Search Documents

By E. Teghtsoonian, K. G. Davis

Cobalt crystals of commercial purity have been tested in tension. Their resolved shear stress-shear strain curves are very similar in form to those for zinc, magnesium, and cadmium. There is an initial linear region for shear strains up to around 150 pct, the ratio of work hardening slope to shear modulus at room temperature being about 2 X x This is followed by an upturn, which is, PLASTIC deformation in metal single crystals with close-packed structures has been found strongly dependent on stacking-fault energy. The high stacking-fault energy hexagonal metals magnesium, zinc, and cadmium have been quite extensively tested, but up to now no data have been available for a comparable hexagonal metal with low stacking-fau1t energy' An however, smaller in magnitude for cobalt than for the other metals. Values for the critical resolved shear stress rise from 97 kg per sq cm at room temperature to approximately 170 kg per sq cm at -196 °C. The Cottrell-Stokes ratio is not constant either for variations in the strain rate or for temperature changes, its value decreasing with strain. investigation into the plastic deformation of cobalt, which has a very low stacking-fault energy, has therefore been undertaken. EXPERIMENTAL PROCEDURES Cobalt crystals in the form of rods 0.3 cm in diam were grown in an electron-beam floating-zone refiner at a rate of zone travel of 25 cm per hr. Details of the growing procedure are given in Ref. 1. The zoned cobalt rods had the following analysis:

Jan 1, 1963

By B. L. Averbach

THE rolling process may be considered as a case of a nonhomogeneous plastic flow. In such a heterogeneous deformation there is no direct general solution, and the plastic deformation varies from point to point as a function of the coordinates. It is practicable to determine these plastic strains only at the conclusion of the rolling process, and the local strains can be studied by observing the deformations produced in a suitably placed grid system. Strains at the surface of a bar after rolling have been reported by MacGregor and Coffin,' but the strain distributions within the bar have not been previously observed. Siebel² has investigated the plastic deformations resulting from wire-drawing by splitting the wire along its axis, milling a grid coordinate system on the inner plane surfaces, and binding the .wire together so that it would pull through a die as a single unit. This method was possible because of the rotational symmetry of the die. In the rolling process, however, such a system was not readily applicable. This paper describes another method of including a grid system, and reports some preliminary data on the plastic rolling strains within a square bar. Experimental Procedure 2.1 mm wide (144 network squares per sq in.) was punched from a thin lead sheet with a steel die and supported in a brass mold by thin copper wires. Pure tin was then poured around the grid to form a solid bar, with the network securely imbedded at. a given position. This bar was then machined to a square 15.2 mm (0.60 in.) wide, and then radiographed. The lead grid was quite adherent and sufficiently ductile to follow the deformation of the bar faithfully. The network lines also remained sharp enough to maintain a high radiographic contrast, and the tin bar, with the grid included, could withstand considerable deformation at room temperature without splitting at the interface. In order to fill the mold, it was necessary to cast the tin at 260-280°C and during pouring the lead grid was supported at short intervals to prevent warping. Some shrinkage cavities were encountered, but only bars which were free of shrinkage in the network region were used. This method is similar to the one employed by Steinberg" in an investigation of the strain distribution in a tensile specimen. Before rolling, the machined bars were radiographed in two directions to obtain accurate initial dimensions of each square and to observe whether the grid was straight and correctly positioned. The rolling was performed in a small hand mill with 2 in. diam rolls at room temperature, and a 20 pct reduction based on the original height was employed. The rolls were clean and no lubricant was used. Halfway through the bar, at the center of the network, the rolls were reversed and the bar extracted. These bars were then radiographed again

Jan 1, 1951

By R. H. Richman

Coarse-grained Fe-Ni-C martensites formed at subzero temperatures were strained in compression at room temperature and the plastic deformation modes examined as a funclion of carbon content. At very low carbon levels, defovmation occurs hy wavy slip; commencing at about 0.05 pct C, mechanical twinning accounts for an increasing proportion of the plastic flow. Beyond approximately 0.4 pct C the deformation appears to be entirely by mechanical twinning. The habit planes of the operative twin modes were determined to be (113), (0131, and "(089)" in decreasing frequency of occurrence. Some of the implicaticms of Ihe o6served deformation modes upon the structure and properties of ferrous martensites are discussed. METALLURGISTS have long sought to explain the mechanical properties of ferrous martensites, particularly the extraordinary hardness and strength of the high-carbon varieties. Until recently the lack of precise knowledge of the structure of martensite crystals was the most serious barrier to understanding; however, the advent of thin-foil techniques for transmission electron microscopy has removed much of the mystery from martensite structure. Observations by Kelly and Nutting,"' and many others since, indicate that Fe-C based martensite crystals are internally twinned to a degree dependent upon the carbon content, and that a martensite plate containing 0.8 wt pct C or more consists of a stack of twin-related lamellae with each lamella on the order of l00A thick. Such a structure would be expected to influence greatly all aspects of metallurgical behavior, and many of the properties of Fe-C based martensites have been rationalized accordingly. Recent independent experiments led Winchell and cohen3 to conclude that the strength of ferrous martensite is derived primarily from solid solution hardening of the iron lattice by interstitial carbon atoms. Strength contributions from precipitation, dislocation-atmosphere interactions, clustering, short-range order, crystallite size, and so forth, were considered to be of secondary importance. In the view of Winchell and Cohen, the twinned structure of martensite serves mainly to limit the effective length of dislocation lines in the lattice, and thereby confers an added measure of hardening. Few properties of metallic crystals are as sensitive to metallurgical structure as are deformation mechanisms. It is somewhat surprising therefore, that, except for metallographic evidence of mechanical twins in strained martensite,4 no systematic examination of plastic deformation

