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By B. A. Wilcox, A. H. Clauer

DURING the course of an investigation on the high-temperature creep behavior of TD Nickel* (Ni + 2) vol pct ThO2), it was observed that the creep fractures were similar in appearance to low-temperature ductile fibrous fractures and creep ruptures by cavitation. Microfractographs of fibrous ruptures are typically characterized by a dimpled appearance, with second-phase particles frequently found near the bottom of the dimples.'-4 These somewhat resemble creep ruptures by cavitation, in that fracture occurs by void formation, with the subsequent growth and final merging of the voids to form a complete fracture.' It is the purpose of this communication to describe the creep fracture of TD nickel and suggest a mechanism for the rupturing process. The discussion is relevant to material crept to fracture in vacuo at a constant stress of 18,000 psi, over the temperature range 900" to ll00°C. The material used in this investigation was 1/2-in.-diam bar stock supplied by Du Pont, contain- ing 2.3 vol pct Tho2. The final fabrication treatment consisted of -95 pct reduction by swaging followed by a 1-hr anneal at 1000°C. Transmission and replica electron microscopy revealed that the material had a fibered structure with a transverse grain size of -1 µ and a longitudinal grain size of 10 to 15 µ. Selected-area diffraction indicated that the fiber axis was parallel to (00l), in agreement with the results of Inman et a1.6 The thoria particle size varied from 80 to 1000Å, with an average size of 400Å, and the mean particle spacing was about 1200Å. The remarkable structural stability7 was confirmed by annealing for 6 hr at 1300°C (about ' 0.9 the absolute melting point). Transmission electron microscopy revealed that the only structural change was a slight decrease in dislocation density. Furthermore, recrystallization or grain growth during creep has not been observed. All specimens were annealed in vacuo at 1300°C for 3 hr prior to creep testing. The following times to rupture were obtained for vacuum creep tests at a constant stress of 18,000 psi: 900°C, 854 hr; 930°C,

Jan 1, 1965

By G. S. Ansell, J. Weertman

The creep behavior of an aluminum alloy hardened with a finely dispersed phase of aluminum oxide was investigated. The as-extruded alloy shows an approximate steady-state creep in which the creed rate depends exponentially on the applied stress. The activation energy of creeb is abbroximately 150,000 cal per mole. The recrystallized alloy shows no steady-state creep. ONE method of improving the creep resistance of a metal is to introduce a finely dispersed second phase into the metal matrix. The improvement of the creep resistance has been qualitatively explained by assuming that the dispersed second-phase particles act as obstacles to dislocation motion. If the main effect of second-phase particles is simply to hinder dislocation motion then it is possible to derive a high-temperature creep equation for a dispersion-hardened alloy in a straightforward manner. In the Appendix of this paper such an equation is derived from a creep model which works very well for pure metals. Recently, F. V. Lenel has fabricated, for the first time, powder extrusions of aluminum-aluminum oxide in a large-grained recrystallized form. This alloy, designated as MD 2100, consists of a fine dispersion of aluminum oxide plates in a matrix of commercial purity aluminum. A considerable amount of investigation has been carried out concerning the microstructure and physical properties of this alloy.&apos; ) The aluminum oxide is present in the form of flakes 130A units thick and 0.3 u on edge. They are dispersed in the aluminum matrix with an average spacing of approximately 0.5 jx. The spacing varies in the range of 0.05 to 1.5 µ. The alloy structure is extremely stable at high temperatures. For this reason the alloy offers a unique opportunity for a fundamental study of creep of a very finely dispersed two-phase alloy. Lenel supplied specimens in both the unrecrystallized and recrystallized condition. This paper reports high-temperature creep experiments carried out on these specimens. The results obtained were rather unexpected. No steady-state creep was observed in the recrys-tallized material. In fact, after some transient creep which takes place upon loading, the creep rate is essentially zero ( < 10-8per min). If the second-phase particles acted solely as obstacles to the motion of dislocations, measurable steady-state creep would be expected. Since none is observed it appears that the main effect of the fine dispersion in the recrystallized material is to inactivate the dislocation sources themselves, rather than hinder the motion of dislocation loops created at these sources. EXPERIMENTAL DETAILS Specimens were tested in wire form, 0.087 in. in diam for the as-extruded alloy, and 0.035 in. in diam for the recrystallized alloy. These samples were held in friction-type wire grips; a gage length of 2.5 cm was used for all the creep tests. The specimens were held at 600°C in the test apparatus for at least 15 hr prior to each test. The tests were run under the condition of constant loading and, since the creep strains were small, can be considered as constant stress tests. The temperature of testing was held constant within 3°C. Elongations were measured with an optical cathetometer which was capable of measuring strains as smaIl as 0.00012. This allowed the measurement of strain rates as low as l0-8&apos;per rnin. In addition to the creep tests optical micrographs were made in order to determine both the grain size and microstructure of these materials. RESULTS Fig. 1 shows a few typical creep curves obtained from the as-extruded material. The elongations were somewhat erratic, but each curve shows a region of quasi-steady-state creep from which an approximate steady-state creep rate can be obtained. In general the higher the stress at a given temperature, the greater the total elongation before fracture. The lower the applied stress, the longer is the region where the creep rate is almost constant. Summary data from the creep tests of the as-extruded material are listed in Table I. The steady-state creep data of the as-extruded material for a range of stresses at a constant temperature follow a creep equation of the type creep rate = K&apos; = A exp (&) [11 where A and B are constants, k is Boltzmann&apos;s constant, T is the absolute temperature, and a the stress. The standard error of estimate of the data received is less than one order of magnitude. As shown in Fig. 2, if one compensates the creep-rate data for the effect of temperature over the range of test temperature, the steady-state creep data roughly follow a creep equation of the type Temperature compensated creep rate = K* = A exp

