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

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

Jan 1, 1965

By R. W. Kraft

A comprehensive analysis of the crystallographic and metallographic structure of several Al-CuAl, lamellar eutectic grains solidified under equilibrium conditions has been performed. A consistent pattern was discovered which was interpreted in terms of a detailed atomistic model of an interface describable as: Interface II {111} AL 11 {211} <101>Al <120> ? Several arguments are presented to substantiate the theory. It is compared in detail with another interface model characteristic of the Wid-manstatten precipitate of CuAl2 in A1 at low Cu levels. In addition, a concept is proposed to help explain the structure of the compound CuAl2. It has been shown that the eutectic alloy between A1 and CuA1, can be forced to solidify as substantially parallel lamellae throughout a relatively large volume&apos; by appropriately controlling the solidification parameters of growth rate, thermal gradients, and impurity level and by causing solidification to proceed in a unidirectional fashion from one end of an ingot to the other. A typical ingot solidified in this manner shows three distinct zones along the length of the ingot, Fig. 1. At the head end is a region consisting of many different grains, some of which are elongated slightly in the direction of solidification. After a few centimeters of growth, this polygrained region gradually merges into the second zone which consists of a very few elongated coarse grains. The third zone at the tail end is a region of eutectic colonies caused by segregation of impurities. Microscopic examination of transverse and longitudinal sections of the ingots reveals that during the initial stages of growth (zone I) the lamellar structure is frequently highly distorted and twisted but that it straightens out in zone 11. This characteristic pattern suggests that nucleation of a eutectic grain begins randomly at the head end of the ingot, and that some particular orientation relationship between the phases is more favorable from an energy consideration than others for one reason or another, so that some grains grow and others which are less favorably oriented do not. The favorably oriented or "low energy" grains continue to grow until excess solute rejected at the advancing liquid-solid interface destroys the parallel lamellar structure by forming a cellular rather than a substantially planar interface. When this occurs, the parallel lamellae fan out and eutectic colonies are formed because the lamellae grow perpendicular to the local interface. Questions naturally arise as to the crystallographic nature of the "low energy" grains. What do the grains which persist into zone II have in common? Can this explain the stability of such grains during growth? To answer the first question it is necessary to determine the crystallographic orientation of the lamellae of each phase relative to one another. This has been done for Al-CuAl2 eutectic alloys by two different techniques on specimens prepared in different ways.2&apos;3 The results were different from each other and from a third orientation relationship between A1 and CuA1, reported for overaged A1-Cu alloys.4 The three orientation relationships are summarized below to illustrate their similarities and their differences. (001) ? 11 (001) A1; [l00] ? 11 [l00] Al Eutectic, Ref. 2 (001) 8 1) (001) A1; [1001 ?11 [1101 A1 Eutectic, Ref. 3 (001) ? 11 (001) A1; [l00] ? 11 [310] Al; Widmanstfitten, Ref. 4 It is not surprising that different orientation relationships were found by Ellwood and Bagley,&apos; and Takahashi3 since the solidification conditions were quite different. Nor is it surprising that Mehl, Barrett, and Rhines 4 found still another value since they were studying another type of alloy. Nevertheless, it would be expected that some logical and systematic pattern could be found if all the alloys were at equilibrium since the same two phases are

Jan 1, 1962

By A. E. Dwight

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

Jan 1, 1960

By T. V. Philip, Paul A. Beck

IN a previous note1 it was pointed out that the available information suggests a distinct correlation between the occurrence of the CsCl-type ordered structures formed in equi-atomic binary alloys of transition elements and the location of the components in the periodic table. A definite increase in the bond strength between unlike atoms, as compared with that between like atoms, is indicated when, in binary alloys of iron group elements, the other component is changed from chromium to vanadium or tantalum, to titanium. Laves and Wallbaum,2 eported a CsCl-type ordered structure for the stable intermediate phase at the equi-atomic composition in the Ti-Fe system (and also in the Ti-Ru and Ti-Os systems). On the other hand, Tagaya, Nenno, and Nishiyama8 found no ordering of this kind in the body-centered-cubic solid solutions in the Cr-Fe system. It was concluded&apos; that the occurrence of a CsC1-type ordered phase of intermediate stability may be expected in the V-Fe system. Preliminary results were described: suggesting that at least some degree of order does exist in the equi-atomic alloy VFe, annealed at 1200° C and quenched in cold water. Using CrK radiation, at least one weak superlattice line was found in the X-ray diffraction pattern which could be indexed as (100). and which disappeared, as expected, when FeK radiation was used. It was found more recently that the impurity phase (presumably VN), previously giving rise to additional X-ray diffraction lines and thus preventing definite indentification of the (111) superlattice line,&apos; can be eliminated by preparing the alloy by arc melting in a helium atmosphere. The alloy specimen melted in this manner had clean surfaces and showed very littte, if any, nitride phase in the microstructure after annealing in vacuum at 1250°C and quenching. The relative intensity of the (100). superlattice line with CrK radiation was greatly increased and, in addition, a fairly strong (Ill) , superlattice line and even a detectable (210) , super- lattice line was obtained, when the powder produced by filing from the 1250°C annealed and quenched specimen was reannealed in vacuum at 625°C for 1 hr. By using a cellulose acetate film as a filter in front of the photographic film in order to absorb the soft radiation resulting from air fluorescence, the background intensity could be reduced considerably in relation to the intensity of the diffraction lines. All three superlattice lines, (100),, (111)., and (210)a, disappeared, as expected, when a radiation other than CrK, was used.1 For the powder reannealed at 625ºC, the strongest lines of the s pattern also appeared weakly, indicating that during an: nealing at 625°C a small amount of transformation took place from the body-centered-cubic to the u phase. However, since all superlattice lines to be expected in the 0 angle range used were actually very clearly present, it was evident that the high temperature body-centered-cubic phase had transformed into a CsCl-type ordered structure before much s phase could form. Reannealing filings for 1 hr at 700°C resulted in complete transformation into the u phase. After 1 hr at 650°C the transformation into IT was not quite complete, the strongest body-centered-cubic diffraction lines were still present, although fairly weak, and only the (100), super-lattice line was detectable (extremely weak). These findings not only confirm the previous conclusionsL as to the existence of a CsCl-type ordered structure in the Fe-V system, but they also indicate that this metastable ordered structure forms at about 600°C preceding the formation of the stable s phase, while at 1250°C the disordered body-centered-cubic phase is stable. The faint (loo) , super-lattice line previously observed in specimens quenched from 1200°C was probably due to the fact that the quenching of the powder in an evacuated fuse:! quartz capsule was not fast enough to prevent completely the ordering reaction on cooling. The present results conform with the suggestion that the A-B bond, in relation to the A-A and B-B bonds, increases in strength from CrFe to VFe to TiFc. It is, therefore, of interest to compare the measured values of the average atomic diameter for these three alloys with the corresponding average atomic diameters calculated from the atomic radii of the elements concerned. ASSUming A-B contacts