Jan 1, 1963

By C. Elbaum

Specimens consisting of several crystals, each with a prescribed geometry and a controlled orientation with respect to both the extermally intposed stress and the highboring crystals, werer deformed in tension at room temperature. It is shown that the influence of a grain boundary on the plastic defolrmation of a mullicrystal depends on the extent to which the presence of the grain boundary, contributes to the necessity 01. multiple slip in the component crystals. MANY investigations were carried out in the past on the plastic deformation of aluminum single crystals, bicrystals, and polycrystals. The various studies of bicrystals aimed primarily at elucidating the influence of grain boundaries on the mechanisms of plastic deformation. In the earlier studies the emphasis was placed primarily on finding the "strength" contributed by a grain boundary. In more recent investigations it became apparent that the grain boundary does not contribute any strength per se but rather acts by influencing the mechanism of plastic deformation in the adjoining grains. The concept thus emerged of the plastic properties of a bi-crystal, and by extension of a polycrystal. depending solely on the mechanism of deformation prevailing in each grain. The contribution of the grain boundaries thus becomes limited to the type of restrictions imposed on each grain by its neighbors. The present investigation of the behavior of specimens consisting of more than two crystals was designed for the purpose of studying the influence of the grain boundary in simple aggregates. The findings of this study further support the concept that the restriction imposed on a deforming crystal by its neighbor constitutes the predominant factor in the plastic deformation of polycrystals. The term "multicrystal", in contrast with single and polycrystals, is used to describe specimens consisting of several crystals. Each one of the component crystals has a prescribed geometry and a controlled orientation with respect to both the externally imposed stress and the neighboring crystals. Two groups of multicrystals were prepared. All the component crystals of both groups of multicrystals had the axial orientation (isoaxial multicrystals) shown in Fig. 2, with the primary slip plane and slip direction both at 45 deg to the specimen axis. In the first group (hereafter referred to as group I) the component crystals were symmetrically oriented with respect to the plane of the grain boundary; the primary slip plane and slip direction were respectively at an angle of 60 and 30 deg to this plane. For the second group (group 11) the axial orientation remained the same and the relative positions of the primary slip plane and slip direction are shown in Fig. 3. EXPERIMENTAL METHODS The material used was aluminum 99.993 pct pure, according to the manufacturer. The specimens were produced by growth from the melt in a horizontal graphite container. In order to maintain the prescribed geometry of the individual crystals of a multicrystal, a technique described elsewhere was used.' The specimens were grown under a small, positive pressure of helium at a rate of approximately 1 mm per min. annealed in air for 24 hr at 640°C and cooled over a period of several hours to room temperature. All the multi-crystals were rectangular in cross-section, 6 by 18 mm (see Fig. 1) and from 150 to 170 mm long. In each group bicrystals, tricrystals and quadru-crystals were prepared as shown in Figs. 1 and 4.

Jan 1, 1961

By E. S. Greiner

Germanium and silicon have been plastically deformed in torsion at elevated temperatures. Slip took place on the four {Ill} planes. Dislocations, revealed by etch pits on a (111) face, occurred in rows that were traces of operative slip planes. THE plastic deformation of germanium and silicon by bending and tension at elevated temperatures has been reported by Gallagher.&apos; Transla-tional slip during plastic flow in these materials, according to Gallagher&apos; and Treuting,&apos; occurs on (111) planes. Recent work by Treuting&apos; indicates the direction of slip to be <1l0>. The present paper describes the plastic flow characteristics of germanium and silicon deformed by torsion. Torsional deformation was accomplished by twisting 1/4x1/4x2 in. specimens held in molybdenum grips and contained in an atmosphere of helium in a transparent quartz tube and heated by an external resistance furnace. The angular displacements were measured on a graduated circle with a pointer attached to the movable grip. Temperatures were measured with a chromel-alumel couple; the hot junction was within the quartz tube and in close proximity to the specimen. Photographs of samples of germanium and silicon twisted at 850" and 1180°C, respectively, are shown in Fig. 1. The germanium was twisted 230" per in. and the silicon 80" per in. These deformations are larger than those used in experiments to be described later and are presented only to emphasize the extensive plasticity of these materials. Germanium A single crystal specimen of germanium (n-type, 7 ohm-cm resistivity) with a (111) plane normal within 3" of the torsion axis, Fig. 2, was chemically polished with CP-4 solution" and then twisted 9" during the twisting of these specimens of germanium, the slip lines from the (lli) plane should have appeared in the four lateral faces instead of in only two. Perhaps the absence of rotational slip is brought about by the square cross-section. A cylindrical specimen would have a more uniform stress distribution in torsion than one with a square cross-section, and may deform by rotational slip. A specimen of germanium (n-type, 5 ohm-cm resistivity) twisted less than 8" per in. at 550°C, was cut to expose the (111) face 19" 28&apos; from the torsion axis, Fig. 4a. This face, after metallographic

Jan 1, 1956

By W. J. Feuerstein

Plastic deformation of the germanium adjacent to the re-growth material has been observed after alloying single crystal germanium with tin. Of several solder alloys investigated, plastic deformution was observed only in the germanium samples in contact with a tin-doped regrowth material. Dislocations were observed to move on a viewed (111) plane following thermal cycling of tin-doped regrowth material on germanium. OBSERVATION of germanium samples to which solder had been fused indicated that plastic deformation, as evidenced by slip arrays of dislocation etch pits, occurred during the fusion of the solder alloy, Figs. 1, 2. The samples had been prepared by placing the solder in contact with the germanium and heating the assembly to approximately 575"C, followed by cooling to room temperature. During this process, the solder first melts, and then as the temperature is further increased, dissolves a portion of the germanium with which it is in contact. During the cooling portion of the thermal cycle, the dissolved germanium is precipitated, and provided

