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By Walter R. Hibbard

BACKOFEN' reported recently that "the deformation texture of cold-drawn OFHC copper wire, after a reduction in area of 97.3 pct, may still be described as a composite of [lll.] and [loo] directions aligned parallel to the wire axis." In the introduction, he indicated that this was in contrast to the work of Hibbard,' who reported a single [111] texture after a reduction of 96.4 pct. Unfortunately Backofen stated that this was a reduction in area when actually it was a reduction in diameter, as is clearly stated in the reference. Moreover, the results of Backofen are in complete agreement with the results of Hibbard. Backofen's 97.3 pct reduction in area is an 83.3 pct reduction in diameter, after which he foundadouble [ll11 and[l001texture with the former predominating. Similarly, Hibbard; after an 86 pct reduction in diameter found a double [Ill] and [I001 texture with the former predom- inating. Hibbard, however, when he drew the wire further to 96.4 pct reduction in diameter, found primarily a single [Ill1 texture as illustrated by Fig. 2 of ref. 3. Here also, Hibbard- reported evidences of the [loo] recrystallization texture found by Backofen. It might also be pointed out that Backofen not only drew his wire 97.3 pct reduction in area but also etched them over 99 pct reduction in area from 0.125 to 0.01 in. diam. Hibbard's wires were drawn directly to size. In summary, the deformation texture of cold-drawn copper wire still may be described as primarily a single Clll] texture after a sufficient amount of drawing, such as 96.4 pct reduction in diameter." a

Jan 1, 1952

By I. Zaplatynskyj, G. C. Kuczynski

SINCE the excellent studies of metal powder compaction executed by Kamm, Steinberg, and Wulff, no work on the subject has appeared in the technical literature. Kamm et al. were the first to investigate quantitatively the distribution of density in a powder compact, as a function of pressure, height and diameter of the die, powder particle size, etc. For this purpose they devised a very ingenious method. They inserted a thin lead grid into a die and then filled the die with powder. During cold pressing, the lead grid -moved downward. Due to its deformability it followed closely the downward descent of the adjacent powder. The die was then radiographed and, from the deformations of the grid openings measured on the radiographs, the density in the vicinity of each opening was evaluated. Their findings led them to the conclusion that the friction on the side walls of the die is a major controlling factor of the density distribution inside the cold pressed powder compacts. However, it is difficult to conduct tests similar to those of Kamm, Steinberg, and Wulff in a processing plant laboratory, which usually lacks the necessary expensive radiographic equipment. The purpose of this note is to describe a method which makes it possible to determine the density distribution in green powder compacts with the same accuracy as the lead-grid method but which is far simpler and faster and requires only standard laboratory equipment. Instead of using a lead grid, the hardness at selected points of the sectioned compact is determined. If the relationship between hardness and density is known the density distribution is readily obtained. This relationship is easily found from measuring hardness and densities of thin compacts. In such compacts the density, for all practical purposes, is constant throughout. The method was tested on a Plast nickel powder, grade FlA-A20, kindly supplied by Plast Metals Co. Thin compacts (height to diameter ratio 0.2) were pressed in a single action cylindrica1 die at various pressures. The density of the compacts was determined by weighing and by measuring the height and diameter with a micrometer. Subsequently the Rh hardness was determined. Up to ten readings were taken on each specimen. The difference in hardness readings on each compact was never greater than three corresponding to about 0.1 g per cu cm uncertainty in density. By varying the compaction pressure of the samples, a whole scale of densities was obtained allowing construction of a set of density-hardness calibration curves. To test the method several compacts of different height were pressed under varying pressures. Die walls were always well lubricated. After pressing, the compacts were mounted in bakelite and halved by grinding, and hardness readings taken along the diameters of the specimens. The distance between adjacent indentations was about 2.5 mm. After hardness readings were translated into densities, contour maps of densities of the compacts were prepared. One of them is reproduced in Fig. 1. The areas encompassed by the curves are labeled with numbers representing the density in g per cu cm of those regions. In Fig. 2 the same results are re-plotted to emphasize the radial density changes at various depths. The results thus obtained confirm the findings of Kamm, Steinberg, and Wulff kentioned previously. They are recapitulated here briefly. 1—The densest part of a compact pressed from one side is at the outer circumference at the top and the least dense part at the bottom, at the outer circumference. Figs. 1 and 2 show this clearly. 2—The density near the cylindrical surfaces of the compact decreases uniformly with height from top to bottom. 3—The density variation increases with the height to diameter ratio. References R. Kamm, M. A. Steinberg, and J. Wulff: Trans. AIME (1941) 171,'R. p. 439 ;MetaLs Technology (February 1941). R.p. Kamm, M. A. Steinberg, and J. Wulff: Trans. AlME (1949) 180, 2R.P. 694; MetalS Technology (December 1948).

