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By M. J. Buerger

Possibly the most puzzling features observed during a single-crystal deformation test are the appearance of slip striae on the surface of the crystal and the strengthening of the specimen.' While the first phenomenon is mainly of theoretical interest, the latter is fundamental to all strain-hardening and cold-working processes in which the deformation occurs by translation. The plastic deformation of crystals has received considerable discussion2 and need not be reviewed here in any great detail. It has been observed, essentially, that after a certain amount of. initial stress is applied, the surface of the crystal becomes covered with sets of parallel striae or rings which appear to divide it into thin slabs or slip blocks.3 The striae are the traces of rational crystallographic planes along which shearing movements are localized, these movements providing the strain which accompanies stress applied beyond pure elasticity. As deformation under the applied stress proceeds the slip blocks shear past one another, although the essentially single-crystal character of the specimen is unimpaired. All of the shearing apparently takes place in the immediate vicinity of the original slip striae without the appearance of new planes of movement.4 Since each increment of strain is attended by an increased stress requirement to continue the deformation, the crystal strengthens during the process.

By Chi-shing Wang

The late Professor P. B. Bucky of Columbia University introduced the principles and techniques of barodynamic experimentation in early 1931 by the application of centrifugal loading to achieve dynamic similitude between models and prototypes of mine structures.1 Later, he and his associates introduced the combined experimental technique of photo- elasticity and the centrifuge to determine the stress distribution in civil engineering structures and mine workings by the use of transparent bakelite models.2,3 The photostress technique, also known as the birefringent-coating method of photoelastic stress analysis, dates back to 1930, when Mesnager published its principles.4 Since then it has been widely applied to experimental stress analyses in many industries. A practical method of observing the dynamic behavior of opaque mine models, which are made of prototype materials, by means of a combination of the centrifugal and the photostress techniques is a new experimental approach under development at the Henry Krumb School of Mines, Columbia University.5 This paper summarizes the development of the barodynamic photostress technique and presents the information obtained from a recent series of experiments in the study of the behavior of rock beams loaded by their own weight. THEORETICAL BACKGROUND Theory of Pure Bending In the general theory of strength of materials, the flexure stress at any point in a beam of any type of cross section which has a longitudinal

Jan 1, 1968

By M. J. Buerger

POSSIBLY the most puzzling features observed during a single-crystal deformation test are the appearance of slip striae on the surface of the crystal and the strengthening of the specimen.1 While the first phenomenon is mainly of theoretical interest, the latter is fundamental to all strain-hardening and cold-working processes in which the deformation occurs by translation. The plastic deformation of crystals has received considerable discussion2 and need not be reviewed here in, any great detail. It has been observed, essentially, that after a certain amount of initial stress is applied, the surface of the crystal becomes covered with sets of parallel striae or rings which appear to divide it into thin slabs or slip blocks.3 The striae are the traces of rational crystallographic planes along which shearing movements are localized, these movements providing the strain which accompanies stress applied beyond pure elasticity. As deformation under the applied stress proceeds the slip blocks shear past one another, although the essentially single-crystal character of the specimen is unimpaired. All of the shearing apparently takes place in the immediate vicinity of the original slip striae without the appearance of new planes of movement.4 Since each increment of strain is attended by an increased stress requirement to continue the deformation, the crystal strengthens during the process.

Jan 1, 1928

By J. J. Kantner

CREEP investigators have made extensive studies to determine the interrelation of stress, temperature and the tensile creep rates of metals. It has been suggested that at small stresses the secondary or constant creep rates obey a simple viscous law. Building upon this suggestion, departure from pure viscosity as stress increases may be expressed mathematically as a consequence of reversibly altered viscosity or "flowability" in the same sense that temperature change reversibly alters viscosity. From the index to alteration of viscosity, a value for the energy of secondary creep may be derived having the magnitude of the free energy of vaporized metal. The suggestion is made that applica-tion of stress alters the energy of secondary creep. Strain energy is argued to be but a minor factor in the energetics of secondary creep. A deformation mechanism involving the large energy associated with secondary creep implies a sort of solid self-diffusion process. Evidence indicates that creep strain above the recrystallization temperature takes place by crystallographically directed self-diffusion at grain boundaries and points of crystal defects. A self-diffusion theory of secondary creep is proposed, embracing the principles of the Dushman-Langmuir theory of solid diffusion. An equation is suggested whereby the rate of tensile creep may be related directly to the physical and struc-tural character of the solid metal.