Jan 1, 1960

By F. V. Lenel, G. S. Ansell

The creep behavior of an aluminum -aluminum oxide alloy, A T 400, fabricated by compacting an atomized aluminum powder, extruding the compact, cold working, and recrystallizing the extrusion, was investigated. This alloy has a dispersion spacing of 1 . Previously Ansell and Weertman determined the steady-state creep rate of a recrystallized aluminum-aluminum oxide SAP-type alloy, MD 2100, with a 0.48-p dispersion. This alloy was found to have a steady-state creep rate of less than 10-6 min-1, too small to be measured accurately. By employing a more sensitive method of measuring creep rate, it was possible to determine the steady-state creep rate of AT 400 alloy, which is somewhat faster than that of MD 2100, at a series of temperature and applied stresses. Above a stress of Burger&apos;s vector, A = dispersion spacing, u = is a shear modulus) the rate follms an equation of the type: Steady-state creep rate K = A exp. where A is a constant, Q is the activation energy for sey-diffusion, and is the applied stress. At stresses lower than the steady-state creep rate drops off sharply and is no longer in agreement with this equation. This behavior is in good agreement with that predicted by the model for dispersion strengthened alloys in the stress and temperature range investigated. The absolute value of the creep rate is, however, four orders of magnitude lower than that predicted if the normal number of active dislocation sources are assumed to be present. It is concluded that in this SAP-type alloy the usual three-dimensional dislocation network is not present. Instead, short dislocation segments extending from one dispersed particle and terminating at a neighboring particle may act as dislocation sources. With this provision the creep model proposed by Ansell and Weertman reasonably accounts for the creep behavior which was observed. RECENTLY, Ansell and Weertman1 proposed a dislocation model from which they derived creep equations to describe the steady-state creep behavior of dispersion - strengthened alloys. Following Schoeck,2 they assumed that the rate controlling process for steady-state creep is the climb of dislocations over the dispersed particles. In order to verify their creep model, Ansell and Weertman determined the steady-state creep behavior of an aluminum-aluminum oxide SAP-type alloy, MD-2100, in both the fine-grained as-extruded, and coarse-grained recrystallized conditions. Since the grain size was the order of the dispersion-spacing, their model was not applicable for the as-ex- truded alloy. It should, however, be applicable to the coarse-grained recrystallized alloy. The results they obtained were rather unexpected. No meas-ureable steady-state creep was observed for the recrystallized MD-2100 alloy. If their model is correct, and if the second-phase particles act solely to hinder dislocation motion, then some measureable steady-state creep would have been expected. On this basis, they postulated that, in this SAP-type alloy, the main effect of the fine dispersion was to inactivate dislocation sources rather than to hinder the movement of dislocations. In order to understand more fully this unusual creep behavior, and to determine the validity of the model proposed,&apos; the steady-state creep behavior of an aluminum-aluminum oxide recrystallized SAP-type alloy, with a somewhat coarser dispersion spacing, was investigated. The results of this study are presented in this paper.

Jan 1, 1962

By Ervin E. Underwood

IT has been recognized for many years that dis-persed particles have great value in raising the creep resistance of metallic alloys. In fact, some of the most successful high-temperature alloys owe their superiority to this factor above all others. A recent observation by Glen1," indicates that even better high-temperature resistance to deformation results in alloys capable of two successive precipitation reactions. The ramifications of this finding are of great interest. Unfortunately, our understanding of the reasons for such notable improvements has not kept pace with technical developments. In an effort to uncover some of the basic facts governing strengthening by particles, a program was initiated at the Battelle Memorial Institute with the primary goal of comparing creep strengths in single-phase and two-phase (precipitating) alloys. The effects of precipitation from solid solution on the creep properties of alloys are generally such that the resistance to creep is increased. However, if alloys are heat treated to different degrees of hardness before creep testing, it is often found that those possessing the maximum hardness initially do not necessarily have the maximum creep resistance. Depending on the stresses and temperatures involved other structures may prove more desirable. Considerations of the above nature indicate the importance of defining the initial state of the alloy. Here, it was decided to start with quenched single- phase alloys in which precipitation and creep deformation proceed concurrently. Equipment and Experimental Procedures Preparation of the Specimens—Four 25 lb ingots were prepared from 99.999 pct Cu and 99.996 pct Al to compositions of 1, 2, 3, and 4 wt pct Cu. Spec-trographic and chemical analyses are listed in Table I. After heat treatments and intermediate reductions, the alloys were cold rolled to 1/8 in. thick sheet. The final cold reductions amounted to 50, 40, 20, and 10 pct for the 1, 2, 3, and 4 pct Cu alloys, respectively. The specimens for creep testing were machined into tensile flats 7 in. long, 3/4 in. wide (at the shoulders), and 1/8 in. thick. The reduced sections were 1/4 in. wide and 21/2 in. long. After heat treatments at 540°C to an ASTM grain size of 1 1, the specimens were quenched into water at room temperature, then electropolished in a glacial acetic acid and perchloric acid solution. The gage marks were Knoop impressions placed 2 in. apart on the reduced sections. Blanks of 1 x 1 in, were cut from the same sheets for the age hardening runs and were given the same grain size heat treatments. The specimens and blanks were stored in a refrigerator at —40°C until needed for testing. Creep Measurements—Creep tests were conducted in a constant temperature room which was maintained at 26° ±1°C. A split-type, hinged, vertical-tube furnace was mounted on a horizontal track so that the specimen could be enclosed suddenly. Thus, it took about 15 min for the specimen to come within 5°C of the test temperature. The temperature variation along the specimen was controlled to about