Jan 1, 1961

By D. F. Gibbons

THIS investigation was undertaken in order to gain further information on the mechanism of plastic deformation of iron at temperatures between room temperature and 77.2°K, and also to contribute to our understanding of the low temperature brittleness phenomenon that occurs in both the tensile and impact tests. It was decided to study as pure an iron as possible and to use the tensile test in order to simplify the problem as much as possible. Two series of iron were used throughout the investigation: iron A, obtained from the National Research Corp. and supplied as gas-free, high purity iron; and iron B, obtained from Fast&apos; and produced by melting iron under purified hydrogen. Typical analyses of samples of both irons, after fabrication, are given in Table I. The main difference in composition of these irons is in their nickel and oxygen contents. Nickel has a very large solid solubility in iron. However, oxygen has an extremely small solid solubility. An attempt was made to reduce the oxygen content still further by remelting under purified hydrogen. This was successful in reducing the oxygen content to -0.0006 pct. However, no results on tests of this iron are included, since difficulty was encountered in fabricating the ingot. Wire specimens 1 mm in diameter were used for the investigation. The wires were produced from the ingots, as supplied, by cold rolling and swaging, with intermediate vacuum anneals at 700°C. Care was taken to reduce preferred orientation in the wires to a minimum by keeping the percentage of reduction in area between anneals of 30 to 40 pct. X-ray transmission photographs showed no indication of preferred orientation. The final grain size of iron A was 20 to 24 grains per linear mm and of iron B, 16 to 18 grains per linear mm. All specimens were tested in the decarburized and denitrided condition unless otherwise stated. The procedure was to pass hydrogen, saturated with water vapor at 26oC, over the specimens at 730°C for 2 hr. The specimens were quenched in iced water and then annealed in a vacuum of - 5x10-6 mm Hg for one day at 560°C to remove hydrogen. Higher temperatures were used for the vacuum anneal but this temperature was found to be quite satisfactory in removing hydrogen. The specimens were slow-cooled after the vacuum anneal. Where it is stated that the specimens were carburized, the specimens were given an identical decarburizing treatment and then carburized by passing hydrogen, saturated with pure n-heptane vapor at 0°C, over the specimens at 730°C. The specimens were then homogenized at 730°C for 2 hr in dry hydrogen. After the carburizing treatment the specimens were given the same vacuum anneal as for the decarburized specimens. The carbon content was determined from the maximum value of the internal friction carbon peak.2 Apparatus Fig. 1 shows a diagram of the tensile apparatus, with half the cooling coil removed. The cooling coil enabled temperatures from 200" to 77.2oK to be obtained. The apparatus was designed to fit a standard Tinius Olsen Universal tensile machine. The apparatus consisted of the rigid plate A which carried two carefully machined hooks H. These hooks attached the plate firmly to the moving crosshead of the tensile machine. The lower grip B was rigidly suspended from the plate A by three stainless steel rods. The upper grip C was joined to the upper grip of the tensile machine by the stainless steel rod E. The lower part of the apparatus was surrounded by a Dewar vessel, which was made a sliding fit inside the brass collar D. The specimen was held in a clamp which fitted into the grip, forming a ball and socket joint (see inset a). This was to attain as nearly pure

Jan 1, 1954

By E. C. Burke, W. R. Hibbard

Plastic deformation in magnesium single crystals was studied by tensile tests at room temperature utilizing an improved preparation and testing technique. Consistent critical resolved shear stress values for basal slip were obtained. The advent of pyramidal slip at room temperature was rationalized upon the basis of grip constraints. A bend-twinning hypothesis was advanced as an explanation of mechanical twinning which occurs as a complex stress-relief mechanism. INVESTIGATIONS of the plastic deformation of magnesium have been limited to the determination of the fundamental kinetics which may be summarized as follows: 1—Twinning on the {102).l 2— Slip on the (001) plane in the [loo] direction at room temperature.&apos; 3—Slip on the {101) or {102) plane in the [loo] direction above 225°C." 4—Critical resolved shear stresses for basal slip in tension at room temperature of 83 g per sq mm with a variation from 57 to 127 g per sq mm." Bakarian&apos; studied the compression of thin wafers of magnesium single crystals and classified the components of the deformation mechanisms as follows: 1—The Basal field: (001) at an angle of less than 20" to the compression surface. Fracture along {101} or slip on (001) followed by {101} fracture. 2—The prism field: (001) at an angle greater than 60" to the compression surface. Twinning on the {102) generally occurring during the early stages of loading, basal slip in the areas of original orientation and (001) slip within twins. 3—The central field: (001) at angles greater than 20" but less than 60" to the compression surface. Slip on the (001). 4—The critical resolved shearing stress for {101} slip above 225°C was 400 g per sq mm. Observations of mechanical twins in hexagonal close-packed metals have been summarized by numerous investigatorsb-&apos; emphasizing a lateral or rotational atomic adjustment, in addition to the pure twinning shear, and the importance of reorienting the basal plane to a position more favorable for continued slip, rather than the resulting small dimensional changes. Criterion for the operative twinning planes has not been clearly established. Schmid and Boas hurmised that an energy condition related to the atom movements is the determining factor. MillerQ bserved that twinning stresses in zinc crystals decreased as the amount of prior deformation increased. Preparation of Specimens Magnesium single crystals % in. in diam x 8 in. long were grown from the melt under an argon atmosphere in a gradient furnace similar to that described by Jillson." Magnesium containing 0.018