Jan 1, 1958

By P. A. Beck, M. V. Nevitt

All binary and a number of ternary u alloys formed by first long period transition elements were examined and found to be ferromagnetic at low temperatures. The Curie temperatures for these alloys were measured. It was found that the correlation of the Curie temperature with composition may be described qualitatively in terms of the contributions of the various component atomic moments to the saturation moment of the alloy. Ternary Fe-Cr-Mo u phase alloys were also found to be ferromagnetic, with a Curie temperature dependent on the iron content and largely independent of the unit cell dimensions. Similar relations were found for the Co-Fe-Cr and the Co-Cr-Mo a alloys, where the Co + Fe content appears to determine the Curie temperature. RECENTLY, it has become increasingly evident that the u phase is some kind of an "electron compound." Several papers1-&apos; discussed the empirical correlation between the composition of the various u phases in alloys of the transition elements and the distribution of electrons in the partially filled d-levels of the component atoms. However, a picture of the latter can be formed only in a more or less intuitive manner, as in the Pauling theory," and the rigorous treatment of these problems is at present prevented by lack of adequate knowledge of the electronic structure of the transition elements in the metallic state. It appeared reasonable to expect that investigation of the magnetic properties, which are related to d-shell electrons, may help in clarifying the physical nature of the foregoing empirical correlation. Qualitative tests of samples of various compositions have shown that certain u alloys become ferromagnetic at liquid nitrogen temperature." The present investigation was undertaken to determine whether or not low temperature ferromagnetism is characteristic of a large variety of u alloys and to establish how the Curie temperatures of ferromagnetic u alloys are influenced by changes in composition and in lattice parameter. In the first portion of the in- vestigation, Curie temperatures were measured for a series of u alloys containing either vanadium or chromium with one or two of the elements manganese, iron, cobalt, or nickel. In the second phase of the work, data were obtained on the Curie temperature of ternary (Fe, Co, Cr)a, (Fe, Cr, Mo)a, and (Co, Cr, MO)U alloys, as a function of composition and of interatomic spacing. Experimental Procedures High frequency vacuum melting in high purity re-crystallized alumina crucibles was employed in the preparation of the u alloys, using metals whose lot analyses are given in Table I. Approximately two-thirds of the alloys were analyzed chemically, the analytical results being in acceptable agreement with the intended compositions, as seen in Tables I1 and 111. The specimens were annealed for homogen-ization in an atmosphere of purified 92 pct He and 8 pct H, mixture or in evacuated and sealed Vycor tubes at temperatures from 780" to 1300°C, depending on the temperature range of the u phase field for the particular composition. The annealing temwerature and time for kach alloy are given in Tables 11 and 111. Curie points were determined by an induction method; the change with temperature of mutual inductance between two coils was observed when the i-u specimen was inserted into the flux path between the coils. The transformer consisted of three coils each containing 1200 turns of 0.0050 in. diam enameled copper wire. The center coil, P in Fig. 1, served as the primary coil, and was linked magnetically with each of the two secondary coils, S, and S? which were connected in series opposition. The primary coil, P, was energized by an audio-oscillator, set at a frequency of 500 cycles per sec, while the signal from the transformer secondary circuit,

Jan 1, 1956

By L. F. Coffin

Monotonic tension and controlled cyclic-strain tests have been conducted on an annealed steel at various strain rates and temperatures in the weep range. Evidence of a strain-induced precipitate reaction abozle 500°C was determined from pronounced cyclic-hardening effects, increase inflow stress, inter granular fracture, drastic decrease in low-cycle fatigue resistance, and loss in tensile fracture ductility, as well as through electron-microscopy examination. It was found that strain rate as well as temperature had a pronounced effect on these observations. A parameter of the form P = T(7.95 - log ip) was determined, which was directly related to the ductility, defined either as the true strain at fracture in the case of simple tension, or as 2N 1/2 ? E p in the case of cyclic plastic strain. A highly satisfactory comparison of the cyclic life as measured and as computed from the ductility predicted by this parameter was obtained for a range of temperatures from 400° to 650°C and for crosshead speeds of 0.002 to 0.2 in. per min. MANY metals subjected to sustained loading at elevated temperatures derive resistance to creep from solid-state reactions of various alloying constituents. These reactions can be many and varied, and occur as a consequence of time and temperature according to reaction-rate principles. Strong evidence exists that many of these reactions are influenced by plastic strain, the argument being put forth that dislocations act as sites for nucleation and growth for the new phase.&apos; Many examples can be cited where plastic strain during transformation influences the structure, and as a consequence affects the properties.2 The low-alloy steels serve as particularly good examples for investigating the effect which aging reactions have on resulting properties. Alloying elements such as carbon and nitrogen, and carbide formers such as manganese, chromium, molybdenum, and so forth, can, by the particular aging reaction which occurs, produce strengthening effects at various temperatures, and so endow strength to the alloy over a broad range of temperatures. These effects have been systematically studied by Glen both during creep3 and for constant strain-rate tension testing.4,5 The work of Glen is of considerable interest in connection with the present study, particularly in regard to the effect of various alloying additions on the true stress-strain curve and on fracture ductility at various elevated temperatures. He has shown that strain-age hardening occurred during plastic straining, which was quite specific both to the temperature of the test and to the alloying element involved. When strain-age hardening was noted at a particular temperature, a .minimum in reduction of area was also obtained. Provided the temperature for the minimum reduction of area exceeded 300°C, all minimum ductility fractures were found to be inter-crystalline in nature. For carbon steels containing molybdenum, two minima in reduction of area were noted, one occurring at 200° to 250°C, the precise temperature depending on the percentage of molyb-

Jan 1, 1964

By A. S. Yue

The interface morphology of the Mg-32 wt pct A1 eutectic has been studied in terms of the freezing rate, the temperature gradient, and the impurity content. For the impure eutectic it has been found that for a given temperature gradient a fast freezing rate favors the formation of a cellular intwface with sub-grain strucfure. This cellular interface can be changed to a planar interface of the same substructure either by decreasing the freezing rate or by increasing the temperature gradient. For the eutectic of highest purity, as purified by zme-refining, no cellular interface was found for any growth condition and only a planar interface with subgrain structure was observed. Furthermore, a layer of liquid adhering to the interface during de-cantation freezes with shapes and sizes of the phase particles different from those in the main eutectic solid. WHEN a molten metal or a binary eutectic liquid with zero freezing range is solidified unidirec-tionally, a cellular interface is usually formed-3 This interface is schematically represented by Fig. 1. The profile of the solid-liquid interface has a corrugated shape, as shown in Fig. l(a), while the decanted interface consists of cells, as shown in Fig. l(b). The cell boundary in a frozen eutectic is distinguishable from the cell interior by changes in particle shapes, as shown in Fig. 4. The formation of a cellular interface, according to Weart and ack,&apos; is attributed to a layer of constitutionally supercooled" liquid generated at the advancing interface by the simultaneous rejection of an impurity by the two phases of the eutectic mixture, which then permits freezing over an appreciable temperature range. This concept has been further elaborated by Tiller, who predicts that even in the absence of an impurity the rejection of solute ahead of each lamella of the eutectic may promote the formation of a cellular interface. More recently, Chilton and Winegard, and

