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By R. E. Reed-Hill, W. H. Hartt

The "(3034) " twin lamellae in magnesium have been reexamined using electron microscope replicas. The double twinning sequence (1011)- (1012) for these lamellae has been reconfirmed. Evidence is presented showing that the irrational habit of these twins is probably the direct result of a need to accommodate the second-order twinning shear. This accommodation vesults in both an external shear in the matrix and an internal shear in the lamella. A model is presented which accounts for the experimental obseruations. HCP metals are generally characterized by strong textures in which the basal planes of the grains tend to be aligned parallel to the rolling direction in sheet or plate and to the axis of wires and rods. Since these directions are normally those in which finished products may be subjected to uniaxial tensile stress, these textures effectively place the crystals of magnesium objects in orientations unfavorable to both basal slip and {1012) twinning, the easily activated deformation systems of this metal. However, when magnesium crystals are deformed near room temperature by a tensile stress nearly parallel to the basal plane, another mode of deformation can occur.',2 This is _a double twin which forms first by twinning on {loll), followed by retwinning on (1012). The resulting twin lamellae are of considerable interest. First, they can be responsible for "brittle fracture''; when a tensile stress axis lies in the basal plane, because the reoriented crystal structure of a lamella is well-aligned for slip while the parent crystal is not. Extensive internal deformation may thus occur while the matrix is still almost undeformed. This deformation can produce a ductile rupture running the length of the twin.3 Complete failure of the specimen may then oc-cure by the spreading of cracks from one twin lamella to another, or by the movement of a crack into a grain boundary and then along grain boundaries. Since the the volume fraction of these doubly twinned elements is normally very small, the fracture may be classed as brittle, although the fracture mechanism is, of itself, essentially ductile. It is quite probable that the ductility transition, normally observed4 in magnesium at or slightly Obove room temperature, is closely associated with these second-order twins. The detailed relationship of these twins to fracture in single crystals will be the topic of another paper. The present paper is concerned with a second important aspect: the irrational habit of these double twins that falls close to {3034), or approximately 7 deg away from the primary (10il) twin habit. There is good reason to believe that this habit results directly

Jan 1, 1968

By Frank S. McKenna, Myron A. Pugacz, Clarence E. Jackson

The notched-bar impact test has proved worth while in certain applications as a test for control of the quality or the heat-treatment of steel. In view of the serious thought that even so simple a test as the tensile test has evoked during the past years, it is not surprising that the notched-bar impact test should have inspired much experimental work. The correlation of the great number of data has not been successful, although steady progress has been made toward a better understanding of this test. Progress has been made, especially, in the isolation of the effects of the many variables that control the results. The stress system imposed on a specimen with a notch is so complicated and unpredictable that no simple evaluation of the test has been possible. Because of this uncertainty, many engineers hesitate to use the notched-bar impact test, and this attitude may well continue until a better understanding of the effects of the variables in the test are available. Without doubt, any additional data that may be presented should be accompanied by as complete a description of the - details of test as possible, so that it may be added to the general fund of information that is to serve as the basis for the theory of the notched-bar impact test. The many factors that may control the test results have been pointed out repeatedly. The importance of the effect of the type and dimensions of the specimen has been recognized. Most of the work reported by American investigators has been limited to small-size (Charpy) specimens tested as a simple beam; two types of notches (Fig. I) have been commonly used. Considerable data have also been presented by many investigators using a small specimen tested as a cantilever beam; this commonly being called the Izod test. Here, however, a shear component of stress makes the stress system even more complex than that present in the simple beam type of test, hence a critical analysis is difficult. Much work has also been reported by investigators using the tension type of specimen. A second variable that must be controlled is the testing temperature. An indication that the tests were performed at room temperature is not sufficient, since in many steels a variation of a few degrees in the actual testing temperature may be sufficient to give an entirely different range of results. Other factors, such as the composition and condition of the material being tested and the speed of test, should also be considered. Many investigators have contributed data and theoretical discussions on the problems encountered in notched-bar test-

Jan 1, 1944

By Ursula E. Wolff

Il.lechanica1 twins have been observed in brigsten single crystals of a variety of axial orientations defornzed at room temperature in tension or bending. The twins formed near the final fracture and were up to 3 p thick. The twinning plane was always of the type (113). Twinning at room ternperature occurred only after considerable prior slip. Twins usually preceded fracture and nucleated cracks. The crack surfaces often alternated between a (001) plane and the twin interfaces. Secondary twins could also nucleate from cracks. In the absence of twinning tensile samples failed by shear; twinned samples failed by cleavage. On the assumption that observed sudden load drops in the stress-strain curves are associated with twinning, a critical resolved stress for twinning of 60, 000 to 65, 000 psi was calculated. MeCHANICAL twinning has been observed in iron and iron alloys at low temperature by a number of investigators.'-7 Similarly, for high-purity tungsten, twinning has been reported for deformation temperatures below 211°K.8-10 In W-Re and Mo-Re alloys, 20 pct Re was determined as the lower limit for twin formation at room temperature." Since the twins are generally very narrow, they are usually identified only by etching techniques. The expected (112) habit plane has always been confirmed by angular analysis of the surface traces. Recently, however, a complete identification by X-ray analysis has been performed on twins in a Mo-35 pct Re alloy.12 During an investigation of the deformation charac- teristics of tungsten single crystals, twins were revealed in tensile and bend samples deformed at room temperature. This paper deals with the conditions for such twinning and the relation of twinning to fracture. EXPERIMENTAL PROCEDURE Tungsten single crystals, 1/8 in. in diam, of a variety of axial orientations were grown from un-doped material by four-pass electron-beam zone melting. A representative analysis is given in the following table: From these crqstals, tensile samples with 1 in. gage lengths were made by surface grinding, leaving shoulders for gripping. The diameter after grinding was 0.082 in. The distorted surface layer was then removed by ele1:trolytic polishing which reduced the diameter of the gage length to 0.080 in. Tensile tests were carried out at room temperature in an Instron machine under two different sets of conditions: a) Rigid mounting; strain rate 0.02 in. per in. per min. b) Gimbal mounting; strain rate 0.002 in. per in. per min up to a total strain of approximately 0.2 pct, then 0.01 in. per in. per min to fracture. Stress axis and growth direction coincided in all samples and are subsequently called orientation.