Jan 1, 1937

By V. S. Tuman

In the first part of this paper, an estimate is made of the magnitude and extent of the thermal stresses which result from mud circulation. Our study is made for the period of relaxation, i.e., when the drilling operations are terminated and mud circulation is discontinued. In the second part, we have shown how the thermal stress can affect the wave propagation. An example is worked out for a Carbondale sandstone (Illinois basin). It is concluded that, in extreme cases when differential temperature is about 100°F, the travel time will be affected by about 2 microsec/ft. For more refined permeability studies, such corrections would be desirable. MAGNITUDE AND EXTENT OF THERMAL STRESSES RESULTING FROM MUD CIRCULATION When geological beds are penetrated by boreholes, it is observed that the formation temperatures increase with depth; however, the temperature profile varies considerably from place to place. During drilling operations, mud pumped from a pit at atmospheric temperature absorbs heat from the lower beds. As a result, the drilling fluid returning to the surface is at a higher temperature than the surrounding beds. The temperature gradient in a well depends on the rate of mud circulation and other factors; normally, this temperature gradient is smaller than the natural gradient in the formations. (See Fig. 1.) The temperature difference between the mud column and the surrounding beds gives rise to therma1 stresses (which are also important in the phenomenon of fracturing), and it is expected that they will affect the transit time of the sonic front in velocity logging.1 It is evident chat beds near the surface will undergo various cycles and will have a complicated dynamical and thermal-stress history. A limestone bed which is just penetrated will act as a source of heat, warming up the cold mud pumped down a few minutes earlier from the surface pit. The same limestone bed a week later will act as a sink, absorbing heat from the drilling mud which has already warmed up sufficiently to be at a higher temperature than the bed in question. No doubt a large section of the hole will undergo a heat treatment, which will make the calculation of the exact magnitude of the thermal stresses very difficult. In the solution of wellbore thermal equation, it is assumed that the rock around the wellbore is elastic and isotropic, and that the system is radially symmetrical. A complete dynamical solution of the thermal stresses set up at different horizons during the drilling operations would require a comprehensive history of the mud circulation, the surface temperature of the pit and the number of hours in which mud was not circulated. CONDUCTION OF HEAT AND THERMAL EQUATION OF STATE

By C. Fairhurst, A. M. Starfield

As a practicing mining engineer, I face many rock mechanics' problems daily and would like to mention one or two examples to illustrate the current gap between laboratory investigations and actual field problems. I would like to endorse Dr. Obert's suggestion that more field measurements and observations should be undertaken. There is an ever-increasing body of data beginning with Hast's results in Sweden,l then measurements at Elliot Lake, Canada, and so on, including our own measurements at White Pine, which clearly indicate that the horizontal stresses underground are often at least as large as the vertical stresses. Visual obsenation of the deformation of roof and pillars (including failure due to horizontal compression) also demonstrates that the horizontal stresses are often most important. Yet almost every laboratory investigation begins with the assumption that the only stresses acting are vertical. Roof spans in layered formations. for example, are calculated on the assumption that the rock behaves as a gravity loaded beam. This is all too often unrealistic. Roof bolts are also often considered to be simply means of suspending the gravity loaded beams. As Dr. Reed has mentioned they are probably, in fact, acting to restrain a beam which is attempting to buckle due to lateral pressure. The fact that moisture can reduce the strengths of some rocks as much as 50 percent has been known for many years. In the mine me are almost always faced with wet rock, yet no one has investigated ways in which this wakening effect can be overcome. as, for example, by waterproofing the rock. C. Fairhurst, University of Minnesota I would like to mention that we have found,2 from stress-relief determinations, that appreciable (over 1000 lb per sq in.) horizontal pressures occur also at the surface in granites quarried in central Minnesota. Whilst I agree that more field measurements are desirable, it is important to point out that most university research is undertaken by graduate students who must attend classes daily. Their research is therefore restricted to the laboratory. A.M. Starfield, University of Minnesota No one denies the importance of obtaining: data from field measurements. It is equally important, however, that field measurements be guided by theory. Much time and money can be wasted by indiscriminate measurement. An example of the value of theory in interpreting measurements is given in Dr. Obert's comments on the time dependent strain observed in a salt mine. He anticipated that the stress at the wall of the opening would change with time because salt is viscoelastic rather than elastic. It can be shown from theory that if an excavation in a viscoelastic medium is unsupported, then the stress at the wall does