Jan 1, 1958

By T. E. Tietz, J. E. Dorn

Activation energies for creep of copper at intermediate temperatures, where crystal recovery was negligible, were determined by the simple technique of rapidly alternating the test temperature between and T2 (T2 = TI + about 10°K) throughout a constant stress creep test. The activation energy for creep H was found to be 37,000± 3,000 cal per mol, independent of stress and strain. The same creep laws as have been previously established for high temperature creep were found to be valid for creep at intermediate temperatures. But the AH was found to be lower than that for self-diffusion in the intermediate temperature range whereas it is known to be equal to that for self-diffusion at high temperatures. IT is now well established that creep at high temperatures can be correlated by the functional relationship&apos;-" e = f(?) s = constant [I] where E is the total plastic strain, f is the function that depends on the stress, ? = f e -- dt, t is the duration of test, e is the base of natural logarithms, AH is the activation energy for creep, R is the gas constant,T is the absolute temperature, and s is the stress. Thus, identical values of are achieved during creep under a given stress at two alternate temperatures at the same total strain. At the same strain therefore where subscripts refer to the two alternate temperature conditions of test. Consequently, the activation energy for high temperature creep is readily obtained with the aid of Eq. 2. Activation energies so obtained have been observed to be insensitive to the creep strain at which they are evaluated, the applied stress, grain size, minor alloying additions,&apos;-&apos; cold worked state, and the presence of thermally stable dispersions of intermetallic compounds in an a solid solution matrix Furthermore, the activation energy for high temperature creep is very nearly equal to that for self-diffusion in all cases where adequate data are available for comparison." " The apparent identity of the activation energies for high temperature creep and self-diffusion strongly suggest that high temperature creep arises from a dislocation climb process. This hypothesis is further strengthened by the fact that the energy of activation for high temperature creep is insensitive to the applied stress," and by the observations that the correlation suggested by Eq. 1 cannot be ex- tended to temperatures below those for rapid crystal recovery. When using the activation energy for self-diffusion, Eq. 1 fails to give the required correlations between creep curves at various intermediate temperatures.&apos; This suggests that the dislocation climb mechanism for creep might be superseded by some alternate mechanism in the intermediate range of temperatures. This investigation was initiated in a preliminary attempt to ascertain the type of creep law that might be valid in the intermediate range of temperatures. Special consideration, however, was given to the determination of the activation energy for creep in this range because the Becker-Orowan&apos;, " and the Mott-Nabarro10 theories for transient creep suggest that the activation energy should increase

Jan 1, 1957

By J. Weertman

High-temperature creep experiments were carried out on indium, lead, and on binary substitutional alloys of In-Pb, In-Sn, In-TI, In-Cd, In-Hg, Pb-Bi, Pb-Sn, Pb-In, and Pb-Cd. The stress at which the power law creep equution breaks down was found to be much smaller for indium and lead than for metals with larger elastic moduli. The exponent over the stress in the power law creep equation was found to decrease upon alloying from values close to 4.5 to values near 3. THIS paper describes a set of high-temperature creep experiments made on high-purity lead and indium and on lead-rich and indium-rich single-phase binary alloys of various metals. These ex- periments were carried out to check two predictions of some creep equations derived by us"2 from a dislocation creep model due essentially to Mott. This model is shown in Fig. 1. Here dislocation loops are emitted from sources, not shown, situated on different slip planes. As the loops expand they come into each others&apos; stress fields and are stopped. However, at high temperatures, as Mott has pointed out.

Jan 1, 1961

By P. Shahinian, J. Weertman

Minimum creep rates of nickel samples were measured in the stress region of 2.5x107 to 2.8xl0 dyne per sq cm and the temperature region of 400° to 1100°C. The creep rate seems to be proportional to (stress) at stresses below 7x10H dyne per sq cm. The activation energy of creep is approximately 65,000 cal per mol. IN a recent theory&apos; of steady-state creep which is based on Mott&apos;s dislocation climb mechanism, the following creep equation was derived for creep in polycrystalline metals (if where K is creep rate, Q the activation energy of self-diffusion, S the entropy of activation of self-diffusion, L&apos; the grain size, L the subgrain size, b the length of the Burgers&apos; vector of a dislocation, u the shear modulus, u the stress, a the critical shear stress, M the density of active Frank-Read sources, v the vibrational frequency of a vacancy, and kT has its usual meaning. This equation predicts a creep rate which depends on the stress through a power law at low stresses. At high stresses the creep rate increases much more rapidly with stress. The theory breaks down for stresses great enough that the inequality holds true. It was the purpose of the present in-

Jan 1, 1957

By J. E. Breen, J. Weertman

The creep rate of polycrystalline tin was studied as a function of temperature and stress in constant stress experiments. The temperature was varied from room temperature to almost the melting point of tin. Activation energies were calculated from tests run at the same stress. It was found that on a log creep rate vs inverse temperature plot the experimental points did not fall on one straight line but on a line which changed its slope in the 90° to 160°C region. Two activation energies for the creep of tin can be calculated from the data: a value around 26,000 cal per mol at high temperatures and a value around 11,000 cal per mot at low temperatures. It is suggested that the discrepancies between the creep activation energies and those of self-diffusion can be accounted for if self-diffusion takes place predominately by Zener&apos;s ring mechanism rather than through vacancy or interstitial movement. SHERBY, Orr, and Dorn&apos; and Dorn&apos; have recently reviewed some of the data on high temperature creep of metals. -The data show that the activation energy of high temperature creep is approximately equal to the activation energy of self-diffusion. This same correlation has also been successfully made between the activation energy of grain boundary relaxation and that of self-diffusion.3,4 The metal tin does not fit into this simple picture. Its activation energies of self-diffusion differ appreciably from that of grain boundary relaxation and of creep. Fensham,5 from a precisely performed experiment, has determined that the activation energies of self-diffusion of tin are 10,500 and 5,900 cal per mol along the C and A axes, respectively. There are two energies because of the anisotropic nature of tin. Rotherham, Smith, and Greenough6 have shown that the grain boundary relaxation activation energy is 19,000 cal per mol (measurements made from room temperature to 100°C). Puttick and King7 found the same activation energy for grain boundary slip in bicrystals of tin (180° to 225°C region). Until recently, there was no high temperature large strain creep data on tin suitable for activation energy calculations. At rather small strains (up to 0.01), Tyte8 had made a series of measurements on tin from which activation energies can be calculated. In Fig. 1 are plotted some of his data on a log creep rate vs inverse temperature graph. It can be seen that Tyte&apos;s work indicates that at a relatively low temperature the activation energy is around 7,400 cal per mol but at higher temperatures the activation energy increases. Since Tyte measured the creep only for small strains, it is doubtful if a