Jan 1, 1957

By R. F. Campell, W. L. Jensen

IT is not uncommon for martensitic high carbon steels having a coarse austenite grain size to exhibit microcracks when polished and etched and examined with a microscope, as described by Davenport, Roff, and Bain.' Whether such cracks exist before etching or are the result of acid attack during etching has been debated from time to time. Fig. 1 illustrates the effect of electrolytic polishing, mechanical polishing and etching subsequent to each polish on microcracks produced by oil quenching from 1800°F a steel containing 1.14 pct C, 0.23 pct Mn, 0.33 pct Si, and 0.45 pct Mo. The austenite grain size was 3-4 on the ASTM scale. Grinding on lead laps followed by either electrolytic polishing with acetic anhydride-perchloric acid solution' or mechanical polishing with Linde "B" alumina on "microcloth" (sometimes referred to as Gamal cloth) revealed microcracks without conventional etching, as shown in Fig. la and b, respectively. These same fields, after subsequent etching with saturated picral, are shown in Fig. lc and d, and the cracks are seen to be typical microcracks; moreover, the cracks appear to be broader and longer than before etching. Although the microcracks were revealed by electrolytic polishing alone, the possibility of acid attack was present; however, the mechanical polish was accomplished without any intermediate etching to remove disturbed metal, hence this is regarded as definite evidence that microcracks are present before etching.

Jan 1, 1954

By J. L. Lummus, Frank O. Jones

A field procedure for determining graphite in drilling mud is presented which is sensitive to 0.25 lbs/bbl and accurate to 20 per cent. The method, utilizing oil flotation principles, is suitable for use in all oil-free water base muds except those containing ligno-sulfonates, lignites, or surface active agents. INTRODUCTION Graphite was proposed as a drilling lubricant as early as 1940, but has not been used extensively until recently.' Graphite has been substituted for oil in certain instances to avoid oil contamination of core samples since it has been found that graphite does not interfere with routine core analysis. A major difficulty in using graphite is the lack of a satisfactory field test for determining the concentration of graphite in mud. DISCUSSION OF METHOD Several possible methods of analysis were investigated, including chemical separation, density fractionation, radioactive tracers, and oil flotation.', ' The investigation indicated that a satisfactory method for field use could be devised using an oil flotation method. It was found that toluene shaken with a highly diluted mud sample would recover sufficient graphite to be apparent in the oil phase. Refinement and standardization of technique made it possible to detect as little as 0.25 lb/bbl graphite and to estimate graphite content to within 20 per cent by using a visual comparison method. The test is limited to oil-free water base muds. Quebracho, phosphates, or barytes in the mud do not interfere with the test but surface active agents, lignosulfonates' and lignites evidently render !he graphite water-wet so that none may be recovered by oil-flotation. PROCEDURE Instructions for determining graphite in mud: 1. Collect representative one gallon sample.- from mud stream. Transfer immediately 350 ml portions of this Sample into four mixing cans labeled A, B, C, and D. Measure out graphite (same as is used to treat mud) for addition to cans as indicated below, using either a specially designed scoop or a balance. Can: A B C D Grams Graphite to Add: none 2 4 6 Stir samples B, C, and D for 15 minutes with propeller type mixer. 2. Clean and rinse well with water four 250 ml volumetric flasks labeled I, 11, 111, and IV. Using a 5 ml hypodermic syringe, transfer the indicated volume of samples from cans A, B, C, and D into designated flasks as follows: From Can: A B C D To Flask: I II III IV Add This Volume of Mud: 4 ml 2 ml 2 ml 2 ml 3. Measure 100 ml fresh or distilled water to each flask and swirl gently to disperse mud. Add exactly 5 ml toluene to each flask. Stopper and shake each

Jan 1, 1953

By S. L. Couling, G. W. Pearsall

MOTT and Hainesl have summarized the available techniques for the examination of aluminum and some anisotropic metals under polarized light. Many of these techniques are rather complicated and cumbersome. This note presents a simplified procedure for using polarized light to obtain information about the crystallographic orientation of any particular grain in a magnesium alloy. Since other hexagonal metals are more anisotropic than magnesium, similar methods might well be applied to them. Ernst and Laves2 produced a double-refracting layer on magnesium alloy specimens by SuCCeSSiVe etches in solutions of perchloric acid in alcohol, magnesium perchlorate in perchloric acid and alcohol, and calcium and magnesium carbonates in water. They examined their specimens under polarized light and were able to determine the direction of the hexagonal axis in any particular grain from a measurement of the extinction behavior of that grain. The disadvantages of their technique were the complexity of the etching procedure and the explosive hazard of the perchloric acid-alcohol solutions. Results equivalent to those of Ernst and Laves were obtained in this investigation after etching specimens for 6 to 8 sec in an acetic picral solution containing 100 parts 6 pct picral, 10 parts distilled water and. 5 parts acetic acid. A. similar etch has been used by George3 in earlier metallographic