Jan 1, 1962

By JAMES SCULLY

For the last 4 years political leaders have found a new subject on which they can safely generalize wihout creating opposition. That subject is commodity prices. Since the four-fold increase in OPEC crude oil prices, public attention has focussed as never before on the subject of commodity prices. To advocate stabilizing commodity prices is akin to supporting motherhood or peace or better schooling. Everyone gives lip service to the concept that stable commodity prices are desirable. It is easier to state the principle than to achieve it. Prices that are stable in terms of one currency may be clearly unstable in terms of a different currency. This has become a troublesome matter since 1971, when the world's leading trading currencies were set free to float in relation to each other. To illustrate: consider copper prices in the interval between the end of 1974 and the end of 1977. During those 3 years, the copper price in pounds sterling on the London Metal Exchange rose by 25 per cent. During that period, however, in terms of the USA dollar equivalent, the price was unchanged. And during that period, in terms of the German mark equivalent the price shrank by 13 per cent while the Japanese yen equivalent fell by 20 per cent. Thus a price that appears stable in dollars, rose in terms of pounds sterling and fell in terms of marks and yen. Had this result been achieved as a consequence of an international effort to stabilize prices, an American would have said the effort was successful. An Englishman would have said it had failed to prevent a price rise. And a German or a Japanese consumer would have been happy to have covered his copper needs at a lower cost in terms of his own currency.

Jan 1, 1978

By Walter Kauzmann

All viscous or plastic flow of incompressible matter is the result of shear strain; the changing shape of any body that is being plastically deformed can be completely described in terms of the shear strain occurring at each point in the body.† Furthermore, the relative amounts of shear strain occurring in different parts of a body under stress depend upon the relative rates of shear strain at those different points, so that if the dependence of the shear rate of any material on the temperature, shear stress, previous history, etc., were understood, the principles of plastic deformation would be known, and we could calculate how a body made of a given material, having a given shape, and subject to a specified system of forces, would change its shape with time. It may be said, then, that the problem of plasticity resolves itself into, first, the problem of the rates of pure shear processes, and second, the application of what is known about pure shear to actual cases. It is the purpose of this work to investigate the former problem —i.e., the dependence of shear rates on temperature, stress, etc.—from the standpoint of .recent developments in the field of chemical-rate theory and with particular reference to the phenomena occurring in the creep of metals and in the plastic flow of crystalline solids in general. It is left for the mechanical engineer, and perhaps the expert in hydrodynamics, to deal with the problem of app1ications.l Resolution of Macroscopic Shear into Microscopic Movements; Resemblance to Chemical Reactions Just as any large body is made up of many small units, or atoms, so macro-scopically observable shear is the result of many microscopic unit shear processes; just as the understanding of the behavior of large bodies demands the understanding of the atoms of which it is made, so the understanding of macroscopic shear demands the understanding of these fundamental unit processes. The study of shear from this "atomistic" point of view has made considerable progress. There has been fairly complete understanding of shear processes in gases for a long time, at least for non-turbulent flow, as a chapter on gaseous viscosity in any text on the kinetic theory of gases will prove' In recent years Andrade2 and Eyring3 have presented important theories for the flow of liquids and amorphous solids. Becker14 Orowan,5 Taylor,6 Burgers,7 and Kanter8 have considered the plastic flow of crystalline solids from this

Jan 1, 1941

By J. D. Livingston

THE hardening of alloys by the precipitation of a second phase has long been an important technological process. One approach towards improving our understanding of this phenomenon has been a correlation of mechanical properties with such parameters as particle size and inter par ticle spacing.' Several reviews of such data have appeared.2-4 A major limitation to this approach has been that for most alloys the particles are submicroscopic in size in the range of optimum hardness. Precipitation-hardening copper-cobalt alloys, therefore, are of interest, because the ferromagnetic properties of the precipitate make it possible to measure particle size, number of particles, and so forth, from magnetic measurements alone.5, 6 Livingston and Becker7 have applied these techniques to a study of precipitation hardening in an alloy of 2 pct Co in copper. It was found from magnetic measurements that nearly all the cobalt to be precipitated was out of solution within a few minutes at 600°C, whereas the peak in tensile yield stress was not attained until a much longer aging time. Thus during the first 1000 min of aging time at 600°C the Yield stress was increasing while a constant volume of precipitate was coarsening, i.e., while particle size and interparticle spacing were increasing. Peak yield stress was reached at an average particle radius of about 70A. The earlier study was confined to one alloy at one aging temperature, so that the volume fraction of precipitate was fixed and, therefore, particle size and interparticle spacing could not be independently varied. The work has now been extended to several alloys of varying percentage cobalt in copper, and to aging at various temperatures. It was hoped that such a study might clarify the relative importance to precipitation hardening of particle size, interparticle spacing, and volume fraction of precipitate. EXPERIMENT The alloys studied contained 0.7, 1.3, 2.0, and 3.2 wt pct Co in copper. They were prepared from electrolytic copper and electrolytic cobalt in a vacuum -induction furnace, worked to 3/8-in.-diam rod, and machined into tensile specimens with a gage section 1 1/2 in. long and 3/16 in. in diam. All specimens were given a solution treatment consisting of a 30-min anneal in nitrogen at 1000° C followed by a quench into iced brine. Subsequent aging was done in nitrogen and followed by a water quench. Average grain diameter was approximately 0.01 in.