Jan 1, 1953

By E. C. Burke, W. R. Hibbard

G. B. Craig (University of Toronto, Toronto, O,nt., Canada)—The advent of pyramidal slip at room temperatures in a magnesium crystal (M2,) and the very low value reported for the critical shear stress are puzzling. Table I1 shows the calculated values (approximate) for sin x cos I in this specimen if all the (10l) planes are considered. If So is the shear stress resolved in the direction of glide, on the glide plane, and U, is the stress operative in yield point tests, then: S,, — 325 (0.169) 55gpersqmm (approximately) for 1101: S,, = 325 (0.465) = 151 gpersqmm (approximately) for (0001): S,, — 325 (0.101) - 32.8 gpersqmm (approximately) Thus, we see the pyramidal plane in which the minimum shearing component operated. Barrett"&apos; stated: "Experiments have repeatedly shown that, when there are several crystallographically equivalent slip systems in a crystal, the one having the greatest resolved shear stress will become active. ..." It does not appear to me that the measurements given are conclusive proof that pyramidal slip operated. E. C. Burke and W. R. Hibbard, Jr. (authors&apos; reply) —Although the low value for the critical resolved shear stress for pyramidal slip may be puzzling, there does not appear to be any basis for questioning the validity of the measurements. Under the influence of constraints, slip systems having decidedly lower shearing components may become operative, e.g., "cross-slip" or the "forced glide" in magnesium reported by Bakarian. Since we believe that pyramidal slip occurred in the specimen because basal slip was inhibited, it is not too surprising to find an operative plane with a lower shear stress. -7 C. S. Barrett: Structure of Metals U94jl p. 2J6. New York. McGraw-Hill Book Co.

Jan 1, 1953

By Y. Nakada, U. F. Kocks, B. Chalrners

THE orientation dependence of work hardening has previously been studied over the entire range, i.e., including special orientations of high symmetry, in aluminum1-3 and silver.* The differences between various orientations are substantial, and the trend is the same in all fcc crystals. However, there are quantitative differences in behavior between aluminum and silver at room temperature, particularly in the (100) orientation. While many experiments on gold have been reported,5&apos;9 none included the special orientations. We therefore undertook tension tests on gold crystals of the axial orientations (100),(110), (Ill), (211), and, as a representative of single slip, one whose Schmid factor was 0.5 (hereafter referred to as m = 0.5). Single crystals of dimensions 1/4 by .1/4 by 6 in. were grown from the melt1&apos; at a rate of 4 in. per hr, using gold of 99.99 pct purity obtained from Handy and Harman. A growth rate of 1/8 in. per hr, or a purity of 99.999 pct,ll produced no difference in results. The crystals were annealed at 1000°C in air for 24 hr and furnace-cooled down to room temperature, after which they were electro-polished in a solution of potassium cyanide (40 g), potassium ferrocyanide (10 g), soda (20 g), and enough distilled water to make 1 liter of solution, at a current density of 0.02 amp per sq mm. After 2 or 3 hr, a very smooth surface was obtained by this method. Nine m = 0.5, two (loo), one (110), three (Ill), and one (211; crystals were tested at room temperature in a floor-model Instron machine at a tensile strain rate of 0.5 pct per min. The accuracy of the stress measurement was k10 g per sq mm up to 500 g per sq mm, k2 pct for higher stresses. The strain measurement was accurate to t2 pct. The scatter of stress at a given strain among the crystals of the same orientation was small, *5 pct being the largest. The representative stress-strain curves for various orientations are shown in Fig. 1. Table I summarizes the work-hardening parameters as used by seeger.12 Results of other investigators are also included in this table for comparison. There are no previous data for the corner orientations. Values for m = 0.5 crystals agree fairly well with those of Berner. Tm is defined as the stress at which the stress-strain curve begins to deviate from linearity of Stage 11. However, in practice this is a very difficult value to estimate because each investigator has a different idea of linearity. Therefore, the comparison with the values of other investigators may not be valid. In the present experiment, (100) crystals had the highest 111, followed by (111) crystals. The work-hardening rate in Stage I1 was highest for the (111) crystal followed by the (100) crystals. Our value for 0x1 of m = 0.5 orientation agrees very well with those of other investigators. 1) Single-Slip orientation (m = 0.5). These crystals were oriented so that the primary-slip vector was contained in one side face. The dimension perpendicular to this side should then not change if single slip indeed takes place. Within the accuracy of measurement, this dimension did not change during the deformation. Since the accuracy is k0.2 pct, the amount of secondary slip is less than 0.7 pct of the slip on the primary-slip system at 30 pct tensile strain. This is in conformity with the results obtained by Kocks" for aluminum crystals. The tensile axis moved toward (211) during the deformation. Slip bands, Fig. 2(a), were very fine and closely spaced. Some deformation bands were observed. There were no clear-cut cross-slip traces such as the ones observed on aluminum m = 0.5 crystals. 2) (111) Crystals. The orientation of the tensile axis was stable during the deformation. From this observation, one can deduce that at least three slip systems must have operated, and probably all six because the remaining three all have cross-slip relation to one of the first three.&apos; It was very difficult to observe the slip markings. Consequently, we could not confirm by this method that six systems were operative during the deformation. At high strains (above 50 pct shear strain), this orientation had the highest stress-strain curve. At 80

