-ray scattering factors of magnesium and aluminum atoms are about the same. Recently, however, Cordier and Detert7 have stressed that during the aging at about room temperature of a supersaturated Al-Mg 10 pct alloy it is possible to detect an increase in resistivity; since, as is well known, such an increase is observed also in most alloys showing preprecipitation, the above authors have interpreted their results as evidence for the formation of magnesium-rich clusters (or Guinier-Preston zones) during the aging. In the course of or ientative investigations on preprecipitation in several aluminum-rich alloys, we also could detect a similar phenomenon in more dilute Al-Mg alloys, see Instituto Sperimentale Metalli Leggeri, Annual Report, 1959, and also Ref. 8. Since the details of our observations, although of a preliminary nature, differ from those of Cordier and Detert and allow one to draw a more advanced picture of the preprecipitation process in Al-Mg alloys, we have thought it useful to report our results in this paper and to comment on them briefly.

Jan 1, 1963

By P. K. Foster, C. M. Payne, A. McNabb

Some measurements of the rate of loss of hydrogen from cylinders of iron and steel are analyzed in terrns of a trapping theory. The apeement is encozcraging and gives rise to estimates for the density of traps in the metal. Furthermore, the results appear to be consistent with the assumption that the diffusion constant D for the steady flux of hydrogen through iron lies on the extrapolation of the linear curve (log D us 1/T) obtained at higher temperatures. IT has been shown in a previous paper1 that the literature relating to hydrogen diffusion in steels contains sufficient evidence to invalidate the application of Fick&apos;s laws to hydrogen diffusion in steel at low temperatures. To account for the deviations from simple diffusion behavior a trapping theory was developed, and the fundamental laws modified accordingly. In the present paper, new data on the evolution of hydrogen from long cylinders are presented, and together with some published data are examined in terms of the requirements of the theory.&apos; Properties of solutions of the basic equations derived previously1 and appropriate to the present experimental conditions are outlined in the first section as they determine the form in which the experimental data must be presented for a comparison of theory and experiment. Two new solutions not previously reported have been derived as described in the Appendix. The experiments and treatment of data are then given in Sections 2 and 3 and the results are discussed in Section 4. 1) THEORETICAL CONSIDERATIONS The hydrogen-diffusion theory1 applied in this paper postulated that lattice-dissolved hydrogen at a concentration C diffuses randomly in accordance with Fick&apos;s first law, but that the lattice contains a uniform density N of traps which can capture and delay hydrogen atoms. kC atoms are trapped per second in a region containing unit concentration of vacant traps while p are released per second in a region containing unit concentration of occupied traps. On this basis it was shown (Eq. [30] of Ref. 1) that, when local changes in the lattice-dissolved concentration C are slow enough for equilibrium to be established with the traps, the system is represented in dimensionless form by the equation:

Jan 1, 1965

By Gerhard Bockstiegel

Kuczynski&apos;s formula has been derived for the case of nonspherical particles. TWO formulae of Kuczynski&apos;s type have been derived, one describing the increase in tensile strength, the other describing the progress of shrinkage of a powder compact. It has been strength,shown that the exponents of all three formulae each contain two magnitudes of different physical characters, viz, the geometrical factor a and the kinetic factor ß. The interrelationships between the three exponents are stated. SOME years ago Kuczynski1 experimentally showed that the radius, x, of the area of contact between very small spherical metal particles and a metallic block is related to the time of sintering, t, by the following equation x = constant tk [11 where k has the value 1/5 or 1/7. Assuming that the metal particles were perfect spheres and the metallic block was perfectly flat, he derived the foregoing equation from theoretical considerations of the process of material transport in metals, and he showed that exponent k is different for different mechanisms of transport, e.g., k = 1/2 for viscous flow (according to Frenkel2), k = 1/3 for evaporation and condensation, k = 1/5 for volume diffusion, and k = 1/7 for surface diffusion. From this Kuczynski concluded that the mechanism of transport was either volume diffusion or surface diffusion, depending on whether the value of k, as found in his experiments, was 1/5 or 1/7. Subsequently. Cabrera8 corrected Kuczynski&apos;s calculations with regard to surface diffusion, showing that the theoretical value of exponent k is 1/5 for both volume and surface diffusion. He supposed that the different experimental values of k were due to slight differences in the shape of the metal particles. An exponential relationship similar to the aforementioned was found by Okamura, Masuda, and Kikuta,4 Masuda and Kikuta, and Takasaki8 when studying the rate of shrinkage on powder compacts during sintering. The authors measured the shrinkage by means of the fraction w = Vp — V./Vp — V,,,, where V,, is the volume of the green compact, V, is the volume of the sintered compact, and V,,, is the volume of the compact in its densest state. This fraction, w, they found, is related to the time of sintering, t, by the equation w == constant tm. [21 Further, Bockstiegel, Masing, and Zapf7 observed that the tensile strength, s, of sintering iron powder compacts can also be related to the time of sintering, t, by an equation of the foregoing type, i.e., s = constant tn. [3] For exponent n the values 0.28 (S=2/7) and 0.35 ( 2/5) were obtained, and the authors pointed out that there might exist a simple interrelation between exponent n as found in their experiments and exponent k in Kuczynski&apos;s equation. The authors supposed that 2k = n, since the strength of adhesion between a metal sphere and a block (as in Kuczyn-ski&apos;s experiments) must approximately be proportional to their contact area, p. x2. Theoretical Considerations This paper is an attempt to correlate the fundamental experiments of Kuczynski&apos;s type with the results obtained with powder compacts as represented by Egs. 2 and 3. In particular, the paper is to show how the rate of sintering is influenced by the geometry of the sintering particles and by the type of material transport. As the geometry of particles conglomerating in a powder compact is very complex, some simplifying assumption has to be made, of course, in order to adapt the problem to mathematical treatment. In the following paragraph a suitable simplification is introduced, and Kuczynski&apos;s formula is derived for the case of nonsphcrical particles. Relation Between Area of Contact and Sintering Time—As the face of contact between two particles in a sintering powder compact is not necessarily a circle (as in the case of spheres sintering to a block), Kuczynski&apos;s formula is modified as follows: Let the perimeter of the face of contact be described by means of polar coordinates R, 4, as shown in Fig. la, so the area of contact, f, is determined by f= 1/2 . S112p[R(Æ) ]2 dÆ [4] Then, let the two particles be intersected by a plane perpendicular to area f. The intersection is shown in Fig. lb. According to the nomenclature in this figure, the distance, h, between the surfaces of the two particles is a function of T and Æ: h = h(r,Æ). For the particular case of spherical particles, as in Kuczynski&apos;s theory, this function becomes: h = constant r2. It shall be assumed here that in the close neighborhood of their

Jan 1, 1957

By H. W. Paxton, G. M. Pound

A method is outlined for taking into account variation in chemical potential of both components in evaluating capillary effects at growing interfaces. The results are compared with experiment, and seem to be in reasonably good accord for Widman-statten ferrite growing in austenite. ENERY pointed out that during the steady-state growth of phases with a rather small radius of curvature at their advancing edge capillarity cannot be neglected. By proper application of the Laplace equation a correction must be made to the activity gradients down which diffusion occurs. Subsequent workers have concerned themselves with attempts to evaluate specific cases by the use and modification of the principles laid down by Zener.2-5 To solve the problem in its simplest form it is necessary to assume thermodynamic equilibrium at the interface and to select some criterion which will allocate the available free energy between reversible and irreversible processes. Zener chose to assume that the division should be made such that the new phase grew at the maximum rate. Other workers have used the same2,3 or different assumptions, e.g., maximum rate of free-energy dissipation,4 minimum rate of entropy production.5 Li6 has proposed that the "thermokinetic potential" should be a minimum at steady state. The purpose of this presentation is to note that most prior treatments have considered variations due to capillarity only in the chemical potential of the mobile constituent, and that a more consistent treatment must involve a consideration of the variation of chemical potentials of both solute -and sol- vent in a binary system.* As an example, the way in which this arises for ferrite growing from austenite may be illustrated by reference to Fig. l(a). The line OABC shows a typical variation of carbon activity with composition at one atmosphere pressure (at a transformation temperature below A3). In the tip of a growing ferrite plate with a hemi-cylindricab leading edge of radius ?, the pressure due to capillarity is*