Jan 1, 1958

By F. W. Jessen, James N. Howell

INTRODUCTION The determination of cloud points has to date been limited to rather transparent oils, visual observation of the formation of a solid phase being the criterion for the standard ASTM D 97-47 method. The need for a quiclc and simple method for determining cloud points under dynamic conditions for opaque crude oils became necessary in a study of fundamental aspects of paraffin deposition from crude oils. PREVIOUS WORK The determination of cloud points in opaque oils by viscosity temperature curves is fairly new, Young' described a method employing the capillary tube principle. No information exists relative to the determination of cloud points of crude or refined oils under dynamic conditions. Shock' noticed that deposition of paraffin from crude oils took place at temperatures at or below the temperature at which a sharp inflection point occurred in the viscosity-temperature curve. This observation indicates a possible correlation between this temperature and the cloud point of the crude oil. Reistle and Vietti1 have reported that when crude oils containing small amounts of asphaltic materials were heated to temperatures sufficiently high to solubilize these materials and immediately cooled the pour point of the crude oil was lowered as much as 70°F. Sachanen\ asribes this effect to the action of colloidal asphaltenes in preventing the formation of the crystalline structure necessary to maintain the oil in a rigid state. At high temperatures, asphaltenes are peptized, and the paraffin crystals formed at these temperatures adsorb the colloidal asphaltenes on their surface thereby hindering further growth of the crystals. Reistle" found, however, that such heating and cooling of crude oils had no effect upon the cloud points. This latter work dealt with a crude oil of fixed composition, and the question immediately arises as to the effect of varying the concentration of asphaltic materials on the cloud point. APPARATUS AND PROCEDURE All viscosity measurements were made with a Bendix Ultra-Viscoson. The Bendix Ultra-Viscoson, which consists of a vibrating probe and an electronic computer. measures viscosity by exciting a thin alloy steel blade on the end of a probe by short electrical pulses in damped oscillation at 28 kilocycles. The blade vibrates longitudinally with an amplilude of less than 55 micron or 20 millionths of an inch. Energy to protlucc this excitation is generated in he computer and transferred to the probe through the connecting cable. The oscillating blade is magnetostric-tive, i.e., it is capable of transforming electrical energy to mechanical energy in the ultrasonic range. Ultrasonic waves are produced in the material surrounding the blade by the oscillating motion of the blade causing layers of the material to slip back and forth over one another at a known frequency. The electronic computer calculates the energy required to produce the sliding motion which is in turn proportional to the viscosity of the material. Actual values of viscosity times density (centi-poise X grams/cc) are indicated on the computer and a continuous D-C signal is provided which is fed into a type 153 Electronic Recorder (manufactured by Brown Instruments Div. of Minneapolis-Honeywell Regulator Co.) The liquid sample container was fabricated from a Lucite cylinder and jacketed by a Luicite water bath. Early experiments using glass and steel sample containers were not satisfactory. since the Ultra-Viscoson was apparently affected by the alterzltion of the magnetic fields surrounding the probe by stresses set LIP in the glass and steel as it cooled. The procedure for determining viscosity-temperature curves was relatively simple. The temperature ot the sample was raised sufficiently high to solubilize all paraffin and asphalts present. After heating, the oil sample was immediately transferred

Jan 1, 1957

By M. R. Tek

General equations relating the pressure drop necessary to sustain the flow of a fluid through a porous matrix at a given rate have been developed. The results indicate that at high values of flow rate the pressure-flow behavior may not necessarily satisfy the usual Darcy equation. The mathematical analysis, carried through the micro-pore geometry and extended through the macro-reservoir scale, indicate that Darcy's law, of limited applicability to certain ranges of Reynolds numbers, can be generalized through the inclusion of some additional parameters. The "generalized Darcy equation" has also been formulated in dimen-sionless form permitting the evaluation of its predictive accuracy with regard to literature data. A comparison between predicted and experimental values indicates that the generalized Darcy equation predicts the pressure drops with good agreement over all possible ranges of Reynolds numbers. INTRODUCTION The limits and the nature of validity of Darcy's law' has been a subject of every-day interest to the industry for many years. It is well known that as the Reynolds number, characteristic of the fluid flow through porous media, becomes large, Darcy's law gradually loses its predictive accuracy and ultimately becomes completely void. For the last 20 years much has been said and written on this subject. Unfortunately little has been accomplished to bring about a satisfactory agreement, at least on the nature of the threshold of validity of Darcy.'s law. Fluid dynamists, geo-physicists, and engineers all had their individual views, explanations, interpretations and concepts on the subject. To some, a mechanistic analogy with pipe-flow proved a satisfactory explanation.' To others,' turbulence, in its random character, was incompatible with the geometric structure of consolidated porous systems. To some,4 turbulence merely represented a factor influencing the permeability measurements and again to others5,6,7 em-pirical or semi-empirical correlations proved satisfactory from an engineering viewpoint. Deviations from Darcy's law at high flow rates have been studied by systematic experiments by Fancher, Lewis, and Barnes.' In an article on the flow of gases through porous metals, Green and Duwezs conclude that the onset of turbulence within the pores appears unsatisfactory to explain deviations from Darcy's law. This view is held by many others. While the subject remained controversial for many years, the development of vast natural gas reserves throughout recent years further justified considerable interest on this problem from the standpoint of gas reservoir behavior. As large amounts of field data became available from the operation of many gas fields, it became evident that the steady-state behavior of gas wells was not, in general, in agreement or compatible with Darcy's law. This suggested a careful reconsideration of all mechanisms which may account for pressure drops in addition to viscous shear. In a series of articles9,10 . Hou-peurt indicated that deviations from Darcy's law may be explained on the basis of kinetic energy variations and jetting effects without resorting to assumptions on turbulent flow conditions. Another article by Schneebeli11 indicates that special experiments by Lindquist clearly demonstrated that the onset of turbulence does not necessarily coincide with conditions of deviation from Darcy's law. This view is also held by M. King Hubbert.12 Starting with the basic pressure-flow relations suggested by Houpeurt, the derivation, development and extension of analytical expressions to -supplement and generalize Darcy's law has been the objective of this work. MATHEMATICAL ANALYSIS Derivation of Dimensionless Pressure-drop, Flow-rate Relations In considering the flow of a fluid through a porous matrix geometrically represented by a succession of capillary passages in the shape of truncated cones,810 an approximate expression may be derived relating viscous and inertial, i.e., total pressure drop to the physical properties of the fluid, geometric properties of the rock matrix and the rate of flow: ?P/?r = µ/k V [ 1 + c(m4 - 1) p V/16n" mµ w] ..........(1) Let us formally set: c (m4 - 1) / 16n" m = a d ......(2) Such a representation is equivalent to assert that the term [c(m4 — 1)/ 16n"m], variable with various porous media and probably highly variable within a given porous medium, may be macroscopically defined as equal to a lithology factor times the aver-age grain diameter d. In view of the usual grain and pore size distribu-