Jan 1, 1964

By J. J. Gilman

The data presented indicate that the critical shear stress and strain-hardening Thedatapresentedrate of a zinc monocrystal depend on the orientation of its slip direction with respect to its external boundaries. The tendency of a crystal to form deformation bands also depends on its shape. THE plastic behavior of pairs of zinc monocrystals in which both members of the respective pairs had the same orientation with respect to the longitudinal axis, but each had different orientations with respect to their rectangular external shapes, were compared in this investigation. The purpose of the investigation was to see what influence the shape or surface of a zinc crystal has on its mechanical properties. In a previous investigation of triangular zinc monocrystals,1 anomalous axial twisting was observed which seemed to be related to the triangular shape of the crystals. Wolff,&apos; in 400°C tensile tests of rectangular rock-salt crystals bounded by cubic cleavage planes, found that, of the four equivalent slip systems, the two with the "shorter" slip directions yielded and produced slip lines at lower stresses than the other two. This observation and the work of Dommerich³ as formulated by Smekal4 as a "new slip condition" for rock-salt: "among two or more slip systems permitted by the shear stress law, with reference to the formation of visible slip lines by large individual glides, that slip system is preferred which has the shortest effective slip direction." More recently, Wu and Smoluchowski5 reported essentially the same effect for ribbon-like (20x2x0.2 mm) aluminum crystals at room temperature. Experimental Chemically pure zinc (99.999 pct Zn), purchased from the New Jersey Zinc Co., was the raw material. Glass envelopes, containing graphite molds and zinc, were evacuated while hot enough to outgas the graphite but not melt the zinc. At a vacuum of about 0.2 micron the envelopes were sealed off and then lowered through a furnace at 1 in. per hr so as to melt and resolidify the zinc and produce mono-crystals. One-half of one of the molds is shown in Fig. la. Each mold consisted of four pieces from a cylindrical graphite rod that was split longitudinally and transversely at its midpoints. Rectangular milled grooves 0.050 in. deep and % in. wide formed the mold cavity when the split halves were assembled with twisted wires. Fig. lb shows the specimen shape obtained when the top and bottom mold-halves were rotated 90" with respect to each other. Good fits prevented leakage and excess zinc was necessary to provide enough liquid head to fill the mold completely. In removing soft crystals from the molds it was impossible to avoid small amounts of bending. However, manipulations were carried out whenever possible with the crystals protected by grooved brass blocks. All specimens were annealed prior to testing. From the top and bottom sections of each crystal, X-ray specimens and tensile specimens 7 to 8 cm long were sawed. The tensile specimens were annealed inside evacuated tubes for 1 hr at 375°C. Next the crystals were cleaned and polished by 2-min dips in a solution of 22 pct chromic acid, 74 pct water, 2.5 pct sulphuric acid, and 1.5 pct glacial acetic acid.&apos; Cleaning was followed by a 10-sec dip in a 10 pct caustic solution, then washed in water and alcohol, and dried. This treatment results in a bright surface covered by an invisible oxide film. The testing grips were a slotted type with set screws and were supported in a V-block during the mounting operations in order to avoid bending the crystals. A schematic diagram of the recording tensile-testing machine is shown in Fig. 2. The machine has been described elsewhere.&apos; The head speed was 0.3 mm per sec for all tests. The crystal orientations were determined by the Greninger X-ray back-reflection method with an estimated accuracy of 1. Description of Crystal Geometry A schematic picture of a rectangular zinc mono-crystal is shown in Fig. 3. ABD designates the front edge of a basal plane (0001) of the crystal, the only active slip plane for zinc at room temperature. Of the three possible (2110) slip directions, the active one is indicated by an arrow. Cartesian coordinates are taken parallel to the specimen edges. The normal, n, to the basal plane (n is parallel to the hexagonal axis) has the direction cosines a, ß and ?. X0 = 90 — y is the angle between the longitudinal axis and

Jan 1, 1954

By J. L. Stokes, L. J. Demer

It has recently been shown&apos; that epitaxial films of silicon carbide deposited on silicon single crystals possess desirable properties for semiconductor applications. There is one apparent disadvantage to such a system, however; since epitaxial deposition is a high-temperature process, it can result in plastic deformation of the silicon substrate. The accompanying Berg-Barrett X-ray diffraction photographs reveal plastic deformation in two silicon semiconductor crystals which occurred when the crystals were coated with an epitaxial layer of silicon carbide at 1150°C. Due to differences in thermal expansion between the silicon substrate and the epitaxial silicon carbide, the silicon was subjected to stresses while still in the plastic temperature range. Both crystals shown were 0.7 in. in diam and 0.0055 in. thick. The crystals were sliced from a larger crystal so that their polar axes were parallel to the [ill] direction. After cutting, the crystals were polished with diamond paste, and etched in HC1 vapor to remove surface damage re- sulting from the cutting and polishing operations. This provided clean, damage-free surfaces on which to deposit the silicon carbide. Figs. l(a) and l(b) are reflection and transmission photographs, respectively, of the same crystal. A smaller portion of the crystal is shown in the transmission geometry, because a vertical slit was

Jan 1, 1965

By B. Ramaswami, U. F. Kocks, B. Chalmers

This paper describes the tempetrature, solute (gold), and orientalion dependence of the plastic rleforlirnlion of silver single crystals. The virgin flow stress, To, and its temperatutre dependence incrense with increase in solute concentration. el decreases with decrease in temperature below room teiirperature and with increase in solute coucentralion. The dependence of 011 on temperature arid solute sontenl is due to the dependence of Ts on the two variables. An increase in ts, due to either the temperature or the solute conlent, results in a decrease of e11 in crystals of single-slip orientation and an increase of 011 in crystals of&apos; (100) find (111) orientation. is orientation-dependent and at all the temperatures and in all the materials studied. The Leveling off of the engineering stress-strain curve in crystals of (100) 07-ientotion at a stress tl, is associated with extensive cross slib. The temperature and strain -rate dependence of tl are similar to those of indicating that a rate process is the cause 01 this phenomenon. The plastic deformation of silrer crystals of (110) orientation is multiple to that of crystals of single-slip orientation. THE work hardening of fcc crystals has been the subject of intensive investigations in the past 15 years. The effect of orientation, deformation temperature, solutes, second phase or precipitates, strain rate, etc., has been studied in a number of fcc metals.&apos;-5 In spite of the considerable amount of work reported on the dependence of work hardening on the orientation, temperature, and solute concentration, certain aspects of the plastic deformation of fcc crystals have not been clarified. For instance, with the exception of a few investigations,6-8 where crystals of multiple-slip orientations have been studied, almost all the studies have been on crystals of single-slip orientations. Hence, a major portion of this study has been devoted to the dependence of plastic deformation on the multiplicity of slip systems and the enhanced possibility of dislocation interactions resulting from such multiplicity. Further, the abnormally low rate of work hardening observed at large strains at certain temperatures in crystals of the (100) orienta-tion 6-8has not been explained satisfactorily. It is the aim of this study to clarify this aspect of the orientation and temperature dependence of the plastic deformation of fcc single crystals. The work-hardening characteristics of single crystals of aluminum of ( 110) orientation have been studied at room temperatur "&apos;12 and above." They have not been studied at temperatures where the virgin flow stress is dependent on temperature or where, in Seeger&apos;s terminology is important. The work hardening of single crystals of (110) orientation is of interest for another reason. As shown in Table I, the dislocation reactions that are possible in the (110) orientation are similar in certain respects to those that are possible in the (100) orientation. Hence, the deformation of single crystals of silver of (110) orientation was studied in the temperature range 100° to 900°K at intervals of 200°K. The effect of solute concentration on the plastic deformation of fcc single crystals of single-slip orientation has been studied by several investiaators.> In all of these investigations—with the exception of Ref. 20—single crystals of identical orientation have not been used, with the result that the orientation dependence of plastic deformation is superimposed on the effect of the solute. In addition, the effect of the solute on the work-hardening characteristics of single crystals of multiple-slip orientations has not been studied by the previous