Jan 1, 1960

By D. E. Peacock, B. Harris

The mechanical behavior of a niobium (columbium)TUNG alloy containing 20 wt pet Ta. 15 wt pet W, and 5 wt pct Mo has been studied in the temperature range 77° to 423°K. All specitrzens tested, apart from those into which oxygen was introduced deliberately, were fully recrystallized at 1500°C, had an average grain diameter of approximately 0.03 mm, and a combined carbon, ox-vgen. nitrogen, and hydrogen content of not not more than 250 ppm The meckatnical behavior of this alloy was found to be similar in seine respects to that of unalloyed bcc transilion metals. Both yield and flow stresses were sensililae to changes in deformation rate and both increased rapidly as the temperature was lowered below 150°C. A detailed examination revealed, however, that most of the temperature dependencc of the yield stress could be accounted for by the temperature dependence of the elaslic, modulus, whish is not true of the unualloyed metals. In lension at moderate strain rates, the trunsition fvom ducfile to hvittle behavior occurred just belour room teunperature bur incveasing the oxygen content from 190 to 200 pptn raised the transition temperature to about 4000K. TUNGSTEN and molybdenum have been found to be very effective high-temperature solid-solution strengtheners of niobium, but the amounts of these elements that can be added are limited if the alloy is to retain useful room-temperature ductility. It has been shown, however, that partial replacement of niobium with tantalum lowers the ductile-to-brittle transition temperature of such alloys and allows larger additions of molybdenum and tungsten to be made. Some of the high-temperature properties of niobium alloys containing these elements have been reported by Bartlett et al.,' and the work presented here describes the low-temperature behavior of one of these, a solid-solution alloy containing, by weight, 20 pct Ta, 15 pct W, and 5 pct Mo. The elastic modulus, the temperature and strain-rate dependence of the yield and ultimate tensile stresses, and strain-hardening effects are discussed and compared with those of unalloyed niobium. EXPERIMENTAL MATERIAL AND PROCEDURE The material used in this investigation was produced from a 6-in.-diameter, double arc-melted ingot. This was can-extruded at about 1150°C to a 3-in.-diameter billet, and after annealing for 1 hr at 1345°C the billet was heated to 1315OC and part rolled and part forged to 0.5-in.-thick plate. The resulting material exhibited a cold-worked structure

Jan 1, 1965

By Walter Kauzmann

All viscous or plastic flow of incompressible matter is the result of shear strain; the changing shape of any body that is being plastically deformed can be completely described in terms of the shear strain occurring at each point in the body.† Furthermore, the relative amounts of shear strain occurring in different parts of a body under stress depend upon the relative rates of shear strain at those different points, so that if the dependence of the shear rate of any material on the temperature, shear stress, previous history, etc., were understood, the principles of plastic deformation would be known, and we could calculate how a body made of a given material, having a given shape, and subject to a specified system of forces, would change its shape with time. It may be said, then, that the problem of plasticity resolves itself into, first, the problem of the rates of pure shear processes, and second, the application of what is known about pure shear to actual cases. It is the purpose of this work to investigate the former problem —i.e., the dependence of shear rates on temperature, stress, etc.—from the standpoint of .recent developments in the field of chemical-rate theory and with particular reference to the phenomena occurring in the creep of metals and in the plastic flow of crystalline solids in general. It is left for the mechanical engineer, and perhaps the expert in hydrodynamics, to deal with the problem of app1ications.l Resolution of Macroscopic Shear into Microscopic Movements; Resemblance to Chemical Reactions Just as any large body is made up of many small units, or atoms, so macro-scopically observable shear is the result of many microscopic unit shear processes; just as the understanding of the behavior of large bodies demands the understanding of the atoms of which it is made, so the understanding of macroscopic shear demands the understanding of these fundamental unit processes. The study of shear from this "atomistic" point of view has made considerable progress. There has been fairly complete understanding of shear processes in gases for a long time, at least for non-turbulent flow, as a chapter on gaseous viscosity in any text on the kinetic theory of gases will prove' In recent years Andrade2 and Eyring3 have presented important theories for the flow of liquids and amorphous solids. Becker14 Orowan,5 Taylor,6 Burgers,7 and Kanter8 have considered the plastic flow of crystalline solids from this