Jan 1, 1958

By Charles Wert

THE diffusion and precipitation of carbon and nitrogen in a iron have previously been investigated using the internal friction as a measuring tool.' Most of this work has been done on rather pure iron; no effect was observed which would indicate that either of these phenomena is affected by the rather small amounts of impurity found in these samples of iron. Fastz observed, however, that both the diffusion rate and the aging properties of nitrogen in iron were sensibly changed by the addition of Vz pet Mn. The diffusion rate at a given temperature is reduced and the nucleation of nitrides is apparently changed somewhat. He observed no such changes for carbon in this alloy. Later Dijkstra and Sladek" extended these observations on nitrogen to other alloys of iron. They found that metals other than manganese also influence the behavior of nitrogen in iron; chromium, molybdenum and especially vanadium affect the diffusion and precipitation of nitrogen even more than manganese does. Their results have been verified in all essential details by this author, who finds in addition that small additions of nickel have about the same effect on the diffusion of nitrogen as the same amount of manganese. The present work was undertaken to study the effect on carbon in iron of these alloying elements. The alloys used had two sources. The material used as a "standard" (designated Fe in this paper) in the measurements was some iron supplied by J. K. Stanley, of Westinghouse Electric Corp., who reported 0.01 pct 0, as the only major impurity. He also made up an alloy of 0.26 pct Ni and one of 0.9 pct Mo using this same iron as a base. They were supplied by him in 2 lb billets, which were sawed into rods and cold formed into 0.030 in. wires for measurement. The alloys of chromium, manganese, and vanadium were prepared by the metallurgy section of the Institute for the Study of Metals, University of Chicago, by adding these metals in turn to vacuum melts of National Research Corp. iron. The small castings prepared in this way were also cold formed into 0.030 in. wires. After these wires had been prepared they were decarburized for 30 min at 730°C in wet Hz. After this treatment, no trace of carbon (as measured by internal friction) could be found. All specimens were then carburized for about 15 min at 710°C and water quenched. By this treatment the internal friction at 40°C was raised to a Q-' ~ 0.015. The diffusion of carbon in these alloys was studied by observing the shape and position of the internal friction peak at 0.9 cycles per sec. These measurements were made using a torsional pendulum in a manner described earlier.' The data are plotted in Fig. 1. It is seen that there is no apparent difference in internal friction between the various alloys. This is in marked distinction to the broadening and shift-

Jan 1, 1953

By L. D. Hall, S. J. Rothman

DIFFUSION coefficients of RaD (PD) and RaE (Bi) in a Bi-0.255 atomic pct Pb alloy have been measured by the methods outlined in a previous paper.' The following changes were made in the experimental procedures: the bath was made up of about 400 to 500 g Bi; and no correction was made for the volume change of bismuth on melting. The data are presented in Table I and Fig. 1. A least-squares analysis of the data yielded D = (0.120 t 0.09) exp ( -9680 + 1070/RT) D- (0.0465 0.001) exp (-8100 + 466/RT). Statistical analysis of the data indicated that the activation energies are significantly different at the 50 pct level, but not at the 75 pct level, while the D values are significantly different at the 97.5 pct level, but not at the 99 pct level. The differences are thus not as clear-cut as they were for lead. However, bismuth diffuses faster than lead in high bismuth alloys as well as in lead. The high activation energies, more than twice the value calculated from viscosities, are in good agreement with the results of Grace and Derge.' No data were obtained at higher temperatures because of gas bubble formation in the capillary. Acknowledgments This work was supported by the Office of Ordinance Research under contract DA-04-200-ORD-178. The authors thank 0. P. Vieria and M. Volpe for help in the experimental work.