Jan 1, 1963

By J. D. Mote, J. E. Dorn

This investigation was undertaken to study the effects of piledup arrays of dislocations on inducing slip, twinning, and fracturing in magnesium bicrystals. A series of variously oriented bicrystals of magnesium having a vertical grain boundary were prepared and tested in tension. It was found that piled-up arrays of dislocations at the grain boundary could, under appropriate conditions, induce slip, twinning- and cracking. The results that were obtained substantiate, at least qualitatively, the general dislocation mechanism for transmission of strain across grain boundaries and the Petch-Stroh concept of fracturing. WHEREAS single crystals of magnesium generally exhibit extensive deformation, coarse-grained poly-crystalline magnesium at subatmospheric temperatures fractures after a few percent elongation.&apos; Although a small amount of ductility is obtained, several features of this fracturing are characteristic of typical brittle behavior. Over a rather broad temperature range the fracture stress is insensitive to the test temperature and the fracture stress increases linearly with the reciprocal of the square root of the mean grain diameter. The course of fracturing is predominantly intergranular, but small fragments of adjacent grains frequently adhere to the fractured surface.2 The brittle behavior of polycrystalline magnesium is attributable to the limited number of facile deformation mechanisms it exhibits at low temperatures. For a general deformation of a randomly oriented polycrystalline aggregate, each grain must exhibit at least five independent mechanisms of deformation to permit accommodation of the imposed deformation from grain to grain.= Although minor amounts of prismatic slip occur in corners of grains where stress concentrations are known to be high, glide in polycrystalline magnesium at low temperatures takes place almost exclusively by basal slip.&apos; The common type of twinning, which takes place on the (1012) pyramidal planes, can under the most favorable orientations, lead to a. strain of only 6.9 pet; the contribution of twinning to the tensile strain would indeed be much less than this in a randomly oriented polycrystalline aggregate of magnesium. Since the three mechanisms of basal slip are coplanar, they are equivalent to only two independent mechanisms, a number insufficient for a general deformation. Consequently, once the permissible twinning has taken place in conjunction with basal slip, no further plastic deformation is possible because of interference to slip at the boundaries of dissimilarly oriented grains. At this stage brittle fracturing takes place due to high stress concentrations at the juncture of slip bands with the grain boundaries; the predominance of intergranular fracturing in magnesium, in preference to transcrystalline fracturing which is prevalent in zinc, has not yet been rationalized. A more atomistic description of the plastic behavior and fracture characteristics of magnesium follows from the analyses made by stroh4 on the stresses induced by piledup arrays of dislocations. Slip first takes place by dislocation motion in the most favorably oriented grains. As the dislocations approach the boundary of a dissimilarly oriented adjacent grain they begin to form an array of dislocations with its attendant stress field. Piledup arrays of screw and edge dislocations introduce high localized shear stresses at the spur of the array; piledup arrays of edge dislocations also induce high tensile stresses localized in the vicinity of the grain boundary. Whereas the shear stresses can induce slip to take place, the tensile stresses, if sufficiently high, can cause fracturing. The localized shear stress will be relieved if sufficient numbers of mechanisms of deformation become operative in the original and the adjacent grain to permit accommodation of the dislocations in the grain boundary. In this event a ductile behavior will be obtained. But if the number of deformation mechanisms is insufficient for complete migration of dislocation arrays into the grain boundary, the tensile stresses due to the edge components of piledup dislocation arrays will continue to increase with increasing applied stress until fracturing takes place. Whereas face-centered-cubic metals have a sufficient number of mechanisms of slip for accommodation of dislocations in their grain boundaries to exhibit ductile behavior, hexagonal-close-packed metals, in general, do not. Consequently, hexagonal-close-packed metals are usually brittle except when conditions such as alloying or temperature permit facile slip by a number of mechanisms. The arguments presented above suggest that the mechanical behavior of magnesium depends on whether or not dislocation arrays in adjacent grains can enter the grain boundary. When such accommodation is possible, ductile behavior is expected; but when such accommodation is impossible, fracturing will ensue. To further test the validity of these arguments it was considered advisable to study the

Jan 1, 1961

By A. T. Churchman

The deformation modes of rhenium have been identified as those typical of the hexagonal metals, titanium, zirconium, and beryllium whose c/a ratios, in common with rhenium, are less than ideal for close packing. Slip is observed on (1010), (1011), and (0001) planes and twinning on (1121), (1122), and (1012) planes. The very high rate of work hardening is believed to be associated with intersecting partial dislocations on two (1010) systems which can combine to form sessile barriers. If the stacking fault energy is low, as postulated by Seeger, these barriers should be strong and not easily bypassed by cross slipping. Such an explanation could also account for the very small temperature dependence of the yield stress which was observed. RHENIUM is interesting scientifically as a member of the group of high melting point hexagonal metals: titanium, beryllium, and zirconium with a c/a ratio less than that for ideal close packing. Unlike them, however, it work hardens at a very high rate. This rate is greater and continues to a much higher degree of deformation than for nickel, normally considered to have a high rate of work hardening. This paper presents experimental observations on the modes of deformation of rhenium and, by comparison with other hexagonal metals, some speculation on the cause of the high work hardening. MATERIALS Johnson, Matthey rhenium powder of both 99.9 pct and 99.5 pct purity, see Table I, was compacted at 10 tons per sq in., part sintered at 1350°C in vacuo, and finally arc melted in a "gettered" argon atmosphere arc furnace to produce small buttons. Little difference was observed in the as-cast hardness or working down behavior of the two purities suggesting that either silicon and potassium do not have a significant effect on the working properties of rhenium or they were lost during arc melting. SPECIMEN PREPARATION The cast structure was broken up by cold-rolling with inter-stage annealing at 1600o or 1800°C in a vacuum high-frequency furnace using a tungsten susceptor. Strip for tensile testing was taken from two thicknesses of material 0.011 and 0.064 in. The former with intermediate anneals at 1800°C had a grain size of 900 grains per sq mm, while the latter with inter-stage annealing at 1600°C had a grain size of 3600 grains per sq mm. A coarse grain size was obtained by secondary recrystallization in a half button cold-worked by 30 pct reduction. Annealing times of from half an hour to several hours at 2200° to 2600°C in a "gettered" argon atmosphere arc furnace1 resulted in grains of up to 2 mm diam.