Jan 1, 1941

By Jean-Jacques Prompsy, J. S. Rinehart

The purpose of the present study was to arrive at a better understanding of the stress fields developed within drill bits under dynamic loading and the influence that these stress fields could have on the failure of the drill bits. Particular emphasis has been given to the influence that bit shape has on the establishment of highly localized, potentially destructive stress inhomogeneities within the bit. This paper covers one phase of a broad study involving three velocity regimes: impacts at very low velocities, 0 to 20 ft/sec, a velocity range in which dynamic effects are just beginning to be found; impacts at velocities ranging from 20 to several hundred ft/sec, arange commonly encountered in practical drilling operations; and impulsive loading through the detonation of explosives, a velocity range in which the dynamic effects are greatly exaggerated and made more identifiable. Specifically, fracturing which develops at the end of a cylindrical bar undergoing a shock produced by impact was experimentally investigated, the impacted area being the face of a truncated cone terminating the cylindrical bar. Fracture characteristics were looked at as a function of impact velocity, area of impacted face and cone angle — parameters of considerable importance in the design of drill bit. EXPERIMENTS The specimens were made of Plexiglas, which enabled the fracture pattern to be easily observed. In Plexiglas, the velocity of a longitudinal wave is about 8,700 ft/sec, and the velocity of the transverse wave about 4,200 ft/sec. The specimens were impacted by a steel cylinder whose lower face was parallel to the terminal face of the experimental bit, as shown in Fig. 1. The impacting mass was shifted up and down on two steel rods, dropping from a maximum height of 11 ft, with the velocity varied between 0 and 6.5 m/sec. The initial mass of the cylinder was 4.1 kg, which could be increased by steps up to 8.8 kg by addition of steel plates. The velocity of the steel cylinder was determined by using an electric circuit; as the cylinder dropped, it contacted two steel wires, the first one starting and the second one stopping an electronic counter. Two similar counters connected in parallel were used to corroborate each other. The velocity was checked at each drop as it had been observed to vary somewhat from drop to drop. The two contact wires were located just above the top of the specimen so as to give a value of the instantaneous velocity of the steel cylinder at impact. The distance between the wires was 40 ± 0.5 mm and the discrepancy between the counters was never more than 0.1 m/sec. Thus the velocity was known to within 3.25 per cent. This precision was sufficient with respect to the precision of the machining of the specimens. A very small lack of parallelism between the face of a specimen and that of the impacting hammer resulted in an oblique impact which required a much lower velocity to break the specimen. The experiments had a twofold purpose — (1) to observe the fracture pattern, and (2) to find relationships between the minimum velocity required to generate a fracture within a specimen and the

By Erwin Pink

It has been pointed out in a previous publication' that, for a given strain rate, serrated yielding can be observed only at certain test temperatures. Fig. 1 shows the results obtained for polycrystalline and re-crystallized tantalum, Va group in the periodic table of elements, where serrations in the course of deformation match the decrease of total elongation. However, there was no evidence of repeated yielding when testing molybdenum or tungsten, VIa group, at similar conditions, i.e., annealed and air-cooled samples (serrations have been found in quenched tungsten2). The reason for the observed serrations in the stress-strain curve are dissolved impurities on interstitial sites of the lattice. Of importance is the concentration of oxygen, carbon, and nitrogen, which are in random solution. Two methods to calculate the limiting concentrations for serrated yielding have been evaluated and applied with more or less success in estimating the role of carbon and nitrogen in mild steel.3 J. Friedel4 has given two equations, which determine the upper and lower strain rates i for the appearance of serrations at a certain test temperature: W denotes the binding energy of the interstitial atom, -1 ev for refractory metals;5 e' the portion of continuous strain in the discontinuous stress-strain curve, measured as -3x10-3; b the Burgers vector, c the concentration, see Table 11, in atom fractions; p the dislocation density, -2 X l09 per cm2 at an average stress ?, -15 kp per mm2 at medium strain. k stands for the Boltzmann constant, T for the absolute temperature, and D for the diffusion coefficient. Table I. Eq. [1], for a given strain rate, determines the minimum temperature, and [2] the maximum temperature, below or above which no "dynamic strain-aging" can occur. According to the calculation, which uses the given quantities, serrations should only be observed within the cross-hatched temperature regions in Fig. 1, and this is in good agreement with the experiment. The effect of varying impurity concentrations is indicated schematically in Fig. 2: only Eq. [I] is affected. Setting Eq. [I] equal to [2], one can calculate the limiting concentration cmin which first causes serrations. The second method uses the aging condition by Cottrell and Bilby6,7 \£i/ \ n. a / where n(t) is the number of impurity atoms, which segregate at a dislocation line of 1 cm length after the time t (t in our case is the time between "repeated yield drops" in the serrated curve, or, the time until the above mentioned strain E' is obtained, i.e., -1 sec for medium intensity or serrations). no is the number of impurity atoms in 1 cm3 and A = Qb4ep[(1 + v)/(l - v)], derived from equations given in Ref. 7. p is the shear modulus, 18,800 kp per mm2 for tantalum, 12,200 for molybdenum, AE the tetragonal distortion caused by interstitial impurities in a bcc lattice (approximately 0.4 for both tantalum and molybdenum) and v Poisson's ratio (0.35 for tantalum, 0.30 for molybdenum). From Eq. [3], combined with the condition for a pronounced yield drop as formulated by cottrel16 (at least one impurity atom segregated at the unit length of a dislocation), again a no min, and hence the concentration Cmin can be calculated.

