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By W. A. Backofen, G. Y. Chin, W. F. Hosford

The ductile fracturing process was studied in single-crystal and poly cvystalline aluminum deformed in tension over a temperature range from 295° to 4.2°K. At temperatures as low as 77°K, the fracture of "inclusion-free" material, including zone-refined aluminum, was by rupture (-100 pct RA). At 4.2 OK, fracture was brought on by adia-batic shear. Metallographic examination did not disclose any voids or slip-band microcracks, thus negating for inherently ductile metals any mechanism of void nucleation by vacancy condensation or of cracking due to dislocation pile-ups. In Izigh-purity aluminum not treated to be inclusion-free, fracture at temperatures as low as 45°K was of the double-cup type and a result of void formation. The reduction-of-area decreased as temperature was lowered, corresponding to the earlier appearance of voids. Such behavior was rationalized in terms of a larger increase, with decreasing temperature, in the .flow stress relative to the strength of the inclusion-matrix interface. Evidence for low-temperature adiabatic shear was found in discontinuous flow at 4.2"K, in the transition to a localized shear fracture at low temperatures, and in the suppression of shear fracture with an elastically hard pulling device. A simple analysis for the initiation of adiabatic shew permitted a general correlation of the various contributing factors. It has been pointed out that the duration of shear depends upon effective mass and elastic stiffness of the deformation system. IT has long been recognized that fracture* may Throughout this paper, the term "fracture" is taken to mean any process that results in the separation of a material into two (or more) parts. Thus rupture as it may be encountered in a tension test leading to 100 pct reduction-of-area is included in this category. occur in a ductile mode, and that the process can be of great practical as well as general interest. Much information about ductile fracture has also been accumulated over this period, but only recently has an understanding of mechanism begun to appear. Ludwik,' in 1926, first reported fracture in a tensile specimen starting with a central crack in the necked section. Since then, other studies have disclosed that such cracks may form by the coalescence of voids nucleated in this region where hydrostatic tension is highest.2-4 Rogers and Crussard et al.' have emphasized void formation and reori-entation along localized shear bands as a mode of crack propagation. pines6 has considered the tensile rod as a bundle of fibers joined by weak interfaces, which subsequently separate to allow individual fiber contraction. The notion of cavity growth and coalescence by purely plastic processes was discussed by Cottrell: who added that the tensile reduction-of-area ought not to be sensitive to temperature. On the other hand, it has been observed that the reduction-of-area is greatly increased if tests are carried out at high temperaturesa or under high hydrostatic pressure.' Fracturing anisotropy in wrought products lends support to the idea of void formation from preexisting flaws strongly aligned by earlier processing.''-l2 There is evidence that many voids result from the fracturing of inclusions or separation at the inclusion-matrix interface Another possibility is that voids grow out of pore volume produced in the initial solidification and never fully removed in later working. In general, a structure 3f particles, pores, and weak interfaces can be expected, at least in materials of engineering interest. Vacancy condensation has been suggested as an alternative mechanism of void formation for materials considered to be inclusion-free.13 Yet experience has shown that tensile reduction-of-area increases with purity, to the extreme of rupture as so often observed in single crystals. Adiabatic shear has an important bearing on ductile fracture. It occurs when the decrease of flow stress, as a result of local temperature rise from heat generated during straining, becomes larger than the increase due to strain and strain-rate hardening. As demonstrated by experiments on punching of plates,14 a large temperature rise may be brought about by rapid straining. Adiabatic flow as a result of the high strain rate reached in an ordinary tensile specimen just prior to separation may account for the cone formation in cup-and-cone fracture;14 evidence of such local heating has been presented.15 For geometrical reasons, however, pure sliding along the conical surfaces is unlikely, and separation under tensile forces is probably an important accompanying feature of the shear.7 In deformation processing operations, a high shear-strain rate may exist at boundaries between plas-

Jan 1, 1964

By J. Greenspan

The anisotropy of fracture and slip, that is, the brittleness and ductility of the beryllium single crystal, is characteristic also of po1ycrystalline beryllium in which the grains are oriented in a preferred manner. Beryllium with grain orientations resulting from hot working either unidirectionally or bidirectionally is ductile or brittle in directions given by the anisotropy and orientation of the grains. Textures developed from various hot-working sequences are given, and tensile results are correlated with textures. Not only texture, but fine grain size is necessary for obtaining high tensile elongation. Ultimate tensile strength and elongation are both correlated with grain diameter. Of particular interest is the case in which unusually high tensile elongations of 30 to 40 pct are obtained when basal planes are oriented to carry THE beryllium crystal (of nominal purity) is probably unique among metals with respect to its unusually acute anisotropy of slip and fracture. While extensive slip can occur on the system (1010) [ll20] starting at about 19,000 psi, the (0001) plane is particularly vulnerable to fracture at 4500 psi or less. Fracture occurs also on the (11zo) plane at about 26,000 psi.1"3 Further, there seems to be no other slip System which contributes significantly to