Jan 1, 1965

By J. N. Hobstetter, J. J. Becker

Slip lines in deformed copper single crystals exhibit very pronounced cross-slip and clustering if the stress axes are not too far from <100>. This orientation dependence seems to persist whether or not attempts are made to reduce the bending constraints of ordinary mechanical tests. THE purpose of this paper is to report some microscopic features of the plastic deformation of copper single crystals. The material used was OFHC copper obtained from the American Brass Co. Single crystals about 3 in. long and 5/16 in. in diameter were made by lowering graphite crucibles containing this copper out of the hot zone of a vertical tubular furnace at a rate of 1 1/4 in. per hr. The furnace atmosphere was nitrogen. The orientations of the crystals were determined by the back-reflection Laue technique.&apos; The X-ray spots usually indicated a slight lineage structure of not more than a degree or two. The crystallography of slip is discussed in Schmid and Boas.&apos; The terms classical slip, cross-slip, and conjugate slip are used here with the same meanings as in ref. 3. Compression Specimen 17 (Fig. 1) was selected because the resolved shearing stresses on eight slip systems dif- fered at most by a factor of 1.2. It was hoped that in this situation such effects as cross-slip might be made more prominent. Two intersecting planes parallel to the stress axis were ground on the crystal, using optical abrasive on a lead lap. The large plane was approximately perpendicular to the plane of the axis and the primary slip direction. Its exact orientation was determined by X-ray. The smaller made an angle of 49" with the larger, measured by reflecting a small light source. The specimen was etched with nitric acid until its diameter had been reduced 0.010 in., and then was given a metallographic polish and very

Jan 1, 1954

By J. Marin, H. A. B. Wiseman

This paper presents results of an experimental study dealing with the plastic stress-strain relations of aluminum alloy 14s-T6 subjected to combined biaxial tension and compression stresses. Plastic stress-strain relations for both constant and various types of variable stress ratios were determined and a comparison made with the simple flow theory of plasticity. THIS investigation was undertaken for two main purposes: 1—to obtain plastic stress-strain relations for Alcoa 14s-T6 when subjected to various combinations of biaxial stresses, and 2—to determine the validity of the flow theory in predicting plastic stress-strain relations for combined stresses. The biaxial stresses used were tension combined with compression. These stresses were produced by subjecting a thin-walled tube to axial tension and torsion. Various types of combined stress conditions were investigated. To provide control test data and information on the influence of biaxial stresses on the strength, the usual constant stress ratio type tests were made. These tests showed that the biaxial yield strength agrees approximately with the distortion energy theory. However, the Prager semi-empirical theory agrees best with the test results. For these constant stress ratio tests the plastic stress-strain relations were found to agree approximately with the flow theory. (For constant stress ratio the flow and deformation type theories are identical.) In view of the fact that the constant stress ratio tests cannot distinguish between the flow and deformation theories, a number of variable and special biaxial stress tests were made. These tests showed that the flow theory is inadequate, since large differences exist between the experimental and theoretical results. Special tests were also conducted to check the validity of the isotropic yielding assumption. This assumption is made in the linear-type flow theory. In these tests specimens were loaded in tension to predetermined values beyond the proportional limit stress. The tension load was removed from the specimen and the specimen was subsequently loaded in torsion to fracture. Other tests were applied with the order of torque and tension loading reversed. The nominal stress-strain curves for these two tests approximately coincide indicating that the assumption of isotropic yielding is valid. In addition, these tests verified the requirement by the slip theory of plasticity that prestraining below 140 pct of the proportioned limit stress in either torsion or tension did not influence the subsequent plastic stress-strain relations in tension or torsion. Another type of test was conducted to check the assumption that the axes of principal stress and strain coincide during plastic flow and variable stress conditions. These tests were conducted by applying combinations of axial tension, internal pressure, and torsional loads such that the axes of maximum principal stress could be rotated through 90" during the loading path. The results of those tests showed that the angle between the axes of principal stress and strain varied greatly and that the assumption of coincidence between axes of principal stress and strain is not valid. Introduction In various metal processes including forming of sheets, rolling of bars, and extrusion of rods, metals are subjected to stresses beyond the yield strength of the material. Often these stresses are not simple stresses acting in one direction, but are combined stresses acting in more than one direction. Structural and machine members are often subjected to combined stresses. To adequately determine the factors of safety for these members, it is necessary to know the plastic stress-strain relations of the material used for various combined stress conditions. Various theories have been proposed for predicting the plastic stress-strain relations for combined stress in terms of the simple tension plastic stress-strain relation for the material. To determine which theory might be adequate, test results must be obtained for various combined stress conditions, in order to compare the actual with the assumed theoretical behavior. Although there is considerable test data available for combined stress conditions in which the principal stress ratios are constant, relatively little test information is available for vari-