Jan 1, 1963

By Toshimi Yamane

The internal friction of cold-worked titanium iso-thermally annealed at temperature below the recrystallization temperature was measured. The internal friction was calculated from the half width of a resonance curve of the specimen which was vibrated transversally by the electromagnetic method. The experimental results were as follows: 1) The specimens annealed for a long time at temperature below the re crystallization temperature after cold working have the strain-amplitude dependent internal friction. 2) The internal friction increased by the cold working was decreased during the isothermal annealing. The reason of decrease of the internal friction is considered to be caused by the annihi-lation of lattice defects. 3) There is a linear relation between logQt-1/Q0-1 and (1/T)2/3 below the recrys-tallization temperature, where Q0-1 is the internal friction standing 24 hr at the room temperature after cold rolling, Qt-1 is the internal friction annealed at T°K for t min. 4) The hardness of the cold-worked titanium does not change by the annealing at 300°C for a long time but decreases by annealing at 400ºand 460°C. METALS, when cold worked, show sharp changes in physical and mechanical properties&apos; The internal friction of cold-worked metals increases sharply and has a maximum value1,2 connected with working de- grees. The increased internal friction of cold-worked metals is recovered by annealing. This phenomenon is the well known effect called Köster effect. The recovery of the internal friction occurs earlier than the changes in tensile properties, hardness, or X-ray diffraction, and is very sensitive to the structure of a metal. The mechanism of the recovery at a temperature lower than the recrystallization temperature is being considered variously by many investigators: there are such views as the annihilation of dislocations by smith,&apos; the rearrangement of dislocations mentioned by Nowick,4 and interaction of dislocation with point defects.5 Smith and Nowick also considered the interaction but it is so difficult for them to explain the rearrangement mechanism systematically, it being not considered a special model; therefore, we do not explain it quantitatively. Experiments measuring the recovery of the internal friction of cold-worked metals were performed by Gordon and Nowick6 on NaCl, and by Smith on copper. In addition, there are many studies, particularly those of measurements on copper by other investigators. There are comparatively many investigations on aluminum and iron which are the cubic system,&apos;-&apos; but only a few on metals of the hexagonal system.10 In view of this, I investigated cph titanium at room temperature and measured the internal friction after annealing isothermally at temperature lower than the recrystallization temperature. SAMPLES AND EXPERIMENTAL METHOD samples for the experiment were cut from a 6-mm titanium plate. The long direction of samples was

Jan 1, 1963

By Rollin E. Hook, Attwell M. Adair

The yield and fracture behavior of recrystallized chromiztm have been studied in order to gain an understanding of the recrystallization embrittlement-rheotropic recovery phenomenon. The duc tile-brittle tensile transition temperature of recrystallized chromium was found to vary from 225 ° to -80°C as the ratio of specimen diameter/mean planar grain size decreased. The applicability of this observation to other bcc metals is briefly discussed. Brittle fracture in recrystallized chromium was found to be initiated predominately from intercrystalline rupture nuclei. Single crystals exhibit a high degree of ductility at 23 "C. The experimental data indicate that grain boundaries play a significant part in the yield and fracture behavim. Pres training significantly reduces the transition temperature, and high temperature aging does not result in re-embrittle-ment until complete recovery or re crystallization occurs. SEVERAL theories have been used to explain the recrystallization embrittlement-rheotropic recovery phenomenon in chromium. Wain, Henderson, and ohnstone&apos; propose a Cottrell dislocation locking mechanism due to nitrogen, and Weaver and Gross and weaver 3 propose a strain-induced precipitation mechanism involving a chromium nitride precipitate. The researches of many investigators seem to leave little doubt that brittleness in chromium is promoted by interstitial impurities. Smith and seybolt4 have shown that the ductile-brittle transition temperature is lowered as the interstitial content is reduced. weaver3 provides evidence for a 150°C reduction in the tensile transition temperature as the nitrogen content is reduced from 20 to 5 ppm. Maykuth and affee&apos; have suggested that the amount and orientation of grain boundary impurities may be responsible for the brittle nature of recrystallized chromium. This suggestion was based on their findings that wrought iodide chromium possessing a fiberous grain structure is ductile in tension at room temperature while a recrystallized grain structure is completely brittle. Previous investigations have not studied this phenomenon sufficiently to determine its cause. Perhaps this has been largely due to previous experimental findings that brittle fracture observed in chromium has been almost entirely transgranular.&apos; In addition McNeil and imb,&apos; who investigated coarse-grained as-cast chromium, describe the point of initiation of fracture as cleavage, close to the (100) plane, near or at grain bound-daries, or at included particles or voids. However, Hook, Adair, and ipsitt found that fracture in coarse-grained recrystallized chromium is initiated by intergranular rupture and then propagates nearly entirely by cleavage. This result, together with their finding that room temperature ductility in bending is observed for single crystals and coarse-grained polycrystalline specimens for which the number of grains through the specimen diameter is small, suggests that grain boundaries may play an important role in the brittle behavior of chromium. The recrystallization embrittlement problem can be resolved into two questions. These are, whether the controlling mechanism is predominately one of crack initiation or crack propagation, and whether brittle fracture is initiated predominately by slip or twin induced intergranular rupture or by cleavage. The following research was designed to study the role of grain boundaries on the brittle fracture of chromium in an effort to resolve these questions. EXPERIMENTAL PROCEDURES, RESULTS, AND DISCUSSION General Procedure. All tensile specimens (except 0.04 in. diam wires) were prepared from 1/4 in. diam swaged rod fabricated from one ingot. Details of fabrication are given elewhere. The results of impurity analysis for the swaged rod and for the