Jan 1, 1956

By O. D. Sherby, J. E. Dorn, C. D. Wiseman

MCLEAN&apos; has shown that the total strain obtained during creep of aluminum polycrystals arises exclusively from the mechanisms of 1) microscopically observable slip, 2) subgrain tilting, and 3) grain boundary shearing. Extensive analyses, however, suggest that the high temperature creep of metal polycrystals is controlled by a single thermal activation process."" These somewhat contradictory observations might be reconciled if it could be shown that the activation energies are identical for each of the mechanisms isolated by McLean. Such identity of the activation energies, of course, would demand that the same unit process controls the functioning of each individual mechanism. Under these conditions the activation energies for creep of single metal crystals and polycrystalline aggregates and for grain boundary shearing should be identical. This paper is primarily concerned with the possible identity between the activation energies for high temperature creep of single crystal and polycrystalline metals. In addition, comparisons will also be made between the activation energies for creep of single crystals and polycrystals with previously reported activation energies for grain boundary shearing.0"8 Materials and Techniques The same high purity aluminum, lead, and tin were used in the creep tests for single crystals and polycrystalline aggregates. Single crystals of aluminum and tin were prepared by the strain-anneal technique, whereas lead single crystals were prepared by growth from the melt. The tensile creep stress was maintained constant by Chalmers-Andrade parabolic-type lever arms. Strains were measured to &0.0002 in. per in. with rack and pinion type extensometers, and temperatures were maintained to within & 0.2"C of the reported values by mercury-thermoregulated resistance-heated silicone oil baths. The previously reported unambiguous technique for determination of the activation energy for creep was employed throughout this investigation.&apos; ." It involves periodic abrupt small changes in temperature during the course of creep, accomplished by rapidly replacing one creep bath at temperature TI by a second bath at T,. The abrupt change in creep rate from i, to & attending the abrupt change in temperature is due exclusively to the change in temperature, since both the stress and the substructure are identical the instant before and the instant after a change of temperature. Therefore, all other factors being identical where AH is the activation energy for creep and R is the gas constant. Results Typical examples of the creep rate vs creep strain data during temperature cycled creep tests of single

Jan 1, 1958

By E. F. Ketterer, D. B. Collyer, A. B. Wilder

The microstructural stability of 59 carbon and low alloy steels after 34,000 hr exposure at 900&apos; and 1050°F, including the weld heat-affected zone, is discussed. The tensile and creep rupture properties of the parent metal of many of the steels before and after 10,000 hr exposure are presented. SEAMLESS pipe has been used for many years at elevated temperatures. When seamless first began to be used, operating temperatures and pressures were relatively low and the steel produced adequately met the existing requirements. The need for knowledge of creep properties and graphitiza-tion was nonexistent. Today the requirements for tubular products have changed considerably. Operating temperatures and pressures are increasing continually and corrosion, particularly at high temperatures, presents a problem. Carbon steels have, under these conditions, certain economic advantages particularly in oil refinery use. However, the use of low alloy steels in the generation of steam power has increased appreciably due to the influence of molybdenum on creep strength and the control of graphitization with chromium. The behavior of carbon and certain low alloy steels after long periods of exposure at 900° and 1050°F (480° and 565°C) has been investigated. The steels were examined before and after 10,000 to 34,000 hr exposure. Results obtained with material exposed at 1200°F (650°C) are not presented due to the severe oxidation and resulting decarburiza-tion after long periods of exposure. The graphitization characteristics of carbon and low alloy steels are of fundamental concern to the users of these materials. This is particularly true where welded joints are employed. In order to evaluate properly the behavior of steels at elevated temperatures, it is desirable to employ not only long periods of exposure under controlled conditions, but to use material with known properties and steelmaking practices. The purpose of this investigation has been to study the microstructure of the weld and the tensile and creep rupture properties of the parent metal after long periods of exposure at elevated temperatures. In the report&apos;.&apos; of a previous investigation data were presented on the microstructure, impact strength, hardness, and oxidation characteristics after 10,000 hr exposure at elevated temperatures. When this investigation was planned, methods for controlling the graphitization characteristics of steel were not established and, therefore, a number of special alloy steels were included in the study. During the exposure of these steels, the influence of aluminum in accelerating the rate of graphitization and the inhibiting power of chromium were established by various investigators. Also, the vanadium-bearing steels, because of their outstanding creep properties, received attention. As a result of these developments, considerable progress has been made in the field of high temperature tubular products, and the necessity for special alloys to prevent graph-itization has been restricted largely to the use of chromium. Material Chemical analysis, deoxidation treatment, and austenitic grain size of the 59 steels discussed in this paper are shown in Table I. The steels were forged to 1x1 in. bars with the exception of steels 12B, 12DX, 12DY, 12DZ, 70, 70A, 72 to 78, 82, and 83 which were machined from heavy wall pipe. All bars were surface ground before exposure. Heat treatment before exposure is shown in Table 11. The majority of the steels included were melted in either a basic open hearth or basic electric furnace; how-