Jan 1, 1957

By P. E. Busby, C. Wells

FURTHER study of data used in determinations of 1—rates of diffusion of boron in austenite and 2—solubilities of boron in the a and phases of iron and steel' has provided an equation for the diffusion of boron in a iron. In brief, the previously published data were accumulated from the results of deboron-izing (and decarburizing) experiments carried out in the range of 700° to 1300°C. Diffusion coefficients (D?) for boron in austenite were calculated using the Grube solution of Fick's law. However, only solubility values were estimated from the discontinuous concentration-penetration curves, Fig. 1, which are characteristic of diffusion in two phases. Dr. Carl Wagner' has recently provided a solution for calculating D values from penetration curves of this type as follows: Cl1.1 —C8/C8- C11.1 = vp ? e ? erf (?) and D = ?/4?2 t where C11,12, C8, C11, and E have the values shown in Fig. 1. D is the diffusion coefficient, sq cm per sec; t is time of deboronizing anneal, see; and ? is a di-mensionless parameter. For a given diffusion experiment, the value of ? can be readily obtained by graphical solution from a plot of y vs the right-hand part of Eq. 1. D may then be evaluated from Eq. 2. The avplication of this solution to previously re-ported results, of which excerpts are given in Table I, permits the calculation of diffusion coefficients for boron in a iron. On the basis of these meager data, it is tentatively concluded that the diffusion of boron in a may be represented by the equation Da = 1011 e-92,900/RT where R is the gas constant, cal X 0C-1 X mol-1; and T is the absolute temperature, OK. Although the frequency factor, 106 sq cm per sec, is admittedly several orders of magnitude higher than expected, the value of Q, 62,000 cal per mol, appears reasonable and is, in fact, very similar to that for the self-diffusion of iron. It is pertinent to mention at this point that the value of Q obtained for the diffusion of boron in austenite by means of the Wagner solution is 19,000 cal per mol and is in excellent agreement with the value previously reported1 in the equation DT = 2xl0-3 e-21,000/RT [4] which was determined by the application of the Grube solution to other data. The fact that determined constants A and Q in the equation D? = A e-Q/RT were practically the same, independent of whether the Wagner or Grube solutions were used in determinations of D values, strengthened the authors' belief that the computed values of D (Table I) using the Wagner solution are reliable. The relative values in Eqs. 3 and 4 for the diffusion of boron in the a and ? phases, respectively, suggest that boron forms a substitutional solid solution in a iron and an interstitial solid solution in ? iron. The same tentative conclusion has been reached by McBride et al.3 on the basis of relative solubilities, atom diameter, and the size of the interstitial hole in a and ? iron. In connection with the data for test 14 listed in Table I, it is of interest to calculate the solubility of boron in a iron using the D value given by Eq. 3. As might be anticipated from the small movement of the interface in test 14, proper substitutions in Eqs. 2 and 1 give a low value, approximately 0.0004 pct B, at 850°C. Apparently at 835°C (test 13) it is possible to obtain 0.0018 pct B, and at 850°C only 0.0004 pct B into solution in the a phase before a second phase appears. These observations are consistent with the Fe-B constitution diagram proposed by McBride, Spretnak, and Speiser.3 References P. E. Busby, M. E. Warga, and C. Wells: Diffusion and Solubility of Boron in Iron and Steel. Trans. AIME (1953) 197, p. 1463; Journal of Metals (November 1953). 'W. Jost: Diffusion in Solids, Liquids, Gases. (1952) pp. 69-71. New York. Academic Press Inc. "C. C. McBride, J. W. Spretnak, and R. Speiser: A Study of the Fe-Fe2B System. Trans. ASM (1954) 46, p. 499.

Jan 1, 1955

By H. W. Mead, C. E. Birchenall

SELF-DIFFUSION of cobalt has been investigated by Ruder and Birchenall,1, 2 Nix and Jaumot,3 and Gruzin.4 The results for a given tem- perature differ by a factor of about six in the extreme cases with no really close agreement between any two sets of data. The first two groups of investigators employed the decrease of surface activity method. Since Ruder and Birchenall have shown that the values obtained from this method are sensitive to the surface preparation, it seemed desirable to perform a few check experiments by a method not open to this objection.

Jan 1, 1956

By C. E. Birchenall, W. Batz, H. W. Mean

AT temperatures between 1095' and 1347ºC, 13 runs have been made on the diffusion of silicon in iron. In two of the runs the couple compositions were entirely within the loop of the Fe-Si system; the base alloys contained 0.0 and 1.0 wt pct Si. The other runs in which the couples consisted of a 2.3 wt pct Si alloy welded to a 3.7 pct Si alloy were a phase throughout. The alloys were made by melting electrolytic iron and commercially pure silicon. Trace impurities were not determined. The butt welded couples were diffused in an inert atmosphere of argon or hydrogen. After cooling, cuts of two mils or greater thickness were machined parallel to the weld interface. The chips were analyzed for silicon. When the concentration and distance data were examined on the conventional probability plot,' no marked variation of the diffusion coefficient with concentration was indicated over the narrow composition ranges employed. Therefore, a single diffusion coefficient is recorded for each run in Table I. The temperatures and atmospheres of the diffusion anneal are listed along with the compositions of the base alloys. For a iron the silicon diffusion coefficient is given by the equation: D = 0.44 e-48,000/RT where R is the gas Constant and T, the absolute temperature. However, since the scatter in the data is fairly large, the activation energy may be in error by as much as 6000 cal per g-atom. The two ? iron points do not permit estimation of the activation energy with any reasonable certainty. They do indicate that the coefficients reported by Smithells2 and Jost,3 based on the work of Fry,4 are much too high. Although very dilute solutions in iron of manganese,5 nickel,8 cobalt,7 and molybdenum8 give dif- fusion coefficients quite close to those obtained for self-diffusion in iron, the silicon values are considerably higher, though of the same order of magnitude. This seems to be consistent with the fact that the silicon atom is the only one of those listed here which is appreciably smaller than iron. The authors are grateful to the Office of Naval Research for their support of this work under Contract N6ori-47, Task order IV, Project NR 031-184, to J. K. Stanley and the Westinghouse Research Laboratories for the silicon alloys used, to several steel companies for the silicon analyses, and to C. Wells, of the Metals Research Laboratory, Carnegie Institute of Technology, for numerous suggestions during the course of the work. References 'C. Wells: Atom Movements (1951) Chapter 2. A.S.M. 2C. J. Smithells: Metals Reference Book (1949) p. 405. Interscience. Pub. Co. 3W. Jost: Diffusion (1952) p. 223. Academic Press. 4 A. Fry: Stahl und Eisen (1923) 43, p. 1039. T. Wells and R. F. Mehl: Trans. AIME (1941) 145, p. 315. "C. Wells and R. F. Mehl: Trans. AIME (1941) 145, p. 329. 7M. F. Hawkes and R. F. Mehl: Trans. AIME (1947) 172, p. 467; Metals Technology (August 1947). .J. L. Ham: Trans. A.S.M. (1945) 35, p. 331.