Jan 1, 1967

By M. E. Fine, A. A. Hendrickson

The critical resolved shear stress and the strain rate dependence of the .flow stress are reported for Ag base A1 single crystals up to 6 at. pct A1 over a temperature ralzge of 4.1° to 470°K. At room temperature the solid solution strengthening is attributed brinciballv to an increase in the dislocation density on alloying. At 42°K the alloys are relatively stronger because the dislocations widen on alloying and are more difficult to cut. In a previous paper, the authors reported the characteristics of strain aging in Ag base A1 alloys.' The variation of the magnitude of the strain-aging yield drops on aging time, aluminum content, and testing temperature strongly indicated that the phenomenon is due to the Suzuki mechanism. In the present paper, the critical resolved shear stress (CRSS) and the strain rate dependence of the flow stress are reported for Ag base A1 single crystals as functions of testing temperature (4.2" to 470") and A1 content (0 to 6 at. pct). Observations on the substructure and measurements of the effect of crystal growth rate are also given. The experimental re- sults appear explainable considering that aluminum additions increase the dislocation density and dislocation width. EXPERIMENTAL METHOD The methods of specimen preparation and tensile testing were described previously.' Briefly, single crystals were grown from the melt in a vacuum (1 x lom5 mm Hg), shaped into tensile samples by a combination of abrading and acid etching, annealed at 850°C in a vacuum (1 x 10" mm &Z) for several days, and furnace cooled to 200'. The testing was done on a model TM Instron using friction grips and a strain rate of about 5 x 106 per sec unless otherwise noted. The various testing temperatures were obtained by immersing the specimens in the following media: 1) 4.2': liquid helium using the apparatus of G. Byrne;' 2) 77°K: liquid nitrogen; 3) 200"K: dry ice and acetone; 4) 415' K: ethylene glycol; 5) 460' \ to 480' : molten Stanalax. In the determination of the CRSS above 296' K, a ratio method was used; the crystals were strained initially at the higher temperature, 0.1 pct shear strain, and then tested at 296' . The ratio of the flow stress between the two temperatures was then multiplied by the average CRSS at 296' K to obtain the value of the CRSS at the high temperature. (The test at 296' showed a yield point resulting from strain aging; the flow stress at 296' K was taken as the lower yield stress.) The ratio method, we believe, is more accurate than using different crystals since

Jan 1, 1962

By J. E. Hanafee, G. J. London

MANY studies of the deformation behavior of materials under a superimposed hydrostatic pressure have shown that materials brittle at ambient pressure behave in a ductile manner under pressure. Thus, with a metal such as beryllium which possesses relatively low ductility, but otherwise exhibits quite useful physical and mechanical properties, hydrostatic pressure may be particularly useful for both forming beryllium shapes and studying its deformation behavior. In fact, it has been found1"4 that polycrystal-line beryllium in both ingot and powder form appears to behave in a more ductile manner on a macroscopic level in a hydrostatic pressure environment, and it has been suggested2 that this is due to activating a new slip mode. Furthermore, Andrews and Radcliffe5 have found pressure induced nonbasal dislocation activity in hot pressed beryllium. Recently6 it has been shown in "c-axis" compression tests under hydro-static pressures up to 28 kbars that the shear stress needed to cause slip with a Burgers vector out of the basal plane (pyramidal slip) does not change with increasing pressure in beryllium with a purity of some 99.5 pct. This material is equivalent or more pure than the beryllium used in the previous pressure studies. Thus, it appears, as suggested by Inoue et al.,3 that the hydrostatic pressure affects the fracture stress rather than the stress necessary to activate pyramidal slip in beryllium. However, in "c-axis" pressure tests on high purity 12 zone pass beryllium (˜50 ppm total impurities) the macroscopic compression stress needed to cause pyramidal slip was considerably lower than that at ambient pressure.6 It has further been shown that alloying beryllium with nickel and copper in the range 2-5 wt pct also favors the occurrence of pyramidal slip in "c-axis" compression tests,7'8 while lower amounts of nickel and copper do not have significant effects. In the present study the combined effect of hydrostatic pressure and alloying high purity beryllium on the shear stress needed to cause pyramidal slip has been ascertained. A 2.5 wt pct Cu alloy was selected as the first alloy to study as this level of copper did favor pyramidal slip at room pressure. A high purity (12 zone pass) single crystal of beryllium 0.3 by 0.1 by 0.1 in. was cut and polished by an orientation and lapping technique8 so that the top and bottom compression surfaces were parallel and within 3 min of arc to the (0001) plane and the sides parallel to the {l010} and {ll20} planes. In these compression specimens, therefore, the resolved shear stress was nearly zero on both the basal and prism planes, and slip was restricted to pyramidal systems. Analysis of slip traces on the two lateral surfaces served to accurately identify the active slip planes.6'9 The pressure unit was a modified piston-cylinder device fitted with a manganin transducer coil arrangement which continuously monitored and recorded the hydro-static pressure. The load on the specimen was measured by a strain gage load cell which operated entirely within the pressure chamber. This load cell was calibrated before and after each pressure cycle at room pressure in situ and the calibration did not vary more than ±1 pet. These techniques and devices have been previously described in more detail.6 Successively higher compressive stresses were applied to the single crystal under a superimposed hydrostatic pressure until fracture occurred. The strain rate was (4.5 ± 2.0) x 10-6 sec-1 and the average rate of pressure application and release was approximately 0.3 kbars per min. As the load on the specimen was applied by the piston which was used to increase the hydrostatic pressure, the pressure increased during the compression test. This increase ranged from 0.0 to 0.8 kbars, and the maximum hydrostatic pressures are quoted in Fig. 1. The lateral surfaces of the specimen were examined in a light microscope after each pressurization/stress cycle so that the stress at the onset of {1122} pyramidal slip could be ascertained. Post compression height measurements allowed the plastic strain in the specimen to be evaluated to within 0.03 pct. The resulting compression stress-plastic strain curve is shown in Fig. 1 with results of a "c-axis" test on a similar Be-2.5 wt pct Cu single