Jan 1, 1954

By R. C. de Lange

An improved replica technique is developed for a nondestructive study of the nucleation and growth of fatigue cracks. Three different growth stages of a fatigue crack were observed. An initial stage of high growth rate is followed by a long period of very slow growth, until finally a third period of high growth rate leads to fracture. THE metal-fatigue process is of a very complex nature. The experimental approach towards fatigue is susceptible to many minor influences which, together with the unavoidable scatter in testing results, makes the interpretation a matter of extreme care. The generally accepted fact that, in a homogeneous material, the fatigue cracks start at a free surface indicates that surface studies may contri-but in an essential way to a better understanding of the fatigue mechanisms. Indeed metallographic observations of the fatigue phenomena have been very fruitful in the last decade. The study of extrusions, intrusions, and persistent slip bands has contributed much to the present knowledge of the early processes in fatigue.&apos; The drawback of the current metallographic techniques lies in the fact, however, that either observations of fatigue phenomena had to be made in a destructive way after an only partly executed test or a sequence of observations on the same test bar was only possible on notched specimens.2 4 In both cases an uncertainty exists as to the nucleation and growth of the fatigue crack in an unnotched test bar, where the crack can start at any place of a large area and develops in a test bar, which is macroscopically

Jan 1, 1964

By N. K. Chen, R. Maddin

Columbium single crystals were deformed in tension and compression. Reorientation by X-rays and stereographic projections of slip traces indicate that plane of slip may be considered as (110). The plastic behavior is shown to be quite similar to the deformation of molybdenum single crystals. STUDIES on the crystallography of the deformation process in body-centered cubic metals have been renewed recently with investigations of iron single crystals1-" and molybdenum single crystals.4 It is now apparent that too many exceptions to the rationalization based upon the ratio of absolute testing temperature to absolute melting point by Andrade5 exist to permit more serious discussion of this type of analysis. The considerations of resolved shear stress utilizing only planes of the type {ll0}, {112), and {123)³,6 permit analysis of the deformation only on the basis of those three types of planes. The suggestions made by Elam7 and by Greninger8 in which the slip process is envisioned as a composite slip on two nonparallel {110) planes can be illustrated schematically in Fig. 1. It may be seen that an unresolved trace on any plane containing a <111> direction may be accomplished by varying the number of atoms participating in the composite process. By further varying the number of atoms in each plane but keeping the ratio of participating atoms constant, jogs could be obtained in the traces and hence wavy slip lines could be produced. Vogel and Brick&apos; studied the behavior of a iron single crystals in which they suggest that the plane of glide is "non-crystallographic" and may be predicted from the intersection between the great circle joining the slip direction and specimen axis with the great circle whose zone axis is the slip direction. In a more recent investigation on iron single crystals, Steijn and Brick" suggest that the slip mechanism may be considered as made up of a type of composite slip occurring on {110} and {112} planes. Evidence for a possible composite nature of the slip process has been presented for the case of molybdenum in the form of analysis of asterism and specimen axis rotation." Definite proof of a composite slip process must, however, await good electron microscopic resolution of the individual traces making up the unresolved optical trace used in determining the acting slip plane. The present investigation was undertaken to study the behavior of columbium single crystals not only in tension but also in compression since the specimen axis migration should indicate the plane or planes of glide in the same manner that the specimen axis migration in tension indicates the direction of glide. The orientations of eleven crystals investigated are shown in Fig. 2. Specific orientations are missing (those in the vicinity of [Ill] and [001] and consequently the effect of orientation on the crystallography of deformation could not be considered. Experimental Procedure The 1/8 in. rods (7 in. long) were subjected to an axial tension in vacuo while at temperatures in the vicinity of 2000°C for 2 to 4 hr. This treatment resulted in large cylindrical grains (about ½ in. long) occupying the entire cross section. A number of these rods were used for the tension studies by observing the behavior of the individual grains. For the compression studies, single crystals approximately % in. long by 1/8 in. in diameter were cut from the rods; the ends were ground parallel. All specimens were polished electrolytically in a solution of 15 cc HF(48 pct) and 85 cc H2SO4 (concentrated) using a platinum cathode, a current density of 0.04 amp per sq cm and a temperature between 25" and 60°C.10 Orientations were obtained using a Laue back-reflection method (3 cm film to specimen distance) with a ½ mm collimator 9 cm long. For the compression specimens, a reference mark was scratched on one of the compression sur-