Jan 1, 1961

By S. R. Dunbas, D. C. Jillson, E. A. Anderson

THE present work was undertaken to furnish information, lacking in the literature, on the deformation mechanisms active in pure titanium at room temperature. Since it was started, Rosi, Dube, and Alexander&apos; have indicated that slip can occur in coarse-grained (2 to 6 mm diameter) titanium on the {1010} and {1011} planes and twinning can take place on the {1072}, (1122) and (1151) planes. Liu and Steinberg,&apos; working with titanium flakes produced by fused salt electrolysis, found evidence of twinning on the {1032$, {1121), {1122}, (1123}, and (1154) planes. The crystals used in the present work were substantially longer (up to nearly 2 in. in length) and possibly purer. Production of Large Crystals It was the purpose of this part of the work to provide single crystal or large grain specimens for use in the deformation studies rather than to study the mechanism of crystal growth. Accordingly, all further exploratory studies on methods were abandoned when it was found that cold-rolled bars sealed in vacuo in individual Vycor tubes and given three or more cycles of 4 hr at 1200°C and three to five days at 850°C, gave large grains. Eighteen specimens about 0.2 in. square x 2 in. long yielded 33 useful grains, ranging from Va in. to nearly 2 in. in length, with an agreeably wide range of orientations, Fig. l. The 0.25 in. thick strip from which the starting specimens were cut had been reduced 67 pct on 18 in. diameter rolls from a scalped, hot-forged (959" to 1000°C), arc-melted, iodide titanium ingot. Thc bar was at room temperature, but the rolls were at 200°C. Reductions of about 0.03 in. per pass were used. The bar was cut into four segments, each of which was rolled in a somewhat different manner. No effect on the growth of large grains was noted. The composition of the titanium, determined on turnings from the ingot scalping operations, is given in Table I. The Rockwell A hardness of the ingot was 26. The standard starting specimens, about 1/4x1/4x2 in., were milled on all four sides, hand polished on 280 and 400 mesh emery papers, etched for 3 min in a 50 HF-50 glycerine solution, rinsed, and dried in alcohol and ether just before sealing them in Vycor tubes. The average specimen weight was 7.5 g, and the tube volume was 6.5 cc. A vacuum of less than 1 micron pressure was applied. The specimen tubes were placed in an evacuated Inconel muffle to minimize the danger of collapse of the glass tubes at temperature. In practice the specimens were first heated to 1200 °C for 4 hr and then transferred fairly quickly to an 850°C furnace where they were held for three to five days. This cycle was repeated at least three times before the specimens were cooled, removed from the tubes, lightly polished and etched on one surface for examinstion. Those in which large grains had not developed were resealed in Vycor and returned to the cycling. Satisfactory specimens (about one out of every four cycled) were polished with emery paper on all four side;, then metallographically polished using ctchinz between wheels to remove distorted metal and, finally, given a very light etch to reveal the grain boundaries. This was necessary because the surface was roughened by the sublimation of titanium under high temperature vacuum conditions. Specimens were identified by TiXl numbers using supplementary letters to designate specific grains.

Jan 1, 1954

By L. T. Lloyd, H. H. Chiswik

The operative deformation elements in a-uranium single crystals under compression at room temperature have been determined as a function of the compression directions. The deformation mechanisms noted may be arranged with respect to their frequency of occurrence and ease of operation in the following order: 1 — (010)-[I001 slip, 2—{130} twinning, 3—{~172} twinning, and 4bunder special conditions of stress application, kinking, cross-slip, {.-176) twinning, and (011) slip. The composition planes of the (172) and (176) systems were found to be irrational. Cross-slip was shown to be associated with the major (010) slip system, coupled with localized interaction of slip on the (001) planes. The mechanism of kinking was found to be similar to that observed in other metals in that it occurred chiefly when the compression direction was, nearly parallel to the principal slip direction [loo] and was associated with a lattice rotation about an axis contained in the slip plane and normal to the slip direction: the [001] in the uranium lattice. The resolved critical shear stress for slip on the (010)-[100] system was found to be 0.34 kg per mm2 In a single test it was shown that under compression in suitable directions twinning on the (130) also occurs at 600°C. DEFORMATION mechanisms of large grained polycrystalline orthorhombic a-uranium have been studied by Cahn.1 A major slip system identified as the (010) with a probable [loo] slip direction and a minor slip system on the (110) planes were reported; the slip direction of the minor system was not determined. The twinning systems that were identified experimentally included the (130) and the irrational (172) composition planes; observations of other traces which were not as frequent and which did not lend themselves to positive experimental identification led Cahn to postulate on the basis of indirect evidence that twinning also occurred on (112) and (121) planes. In addition to the foregoing slip and twinning mechanisms, Cahn also observed kinking and cross-slip in conjunction with the major (010) system; the cooperative cross-slip plane was not identified. The availability of single crystals to the present authors has enabled them to check these results, particularly with reference to the doubtful mechanisms and the preference of operation of any one mechanism in relation to the direction of stress application. The tests were confined to compression only, primarily because of experimental limitations imposed by the size and shape of the available crystals. The tests were performed at room temperature except for one crystal compressed at 600°C. The compression directions were chosen to obtain a representative coverage of one quadrant of the stereo-graphic projection. To test the existence of some of the deformation elements that were reported by Cahn, but were not found in the present study, several additional crystals were compressed in specifically chosen directions considered most ideal for their operation. Experimental Techniques The single crystals were obtained by the grain coarsening technique described by Fisher? They grinding and polishing on rotating laps, with final surface preparation performed in a H3PO4-HNO3 electropolishing bath. A typical crystal readied for compression is shown in Fig. 1; their dimensions were rather small and depended upon the testing direction. Crystals isolated for compression in a direction close to the [010] axis, which lay roughly parallel to the longitudinal axis of the polycrystalline rod, were about 3 to 4 mm long and 5 mm2 in cross-section, while those prepared for compression in other directions were smaller. Most of the crystals were free from twin markings and showed no evidence of Laue asterism. Several crystals, however, contained twin traces prior to compression; these were identified prior to compression so as to clearly distinguish them from those initiated during deformation. The origin of the twin markings prior to deformation may be ascribed to two sources: thermal stresses and specimen handling during isolation and preparation. Two other types of imperfections in the crystals should be mentioned: inclusions, which were probably oxides or carbides. and three of the crystals contained a small number of spherical included grains (<0.01 mm diam), which were remnants of unabsorbed grains from the coarsening treatment. The volume represented by these imperfections was small, and their presence presented no difficulties in the interpretation of the macrodeformation processes during subsequent compression. Two compression fixtures were employed: crystals A, B, C, E, and G were compressed in a hand-operated screw-driven jig whose compression platens were designed to minimize axial rotation;