Jan 1, 1970

By D. H. Baldwin, R. E. Reed-Hill

Six compositions of polycrystalline ZY-0 alloys, containing up to 4.2 at. pct 0, were tested in tension between 77° and 600° K. The data obtained from each of the compositions corresponded closely to a rela-ion between yield stress and absolute temperature of the form In s/so = BT, where oo is the yield stress extrapolated to zero degrees and B is a constant. In agreement with others who have observed this relationship, it is shown that the activation energy may be expressed as Ho In so/s. In the present specimens Ho is approximately 18,000 cal per mole and is apparently independent of temperature and composition inside the limits of the investigation. It is also demonstrated that this form of activation energy cowesponds to a strain rate sensitivity parameter RT/Ho. Oxygen was also noted to have an effect upon the operative deformation mechanisms. With increasing oxygen concentration there was an increased tendency to observe both nonbasal slip and cross-slip phenomena. Oxygen does not seriously inhibit twinning more than it does slip. Twins were observed in all specimens tested. It is becoming increasingly evident that interstitial atoms in solid solution are able to interact strongly with mobile dislocations. Stein, Low, and seybolt,&apos; have shown that, if the carbon concentration in bcc iron is lowered below the solubility limit, its flow stress temperature dependence is markedly reduced. This suggests that carbon atoms in interstitial solid solution may be responsible for the pronounced temperature dependence of the flow stress normally observed in iron. This view has recently been challenged by Leslie and sober2 who observed a strong flow stress temperature dependence in iron to which a trace of titanium had been added in order to remove carbon atoms from solution. Since the interstitial concentration must be reduced below approximately 1 ppm in order to produce a pronounced effect on the flow stress temperature dependence,&apos; studies of the effect of interstitials on the flow stress in iron necessarily involve serious experimental difficulties in alloy preparation. There are other metals, however, in which strong effects of interstitial solutes upon both the flow stress and its temperature dependence are observed. Of particular significance is zirconium which, according to Domagala and Mcpherson, 3 is capable of dissolving 28.6 at. pct O. The O-Zr alloy system is an almost ideal system for studying the interaction of interstitial atoms with deformation modes since it is possible to form alloys capable of study over an extensive range of compositions. Mills has made such a study using single crystals oriented primarily for single prismatic slip4 and has found an effect of oxygen concentration on the flow stress temperature dependence analogous to that observed in iron due to carbon by Stein, Low, and Seybolt. The present paper is specifically concerned with the effect of oxygen on deformation in polycrystalline zirconium. Although plastic flow in this type of specimen is much more complex than that reported for the single-crystal work, and involves both slip (on several different types of planes) and mechanical twinning, the results of this investigation are in general agreement with the single-crystal observations concerning the effect of oxygen on the temperature dependence of the flow stress. In addition, they also demonstrate that oxygen affects the acting deformation systems. This is in contrast to single-crystal results4 that showed only single slip on a prism plane. EXPERIMENTAL PROCEDURE Material. High-purity hot-rolled zirconium strip, 0.2 in. thick by 4 in. wide, of 0.10-mm average grain diameter, was used for forming alloys. It was obtained from the Carborundum Metals Co., Akron, N.Y., whose analysis indicated the major impurities were, in wt ppm: Hf, 540, C, 145; Fe, 100; and 0, <80. The plate texture was similar to a wire texture, with basal planes generally parallel to the rolling direction and basal poles randomly distributed about the rolling direction. The heat treatments described below did not appreciably alter the basic texture. specimen Preparation. Small threaded-end tensile specimens were machined from the plate with axes perpendicular to the rolling direction. These transverse specimens had gage sections 1 in. long by 0.060 in. in diam. The small gage section diameter was dictated by the fact that the alloys were formed by dif-