Jan 1, 1970

By Robert Lowrie

Nine intermetallic compounds were tested in tension at various temperatures. Seven exhibited extensive plastic deformation at elevated temperatures. Correlations of tensile strength and elongation are attempted with melting (decomposition) temperature, valence electron configurations of the component elements, heat of formation, crystal structure, density, and volume decrease accompanying compound formation. A LTHOUGH intermetallic compounds have been -tX known for many years, the study of their mechanical properties, particularly in tension, is just beginning. The problem has been unattractive because of the well-known, erratic behavior of brittle materials tested in tension. The strong influence of surface or internal flaws as stress raisers in non-ductile materials and the effect of eccentricity of loading in superimposing bending stresses on the state of tension in the specimen are extremely difficult to mitigate and impossible to completely eliminate. Thus, tensile properties determined for brittle materials, such as intermetallic compounds at temperatures low in comparison to their melting points, are at best only general guides to the values to be expected in an ideal test of a perfect specimen of the material. It is, nevertheless, surprising that apparently no attempt was made to follow up the pioneer work of Tammann and Dahl1 in this field. Working with crude apparatus, these investigators succeeded in showing unequivocally that at temperatures sufficiently close to their melting points (from 75" to 400°C for the compounds tested) intermetallic compounds did exhibit plasticity. This was indicated by the appearance of slip lines on the surface of the specimen. No observations of strength were made in these tests, which were of a compressive or indentation type. Rossi2 in 1932 attempted to study the physical and mechanical properties of single crystals of a group of intermetallic compounds. However, he was able to prepare only one material, Cu2Z8,, in the form of large, defect-free, single crystals. Thus, he was able to report only the relative fragility of the compounds at room temperature. He reported one compound, Ag,Zn,, to be somewhat plastic at room temperature and Cu,Si to be friable, the latter in agreement with results reported herein. Although test results are available only in classified literature, it has also been announced that MoSi, possesses some ductility at elevated temperatures." In 1948 and 1949 Savitskii and Savitskii and Baron -ublished their work on the hot extrusion of Mg-Zn, Al-Mg, and Cu-Zn compounds. Under the favorable state of stress existing for this process MgZn, MgZn,, MgZn,, ß (Al-Mg), ? (Al-Mg) and 0 (Cu-Zn) could be reduced by amounts up to 90 pct at elevated temperatures. These authors also report that hardnesses of Mg-Zn compounds decrease from room temperature values of about 300 kg per sq mm to 30 to 50 kg per sq mm at 325°C. They found that alloys consisting solely of one Mg-Zn compound were most resistant to softening on heating, mixtures of a compound and eutectic less resistant, and mixtures of two compounds least resistant. The more rapid softening of mixtures of

Jan 1, 1953

By R. M. Rose, D. P. Ferriss, J. Wulff

Single crystals of tantalum were grown by multipass zone melting in an electron beam apparatus. Tension tests of these crystals at 4.2 x 10&apos;* per sec-gave a resolved louler yield stress of 7300 psi at with a chisel edge; total uniform deformation increased from 1 to 2 pct at 77°K to over 20 pct at 300°K. This, and slip traces, indicated that deformation is more inhomogeneous at lower temperatures. Deformation occurred exclusively by slip in <III> directions, on planes in the <111> zones. Cross slip was frequent, particularly for those orientations where the resolved shear stress on the cross system was comparable with that on the primary plane. The existence and magnitude of the upper yield point were found to be sensitive to orientation. This effect was related to the circumvention of dislocations which were "locked" by interstitial atoms, by double cross slip, or composite slip, of screw dislocations. Prestrainirg at 300°K did not remove the upper yield point in subsequent tension at 77°K. Also, this treatment was found to cause yield points, where none existed for the unprestrained material. This behavior was also rationalized in terms of the circumvention mechanism. The mechanical properties of polycrystalline tantalum have been investigated by several workers,1"4 and may be summarized by pointing out the following features: a) Sharp rise of yield stress with decreasing temperature below room temperature. b) Response to strain aging at 300" to 400"C. c) Yielding with upper and lower yield-point phenomenon at and below room temperature. d) Low strain hardening below room temperature. e) Reluctance to twin except at very high strain rate. Furthermore, tantalum is ductile at ordinary strain rates as low as 4.2"K.&apos; This feature, in particular, makes tantalum unique among the high melting point, bee transition metals of Groups V and VI in the periodic system. Therefore, a more fundamental and detailed knowledge of the low-tempera- ture deformation of tantalum is required. Since high purity and the absence of grain boundary effects make such a study most productive and unambiguous, the method of electron beam zone melting was selected for the preparation of test specimens. This technique has the further advantage that crystals may be seeded in order to obtain any desired orientation. EXPERIMENTAL The electron beam zone-melting equipment was constructed as a modification of that described by Calverley, Davis, and Lever? All crystals were made by three passes of the molten zone at 4 mm per min to achieve an optimum purity commensurate with economy of time and material. Table I reports the chemical analyses of the starting and refined metal. It will be noted that there remain some 50 to 70 wt ppm of interstitial elements, while all substi-tutional elements have been removed by evaporation. Tungsten is picked up by evaporation of the cathode filament wire. Crystal seeding was normally successful within 3 deg, and the orientation of all crystals are given in the standard stereographic triangle in Fig. 1. Tensile bars were prepared from the crystals by centerless grinding to the shape in Fig. 2. Specimens were then electropolished to remove 10 pct of the diameter in order to remove worked material and to prepare a metallographic surface for subsequent deformation trace observations. All specimens were held in the split bushing grips as indicated in the cross section view of Fig. 2. All tests were made at a strain rate of 2 112 pct per min in an Instron testing machine.