Jan 1, 1956

By W. D. Robertson, R. E. Reed-Hill

DEFORMATION of magnesium crystals in a direction parallel to the basal plane has a special significance as a result of the preferred orientation characteristic of cold worked and recrystallized polycrystalline magnesium sheet and extruded rod in which the basal plane tends to lie in or near the plane of the sheet or the axis of a rod. The principal objective of the present study is a determination of the modes of plastic deformation in magnesium single crystals in this orientation. Evidence for nonbasal slip in magnesium has been presented by a number of authors. Schmid and Was-serman&apos; indicated that pyramidal slip on {1011} < 1120> or {1012} <1120> could occur above 225°C. Bakarian and Mathewson2 stablished that the slip system {1011} <1120> operates at high temperatures and that 225°C was a lower limit for pyramidal slip. The latter authors also showed that the critical resolved shear stress for {1011} slip was 400 g per sq mm at 330°C, while that for basal slip was 66 g per sq mm at the same temperature. Thus, at 330°C basal slip should be expected for all orientations except those in which the stress axis lies almost in the basal plane. More recently Burke and Hibbard3 oserved pyramidal slip at 25°C, when the stress axis was 6" to the basal plane and 14" to a <1120> slip direction. The critical resolved shear stress for pyramidal slip was 52 g per sq mm, which is only slightly greater than their value for basal slip (46 g per sq mm). Chadhuri, Chang, and Grant4 have observed non-basal slip in creep tests with polycrystalline specimens in the temperature range 250" to 350°C. The observed slip bands, which were extremely irregular in appearance, can be explained in terms of cooperative slip on {1011} and (1010) planes which have a common slip direction. Prismatic (1070) slip in polycrystalline magnesium was observed by Hauser, Landon, and Dorn.5 It was found to occur at low temperatures (78" and 195°K) and it was accompanied by cross slip in which the cooperating plane was the basal plane. Since prismatic slip occurred only at regions of high stress concentrations, the critical resolved shear stress could not be determined. Experimental Procedure The present work was performed on crystal specimens which were all cut from the same large single crystal. The original cylindrical crystal, 0.5 x 7 in., was grown in a Bridgman type furnace in which the temperature gradient was moved past the stationary crystal in the manner described by Jillson6 and Burke.&apos; High purity magnesium was furnished by the Dow Chemical Co. with the following spectro-graphic analysis in weight percent: 0.003 pct Al, <0.01 pct Ca, 0,002 pct Cu, <0.001 pct Fe, 0.008 pct Mn, <0.001 pct Ni, <0.002 pct Pb, <0.01 pct Si, <0.001 pct Sn, and <0.01 pct Zn. The large crystal was cut into four cylindrical pieces about 1.5 in. long. A flat surface parallel to the basal plane was made by hand grinding with lubricated metallographic paper on one side of each cylinder. In order to prevent bending in subsequent cutting operations, the crystals were supported by

Jan 1, 1958

By H. C. Chao, L. H. Van Vlack

Small MnS inclusions with known crystallographic orientations were placed inside powder compacts of low-carbon steel. After the metal was axially campressed with negligible end friction, the deformstions for the metal and the inclusions were compared. The MnS inclusions deformed more when the [100] direction was aligned with the compression axis than when the [111] direction was parallel to this axis. The deformations of the inclusions in the two principal radial directions were equal for each of the above orientations. Inclusions with [110] compression alignments did not deform with radial symmetry. The relative deformation of the inclusion and metal was closely dependent upon the relatiue hardness of the two phases. The relative deformation of the two phases was not sensitive to the rate of deformation. RECENT studies by the authors1.&apos; suggested that the plastic deformation of MnS in steel would probably be highly sensitive to the orientation of the inclusions and to the temperature of the metal. This paper reports an investigation of these factors upon MnS behavior within steel. Manganese sulfide (MnS) possesses an NaCl-type structure and typically has extensive (l10) {110} slip as a separate (noninclusion) crystal.&apos; A secondary slip system, ( l 10) { l l l}, has also been observed where the major slip system is restricted. In general, MnS inclusions must be rated as a highly deformable second phase.3 The amount of sulfide deformation varies, however, with several composition and processing factors. Some of these have been only partially assigned. For example, it is known that minor amounts (<0.01 pct) of silicon within free-machining steels will increase the amount of MnS deformation,4 but the mechanism of the added deformation can only be surmised at the present. Manganese sulfide and steel have sufficiently comparable deformation characteristics so that slip which is started in steel may be continued through the sulfide inclusions and back into the steel if the crystal orientations are favorable.5 A more detailed discussion of previous work on the plastic deformation of NaC1-type crystals and on the plastic deformation of inclusions within a metal is given in Chao&apos;s work.6 EXPERIMENTAL PROCEDURE The manganese sulfide which was used in this study was prepared by previously described methods.&apos; Single crystals of MnS, both as cleavage cubes and as spheres, were oriented within steel powder compacts so that the desired crystal directions were parallel to the direction of axial compression. A four-stage hydrostatic compaction procedure was used and involved the following steps. In the first stage part of the powder was placed in a metal die 1 in. in diameter with a thick (1 in. OD, 5/8 in. ID) rubber liner which had one end plugged. The steel powder was hand-rammed, making it as dense as possible before placing a carefully sized MnS crystal (either as a sphere or as a cube) near the center. The crystal was oriented with the chosen direction vertical; viz., [001], [011], or [111], with the aid of a X10 microscope. A pair of tungsten wire threads 0.020 in. in diameter was inserted along the side of this (&apos;core compact" to locate the desired plane after the compression tests. After the crystal was positioned in the center of the die, more powder was added and carefully rammed by hand. The die was then capped with a rubber plug of the same hardness and thickness as that of the liner. The whole assembly as shown in Fig. 1 was compacted by a ram load of 54,000 lb (about 70,000 psi). In the second stage a smaller, 3/4-in, rubber-lined die was used to give a stress of approximately 120,000 psi. The above process was repeated with the initial compact serving as a core for a larger compact. The final product after sintering was a cylinder 1 cm long and 1 cm in diameter, having a density of 7.54 g per cu cm. This was close to the theoretical density since the metal contained a non-metallic phase. There was no evidence of MnS deformation during the hydrostatic compaction or subsequent sintering. Elevated-temperature hardness data were obtained by procedures previously described.2 Compression tests for inclusion deformation utilized the cylinders which were described above. The critical problem in these tests was the lubri-