Jan 1, 1953

By L. D. Jaffe, H. C. Mann, E. L. Reed

It has been generally believed that fracture originates at a point and, if the stress is suficient, propagates across the material from this point. Evidence to the contrary is given in Fig 1. This micrograph shows an area close to the fracture of a steel containing The material had been quenched from 1675°F and tempered at 1150°F as a round about 10 in, in diam, and had a static tensile strength of 132,000 psi and a static yield strength of 105,000 psi. The steel was broken in 3000 cycles of reversed bending at a nominal max. fiber stress of 110,000 psi at a speed of 10,000 rpm. It was in the form of a standard R.R. Moore specimen with 45" V-notch, 0.015 in. radius and 0.220 in. diam at base of notch. The fractured edge in Fig 1 is part of the central portion of the specimen which broke during the final sudden fracture. Attention is directed to the short cracks which appear as dark lines within the specimen. Similar cracks were found in another specimen of the material, broken in 1,798,000 cycles at a nominal stress of 40,000 psi. The cracks were found in several areas close to the path of the final sudden fracture. This final fracture appeared microscopically to be wholly brittle and transcrystalline. Closer to the surface of the specimens, near the path of progressive fracture, which presumably advanced gradually during many cycles, there was microscopic evidence of some local deformation, but no microcracks. Neither were microcracks observed in areas distant from the main fracture path. The following explanation is offered: In the sudden fracture of the specimen, a crack propagates along a crystallo-graphic plane, with little or no plastic deformation of the adjacent material, until it reaches a grain boundary or a particle of carbide or inclusion which stops its advance. (The particle or boundary may be outside the plane of polish and not visible in the micrograph.) A stress concentration occurs about the end of the stopped crack. One or more new cracks are likely to start in the zone of this stress concentration. They may lie in the same grain as the first crack or in an adjacent grain. New cracks may occasionally start in a nearby but not adjacent grain whose orientation with respect to the stress leads to more ready fracture than does that of the grain between. Once started, these cracks propagate along crystallographic planes in their grains and the process repeats. This leads to discontinuous, branching chains of microcracks. As the process continues, microcracks probably tend to link up by fracture of intermediate material under the influence of increasing stress concentration. Occasionally, too, there may be a series of nearby grains of similar orientation so that there is a certain continuity of fracture across them. In either case the effective size of a crack is increased, resulting in greater stress concentration at its ends and a greater likelihood of further increase of size of the continuously-fractured region. When one continuous crack crosses the entire specimen, macroscopic fracture has occurred. The fractured edge of the specimen in Fig 1 represents a series of microcracks which became continuous across the entire specimen. The short, dark-appearing cracks in the figure did not become continuous over a large area. The row of microscopic stress concentrations at their ends may link up with those of the "main crack" outside the plane of polish. The above explanation does not imply that microcracks develop at the same rate in all portions of the specimen. They will develop most rapidly where the macroscopic tensile stress and macroscopic stress concentration are greatest. Viewed on a scale large compared to the grains, the fracture would appear to progress continuously across the specimen. Although Fig 1 shows a specimen broken in a fatigue test, it is believed that the microcracks discussed do not depend on the repetitive nature of the stressing used, since they are in the region where "sudden" fracture occurred, presumably in a single stress cycle. The whole process of microcrack propagation outlined above is thought to have occurred during this single cycle. It is believed that discontinuous crack propagation may be universal in brittle transgranular fracture of crystalline solids. Further experiments are under way.

Jan 1, 1950

By P. A. Beck

ACCORDING to the traditional definition,1 re-x crystallization is a process taking place upon annealing of cold worked metals, characterized by the appearance of new strain-free grains, growing at the expense of the cold worked grains until ultimately the new crystals completely replace the cold worked structure. In metals like brass this process was observed long ago to take place simultaneously with the return of the mechanical properties to those characteristic of well annealed material. The above definition implicitly assumes that the matrix in which the new grains are growing is essentially still in the cold worked condition at the time it is absorbed by the new grains, i.e., that the energy stored in the metal during cold working is not greatly decreased by recovery, prior to recrystallization. Accordingly, the bulk of this energy is assumed to serve as the driving force for the process of recrystallization. Recently, a great deal of evidence accumulated, indicating that the traditional concept may be considerably in error. Suzuki' found that by far the largest portion of the stored energy of cold work in compressed polycrystalline copper is released in the early stages of annealing, well in advance of recrystallization. Thus, the new recrystallized grains are undoubtedly growing in a matrix which is, at least energetically, no longer in the cold worked condition, but has nearly returned to the annealed state. It is true that in Suzuki's experiments the major hardness changes due to annealing were observed to take place concurrently with the formation and growth of the new grains, but this process apparently involved the release of only a minor residual fraction of the stored energy of cold work. Confirming in this respect the views of Wood," several recent investigations by various techniques lead to the conclusion that the grains of many, if not all, metals in the cold worked condition consist of small, slightly disoriented "crystallites" or "sub-grains".* (After appreciable deformation at room temperature, the subgrain size in copper appears to be about 7.104 cm and in high purity aluminum about 2.10-4 cm.) Recent investigations which demonstrated this phenomenon most convincingly are those of Heidenreich8 with hammered high purity aluminum, of P. B. Hirsch and collaborators7,8 with cold worked polycrystalline aluminum, copper, nickel, iron, gold, etc., and of Warren and Averbach9 with a rolled copper plus 2 pct Si single crystal. In addition to the existence of slightly disoriented sub-grains, the cumulative evidence from these investigations also shows that in the cold worked condition the subgrains themselves are severely strained. With regard to the early stages of annealing, Heiden-reich's results indicate that within the subarains of hammered high purity aluminum the strain gradually disappears, without discernible migration of the subboundaries. This recovery process presumably accounts for the major portion of the energy release