Jan 1, 1962

By R. A. Ritter, J. P. Batycky

A numerical technique has been developed to permit estimating the pressure gradient associated with laminar flow of thixotropic liquids through long Pipelines. For this purpose the pipeline is divided into a number of radial and longitudinal increments within which rheological properties of the fluid may be considered as constant at any time. Then, provided only that the fluid flow curve is defined at every duration of shear, it is possible to predict the instantaneous pressure gradient at any cross-section along the pipeline for each desired flow rate and pipe size. The technique consists of an iterative integration of shear rate to establish the appropriate value of the wall shear stress at each location. Consistency of fluid in the increment is determined by the flow history of that increment, while the radial flow associated with variations in velocity profile is accounted for by adjusting the width and radial position of the increment. A number of pressure profiles, computed at each of several flow rates, provide a convenient basis for pipeline design and pump selection. INTRODUCTION In recent years considerable attention has been given to predicting pressure drop associated with the isothermal laminar flow of time-independent non-Newtonian fluids in pipes and annuli. 6,11,12 The approach generally has been to develop analytical relationships between flow rate and pressure drop based on simple constitutive models which hopefully provide an approximate description of the rheological properties of the fluid. Analytical solutions are highly desirable since the influence of all pertinent parameters can be readily determined. Unfortunately, however, this approach is restricted to simple flow geometries and- frequently leads to erroneous results due to inadequacies in the model. In certain cases a solution may be obtained through applying appropriate numerical techniques.l,14 For example, a digital computer program is available for predicting the velocity profile and pressure drop encountered by any Newtonian or time-independent non-Newtonian fluid flowing under laminar conditions in a cylindrical pipe or annulus.l In this paper the consistency behavior of the fluid need only be described in terms of basic rheological data. Analyzing flow systems involving fluids with time-dependent rheological characteristics is considerably more complicated since substantial changes in consistency may occur because of sustained shear action. This sensitivity to shear frequently persists for several hours. Consequently, variations in pressure drop and/or flow rate resulting from the aging process and addition of unsheared or partially sheared fluid to the system must be considered for purposes of pipeline design. This paper outlines a numerical method for predicting the transient and steady-state laminar flow behavior of a thixotropic liquid in a pipeline of arbitrary length (i.e., at a specified constant flow rate, the instantaneous pressure gradient may be determined at any time after start up and at any location along the pipeline). Several such pressure gradient profiles, computed at several flow rates, may be combined to produce a complete portrait of the system response. This flow portrait provides a reasonable basis for pipeline design and for selecting a suitable pump characteristic. TIME-DEPENDENT RHEOLOGICAL BEHAVIOR The most familiar time-dependent rheological properties are those exhibited by thixotropic liquids. Many of these materials, particularly thixotropic crude oils, generally display an apparent yield stress in that a finite pressure gradient is required to initiate flow. Then, under the influence of sustained shear at a constant shear rate, the consistency systematically decreases to some final limiting value. The shear stress obtained at

By T. K. Perkins, L. E. Bartlett

Values of rock surface energy (i. e. energy required to form a unit area of new surface) are useful for interpretation of drilling and fracturing phenonema This paper describes the adaptation of a cleavage technique (splitting of large rocks under controlled conditions) for measuring surface energies. Values of surface energy obtained at room temperature and at low crack extension rates are reported for a variety of sandstones and limestones. Elastic moduli, tensile strengths and compressive strengths of the samples are also reported. The values of Young&apos;s moduli (measured in bending) are relatively low, probably because of the low stress levels imposed. Measured values of surface energy me generally higher than anticipated and probably reflect inelastic yielding near the extending tip of the crack. INTRODUCTION The technology of petroleum production includes many operations such as drilling and fracturing, which involve rock breakage. One of the fundamental properties of a rock needed to fully explain breaking and fracturing phenomena is the surface energy (i. e. the energy required to form a unit area of new surface). In this paper we describe an adaptation of the cleavage method (splitting of the rock under controlled conditions) to utilize large rock samples. Application of the theory of elastic cantilever beams and the Griffith concept of mechanical stability permits the calculation of surface energies from simple measurements. Values of surface energies obtained at room temperature on dry samples and at low crack extension rates are reported for a variety of sandstones and limestones. Measured values of Young&apos;s Moduli, compressive strengths and tensile strengths are also reported for the rocks. THE EXPERIMENTAL METHOD Equipment designed to cleave large rock samples is shown on Fig. 1. This equipment consists essentially of two steel blocks cemented to a rock sample and forced apart with a steel rod. A ball joint and a pivot prevent bending stresses in the rod. A differential thread arrangement permits the rod to advance only 0.012 in./revolution of the driving nut. The axial force in the rod is measured with type FA-50-12 Baldwin Lima Hamilton strain gauges and a BLH type 20 strain gauge reader. Separation of the blocks is measured with a Starrett 656617 dial gauge. The massive nature and design of the equipment minimize the amount of elastic energy stored in the steel parts as the stress in the rod is increased. This will permit the rock to split under controlled conditions as will become clear later. Fig. 2 shows a sketch of the rock sample during cleavage. Guide slots are cut longitudinally along the rock sample as suggested by Berry.1 An initiating slot is also cut across the top of the block to a depth of 1 to 2 in. During cleavage, elastic energy is stored in the flexed beams of rock of length C. If the length of steel rod L is held constant and the crack extends in length, then the elastic potential energy stored in the rock decreases. However, surface energy must be supplied as the crack extends in length. Griffith6 has proposed the following criteria for mechanical stability. The crack will extend as long as the potential energy available is greater than the surface energy required. However, the crack will stop extending when the change in potential energy with change in crack length is just equal to the change in surface energy with change in crack length. See Eq. 1.

By Frederick T. Williams

THE purpose of this paper is to discuss the relative merits of the large 31/8 in. machine and the small 21/4-in. tappett machine in driving development-headings ; and although the . data here presented were obtained from cross-cut headings alone, experience has shown that the results are equally true in drifting, raising and winning. Recently we drove two parallel cross-cuts through the same formation, using a 3k-in. machine at the breast of one cross-cut., and a 2k-in. machine of the same make at the breast of the other. The results of this work afforded an ideal comparison, since in both cases the headings were advanced through rock practically of the same hardness and breaking-properties ; the amount of sludging was equal, and there was no difference in the condition of the steel or the machines, in the air-pressure or in the experience of the operating-crews. Some operators in the Cripple Creek district contend that there is ground which cannot be handled with the small machine, the holes being too small to contain enough powder to pull the ground, etc. The results obtained in working the property of the Portland Gold Mining Co., however, show that the ground worked by them does not fall in this class. During a period of two years there have been driven, with the small machine, 4 miles and 308 ft. of development-headings, through a diversity of ground, including Pike&apos;s Peak granite (a coarsely porphyritic type of granite), highly indurated, andesitic or phonolytic breccia, true massive andesite, trachytic phonolyte, tuffas, and along dikes of decomposed basalt and hard phonolyte; in every instance a satisfactory record was made. The headings here described were driven through highly indurated, andesitic breccia, having a hardness of from 5.2 to 7.2