Jan 1, 1969

By G. T. Hahn, C. N. Reid, A. Gilbert

An evaluation is made of the possible cautsal relationship between twinning and fracture in molybdenum. For both single and poly crystalline material no instance of twin-induced fracture was observed. Instead brittle fracture was found to be slip-induced at heterogeneities. For single-crystal material, the yield stvess in compression and the fracture stvess in tensiow obey a similar angular- relationship which follows approximately a 1/cos2 ? law. where 0 is the angle between the specimen axis and the nearest (100) plane. This sittlilarity between yield and fracture behavior casts doubt on the interpretations made previoltsly that a 1/cos2? relationship supports a critical normal fracture stress criterion. SINCE fracture in brittle materials takes place at stresses an order of magnitude lower than the theoretical strength of the lattice, it must be postulated that some stress-concentrating effect is operative during the fracture-initiation process. Several mechanisms have been proposed whereby the necessary stress concentrations could be produced. The well-known Cottrell mechanism1 describes a dislocation interaction which can lead to the formation of an incipient cleavage crack on a cleavage plane, and both zener2 and stroh3 have discussed models which predict the stress concentration at the intersection of a slip band with a grain boundary. When twinning occurs twin/twin intersections and twin/grain boundary intersections represent another possible means of fracture initiation. Although still controversial, the concept of twin-induced fracture is supported by a weighty mass of evidence, which has been reviewed in a recent paper.4 This investigation was conducted in order to assess the extent to which the brittleness of molybdenum can be ascribed to this cause. Emphasis was placed on seeking direct metallographic evidence for twin-induced fracture such as arrangements of twins located at the fracture origin. EXPERIMENTAL PROGRAM Materials. The experimental materials are described inTable I. From the chemical analyses and estimates of the amounts of interstitials likely to be retained in solution,5 it is concluded that all were mul-tiphased systems. X-ray diffraction experiments6 showed no evidence of preferred orientation in the polycrystalline materials. Single crystals were grown from Molybdenum X and Y using the floating-zone technique,&apos; in a vacuum of better than 3 x 10-5 Torr. However difficulties were experienced with Molybdenum X due to violent gas evolution from the molten zone, and additional crystals (Crystals 3 to 6) were produced by annealing for 5 1/2 hr at 2300°C under a vacuum of 10-4 Torr. Techniques. A series of tension, compression, and bend tests was conducted. Tension tests were used to demonstrate brittle behavior, to measure brittle-fracture stresses, and to provide fractured specimens for metallographic inspection. Compression tests were employed in order to obtain some ductility and a measure of the yield stress. Furthermore, it was considered that compression loading would permit the study of crack nucleation in the absence of propagation. The bend tests were conducted to facilitate identification of the fracture origin, which would be expected to be at, or near, the tensile surface of the sample. Tests were carried out at temperatures between 78" and 298°K attained by means of a liquid-nitrogen evaporator of modified Wessel design.&apos; Specimens were fashioned by mechanical grinding, and, prior to heat treatment, were electropolished at 10 v in a 3:l mixture of ethyl alcohol and sulfuric acid, using a stainless-steel cathode. Except where noted, a strain rate of 4 pct per min was used. All specimens had a gage section 0.75 in. long; diameters of 0.10 and 0.20 in. were adopted for the tension and compression specimens, respectively, the former of single shoulder design, the ends being gripped in split collets with a conical bearing surface. In the bend test, electropolished specimens measuring 0.080 by 0.25 by 1.25 in. were deformed at 78°K by four-point loading. The bending device had spans of 1 in. between the outer and 4 in between the inner fulcra; it was stressed between the compression anvils of the Instron machine at a constant deflection rate. EXPERIMENTAL RESULTS Polycrystals. Tension and Compression Tcsls. It is apparent from Fig. 1(a) that above 170°K fracture of Molybdenum X takes place at stresses equal to or greater than the compressive yield stress whereas

Jan 1, 1967

By A. Wahab Khair

This paper presents an analysis of fracture mechanisms in coal subjected to bi-axial state of stresses, indentation of laterally con- fined coal specimen. Coal specimens were loaded to failure by the straight wedge indenters at various lateral confinement pressures. Strain distribution and acoustic emission characteristics of coal specimens under stress were recorded. The influence lines of vertical forces acting on the horizontal straight boundary of the coal specimen for each type of wedge indenter have been established using holographic interferometry technique. The effects of wedge indenter angle, confinement pressure, and coal anisotropy on fracture types, failure modes, and post-failure conditions were studied. The results indicated that combined application of holographic interferometry and acoustic emission monitoring techniques is not only suitable for studying deformability of heterogeneous and microscopically discontinuous material under stress but it also enhances the mode of fracture during the post failure stage.