Jan 1, 1963

By Y. C. Liu, W. R. Hibbard

An analysis of the relationship between the deformation and recrystallization textures in face-centered-cubic metals is presented. The analysis assumes that orientations of the secondary as well as the primary textures are related to the deformation texture. The effect of alloying elements on the recrystallization texture of copper-base alloys is also discussed. ROTATIONAL relationships based on prior orientations have been used to derive both the primary and secondary recrystallization textures."" This similarity suggests that, if the secondary texture arises from grains formed during primary recrystallization, as proposed by Dunn: and if primary recrystallization derives its lineage from the deformation structure, then the orientations obtained in secondary recrystallization .as well as those obtained in primary recrystallization should be related to the deformation texture. The following discussions are

Jan 1, 1956

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.&apos; 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 Carl Wagner

This paper contains solutions of the differential equation of diffusion in binary alloys if the diffusion coefficient is an exponential function of the concentration of one of the components. THE general differential equation for one-dimensional diffusion in a binary system can be written as: where c is the concentration of one of the two components in any suitable units; x, the distance from a reference plane; t, time; and D, the diffusion coefficient. Hartley and Crank&apos; have pointed out that eq 1 with conventional length units for measuring the distance x holds only if the alloy can be regarded as a rigid framework. In general, this is not the case, especially if the lattice parameter varies appreciably with composition. If a modified coordinate system is used instead of an orthodox system based on the centimeter a:: length unit, eq 52 is obtained, which has the same general form as eq 1 and is generally valid. The necessary transformations are presented in the appendix. If&apos; D is independent of concentration, analytical solutions of eq 1 are known for numerous boundary conditions. If D depends on concentration, solutions based on known analytical functions are not available. Among others, Boltzmann2 and Matano3 have shown that the concentration c depends only on (x/t1/2) in the case of diffusion between two semi- infinite spaces with uniform initial concentrations: c = c, for x < 0, t = 0, i.e., x/tl/2 = — x [21] c = c2 for x > 0, t = 0, i.e., x/tl/2 = + a Moreover, Boltzmann and Matano have shown how D may be calculated as a function of concentration over the whole range of composition from c -c, to c = c2 if c as a function of (x/t1/2) for the initial conditions stated in eq 2 has been determined experimentally. Thus, for instance, in principle, the diffusion coefficient in silver-gold alloys may be calculated as a function of concentration for the whole range of composition from only one diffusion experiment with a couple of pure silver and pure gold welded together. If the diffusion coefficient D as a function of concentration c is known, a solution of eq 1 for boundary conditions as stated in eq 2 with arbitrarily chosen values of c, and C2 may be wanted. For instance, if the diffusion coefficient in an alloy A-B as a function of concentration has been derived from an experiment with a diffusion couple involving 0 and 30 pct B as initial. concentrations, the calculation of the concentration distribution in a diffusion couple involving other initial concentrations, e.g., 5 and 20 pct B, may be desired. This problem may be solved by numerical or graphical integration of eq l. The solution of an ordinary differential equation of second order, which results from using (x/t1/2) as an independent variable, can be computed quite rapidly if two conditions for the same value of the independent variable are given. In eq 2, however, two conditions are given for two

Jan 1, 1953