Jan 1, 1955

By E. S. Machlin

The possibility that formation of voids under creep-rupture conditions may take place by the condensation of vacancies has been investigated theoretically. It has been concluded that nucleation of voids under creep-rupture conditions by vacancy condensation is highly improbable. However, growth of pre-existant voids by vacancy condensation is probable. A number of predictions made in this theory have been verified by the data. It has been predicted and checked that the product of rupture life and steady-state creep rate for preannealed metals and single phase alloys is an approximately invariant quantity, independent of stress, temperature, and atomic number for a given type structure. The direction of the effect of cold work on this product has been predicted and found in agreement with experiment. A number of experiments to evaluate the vacancy condensation mechanism further are described. SEVERAL papers have appeared recently which speculate on the origin of voids formed at grain boundaries under stress.&apos; &apos; The object of this paper is to examine quantitatively the proposition that the voids produced in a creep test are a result of vacancy condensation. A result of this paper is a theory of creep-rupture. Void Nucleation Application of standard nucleation theory" to the problem of void nucleation leads to the following conclusions: 1—Homogeneous nucleation of voids requires a supersaturation ratio (concentration of vacancies in supersaturated to that in saturated solution) of 400 for a reasonable surface energy of 1000 erg per cm-and 1.4 for the improbably low surface energy of 10 erg per cm. 2—Heterogeneous nucleation of voids at plane interfaces between two phases requires a supersaturation ratio of 2.5 for a typical contact angle of 145 3-—Void nucleation about a solid particle may be accomplished at a supersaturation ratio of 1.17 for a typical value of work of adhesion? of 60 erg per The work of adhesion is the surface work 10 replace two solid-vauor surfaces by a solid-solid interface. enr &apos; between an oxide and a metal in the presence of a surface active element such as sulphur. Estimates of the supersaturation ratio at which voids are produced in diffusion experiments yield a maximum of 1.01. Inasmuch as the foregoing mechanisms of void nucleation probably will not operate at this level—too low a surface energy is required—the investigatol. is led to the conclusion that voids must already exist. That is, nucleation of voids probably does not occur. Rather, existing submicroscopic voids grow out to visible size. Already existing voids might be produced during solidification or working. Supercritical sized parlicles which contain cracks may act as heterogeneous void nuclei. Gas pockets may act as void nuclei. Experiments are desired to determine the nature of the heterogeneous void nuclei which grow out to voids in both diffusion and creep experiments. Void Growth Void growth might occur in at least two possible ways, depending upon whether the already existing void nuclei are at grain boundaries or within the grains. In the case of a spherical void far from a crystal boundary, vacancies are generated during creep as a consequence of the migration of suitable dislocation jogs&apos; and are also annihilated at sinks. Under these conditions, a steady-state concentration of vacancies is built up in the crystal, defined by the condition that for any differential volume the rate of generation of vacancies in that volume equals the rate of annihilation of those vacancies." This equality would lead to the development of a gradient of vacancy concentration radially outward from the void surface up to a radius where the vacancy lifetime becomes equal for all directions of vacancy migration. The distance over which this vacancy concentration gradient extends equals about 2vD,T* where D, is the vacancy diffusivity and T:&apos; the vacancy lifetime in a crystal outside the gradient in a zone of constant vacancy concentration. The vacancies generated in the region over which the gradient exists will annihilate more often at the void than elsewhere. Approximately a little over one-half the vacancies generated in the gradient zone will annihilate at the void. Hence, the growth rate of the void is given by on where R is the radius of void in centimeters, is the atomic volume, and R is the rate of generation of vacancies, number per centimeter" per second. R D and T* may be estimated in terms of other physical parameters." In particular, R = n.j e/b [3] where n is the average number of vacancy produc-

Jan 1, 1957

By N. J. Grant, A. W. Mullendore

Three aluminum alloys of 0.94, 1.92, and 5.10 pct Mg, prepared from very high purity metals, were tested at 500°, 700°, and 900°F in creep rupture. The degree of strengthening through solid-solu-tion alloying and the effects on the deformation characteristics and fracture were examined. The ductility of the alloys as a function of stress and temperature was closely followed. STUDIES of the creep process in pure metals in recent years have done much to expand the understanding of the fundamental deformation and recovery processes that contribute to overall creep behavior. In order that this knowledge may be applied to commercial alloys, it is necessary to know the principles governing the effect of alloying on the mechanisms of creep. A limited amount of work has been performed in this field, but few investigators have attempted to follow the changes in particular creep mechanisms with alloying. Recently, studies of the effects of solid-solution alloying on the plastic properties of aluminum have been conducted by Dorn, Pietrokowsky, and Tietz,1 Sherby, Anderson, and Dorn,2 and Sherby and Dorn.3 This paper presents the results of an investigation of the effect of solid-solution alloying of high purity aluminum with magnesium on the creep-rupture properties, and correlates these observations with changes in the creep mechanisms. This work is thus an extension of the creep-rupture observations of Servi and Grant4,5 and the deformation studies of Chang and Grant.6,7 Experimental Procedure Three alloys of aluminum containing approximately 1, 2, and 5 pct Mg were tested. These alloying additions are all within the solid-solubility limit at the testing temperatures.&apos; The analysis of the materials is presented in Table I. The tests fall into two categories: l—creep-rup-ture tests at 500°, 700°, and 900°F, and 2—structure study tests performed primarily at 700°F. Speci-mens of 0.160 in. diameter with milled flats for metallographic observations" &apos; were utilized for the structure studies. All specimens were annealed in one step to give the desired grain size for the tests. Table II presents the annealing data and final grain sizes. The specimens were polished electrolytically before testing with Jacquet solution (2/3 acetic anhydride, 1/3 perchloric acid) at 25" to 30°C, and 15 to 20 v. Creep-rupture testing was performed under constant load with the apparatus previously described." Results and Discussion Creep-Rupture Properties: The log-log plots of creep-rupture data are presented in Figs. 1 and 2. For these very pure single-phase alloys, the minimum creep rate and the rupture life both exhibit straight-line dependence on stress in this method of plotting as they have for commercial alloys0,10 and for pure aluminum." Curve breaks, based on the use of straight-line segments, at 500°F have been found by metallographic study to correspond to a transition from low to high temperature behavior and so represent zones of equicohesion. Specimens on the high creep-rate side of the break showed normal granular deformation processes whereas those on the low creep-rate side showed rapidly increasing grain-boundary sliding and migration with extensive evidence of intercrystalline cracking at 500°F. Two micrographs of the 0.94 pct Mg alloy, Fig. 3, show the increased participation of the grain boundary in the deformation process at 500°F with decreasing stress. In Fig. 3a is shown the structure of a specimen which exhibits little deformation along the grain boundaries and failed transgranularly; in Fig. 3b is shown the increased deformation along the grain boundaries at a lower stress for a specimen which showed appreciable intercrystalline cracking. The severity of intercrystalline cracking increased with increasing magnesium content at 500°F. Intercrystalline cracking disappeared in most of the specimens at 700°F and persisted only in the 5 pct Mg alloy at high creep rates. At 900°F all of the specimens deformed with extensive grain-boundary participation, including extensive grain-boundary migration. None of the alloys at 900°F showed intercrystalline cracking.