Jan 1, 1953

By A. D. K. Laird, C. A. Johnson

Drag coefficients for a cylinder being towed through water at constant velocity and also at constant linear acceleration were measured. Drag coefficients for constant velocity towing showed reasonable agreement with previous results. The drag coefficients found for constant acceleration showed little correlation with either the magnitude of the acceleration or the value of the modulus AD/V2 and tended to be slightly lower than those for constant velocity. INTRODUCTION For the design of offshore structures, wave forces acting on immersed cylinders are of importance. Several investigations have been made of these forces and of how they can be predicted from wave theories. A paper by Crooke' summarizes much of the work already done. More recent research by the Wave Research Laboratory at the University of California, Berkeley, has added much to the body of data collected under ocean wave conditions, but has not found a reliable method of force prediction from basic theories of wave motion. The present investigation is part of a long-range program to collect data with which to test current and future theories and correlations. The immediate objective was to measure drag forces on a circular cylinder subjected to linear accelerations over the range of Reynolds numbers between l04 and 105 where the drag coefficient was a constant for constant velocities. In particular, the effect of constant acceleration from rest and from uniform motion was to be investigated. The effect of acceleration may be evaluated in terms of drag coefficients. A useful resistance coefficient, C, is defined by the equation for total drag force, D, exerted by the fluid on the cylinder. DT =CSp V2/2.........(1) The coefficient C may be plotted as a function of the parameter AD/V2. Here D is the diameter and S is the projected area of the cylinder. The acceleration and velocity are A and V. The mass density of the fluid is p. An alternate drag coefficient, C, corresponds to the total force of the fluid opposing the motion minus the virtual mass force. This drag coefficient, arising from the velocity of the fluid, may be compared with that for the same cylinder in uniform motion. The similarities and differences between this coefficient as calculated for accelerated and for steady motion are of interest in the inverse process of predicting drag forces on cylinders under arbitrary conditions. One serious difficulty in this method is the specification of the virtual mass which depends also on the flow picture about the cylinder.1 EXPERIMENTAL EQUIPMENT The experiment was performed in the combination wave and towing tank at the Engineering Field Station of the University of California. The tank is 200 ft long, 8 ft wide, and 6 ft deep. The tow carriage is externally propelled by a cable, and the velocity of the carriage is maintained essentially constant by means of an am-plidyne. For the purpose of the present investigation, the speed control of the amplidyne was modified by inserting a linear speed control rheostat, which was rotated at a constant speed by a small d-c motor equipped with a slip-clutch. Accelerations which were constant over a reasonable length of time were thus produced. The magnitude of the acceleration depended upon the speed of the d-c motor and the limiting speed of the carriage. Data were obtained for a range of accelerations of 2 to 10 ft/sec,2 and a range of velocities of 2 to 15 ft/sec. An accelerometer (Statham Type C-2-350) with a range of ±2g was attached to the carriage and connected to a Brush analyzer and penmotor. A continuous coil of wire with 10 turns/ft wound around a fixed wooden form extending for a distance of 40 ft along the length of the tank was connected by an electrical contact mounted on the carriage to a Brush analyzer and penmotor, to give the time-position history for each run. The test cylinder was machined from solid aluminum alloy, 17-ST. to a diameter of 1.250 in., and could be

Jan 1, 1957

By G. K. Manning, W. E. Few

WORK on the effect of vacuum heat treatment of 0.040 in. diam sintered and wrought molybdenum wires has been sponsored by the Office of Naval Research at Battelle for the past several years. An electrical resistance furnace' capable of maintaining a vacuum of less than 0.1 micron of mercury at temperatures as high as 4000 °F was used for heat treating the wires. Early in the work, it was found that the introduction of a few microns pressure of oxygen into the furnace resulted in a rapid increase in the oxygen content of the wire specimens and the appearance of a discrete oxide phase. Subsequent elimination of the oxygen atmosphere caused the disappearance of the oxide phase. This was used to determine the solid solubility of oxygen in molybdenum over the temperature range of 2000" to 3000°F.2 It was observed that, with the disappearance of the oxide phase, the wires regained some ductility. Single-phased wires possessed from 5 to as much as 40 pct elongation in 2 in. Later, attention became centered on determining the cause of this wide range in ductility. Wires containing less than 0.002 pct C, less than 0.0007 pct 0, less than 0.0005 pct N, and less than 0.00003 pct H exhibited the erratic ductility noted above. These percentages represent approximately the limit of accuracy of presently available methods of analysis and thus it became apparent that chemical analysis would be of little help in the study. A number of possible explanations for the wide range in ductility were suggested during the course of the work. It was first suspected that variations in the grain size of the recrystallized wire specimens might be responsible. Wire from several lots of material was available. One of these lots tended to develop very large grains when recrystallized, the others all developed an ASTM grain size of 3 to 4 when heated above 2700°F. No correlation between grain size and ductility could be found. It was thought that back diffusion of oil from the diffusion pump might cause contamination of the wire, principally with carbon, but when wires were treated without cooling the cold trap in the pumping system,