Jan 1, 1965

By J. E. Burke, A. M. Turkalo

IN 1923 Desch¹ pointed out that the grains in a metal which is anisotropic with respect to its thermal coefficient of expansion would contract differently upon cooling, and that the stresses developed might approximate the plastic strength of the metal. More recently Boas and Honeycombe2-5 studied the behavior of several metals upon thermal cycling and observed that the stresses developed in arlisotropic metals are great enough to produce slip lines in individual grains and a roughening of the specimen surface. This phenomenon they have named "thermal fatigue." The mechanism they propose involves essentially a kneading of the grains, the deformation being alternately in compression and tension in a given grain as the temperature is changed in one direction and then the other. The present work was undertaken to investigate the possibility that an additional mechanism might operate to produce plastic deformation during thermal cycling—a "thermal ratchet" that depends upon a combination of grain boundary flow to relax the stress that develops between differently oriented grains upon raising the temperature and transcrys-talline slip to relax the oppositely directed stress which develops on lowering the temperature. Thus, thermal cycling should produce a nonreversible distortion such that certain grains will change shape differently from their neighbors with a simultaneous displacement being produced at the grain boundary. Temperature Dependence of Grain Boundary and Grain Strength The critical resolved stress for the initiation of slip in metal grains is only mildly affected by temperature." For example, in cadmium it decreases from 0.15 to about 0.05 kg per sq mm when the temperature is increased from 20° to 458°K and further temperature increase causes little further decrease. On the other hand, the work of KG1 indicates that the grain boundaries behave in a viscous fashion that can be described8 by the expression: t = BVexp(Q/RT) [1] t is the shearing stress on the boundary; B, a constant; V, the flow rate at the boundary; Q, the activation energy for grain boundary flow; R, the gas law&apos;s constant; and T, the absolute temperature. Eq 1 indicates that the stress necessary to cause a given grain boundary flow rate, V, decreases rapidly with increasing temperature. The value of the constant B is such that at sufficiently low temperature and ordinary strain rates deformation will occur preferentially by slip rather than by grain boundary flow. There is considerable evidence to indicate Consider the bicrystal shown in Fig. 1. In grain 1 the slip plane lies 45 " to the boundary while in grain 2 the slip plane is 90" to the boundary. The coefficients of expansion of the grains in a direction parallel to the length of the crystal are a1 and a, with a, > a2 for the orientations shown. The sequence of events that can occur upon heating and cooling this specimen is illustrated schematically in Fig. 2. Initially there is assumed to be no stress in the specimen (A). Upon heating, grain 1 attempts to become longer than grain 2, but is constrained by grain 2. Thus grain 1 is loaded in compression and grain 2 is loaded in tension, and a shearing stress is present across the boundary (B). As the temperature is increased, the stress will build up, and finally grain 1 will be plastically deformed by slip, since the greater stress is resolved on its slip planes. Any further heating will result in more slip and the stress will remain constant until some temperature T* is reached where the stress can be relaxed by grain boundary flow.† At this relaxation temperature (C) a step will appear between grain 1 and grain 2. Further heating above T* will cause grain 1 to become relatively longer, but no stress will appear because the grain boundary is too weak to support the stress (D). Upon cooling again, at T* (E), the grain boundary will again be able to support a shearing stress, and upon cooling further, grain 1 will be loaded in tension and grain 2 in compression (F). When the decrease in temperature below T* is sufficient to impose the critical shear stress upon the slip plane of grain 1, it will be stretched by slip.

Jan 1, 1953

By N. J. Grant, H. Brunner

This paber is concerned with the determination of equations relating elongation to the amount of shear taking place both along grain boundaries and in slip planes of poly crystalline aggregates during creep. Certain discrepancies with previously used equations are pointed out. Grain boundaries were observed to become serrated during creep, but it is shown that this does not necessarily prevent further grain boundary sliding. Direct obser-vations of subgrain boundary ingration lead to the conclusion that this migration facilitates sliding along serrated grain boundaries. It is bointed out that the state of stress at triple boints is still unknown. MOST of the mechanisms of deformation contributing to elongation are shear processes, such as slip, kinking, grain boundary sliding, and twinning. For quantitative investigations of individual deformation mechanism it is necessary to know the equation which permits the calculation of speci-tnen elongation from measured amounts of shear. This calculated elongation must then be compared with the observed total elongation. The authors&apos; special interest concerned grain boundary sliding during creep. Although this subject has already been investigated quantitatively by McLean,&apos; Rachinger,&apos; and Fazan, Sherby, and Dorn, calculations indicated that none of the equations used thus far to relate shear with elongation were sufficiently well founded. A basic study of this relationship was thus made and the results of this study (which do not entirely agree with those previously used) are presented. Most of the ideas set forth apply not only to grain boundary sliding but to other mechanisms of shear as well. THE SPEAR-ELONGATION RELATIONSHIP Basic Models—The relationship between shear and elongation is trivial in the simplest case of shear, which is shown in Fig. l(a). The vector A; designates the displacement across the shear interface, and Au, and Aut are its components parallel and normal to the tensile direction, respectively. It is evident that the specimen elongation due to shear is equal to the longitudinal component of the shear vector, and it should be noted that the normal component does not contribute to the elongation of the specimen (there are, of course, two normal components in a three-dimensional model). The model shown in Fig. l(b) may be applied to mechanical twinning and to subgrain boundary tnigration. In this case the width (h) of an already existing shear band increases by the migration of an interface, but the shear angle y (angle of mis-orientation in the case of a subgrain boundary) remains constant. The geometrical relationships indicated in Fig. l(b) permit this case to be reduced to the one shown in Fig. l(a). For the resulting elongation A6 we find: where AV/V = fraction of the volume of the specimen swept by migrating interfaces , and 1 = length of specimen. Thus, assuming for example that the angle of mis-orientation is 1 deg, and that P = 45 deg, we find that the specimen elongates 0.87 pct of its length if the entire volume of the specimen is swept once by such a subgrain boundary. An example of deformation by migration of subgrain boundaries is shown in Fig. 2. The specimen shown was repolished after 9.8 pct creep strain and the test then continued for another \ pct. Since the shear vector has, in general, a component normal to the surface, subgrain boundary migration results in the formation of an inclined band delineating the region swept by the subgrain boundary. These inclined bands become clearly visible when observed with oblique illumina-