Jan 1, 1955

By J. T. Brown

AS far as could be ascertained, no one had previously investigated the creep strength of silicon poly-crystals. Literature has appeared showing evidence for plastic deformation in silicon single crystals and whiskers.*1"6 Also the fact that germanium, a material of similar crystal structure to silicon undergoes plastic deformation under stress at temperatures above about 60 pct of its melting temperature, has been known for some time.2"4&apos;7 This investigation was performed for the purpose of determining the strength and ductility of silicon polycrystals under creep conditions that would give fairly long times to rupture. PROCEDURE The silicon specimen blanks were obtained by first placing granulated transitor grade silicon (99.999 + pct pure) in a silica crucible. The crucible was surrounded by a graphite susceptor, and induction heating was used for melting the silicon in a vacuum furnace. Blank specimens were formed by freezing molten silicon onto a polycrystalline seed of silicon in a vacuum furnace. The seed was attached to a motor driven revolving rod. As silicon solidified, this rod was gradually withdrawn from the melt. A shape with a contracted center section was obtained by varying the rate of withdrawal from the melt. Specimens for the creep-rupture tests were ground from these "pulled" blanks. Creep-rupture tests were performed in spring loaded machines under constant load at 1800" and 2000° F. RESULTS AND DISCUSSION A test specimen which was sectioned longitudinally is shown in the photomacrograph in Fig. 1. Very little deformation has taken place in the portion of the specimen shown, however, slip lines from several slip systems within the same grain, and deformation band formation was seen. The elongated appearance of the grains is due to the method of growing the specimens. One of the most interesting aspects of the results obtained from the creep-rupture tests was the high strength and the accompanying large amount of ductility. The data obtained is listed in Table I which shows the stress to rupture in 100 hr at 2000°F is between 8000 and 9000 psi. This indicates that silicon&apos;s strength at 2000°F is about equal to that of the best commercial super-alloys. It is important to mention that silicon has less than 1/3 the density of iron-, nickel-, and cobalt-base alloys. The usual type alloys for high-temperature applications

Jan 1, 1960

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.&apos; 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 Walter A. Backofen, Donald H. Avery

Intense primary and cross-slip traces were observed in easy glide on Cu: 6 pct-A1 single crystals deformed in tension. A mechanism of cooperative source operation is developed which recognizes that both the applied stress and that resolved from dislocation arrays contribute to the stress on a source. By considering the stress from arrays, the activation of secondary systems in easy glide and the difference in appearance of slip markings on pure and solid-solution crystals are explained. Furthermore the cross-slip system is predicted to be second favored during easy glide for a large range of orientations. FROM many studies of easy glide in fcc metal crystals, a pattern of observations has developed which still requires full explanation. In pure copper, aluminum, and silver, the easy-glide, slip traces are fine and uniform with steps 50 to 100A on the primary* system.1-4 Yet it has not been at all clear why slip in the pure materials should occur in this way. On the contrary, one might expect, with simple slip and a low hardening rate, that the weakest sources on the primary system would operate extensively to produce strong slip traces. In a brass, however, intense slip steps up to 0.5 are found on both primary and cross-slip system4,6-9 seeger10 has pointed out that in a material of low stacking-fault energy such as a brass, extensive easy-glide cross-slip could not be thermally activated, but rather must originate on the cross-slip plane. In further explanation, the wilsdorfs4 and seeger10 noted that only the cross-slip system would not harden differently than the primary, whatever the latent hardening tendencies of other systems; therefore, in brass, which exhibits high latent hardening, the cross-slip is the only secondary system which could be expected to operate extensively, once it became active. The explanation of how the cross-slip system, on which the applied stress is low, becomes activated has been related, in a nonspecific way, to pileups by Hirsch11 and Honeycombe.l2 In the work to be described, deformation traces on solid-solution Cu: 6 pct A1 single crvstals were studied with conventional light microscopy and a mechanism proposed to explain both the observed activation of secondary systems in easy glide and the difference in appearance of slip markings on pure and solid-solution crystals. EXPERIMENTAL In preparing the Cu-A1 single crystals, rectangular bars approximately 0.4 in. by 0.4 in. by 6 in. were first machined from ingots made by vacuum melting copper of 99.999 pct and aluminum of 99.99 pct purity. They were then packed in powdered graphite and the crystals grown in a modified Bridgman apparatus at a rate of 5 mm per hr under an atmosphere of purified nitrogen. Crystal perfection as indicated by Laue back-reflection spots was good except for the last inch to freeze, which was discarded. Orientations so determined are shown in Fig. 1. Tensile specimens with a reduced gage section were obtained by masking the ends with electrical tape and chemically polishing in a solution of 20 pct HNO3, 24 pct HAc, 52 pct H3PO4, 2 pct Hcl, and 2 pct H20 at room temperature.13 Finally, the specimens were electropolished in a 30 pct ortho-phosphoric acid bath at 12 v. Tensile deformation was performed in an Instron testing machine at a strain rate of approximately 1 pct per min. During easy glide, extensive cross-slip was observed with all crystals, in spite of the low Schmid factor on this system, and in no case was any other secondary trace encountered. A certain sequence of slip-line development was associated with the extension. At yielding, intense primary traces passing completely through the crystal developed at some point on the gage section, generally near the grips; weak cross-slip traces also appeared, extending from the primary traces into the adjacent undeformed crystal, Fig. 2. Further extension led to primary traces adjacent to the first-formed and connecting with those of the cross-