Jan 1, 1960

By Erhard Hornbogen

Twins were propagated into large, well-annealed crystals of a, iron-phosphorous and a, iron-molybdenum solid solutions. Strain fields caused by interaction of these twins were made visible by precipitation. These strain fields can be explained by assuming that transmitted and reflected plastic waves are created when a twin strikes an obstacle with high velocity. The twin front itself can be regarded as a shear wave that may be able to develop a one-dimensional shock front. The occurrence of {WO} fracture by the reflected stress is also discussed. The described effects were not found when twins propagated at lout velocity into disturbed crystals, for example, into crystals previously deformed by slip. DEFORMATION twinning leads to shearing of a crystal lattice under external load. The shear appears to be homogeneous over a large number of crystal layers. In a iron, shear occurs on the (112) planes and in the <1ll> directions. The formation of a twin proceeds by the movement of partial dislocations that change the stacking at the twinning plane.l, In the bcc lattice, this partial dislocation can be created by dissociation of a sessile a/2[111] dislocation that lies in the (112) plane: Cottrell and Bilby&apos;s spiral mechanism can explain the homogeneous shear, but has not been proven experimentally. Nevertheless, this mechanism can explain the possible high velocity of formation of a twin. In Cottrell and Bilby&apos;s model, as in other models of twinning or phase transformation, a much higher energy is required to spread the first stacking fault than to add new layers by further movement of the partial dislocations. The dislocations will therefore become accelerated proportional to the difference between the stress, tN, to nucleate and tp to propagate the twin. It has been assumed3,4 that tn is the stress required to make two partial dislocations of apposite sign pass for the first time. After the first layer of new stacking has been formed, the maximum stress is TN=Gb/4pd where G is the shear modulus, b is the Burgers vector of the partial dislocation, and d is their perpendicular spacing so that the amount of shear is S = b/d. From this formula, a value of 25 kg per mm2 has been estimated for twinning in Zn3. The measured values are smaller, but local internal stresses may help to provide the necessary stress. For a iron, a higher value can be expected, mainly due to the higher value of G. That agrees with the observation that "burst" twinning occurs if the yield strength is in-

Jan 1, 1962

By N. K. Chen, R. B. Pond

IN the study of slip band* formation, there have been many examples to show that they do not always appear as lines traversing the entire crystal, but as segments whose ends seem to vanish in their path through the crystal. This characteristic appearance of slip bands has been witnessed under the optical microscope at various magnifications&apos;-&apos; and also under the electron microscope.&apos; A typical example of this behavior seen with the optical microscope is shown in Fig. 1. However, the slip band studies were generally conducted on polished surfaces of single or poly-crystalline metals which had been previously deformed; i.e., the load was generally released so that the observation could be made. Any picture of slip bands so obtained can represent the surface phenomenon only in a static state of the strained material. The conditions prior to their formation cannot be definitely and clearly assigned. Thus, while a segmented slip band may suggest that slip is a growth process as supposed by the theory of the nucleation of slip,V he usual appearance of suddenly and fully developed slip bands around the crystal has generally been considered as a consequence of uniform shear of the entire slip plane akin to a cataclysmic process. Little clear-cut information is available with regard to the speed at which a slip band forms, its direction of motion, the geometry of its position with regard to its neighbors, and its dependence on orientation. A description is given in this paper of experimental apparatus by which the progressive formation of slip bands can be recorded while the specimen is undergoing deformation. Qualitative and quantitative data on the dynamic formation of slip bands will be presented with special interest concerning the propagation of slip bands, the spacing of slip bands, and their relations to strain hardening. Views on the formation of slip bands are discussed and a mechanism of the unit process involved in the formation of a slip band is proposed. Preparation of Specimens Single-crystal specimens of high purity aluminum (99.997 pct), 1/8 in. square in cross-section and 1% in. long in gage length, were made by the method of gradual solidification from the liquid state. Since no machining work could be introduced in preparation of crystals of such small size, a special mold was designed for casting them to final shape. The mold consisted of two, separate, high purity graphite blocks. Generally, 20 molds were packed together in one container so that 20 specimens could be obtained by one casting operation. This was desirable since it was possible by this method to obtain groups of crystals with similar orientations. The as-cast crystals were carefully clipped from the gate, etched, and homogenized for 24 hr at 600°C. They were then very gently polished using a 4/0 paper, re-etched, and finally electrolytically polished after the method previously described by Chen and Mathewson.6 The crystallographic orientations were determined using a back-reflection, Laue method. Tensile Testing and Photographic Method The tensile testing equipment for these tests was composed of a specially designed microtensile machine, microload cell and microclip gage with necessary appurtenances. The members of the microtensile machine consisted of three parts, as shown in Fig. 2. The chassis is equipped with an oil cylinder, A, and piston, the piston being part of the movable cross-head, B. Pressure in the oil cylinder is controlled and regulated by an external pneumatic-hydraulic cell, C, which is connected to the cylinder by a Vs in. high pressure copper tube. This cell is half filled with hydraulic oil and has a needle valve, D, on the oil exit side as well as a needle valve, E, on the gas inlet side. A quick-acting valve, F, as well as a pressure gage is provided for the gas side. The oil exits into the load piston on the microtensile machine. By connecting a tank of inert gas to the gas inlet, regulated pressures were provided over the oil so that the oil would leave the cell at a rate determined by the setting of the exit needle valve, the gas pressure, and the pressure of the oil in the load piston of the microtensile machine. With this pneumatic-hydraulic appurtenance it was possible to