Jan 1, 1960

By R. Maddi, I. R. Kramer

The delay time for the initiation of slip was studied in single crystals of a brass, aluminum, and ß brass. A delay time for slip was found in ß brass when the specimens were tested below room temperature; however, one was not found for a brass or aluminum. A general theory for the existence of the brittle transition temperature is proposed. A LTHOUGH a considerable amount of effort has A been devoted to the study of the deformation and fracture of single crystals, the vast majority of the work was concerned with static tests or with tests carried out at relatively slow strain rates. The necessity for the study of a possible incubation time for slip becomes apparent when the various theories which have been postulated for the elucidation of the mechanism of slip are considered. The existence of an incubation period would strongly indicate that slip occurs by a process of nucleation and growth; whereas the absence of an incubation would present rather convincing evidence that slip occurs by a cataclysmic process. In addition to shedding light on the process of plastic deformation, an understanding of the early stages of plastic deformation may be helpful in finding an explanation for the brittle behavior of the body-centered metals under certain conditions. It is well known that these metals, such as iron, molybdenum, tungsten, ß brass, etc., will become brittle as the test temperature is lowered or the strain rate is increased. In spite of the fact that this subject has received considerable attention since the turn of the century, no adequate theory exists today which explains the phenomenon. In the ductile temperature range the metal breaks with a "fibrous" fracture after considerable slip has taken place. In the brittle temperature range the metal fails essentially by cleavage on the {loo) planes: however, some plastic flow is always present even in the most brittle fractures. It is possible, as will be explained later, to ascribe this brittle behavior to the length of the incubation time for slip. Clark and Wood,&apos; using polycrystalline metals, showed that a delay time existed for the yield point in mild steels and that the delay time depended upon the applied stress. These authors stated that the delay time was observed only with those materials for which the stress-strain curve showed a definite yield point. In their work only the mild steel specimens exhibited a delay time at the yield point, while the other materials studied-type 302 stainless steel, SAE 4130 normalized steel, SAE 4130 quenched and tempered steel, 24s-T aluminum—did not show a delay time. These authors&apos; in an extension of their work, found that as the temperature was lowered the delay time was increased. It is, then, the purpose of this investigation to measure or to set an upper limit on the delay time for plastic flow in single crystals of a brass, aluminum, and ß brass. The delay time will also be studied as a function of temperature. The incubation time may be measured by determining the length of time the specimen will support a stress without slip occurring when the stress is greater than the static critical resolved shear stress. In order to accomplish these measurements use was made of a pendulum which was so designed that a single crystal specimen could be placed at various positions along its length. When a pendulum is struck by another pendulum of the same length, an elastic wave is transmitted down the bar with the velocity of sound in the material and is reflected from the far end of the bar. The reflected wave then travels back and unloads the stress until it reaches the impacted end of the bar and the two pendulums separate. The length of time that the specimen is subjected to the stress is equal to the time it takes for the stress wave to travel twice the distance from the specimen to the end of the bar. The stress applied to the specimen is governed by the velocity of impact of the two pendulums. The stress at which the specimen first suffers plastic: deformation was determined in these experiments by examining the specimen under the microscope for the first appearance of slip lines and by measuring the residual strain after each impact. In these experiments the critical resolved shear stress was approached from the low stress side and no attempt was made to determine it exactly. To determine it exactly, it would have been necessary to find that stress at which slip would have just started. However, since the stresses were increased in rather small increments the critical stress is believed to be approached rather closely, as will be seen from the experimental results. The critical stress will be taken as the highest stress obtained before the onset of plastic deformation. The stresses

Jan 1, 1953

By R. Maddi, I. R. Kramer

C. S. Roberts (Dow Chemical Co., Midland, Mich.)— In this study we have seen another example of how modern electronic instrumentation can be of great value to metallurgical research. The authors have shown much ingenuity in their experimental work. However, I wish to point out that anelasticity theory tells us that we must be cautious when we use pulse methods for measurements which are to be correlated with knowledge of static stress-strain behavior. The basic stress calibrations used by the authors depend on the use of static moduli combined with the pulsed strains. No recognition of a possible modulus defect has been indicated. The general agreement of critical resolved shear stresses may indicate that a

Jan 1, 1953

By L. B. Harris

Continuous cyclic unloading during tensile work hardening of polycrystalline zinc at room temperature enables specimens to sustain greatly increased extension. Such enhanced ductility is associated with creep-type extension, during which the cyclic component appears to promote relaxation of internal strains. It is possible to trace the transitions from tension, through enhanced cyclic extension, to fatigue and relate the observed behavior to simpler types of deformation. DISTINCTIVE deformation behavior has been shown to occur when loading includes both cyclic and unidirectional components. For aluminum and copper extended by a sequence of progressively biased strain reversals, coffin1 observed greater fracture ductility and lower flow stresses than during monotonic tension. This may be compared with the reduction in hardness obtained from conventional fatigue softening. But fatigue softening is accompanied by enhanced fatigue life,&apos; whereas Benham3 found that fatigue life was reduced when copper continuously extended during axial load cycling. The corresponding specimen elongation, for large cyclic load amplitudes, was greater than during normal tension. Under different conditions, Bendler and wood4 found that torsional fatigue initiated extension in copper under low tensile loads previously in equilibrium with the specimen; fatigue life was again reduced. Thus there is a type of cyclic softening which is associated with reduced fatigue life and which occurs when the cyclic loading is accompanied by a unidirectional strain component. Further, the fracture ductility or extension obtained from the unidirectional component can exceed that obtained in the absence of cyclic load. Specimen extension was not initiated by axial fatigue at small load amplitudes;3 hence Benham&apos;s work distinguishes between fatigue at large and small amplitudes, the former often being linked with unidirectional deformation because of similarities in strain Structure. The initiation of tensile extension during torsional fatigue,4 however, occurred with small amplitudes. Comparable changes in behavior have been ob- served during creep. kennedy&apos; found that combined cyclic and creep stresses on lead at 32°C increased the rate of elongation over that for simple creep, the consequence being a reduction in creep life. It was also demonstrated that small cyclic stresses applied after creep deformation initially increased recovery, but that prolonged application produced only normal fatigue hardening. It is clear that physical properties can be changed by interaction between the cyclic and unidirectional deformations, but owing to the number of different ways in which the deformations can be combined and the large number of possible variables for each combination, trends of behavior become easily obscured. One definite conclusion is that enhanced ductility or increased extension can be obtained by cyclic action, and it is this process that has been investigated for the tensile test by measurements of the extra tensile strain produced by the addition of a cyclic tensile component. EXPERIMENTAL PROCEDURE Material. Specimens were 99.99 pct Zn wire of 1.6 and 2.0 mm diam. Mean grain diameter was 0.02 mm, sufficiently small to give a ductile necked-down fracture under all loading conditions. All experiments were conducted at an average temperature of 20°C. Normal Tension. Unidirectional tensile curves at different strain rates were obtained from an In-stron testing machine, on which load-time curves were recorded autographically, using gage lengths of 5 and 10 cm. Straining was at constant cross-head velocity, and quoted strain rates are with reference to initial specimen length. Measurements of total elongation under simple tension were also made on the tensile machine that had been modified to incorporate an added fluctuating load. Combined Tension and Rapid Cyclic Load. An electromagnetic vibrator was coupled to the elastic beam of a Hounsfield ensometer- and driven sinus-oidally from a power amplifier at frequencies from 20 to 360 cps, the flexible connecting links on the tensometer being replaced by rigid fixtures to eliminate lateral vibration in the specimen. One end of the specimen was pulled by the normal extension drive of the tensometer while the other end, fixed to the elastic beam and vibrator, was subjected to rapid oscillations of load. It was thus possible to apply cyclic load to a tensile test without altering the rate of extension of the specimen