Jan 1, 1963

By Bernard S. Borie

THE U-A1 binary system has been studied by Kaufmann and Gordon.&apos; They have shown that three intermetallic compounds occur in the system: UAl², UAl², and a third compound tentatively identified as UA15. UA1³ is simple cubic, a, = 4.26A. Its unit cell contains one formula weight, and it is iso-morphous with AuCu³. UA1² is face-centered cubic, a, = 7.72A, with eight formula weights per unit cell. Rundle and Wilson have shown that it is iso-morphous with Cu²Mg.² A Debye-Scherrer pattern of the Al-rich compound indicated a more complex structure than either UA1² or UA1³. The following is a report of an investigation of the crystal structure of this compound and a determination of its stoi-chiometric formula. A melt of uranium (99.9 pct pure) and aluminum (99.9 pct pure) was prepared which contained about 25 pct U by weight. It was cooled from 950" to 650°C at a rate of 500" per hr and then taken from the furnace and air cooled. An X-ray diffraction pattern of the ingot showed only lines of aluminum and the Al-rich compound. Filings from the ingot were reacted with a solution of sodium hydroxide, producing a fine black powder, the diffraction pattern of which showed no traces of aluminum. A comparison of the Debye-Scherrer pattern of our sample with the data published by Kaufmann and Gordon1 showed that it is identical with the Al-rich phase which they reported. Single crystals were obtained by cooling the melt more slowly (about 50°C per hr). After reaction with sodium hydroxide, the crystals appeared as small black needles attached to the ingot surface. Cell Size, Space Group, and Uranium Positions A series of Weissenberg photographs for rotation about two of the crystallographic axes, taken with copper radiation filtered through nickel foil, revealed an orthorhombic cell of dimensions: a = 4.41 ± 0.02A b = 6.27 ± 0.02A c = 13.71 ± 0.03A Reflections of the type hkl were observed only if: h + k + I = 2n, of the type hkO only if: h = 2n and k = 2n, of the type h01 only if: h + 1 = 2n, and of the type Okl only if: k + 1=2n. Hence, the cell is body-centered with an 001 glide plane. The evidence for the existence of the glide plane is the observed extinction of 23 possible re- flections of the type hkO with at least one index odd. There are only two space groups consistent with these data: C"" — I2ma and D28 2h — Imma.³ he possible sets of atomic positions for these space groups are: 12ma: (0 0 0; ½ ½ ½) + 4: (a) x 0 %; x % % (b) x ¼ z; x ¾ Z 8: (c) x y z; x y z; x, ½ + y, Z x, M - y, z Imma: (0 0 0; ½ ½ ½) + 4: (a) 0 0 0; 0 ½ 0 (b) 0 0 ½; 0 ½ ½ (c) ¼ ¼ ¼; ¾ ¼ ¼ (d) ¼ ¾ ¾ ; ¾ ¾ % (e) 0 ¾ Z; 0 ¾ z 8: (f) x 0 0; x 0 0; x 1/2 0; x ½ 0 (g) ¼ Y ¼; ¾ Y ¾; ¾ y ¼; 1 y ¼ (h) 0 y z; 0; ;; 0, ½ + y, z; 0, l/2 - Y, Z (i) x 1/4 z; x ¾ z; ¼ z; x ¾ z 16: (j) xy z; x y z; x y z; x y z; x, ½ + y, Z; x,½ - y, z; x, ½ - y, z; 11 1, + y,Z Though density measurements on different samples were found to vary somewhat, they were all within the range 5.7 * 0.3 g per cu cm. If it is assumed that the unit cell contains four formula weights of UAl,, it is 6.5 g per cu cm. If there were as many as eight uranium atoms per unit cell, the

Jan 1, 1952

By C. A. Queener, W. L. Mitchell

In recent years bismuth telluride has received considerable attention, primarily due to its value as a thermoelectric material. Since there seems to be little dependence of thermoelectric effect upon crystal orientation1 many of those who have previously worked with this material have been unconcerned with knowing its crystallographic angles to any degree of accuracy. However, when one studies deformation modes, lattice stresses, or the aniso-tropy of mechanical properties of a material, knowledge of the interplanar angles and their relationships as depicted in a stereographic projection becomes essential. Lange2 originally published crystallographic data which described the structure of bismuth telluride as rhombohedral with the space group A more recent work by Francombe3 presented data which corroborated and refined the original findings of Lange. In addition, Francombe established that there is no coexistence of rhombohedral and hexagonal lattices in bismuth telluride as was suggested by Vasenin and Konovalov,4 and that the structure can be treated as a pseu do hexagonal structure with an axial ratio, c/a, of 6.95 for convenience of presentation and study. The interplanar angles and standard projections for several unalloyed hexagonal metals have been previously published,5-9 but the present work appears to be unique in that it presents data for a rhombohedral compound in pseudohexagonal form. As a pseudohexagonal structure, this material has an extremely large axial ratio as compared to the usual range of approximately 1.5 to 1.9 for the hexagonal metals. Since the interplanar angles are a function only of c/a, the angular relations between various planes for Bi,Te3 will be grossly different

Jan 1, 1965

By R. E. Frounfelker, W. M. Hirthe

INVESTIGATORS in the areas of plasticity, crystal growth, and stress analysis have a need for crys-tallographic data such as the interplanar angles. This information is utilized in the form of a stereo-graphic projection from which orientation determinations can be made. Calculations of mechanical properties, such as the critical resolved shear stress, require values for the angles between directions as well as the interplanar angles. Only a limited amount of this data is available for tetragonal crystals. The equations for these angles are relatively simple but because of the large numbers of angles involved and the infinite number of structures that could be investigated, it was decided to program these calculations on a high speed digital computer. The angle, 8, between two crystal planes (h1 k1 l1)