Jan 1, 1956

By J. J. Gilman

RECENT experiments have shown that the mar-tensite reaction in a standard tool steel is influenced by the history of the reacting austenite. The martensite reaction proceeds to a given extent at a higher temperature in austenite formed from an annealed spheroidal structure than it does in austenite formed from tempered martensite: that is to say, a prequench lowers the temperature range of the martensite reaction in this steel. Furthermore, a prequench alters the appearance of the martensite as compared to martensite formed from "virgin" austenite. The steel used for this work was a manganese nondeforming tool steel of the following composition: C, 0.85 pct; Mn, 1.43; Si, 0.23; Ni, 0.12; Cr, 0.59; and W, 0.59. A piece from a rolled bar was forged to Vz in. sq and annealed to a spheroidal structure. Disks 1/8 in. thick were used in the experiments. Several sets of the specimens were prepared and austenitized in lead at 1475°F. Three sets were held at 1475°F for 15 min, quenched in water, and immediately reheated to 1475°F. After this quench the three sets were held for 5 min, 30 min, and 3 hr, respectively, at 1475°F and then the individual specimens in each set were quenched in molten baths to 325", 300°, and 275ºF, respectively, and held for 15 sec. Immediately after the quenching treatments? the specimens were tempered at 600°F for 30 sec to darken the martensite and then were quenched in water. The holding times were short enough to avoid isothermal transformation. Three other sets of specimens were given the same final quenching treatments as the first three, but they were austenitized at 1475°F for 20 min, 35 min, and 3 hr and 15 min, respectively, without an intermediate water quench. The two individual specimens from each set were quenched together in order to eliminate quenching errors. Several experiments were run in this way but only the six sets referred to are described in detail because they all yielded essentially the same results. By means of the stated heat treatments the martensite reaction was investigated for: 1—austenite formed from an annealed structure, and 2— austenite formed from tempered martensite. The martensite reactions of the two types of austenite differed significantly. This is shown by Figs. 1 and 2. Comparison of the photographs on the left in Figs. 1 and 2 with those on the right shows that less martensite was formed by a quench to a given temperature from prequenched austenite than from austenite formed from an annealed structure, that is, the prequench suppressed the martensite reaction. The effect was observed for specimens austenitized 20 min, 35 min, and 3 hr and 15 min. A comparison of Figs. 1 and 2 shows that the martensite reactions in both sets of specimens occurred at lower temperatures with increased austenitization time. This was caused by the increased dissolution of residual carbides with time at 1475°F. However, the difference in amount of martensite formed in prequenched austenite as compared to virgin austenite was approximately the same for all three austenitization times. One further observation should be noted. The needles of the martensite formed from virgin austenite are somewhat longer on the average and show less of a tendency to cluster than those of martensite formed from prequenched austenite. This causes the martensite on the right in Figs. 1 and 2 to have a more acicular appearance than the martensite on the left. Since the sets of specimens used in this work were austenitized for identical total lengths of time and the effect of a prequench on the martensite reaction existed for specimens held at the austenitizing tem-

Jan 1, 1953

By J. W. Spretnak, R. Speiser, A. M. Adair

THERE are sufficient arguments and evidence to indicate that boron should be adsorbed to existing austenite grain boundaries during the austen-itizing treatment. Accordingly, it is possible that boron contributes to the hardenability of heat-treatable steels by the reduction of the interf acial energy of austenite grain boundaries, at which sites are nucleated heterogeneously the decomposition products of austenite. Such a reduction in interfacial energy would reduce the total energy that can be borrowed in these heterogeneous nudeation processes and thus retard the initiation of transformation. This investigation was undertaken in an attempt to determine the effect of boron on this interfacial

Jan 1, 1956

By L. D. Jaffe, W. P. Clancy, D. C. Buffum

Many earlier workers have suggested that the temper brittleness of steel is associated with the presence of carbon or nitrogen. Nevertheless, no investigations on the effect of removal of these elements upon susceptibility to temper brittleness have been published. It was therefore decided to determine whether temper brittleness would develop in an iron alloy ...__, ing very little carbon and nitrogen. The alloy, in the form of a 10-lb ingot, was prepared by melting purified materials under . argon. Its composition, in per cent, was: This analysis, except for carbon content, is within the specified range for SAE 3140, which has been demonstrated by previous work at this laboratory2 to be markedly susceptible to

Jan 1, 1950

By P. Payson

EMBRITTLEMENT of hard-tempered martensite (500°F embrittlement) appears to be coincident with the beginning of the third stage of tempering. During the first stage, primary martensite of steels containing over 0.25 pct C decomposes to a mixture of c carbide and martensite of appreciably constant carbon content close to 0.25 pct.' During the third stage of tempering, cementite forms. In steels with

Jan 1, 1955