Jan 1, 1964

By J. E. Dorn, L. A. Shepard

LOW and Gensamer&apos; demonstrated a number of years ago that the yield point phenomenon in mild steels was associated with the presence of fer-rite soluble carbon or nitrogen. More recently the yield phenomenon in body-centered-cubic metals containing interstitials was rationalized by Cottrell&apos; in terms of a simple dislocation model. Interstitial atoms interact with dislocations in two ways; they cause not only local expansions but induce local tetragonality in the lattice. Consequently, interstitial~ interact with the hydrostatic tension and shear components of the stress about dislocations. They tend to migrate toward the expanded regions of edge dislocations and to assume sites that relieve the shear stresses of screw dislocations. Thus, a dislocation saturated with solute atoms constitutes a lower free energy state than that obtained when the dislocation threads through the average composition regions of the matrix. A greater stress will be required to separate the dislocation from its atmosphere than to move the dislocation through the matrix. This factor gives rise to the upper yield stress, which is required to unleash a series of dislocations in a localized region. This local yielding is propagated across the specimen to form a thin band of plastically deformed material known as a Lueder&apos;s band, making an angle of about 45" to the stress axis. Once the band has formed, deformation continues at the lower yield stress by the spreading of the Lueder&apos;s band in the direction of the applied stress. Undoubtedly the spreading of Lueder&apos;s bands at the lower yield stress is accomplished by the high stress concentrations at the band fronts, which serve to induce continued unlocking of new dislocations in advance of the migrating band fronts. Cottrell and Bilby have shown that the dependence of the yield point on temperature can be deduced by assuming that thermal fluctuations aid the stress in unlocking small dislocation loops from their solute atmospheres. Once a loop that exceeds a critical size has been nucleated, the entire locked diqlocation is released and can migrate. Fisher4 simplified this analysis by assuming that the locking forces were short range, so that if the dislocation loop were displaced only one Burgers vector from its atmosphere, it would be unlocked. Applying his model to the special case of delayed yielding under a constant stress of the order of the upper yield strength, he demonstrated that the delay time 7 for yielding should depend on stress and temperature according to where A and B are constants, G is the shear modulus, and u and T are the resolved shear stress and absolute temperature, respectively. Cottrell and Bilby, Fisher, and Fisher and Rogers&apos; have shown that the above deductions are at least in qualitative harmony with the experimental facts. A number of investigators5-0 have shown that the yield point phenomenon can also be induced in sub-stitutional alloys of face-centered-cubic metals. In general such yield points are not as pronounced as those encountered in body-centered-cubic metals containing interstitials. The yield point phenomenon in these materials is usually enhanced by prestrain-ing at low temperatures and aging at intermediate temperatures. Undoubtedly the yield point phenomenon induced by strain aging substitutional alloys also results from locking of dislocations. But the locking of dislocations in substitutional alloys of face-centered-cubic metals differs somewhat from interstitial locking of dislocations in body-centered-cubic metals. Substitutional elements in face-centered-cubic lattices cause only radial displacements of the adjacent lattice points. Consequently, only the edge components of dislocations can be locked by the mechanism suggested by Cottrell. Additional locking, however, can be obtained by the Suzuki mcchanism.10 In face-centered-cubic metals, dislocations exhibit lower energies when they are present in the

Jan 1, 1957

By F. N. Rhines, B. H. Alexander

MUCH attention has been directed to the effects of grain size upon the properties of alloys, but there has been scant study either of the conditions that determine the pattern and dimensions of den-drites in metal systems, or of the influence of their shape and size upon the overall properties of cast-ings. The aim of the research that is about to be described has been to investigate the effect of vari-ous factors upon the mode of formation of dendrites in alloys by measurements of the distance between adjacent dendrite arms (dendrite spacing). Early investigators, including Grignonl and Tschernoff,2 showed that a metal dendrite is com-posed of a tree-like system of stalks and branches arranged in a simple geometrical pattern. North-cott and Thomas3 demonstrated that, in the face-centered cubic solid solutions of copper-base, these stalks and side arms all lie in (100) directions in the crystal. Several investigators, including Sauveur and Chou,0 Sauveur and Reed,&apos; and Martin and Mar-tina have reported that the addition to steel of alloy-ing elements, such as nickel, chromium, and molybdenum, not only makes the dendrites easier to reveal by etching, but makes them coarser. The latter authors8 proposed that the coarsening of the dendrites is roughly proportional to the increase in the temperature range of freezing, caused by adding the alloying elements. Sauveur and Chou6 showed, in addition, that the dendrites are coarsened by a decreased rate of cooling of the casting. Measurement of Dendrite Arm Spacing Among the physical conditions that could be ex-pected to have an influence upon the dendrite arm spacing, that appears in a cast metal, are: composi-tion, rate of freezing, crystal structure, and type of constitution. The relationships obtaining between these variables and the dendrite dimensions have been examined, in the present research, by measur- ing the arm spacing in a wide variety of alloys, listed in tables II through VI. Alloy compositions are recorded in the tables by showing the symbol of the major metal followed by the percentage and symbol of the alloying agent; thus, "Al-10Ag" is an aluminum-base alloy containing 10 pct of silver. Although none of the alloys were analyzed, an im-pression of their degree of purity may be obtained from that of their component metals given in table I. Five hundred grams of each alloy was made by melting in small clay-graphite crucibles in an elec-tric muffle furnace. After alloying the temperature was adjusted to 50" to 75°C above the liquidus and the melts were poured into cast iron molds, at room temperature, the molds having a wall thickness of 1 in. and a cavity 11/2 in. sq in cross-section. Each ingot, thus cast, was sectioned at mid-height and the sectioned surface was polished and etched for metallographic examination. Dendrite spacing meas-urements were made at three positions, namely, ad-jacent to the mold wall, midway between the wall and the center of the ingot, and at the center (desig-nated e, m, and c respectively, in the tables). A typical series of microstructures is presented in fig. 1. For each measurement, the average was taken of the dendrite spacing of several grains covering a zone about 2 mm wide. Only those grains which had a major dendrite axis nearly in the plane of polish were selected in order to eliminate corrections for orientation differences from grain to grain. Although the dendrite spacings were measured to the nearest thousandth of a millimeter, the values listed in the tables are thought to be significant only to the nearest hundredth of a millimeter. The larg-est difference in readings found, when various ob-servers rated the same specimens, was 0.012 mm; the largest difference between corresponding meas-urements upon duplicate specimens was 0.027 mm.

Jan 1, 1951