Jan 1, 1984

By Sherwin F. Kelly

THAT gold ores occur in Georgia is a fact apparently not widely known outside of that state, yet in the last hundred years nearly $18,000,000 worth of gold has been mined there. The discovery of gold-hearing quartz was made in 1823 on the "Forty Acre Lot" (which now belongs to the Columbia Mining Co.), in McDuffie County, and about seven years later the first stamp mill on record was erected near there. In recent years Georgia&apos;s gold production has dwindled to an insignificant figure. However, with the increase in gold price, interest in this district has been revived, so an electrical geophysical survey was undertaken to aid in discovering new quartz veins, on a part of the Forty Acre Lot, the adjoining Hamilton mine, and the nearby Woodall property.

Jan 1, 1934

By Edward B. Cook

INTRODUCTION. THE installation of the Gayley Dry-Air process appealed specially to the management of the Warwick Iron & Steel Co., for the. reason that for fifteen years records had been kept at the works of the company, showing the amount of water entering the furnace in the form of aqueous vapor, and careful observations had been made of its effect upon the working of the furnace. Some years had proved much worse in their effect than others, on account, not only of excessive moisture, but also of great variation in the moisture from day to day, and sometimes within a few hours. It had been found impossible to. make a satisfactory percentage of high-silicon foundry-iron in summer, even on high fuel; and for some years the endeavor had been made so to arrange the sales that, during July and August, only a small percentage of the iron produced would be required to carry more than 2 per cent. of silicon. Our larger furnace, running on basic iron, year after year, produced in February a tonnage 20 per cent. higher than in August, on a much lower fuel-consumption, while, at the same time, the summer months were marked by ? messes," tuyeres closed by slips, and other irregularities, constituting serious additional business losses. It will be easily understood, therefore, that the records made at the Isabella furnace after the installation of the dry blast in 1904 possessed special interest, and were closely watched by us. On the basis of our own experience, we argued that if the moisture could be kept low, and also uniform, the cost of installation would be more than justified. The subject was brought before our Board of Directors in the fall of 1905; and in the spring of 1906 it was decided to install a plant of sufficient capacity to treat 70,000 cu. ft. of air per min., an amount

Nov 1, 1908

By W. L. Phillips

Single crystals of aluminum, brass, and copper oriented for (100) and (110) slip were extended at 25°, 400°, and 600°C in simple shear. Aluminum specimens oriented for nonoctahedral slip began to shear at a higher critical resolved shear stress than specimens oriented for octahedral slip. Parabolic stress-strain curves were obtained from zero strain. The initial rate of parabolic hardening was lower for specimens sheared on the (100) plane in a close-packed direction <110>, than for specimens sheared in a nonclose-packed direction <100>. metallographic evidence, however, showed that all slip traces could be explained in terms of (111) <100> slip. All attempts to cause nonoctahedral slip in copper and 70-30 a-brass single crystals were unsuccessful. Instead of shearing, the crystals bent, allowing {111} type planes to come into action. NONOCTAHEDRAL slip in aluminum has been reported under three different conditions: first, as the main mode of slip in tension experiments at elevated temperatures;&apos;-&apos; second, as the main mode of slip in direct shear experiments at room temperat~re; and third, as a minor mode of deformation, i.e., as cross-slip, in tension, shear, and bicrystal experiments at room and elevated temperatures."-l2 However, as far as the author knows, nonoctahedral slip has not been reported in either copper or 70-30 a-brass. The present study was undertaken to determine whether nonoctahedral slip could be obtained in aluminum, brass, or copper at room or elevated temperatures when the shear stress was approximately constant over the cross-section, a maximum at the center, or a maximum at the surface. EXPERIMENTAL PROCEDURE A detailed description of the crystal preparation and shearing apparatus has been given previo~sly. Cylindrical crystals 1/2 in. in diam and 8 in. long were grown from the melt in a temperature-gradient furnace. The aluminum contained 0.001 pct Zn, 0.001 pct S, and 0.001 pct Fe; the 70-30 brass contained 0.015 pct Pb, 0.001 pct Fe, 0.01 pct Ni, 0.02 pct Sn, and 0.005 pct Se; the copper was certified OFHC of 99.98 pct purity. All samples were electropolished prior to testing. The shear apparatus was a modified Bausch type. The strain sensitivity was 4 x lob4 Load was applied by clamping the rods attached to the shear plates in an Instron tensile machine. The rate of loading was 0.02 in. per min. In all cases a 1/8-in. gage length was used. For the tests performed at 400° and 600°C the shear plates, collars, and rods were made of stainless steel. These elevated-temperature tests were performed in an argon atmosphere. A) Aluminum at Room Temperature. Values of a and ß for the various slip planes and slip directions investigated are shown in Table I where a is the complement of the angle between the specimen axis and the slip direction, and ß is the angle between the specimen axis and the normal to the shear plane. The shear stress is a function of a (assuming ß - 0);10 when a is less than 27 deg, the shear stress on the slip plane for which the specimen is oriented has a maximum at the center of the crystal; at a = 27 deg the shear stress is constant across the slip plane; for a greater than 27 deg the shear stress is a minimum at the center. Fig. 1 shows the stress-strain curves for specimens cut from crystals 1, 2, and 5, which were sheared on the (010) plane in the [loll direction at room temperature. These three crystals have shear-stress distributions corresponding to the three dif-