Mar 1, 1906

By A. E. Wells, H. O. Hofman, R. P. Reynolds

A Discussion of the Paper of H. O. Hofman, R. P. Reynolds and A. E. Wells, read by title at the London Meeting, July, 1906 ; presented at the New York Meeting, April, 1907, and printed in Bi-Monthly Bulletin, No. 13, January, 1907, pp. 37 to 52. GEORGE A. PACKARD, Boston, Mass. (communication to the Secretary*) :-The very interesting results obtained by Prof. Hofman and his assistants came to my attention when I had temporarily assumed charge of the metallurgical department of the Missouri School of Mines, and had found it, pending the completion of a new building, lacking a furnace in which to roast ore preparatory to the customary lead blast-furnace run. An attempt at lime-roasting had been already determined upon, but the use of a charge which would make a slag of definite composition was a new idea. The results following were obtained by Messrs. Aubrey Fellows, J. C. Long, E. R. Wash, and Dr. T. C. Tseung, under my supervision. It is regretted that the data are not more complete; but the work was done simply incidentally to securing the desired ore for the blast-furnace, with no idea of obtaining any results of especial interest. It is submitted because of the metallic lead obtained, no notice of which has been seen elsewhere. The ore was an aggregate of several lots of concentrates, apparently from Missouri ores. The analysis follows, with that of the limestone and sandstone used, as far as made:. Ore, SiO2, 3.04; Fe, 0.77; CaO, 2.53; Pb, 68.74; Zn, 5.77; S, 13.9 per cent.; limestone, SiO2, 1.0 ; CaO, 54.35 per cent.; sandstone, SiO2, 99.8 per cent. The converter was made in the shops from a sheet of No. 14 iron riveted in the shape of a truncated cone, 20 in. in diameter at the top, 15 in. at the bottom and 22 in. high. A grate of No. 8 iron, 17 in. in diameter, with 130 s-in. holes placed at about 1.25-in. centers, was held in place by the shape of the

Jul 1, 1907

By Eugene F. Poncelet

Glass squares compressed on edge by steel jaws in poor contact with them developed jagged "partial-contact" cracks caused by the formation of local tensile stresses. Compressed by steel jaws in perfect contact, they developed smooth "release cracks" during release of the pressure, caused by the formation of local tensile stresses during the release of the pressure. All these cracks were parallel to the pressure. A Microflash photograph of a disintegrating specimen under sufficient pressure reveals a network of fractures roughly normal to each other, also "release cracks" and a disintegration cloud. The Griffith theory is amended to account for the formation of a first crack. A new theory, based on the theory of thermal agitation and wave propagation, is proposed to account for the progress, velocity and forking of cracks. The network of fractures is shown to have been caused by reflection at a free boundary of pressure pulses emanating from a first crack. Postulating equal distribution of energy in the pulses emitted on either side by a crack in particles, the smaller fragments are shown to continue fracturing preferentially while some of the coarser fragments remain as residual pieces. As comminution of the smaller fragments proceeds, the solid is reduced to a collection of residual particles of smaller and smaller sizes, accounting for the disintegration cloud. Experimental Procedure Apparatus A crushing device was built, consisting of a steel frame and two polished, hardened steel jaws to crush plate-glass samples. This device was placed between the plates of a hydraulic press (Fig. I). For centering the pressure, the upper jaw was guided vertically and provided with a rounded top. Later it was replaced by a steel jaw ground out of a 2½-in. steel ball, the lower surface being ground to an optical flat (Fig. 2). Four rollers were used to eliminate side thrust. Screws and centering blocks served to center the specimen in the crushing device. Hard steel shims placed under the shoulder of the upper jaw limited the "follow through&apos;&apos; of the jaw after failure of the specimen. Stress distribution was first examined with a polariscope mounted on an optical bench, using monochromatic light. It was found convenient to mount polaroid, quarter wave and monochromatic plates directly on the device itself. A Microflash unit* was used as light source for the photographs. A gold-paint pattern was fused on the plate-glass specimens and connected into the spark-

Jan 1, 1947

By Eugene F. Poncelet

Glass squares compressed on edge by steel jaws in poor contact with them developed jagged "partial-contact" cracks caused by the formation of local tensile stresses. Compressed by steel jaws in perfect contact, they developed smooth "release cracks" during release of the pressure, caused by the formation of local tensile stresses during the release of the pressure. All these cracks were parallel to the pressure. A Microflash photograph of a disintegrating specimen under sufficient pressure reveals a network of fractures roughly normal to each other, also "release cracks" and a disintegration cloud. The Griffith theory is amended to account for the formation of a first crack. A new theory, based on the theory of thermal agitation and wave propagation, is proposed to account for the progress, velocity and forking of cracks. The network of fractures is shown to have been caused by reflection at a free boundary of pressure pulses emanating from a first crack. Postulating equal distribution of energy in the pulses emitted on either side by a crack in particles, the smaller fragments are shown to continue fracturing preferentially while some of the coarser fragments remain as residual pieces. As comminution of the smaller fragments proceeds, the solid is reduced to a collection of residual particles of smaller and smaller sizes, accounting for the disintegration cloud. Experimental Procedure Apparatus A crushing device was built, consisting of a steel frame and two polished, hardened steel jaws to crush plate-glass samples. This device was placed between the plates of a hydraulic press (Fig. I). For centering the pressure, the upper jaw was guided vertically and provided with a rounded top. Later it was replaced by a steel jaw ground out of a 2½-in. steel ball, the lower surface being ground to an optical flat (Fig. 2). Four rollers were used to eliminate side thrust. Screws and centering blocks served to center the specimen in the crushing device. Hard steel shims placed under the shoulder of the upper jaw limited the "follow through&apos;&apos; of the jaw after failure of the specimen. Stress distribution was first examined with a polariscope mounted on an optical bench, using monochromatic light. It was found convenient to mount polaroid, quarter wave and monochromatic plates directly on the device itself. A Microflash unit* was used as light source for the photographs. A gold-paint pattern was fused on the plate-glass specimens and connected into the spark-