Jan 1, 1962

By L. Guttman, C. S. Barrett, J. S. Bowles

THE transformation from the face-centered cubic (Al) to the face-centered tetragonal (A6) structure in certain alloys of the indium-thallium system reported in the preceding paper1 exhibits many interesting crystallographic and metallo-graphic features, most of which presumably are similar to those of other cubic to tetragonal transformation such as, for example, the one which occurs in the chromium-manganese system,2 the one which, judging by microstructures and X-ray pat-terns,3 probably occurs in the copper-manganese system, the ones accompanying ordering in FePt,4 Copt,&apos; and AuCu,5 and the transformation near 115°C in barium titanate.6,7,8 If, as mentioned in ref. 1, the transformation is second order, the phases in equilibrium do not differ in composition, and it is both possible and likely that the mechanism is a diffusionless one. The present paper reports the results of a detailed study of the indium-thallium transformation and presents a theory for the atomic movements of the transformation which accounts for the observations. Experimental Crystallography of Transformation Markings The transformation from cubic to tetragonal in the indium-thallium alloys produces microstruc-tures of the type illustrated in fig. 1. These structures are observable either as relief effects produced on a smooth surface by the transformation, or after polishing and etching. These microstruc-tures are markedly similar to those found in copper-manganese alloys: iron-platinum alloys," and barium titanate,7,8 where it has been demonstrated that the lamellae are parallel to the (101) planes of the original cubic crystal. That the observed lamellae in indium-thallium alloys are also parallel to the (101) planes was proved by the following analyses performed on single grains in polycrystal-line samples containing 20.75 atomic pct T1. A study of the microstructures of a number of specimens revealed the fact that in many specimens the transformation markings continued unchanged in direction across the (111) interfaces of annealing twins. This at once demonstrates that the lamellae are parallel to a plane that is common to both parent and twin orientations, i.e., a plane in the zone <112>. This conclusion is compatible with the lamellae being parallel to (101) planes. To make a more complete determination of the habit plane of the lamellae, two grains were selected in which annealing twins ({Ill) twins) had been present in the high-temperature modification (cubic). The traces of the annealing twins, and of the transformation markings in both parent and twin crystals, were plotted together in stereographic projection, and a parent-twin pair of orientations was found that accounted for all lamellae as (101) planes. The projection of one of these twinned grains is reproduced in fig. 2. In view of these results the probability of there being another solution for the habit plane remote from (101) is very small, but to explore the possibility that the habit plane deviates slightly from (101), a more precise analysis was undertaken. In this, the orientation of a grain in the cubic modification was determined from a Laue back-reflection photograph taken with the sample at 90°C. The traces of the lamellae that formed in this grain on cooling were plotted in the stereographic projection

Jan 1, 1951

By A. E. Dwight

Lattice parameters were determined for eighteen equiatornic alloys of the CsCl-type structure, ten of which were previously un-reported. It was found that fomation of the CsCl-type structure in binary alloys of the transition elements is largely dependent on position of the elements in the periodic table. The relative size of the two elements was not found to be a controlling factor. A recent paper by Beck, Darby, and Arora1 corre-lates the occurrence of CsC1-type ordered structures with the position of the constituent elements in the periodic table for the first long period. It was also suggested that a definite increase in relative bond strength between unlike atoms occurred when, in binary alloys of iron-group elements, the other component is changed from a chromium-group element, to a vanadium-group element, to titanium. A later paper by Philip and Beck2 noted that the lattice contraction increased in the order CrFe, VFe, and TiFe. It was also noted by Philip and Beck2 that the lattice contractions of CsC1-type alloys decreased in the order: TiFe, TiCo, and TiNi, which is an apparent reversal of the contractions expected from the position in the periodic table. It was suggested that the increasing lattice contraction is an indication of increased stability, i.e., greater A-Bbond strength. The present investigation was carried out to determine whether the relation of the position in the periodic table to the formation of the CsC1-type structure was also correct for alloys involving the second and third long-period elements. A systematic search was made for CsC1-type structures among equiatomic alloys and for those found, the lattice contraction was determined. EXPERIMENTAL TECHNIQUE The elements Y, Gd, Ti, Zr, Hf, V, and Cb are designated the A group and the elements Mn, Re, Fe, Ru, Os, Co, Rh, Ir, Ni, Pd, Pt, Cu, Ag, and Au are designated the B group. Equiatomic alloys were prepared for 57 AB combinations. The alloys were arc melted in a multicrucible furnace3 in buttons ranging from 5 to 20 g. Chemical analyses were not made, as the charge weights agreed closely with those of the buttons after melting. The alloy buttons were homogenized at 800° to 900°C. Metal log raphic and X-ray specimens were prepared and heat treated at temperatures from 600° to 1200°C. Specimens for X-ray diffraction were usually ground to a powder in an agate mortar; however, needle-shaped solid specimens were used when the alloy was sufficiently ductile to permit their preparation. Diffraction patterns were taken with a Straumanistype Debye-Scherrer camera using filtered Cu or Co radiation. The lattice parameters were obtained in A by plotting the calculated a0 values against the cos29/sin 0 + cos2?/? function and extrapolating linearly to ?= 900. Metallographic control specimens were polished on cloth wheels with diamond paste and etched with various phosphoric and nitric acid reagents. RESULTS The eighteen equiatomic alloys listed in Table I gave evidence of a cubic structure with two atoms in the unit cell, although two of these cubic structures exist only at elevated temperatures and transform to a tetragonal structure on quenching. Nine of these eighteen alloys gave diffraction patterns with super-lattice lines showing that the structure is of the CsC1-type. The lack of superlattice lines in patterns of the other nine alloys may be attributed to the small difference in atomic scattering power of the components. Metallographic study indicates the occurrence of nine narrow single-phase fields at the AB composition. Any or all of these nine may also have a CsC1-type structure. The VFe alloy was found to have a CsCl-type structure by Philip and Beck2 through the use of CrKa radiation (for which the scattering factor of V is anomalously low), whereas the Cu radiation used

Jan 1, 1960