Jan 1, 1962

By J. L. Lytton, T. E. Tietz

The recovery of flour stress of recrylstallized are-cast molyhdenum after 10 pet prestrain at 150°C was studied for recovery temperatures of 725o 801o and 901oC. The yield phenomenon observed after recovery was such that the yield drop diminished and disappeared as recovery proceeded. A fractional flow-stress recovery parameter fr, was developed and it was shown that, independent of recovery ternperatzwe, equal f, values of about 0.16 produced superposition of stress-strain curves except for the initial yield phenomenon. The activation energy for low degrees oj recovery was found to he 32,600 cal per mole, in close agreement with a reported valzie for difjzdsion of carbon in molybdenum. For values of fr greater than about 0.15 where recovery was thought to predominate over strain aging, the activation energy varied from 43,600 to 82,500 cal per mole and increased with increasing recovery and recovery temperature. A 10 pet pre-strain shifted the ductile-brittle transition temperature, as indicated by tensile elongation, from 10°C. to about -22"C. A 100-hr recovery anneal at 801oC was shown to shift the transition temperature to about —5oC, the major shift occurring during the first hour of recovery. ThE recovery of cold-worked metals is accompanied by changes in the arrangement of the dislocations generated during cold work. In recent years, the use of transmission electron microscopy has allowed direct observation of some of the dislocation configurations formed, such as "tangles", networks, cells, subboundaries, and loops. These observations have recently been reviewed by Keh and Weissmann.&apos; Accordingly, some understanding has been gained concerning the nature of the dislocation rearrangements involved. The relationship between recovery and the decrease of mechanical strength, however, has only recently been explored. Previous efforts of the authors were directed toward investigating the decrease of tensile flow stress of aluminum and Al-1 pet Mg during recovery2 and the effects of concurrent elastic and plastic strain on the flow-stress recovery of aluminum.3 In addition, an investigation of the effect of four different solute additions on the tensile flow-stress recovery of aluminum has been made.4 Many important metals, however, have the bee crystal structure, e.g., iron, molybdenum, tungsten, vanadium, columbium, tantalum, and chromium. These metals might be expected to behave differently during recovery from those with other crystal structures for two reasons. First, the previous and present investigations of aluminum and its alloys have shown that tensile flow-stress recovery is strongly affected by foreign atoms in the lattice. In the bee metals, interstitial impurities are usually present and might be expected to have various effects upon both flow behavior and recovery. For example, heterogeneous yielding might occur during prestraining. The diffusion of these interstitials can also relock dislocations during recovery so that a yield point might be obtained upon restraining (strain aging). Second, some of the bee metals (e.g., iron, molybdenum, and tungsten) undergo the familiar structure-sensitive ductility transition and exhibit brittle fracture at suitably low temperatures. It is of considerable interest to determine the effects of recovery on the transition temperature of such metals. The purpose of the present investigation was to extend our knowledge of flow-stress recovery to the bee metals and to study the effects of recovery on the ductile-brittle transition temperature. Unalloyed recrystallized are-cast molybdenum was chosen as a test material, since it exhibits a well-defined ductility transition near room temperature. As in the previous studies, the degree of recovery was measured in terms of the decrease of tensile flow stress. Prestraining and restraining were carried out at 150°C to avoid the possibility of brittle fracture. EXPERIMENTAL PROCEDURE The are-cast molybdenum sheet used in this investigation was obtained from the Climax Molybdenum Co. of Michigan. It was 0.060 in. thick by 10

Jan 1, 1964

By C. D. King

A QUARTER century ago this country was producing an extraordinary quantity of iron and steel, with a decisive influence on the outcome of the first World War. Today this country is again demonstrating its industrial capacity with telling results. If this lapse of time has confirmed the opinion that man learns little from experience with respect to human relationships, at least we can derive some consolation from the knowledge that in the same period we have made huge strides industrially, and particularly in the steel industry. The differences represented by 25 years are striking, and have resulted from a multitude of changes that have contributed to the present-day high state of our pig iron and steel manufacture.