Jan 1, 1954

By N. K. Chen, R. Maddin

In the extension of molybdenum single crystals at room temperature, the slip planes were found to be of the type (1101; the slip direction <111>. Theories of plasticity of body-centered cubic metals have been examined, and an explanation based upon planes of highest atomic density seems plausible to explain the plastic behavior of molybdenum single crystals. IN body-centered cubic metals, slip has been reported to occur on several planes; these are of the type {110), {112), and (123). Andrade has correlated&apos; the operative slip planes in body-centered cubic metals with the testing temperature relative to the melting point. In this correlation, if T is the absolute temperature at which slip takes place and Tm the absolute melting point, then the acting slip planes in body-centered cubic metals may be arranged as shown in Table I. However, deviations from this correlation have been reported in iron and iron-silicon alloys2 and also in molybdenum deformed at a temperature around 2400°C." In the case of iron and other body-centered cubic metals or alloys in which all three slip planes have been reported to be active at any one temperature, the crystallographic mechanism of slip is not well understood. Numerous investigators in this field have assumed that the resolved shear stress is a deciding factor. Such considerations were given by Gough in his experiments with repeated torsion of iron single crystals4 and recently by Opinsky and Smoluchowski in their study of iron-silicon alloys," and will be dealt with later in this report. A third possibility is that slip lines in body-centered cubic metals may be formed by alternate slip on nonparallel (110) planes and not by slip on any plane of higher indices. This was advanced by Elam in the case of ß brass." Since (1101 planes are planes of highest atomic density in the body-centered cubic structure, this hypothesis would be in accordance with the plastic behavior of metals in other systems, namely, face-centered cubic and hexagonal close-packed. Experimental evidence in support of this hypothesis is lacking. Nevertheless the work of Barrett, Ansel, and Meh12 has definitely demonstrated that the slip resistance on {110} planes in iron is very much smaller compared with that on (112) and (123) planes. In the present investigation, molybdenum single crystals were carefully documented as to the operative slip planes and lattice reorientations after plastic extension at room temperature. In three crystals studied, (110) planes were found to be active invariably rather than the (112) planes, which were previously reported for molybdenum at this temperature&apos; and predicted by Andrade&apos;s theory.&apos; In two other cases (112) and (123) planes seemed to operate together with (110) planes as active slip planes. However, it is believed, after careful analysis of crystallite and lattice rotations, that slip on (112) and (123) planes may be spurious. Particular reference will be made to the formation of asterism, lattice rotation, and crystallite rotation in an attempt to show that slip apparently observed on {1121} and (123) planes is actually slip on nonparallel {110} planes. Materials and Treatment Sintered molybdenum rods ? in. in diam, obtained from the Fansteel Metallurgical Co., were reported to have a purity of 99.9 pct.* One specimen, Mo-13, ¼ in. in diam, was supplied by Westinghouse Electric Corp. Single crystals were prepared, using the technique devised by Chen, Maddin, and Pond." Mo-13 was ¼ in. in diam x 7 in. long with a reduced gage section of 0.200 in. in diam x 3 in. long. The center of

Jan 1, 1952

By N. K. Chen, R. Maddin

Single crystals of molybdenum were extended at temperatures from 1300° to 2500°C. It was found that with increasing temperatures, the yield becomes more pronounced and the number of slip bands for equal amounts of elongation decreases. Slip at high temperatures fragments the structure. OTHER than the investigations on sodium and potassium by Andrade and Tsien,&apos; the researches of Steijn and Brick&apos; on a iron single crystals at low temperatures are about the only studies of the influence of temperature on glide of body-centered cubic single crystals. The effect of test temperature on glide has been rather widely investigated with hexagonal crystals" and less widely with face-centered cubic crystals. ~~ a result of these studies it can be said that, in general, the onset of plastic flow as measured by the initial rate of strain hardening becomes more abrupt with increasing temperature, and the value of the yield decreases with increasing temperature. Strain hardening, however, is markedly affected by changes in temperature except at very low and very high temperatures where the strain hardening rate becames constant. In the present investigation it is shown that temperature affects the glide of molybdenum single crystals in much the same manner as crystals of other classes, it., for comparable strains the number of slip bands decreases with increasing temperature; shear along the slip bands increases with increasing temperature; the yield becomes more pronounced with increasing temperature of test; and the strain hardening approaches a constant at very high temperatures. In addition, it is shown that, in agreement with the work of Tsien and Chow, Qlip occurs on (110) planes in <Ill> directions. It is further shown that slip at high temperatures fragments the structure into either irregular sized cells or bent atomic planes which are roughly aligned in crystallographic directions. Experimental Procedure Single crystals 3 mm in diameter by about 25 mm long were prepared using the technique previously described.&apos; The furnace in which the crystals were grown served as the extension apparatus for the tension tests. It consisted of a 4 in. water-cooled brass tube 20 in. long which was continuously evacuated at the bottom. Two water-cooled copper electrodes held the specimen by means of spherical collets secured in place in the electrodes by set screws. These electrodes served also to transmit power and stress to the specimen. The lower electrode was clamped to a stand, while the upper electrode was fastened to one side of a lever arm flexibly supported at the top through a slightly offset pinion. A metal bellows operating elastically was attached to the upper electrode to affect a vacuum seal and allow freedom of motion. The level of the arm was adjusted by rotating a graduated nut. Rotation of the electrode was prevented by a key fitted into a groove. After the specimen was mounted and the vacuum secured, the lever arm was adjusted so that the bellows was at its relaxed position. This insured that the total weight of the specimen, the upper electrode, and the downpull of the vacuum were balanced by the horizontal beam. Since the specimen was heated by its own resistance, expansion of the specimen proceeded freely by this arrangement. During the time of heating the specimen, the beam was maintained in a horizontal position by turning the nut at the top. By graduating the lever arm and using a known dead weight on the lever arm to supply a tensile stress, the graduated nut could be read to 0.0001 in. extension. Since

Jan 1, 1955

By Charles L. Bauer

WHEN a single crystal is annealed following plastic deformation recrystallization usually occurs rather than polygonization. Consequently, re-crystallization has received the overwhelming amount of attention albeit the intrinsic mechanisms by which dislocations rearrange and annihilate one another are just as well revealed by crystal polygonization. It is the purpose of this note to demonstrate the usefulness of studying the polygonization process by means of an etch-pit technique in sodium chloride. Sodium chloride deforms easily (the slip system is of the [110], (110) type), readily cleaves on (100) planes, and can be chemically etched so as to reveal the intersection of dislocations with a free surface. Thus it is possible to observe the distribution of dislocations after a crystal has undergone a specific deformation and annealing cycle. Various phases of the polygonization process

Jan 1, 1965