Jan 1, 1947

By Eugene F. Poncelet

GLASS squares compressed on edge by steel jaws in poor contact with them developed jagged "partial-contact" cracks caused by the formation of local tensile stresses. Compressed by steel jaws in perfect contact, they developed smooth "release cracks" during release of the pressure, caused by the formation of local tensile stresses during the release of the pressure. All these cracks were parallel to the pressure. A Microflash photograph of a disintegrating specimen under sufficient pressure reveals a network of fractures roughly normal to each other, also "release cracks" and a disintegration cloud. The Griffith theory is amended to account for the formation of a first crack. A new theory, based on the theory of thermal agitation and wave propagation, is proposed to account for the progress, velocity and forking of cracks. The network of fractures is shown to have been caused by reflection at a free boundary of pressure pulses emanating from a first crack. Postulating equal distribution of energy in the pulses emitted on either side by a crack in particles, the smaller fragments are shown to continue fracturing preferentially while some of the coarser fragments remain as residual pieces. As comminution of the smaller fragments proceeds, the solid is reduced to a collection of residual particles of smaller and smaller sizes, accounting for the disintegration cloud. EXPERIMENTAL PROCEDURE Apparatus A crushing device was built, consisting of a steel frame and two polished, hardened steel jaws to crush plate-glass samples. This device was placed between the plates of a hydraulic press (Fig. 1). For centering the pressure, the upper jaw was guided vertically and provided with a rounded top. Later it was replaced by a steel jaw ground out of a 2 1/2-in. steel ball, the lower surface being ground to an optical flat (Fig. 2). Four rollers were used to eliminate side thrust. Screws and centering blocks served to center the specimen in the crushing device. Hard steel shims placed under the shoulder of the upper jaw limited the "follow through" of the jaw after failure of the specimen. Stress distribution was first examined with a polariscope mounted on an optical bench, using monochromatic light. It was found convenient to mount polaroid, quarter wave and monochromatic plates directly on the device itself. A Microflash unit* was used as light source for the photographs. A gold-paint pattern was fused on the plate-glass specimens and connected into the spark-

Jan 1, 1944

By B. H. Kear

Clustering of slip bands in different systems has been observed in both ordered and disordered Cu3Au crystals compressed in the <110> orientation. Certain features of the slip band patterns are explained in terms of reactions between dislocations with Burgers vectors at 120 deg; in a few rare cases, the slip band evidence suggests that the Products of such reactions form diffuse tilt boundaries between the differently slipped regions of the crystal, similar to the known behavior of ionic crystals, but not nearly so well defined. WHEN crystals with orientations favorable for multiple slip undergo plastic deformation, slip may occur in different systems in localized regions, so that clusters of slip bands are developed. This phenomenon has been observed in fee1-4 metals and also in ionic crystals having the sodium chloride structure.5-8 In the ionic crystals, the boundaries formed between the differently slipped regions of the crystal assume characteristic orientations and are associated with macroscopic tilts that are plainly visible on the sides of the crystal. Recently, this interesting feature was explained in terms of the formation of diffuse low-angle boundaries as a result of interactions between families of glide dislocations in the different systems meeting in the boundaries.9 This paper describes an attempt to obtain similar evidence for boundary formation in an fee crystal. The alloy Cu3Au was chosen for the present study simply because this material is currently being used in a general study of differences in deformation behavior of the ordered and disordered phases of this alloy, which will be described elsewhere. EXPERIMENTAL PROCEDURE The two specially oriented compression specimens used in the present study were prepared from a melt-grown single crystal by careful cutting, grinding and polishing. The finished specimens were about 6 mm by 2 mm in cross section by 6 mm tall, with their ends parallel to (101) and sides parallel to (111) and (121); the broad faces of the specimens were made parallel to (711). Both specimens were annealed in an evacuated quartz tube at 850oC for several hours, slowly cooled to 500°c, and then quenched into water in order to obtain the disordered state for the alloy. One of the specimens was partially ordered (with S- 0.8) by reannealing at 350oC for 100 hr. After these annealing treatments, both of the specimens were electropolished. 10 Finally, the specimens were compressed in the [loll orientation and their stress-strain curves were recorded. The deformation was carried out in increments of a few percent strain. At each stage in the deformation the specimens were unloaded, removed from the compression jig, and examined optically for slip bands. Before reloading, the specimens were repolished, so that the observed slip band patterns were characteristic of a particular stage in the deformation. EXPERIMENTAL RESULTS Fig. 1 show!; the stress-strain curves for the ordered and disordered specimens and also indicates the stages 1, 2, and 3 where the deformation was interrupted for examination of slip bands. The curves show marked differences in flow stress and in work hardening rate in the two specimens, as observed by previous workers.11,12 Also, it was found, in agreemement with the observations of Taoka and Sakata,&apos;3 that the plastically deformed disordered alloy showed the characteristic coarse slip bands of alloys, whereas the ordered alloy exhibited a fine slip band structure similar to that of pure metals. Slip Band Observations. In what follows, the description of the slip band patterns, with accom-

Jan 1, 1962