Jan 1, 1944

By D. S. Hutton, W. C. Leslie

S. Floreen (1nteumtio)lal Nickel Co.)— One fairly simple way to differentiate between embrittlement due to surface microcracks or due to a dislocation barrier effect might be to load a brittle rock salt crystal in tension to some stress just below the fracture stress and then immerse the loaded crystal in water. If a surface film is retarding plastic flow then one should observe some plastic deformation of the rock salt as

Jan 1, 1962

By Abbas Ali Daneshy

A study of the mechanics of hydraulic fracturing shows the fracture initiation pressure to be a function of the in-situ principal stresses, the formation and fluid properties, and how the wellbore has been completed. The orientation of the hydraulic fracture is perpendicular to the least in-situ principal stress. The geometry of the induced fracture depends on the treatment fluid properties, the injection rate and volume, fluid leak-off and formation properties.

Jan 1, 1974

By W. R. Clough, M. E. Shank

IT has been noted in a study of the flow and fracture of nodular cast iron under biaxial stress conditions (complete results of which will be published later) that when this metal is subjected to stress it may undergo a striking density change. Such behavior was first determined by strain gage measurements made on tensile test specimens, and has since been substantiated by other types of measurement. The chemical analyses and mechanical properties of several nodular irons to be discussed here are given in Tables I and 11. Tensile data for iron A was obtained from a hollow cylindrical combined stress specimen of the same dimension as those used by L. F. Coffin, Jr.1 in his investigation of gray iron properties. Standard 0.505 in. solid tensile-test bars were used for irons B and C. On each specimen type, A-8 wire resistance strain gages were used—two diametrically opposing gages in the axial direction, two in the tangential or hoop direction. By subtracting elastic strains from the measured strains, the plastic strains could be calculated. By assuming that radial and tangential strains are numerically equal, a measure of permanent volume change can be obtained by summing the plastic strains. This appears to be a good assumption, since the metal either fractured, iron A, or readings were discontinued, irons B and C, long before necking took place. This calculated variation of volume increase with stress is given for irons A and B in Fig. 1. Data for iron C is almost identical with that for iron B. The volume change indicated by Fig. 1 has been substantiated by a more direct type of density measurement. A method developed by S. G. Fletcher and&apos; Morris Cohen,&apos; and completely described in the discussion of their article, has been used. The accuracy of specific volume measurement has been estimated as 0.00002 cu cm per gram. Essentially the method consists of weighing a sample in air and then immersed in water. Measurements were made before and after straining the material. The results shown in Table I11 were obtained by means of half-size (0.252 in. diameter, 1 in. gage length, 3/8-16 threads) tensile specimens. Initial measurements were made on the whole specimen before stressing. After stress-

Jan 1, 1955

By C. W. Burrows

The burden a man can endure depends on its magnitude and the number of times it is applied, as well as on many other factors. The resisting power of steel likewise is dependent on many factors. The maximum load it can support indefinitely is much less than its possible momentary burden. A light load straining the metal far within its elastic limit, if repeated indefinitely, ruptures the metal. The magnitude of the stresses that may be alternately applied and removed without rupturing the material depends on the number of repetitions of the cycle; the intervening periods of rest; the thermal, electric, and magnetic conditions, as well as the presence of secondary streessses. While we are unable to formulate the law between the magnitude of repeated stresses necessary to produce rupture and the length of time during which these alternating stresses may be applied before rupture, my experience is that the time increases as the magnitude of the force decreases, according to a law which! to a first approximation, is exponential. In other words, F = Ce-t where F= magnitude of alternating stresses; t= time for which stresses are continued; C = constant, which depends on the conditions under which the operations are carried out. It is quite probable that the same type of law holds for the magnitude of a continuous force and its duration. When a rod of steel is subjected to the blows of a drilling hammer several things happen. First, one end is struck by the hammer and the other end is driven into the rock, thus causing a bodily displacement of the entire material of the steel drill. The greatest stresses involved in this bodily displacement are located at the two ends of the steel and manifest themselves by the distortion of these parts. Second, after the blow has been delivered, the steel drill, due partly to its own resiliency and partly to the resiliency of the rock, experiences a vibratory motion as a whole, this motion is quite similar to the bouncing of a rubber ball thrown violently upon a smooth pavement. Third, the free vibration of the drill is determined only by its own natural period of vibration. This motion involves all the characteristics of any vibrating body emitting sound. Certain elements of the rod will experience alternations of condensation and rarefaction and, in these regions, the individual steel

Jan 1, 1922