Jan 1, 1953

By Harry L. Brown, Philip E. Armstrong

Young&apos;s modulus doto ore presented for W, Mo. Ta. V, Cr. Ni, Ti, and Zr as a function of temperature up to about 0.7 of the melting points. A plot of reduced temperature us reduced modulus produces a general correlation except for titanium and zirconium. Young&apos;s modudlus data for some representatiue commercial graphites are given up to 2400°C. All results were obtained from longitudinal resonance-frequency measzrrements of 4-in. long samples, corrected for simultaneously measured thermal expansion. Comparison of poly crystalline and single-crystal tungsten behavior indicates that all the observed modulus values are frequencv -dependent at the higher temperatures. STATIC measurements of elastic properties of materials at elevated temperatures are extremely difficult to make since the elastic behavior is obscured by relatively large first-stage creep effects. Dynamic methods which avoid this difficulty by utilizing the measurement of the resonance frequency of a simple vibrational mode have been described in the 1iterature.l-3 The authors have extended the operating temperature range of this type of measurement to above 2000°C and have described the equipment elsewhere.~ The Young&apos;s modulus data presented here were obtained with this equipment, using samples about 4 in. long and 1/4 in. diam, supported horizontally at the center and excited to the fundamental longitudinal resonance frequency. Young&apos;s modulus was calculated by the formula: E = 4f2f2p where E = Young&apos;s modulus, / = frequency, 1 = length, and p = density. Dilatometric data were obtained simultaneously by optical measurements of the change of length of the sample. For the metals tested, an attempt was made to obtain modulus values that would be representative of the pure, strain-free, randomly oriented material. All of the graphites studied exhibited a high degree of elastic anisotropy, while the method assumes an isotropic homogeneous material. However , when the values for Young&apos;s modulus obtained for AUC graphite were compared with those taken from static measurements at room temperature they were found to be only about 4 pet higher. This is excellent agreement considering the low precision of modulus calculations from stress-strain curves. The difficulty in using data of apparent Young&apos;s modulus for anisotropic materials arises when the attempt is made to use these data and shear-modulus data to obtain Poisson&apos;s ratio. The results are usually meaningless and sometimes absurd.&apos; RESULTS Table I lists the sources, impurity content, thermal history, and dilatometric constants of the metal samples that were investigated. All the metal samples were tested under a vacuum of 1 to 5 x 10-5 Torr. Where our dilatometric data agreed with previously published data, the table lists the previous values and the literature reference. Where no reference is given, the constants were determined from our dilatometric data. Table II presents the modulus data in units of millions of psi as a function of temperature in degrees centigrade. The numbers were obtained from curves fitted to the experimental data. For some types of calculations, such as those attempting to correlate creep data, the slope of the modulus curve is of interest, and this information also is reported in Table 11. It is always tempting to try to fit physical-property data into some general pattern and then use this pattern to predict the behavior of other similar materials. The general pattern for an elastic modulus of a metal seems to be a linear deoro- with increasing temperature Over the range between 0.1 and 0.4 of the melting temperature, then a progressive1y decreasing value up to the melting point. Metals appear to retain finite moduli

Jan 1, 1964

By R. L. Fleischer, W. F. Hosford

Tensile data for coarse grained aluminum Polycrystals suggest that the "grain size" effect is not due to dislocations piled up at grain boundaries but rather is primarily a relative size effect due to surface crystals being weaker and less confined. STUDIES directed at interpreting hardening of poly-crystalline metals normally identify their strain hardening properties with those in some particular type of single crystal.1"4 The recent recognition in face centered-cubic metals of a nearly linear stage with rapid hardening occuring at comparable rates for both polycrystals and single crystals, suggested that the same process or processes determine both cases and hence that there exists some justification for the use of single crystals to understand polycrystals. Further evidence for the above view may be found by an approach initiated by Chalmers:5 By using bicrystals of controlled orientation it is possible to begin to assemble a polycrystal and also to study grain boundary effects in detail. In this way it has been found that a single grain boundary affects easy glide but not the subsequent stage II hardening.6 This result suggests that a sensitive way to observe grain boundary effects in polycrystals would be to vary grain size and measure easy glide. As will be seen, easy glide is only possible for coarse-grained samples, and hence the results will serve to fill in the gap in measurements between single crystals and bicrystals on one hand and fine-grained polycrystals on the other. One problem inherent in comparing single crystals with polycrystals is the uncertainty as to what slip systems are acting in a polycrystal. To compare the two types of samples, rates of shear hardeninn---L. on the acting -planes are needed. and these may be computed only if it is known what particular systems are active. The acting systems were examined for a coarse-grained polycrystal and it will be shown that the systems supplying the preponderance of slip can be determined with little ambiguity. EXPERIMENTAL PROCEDURE Twelve samples of aluminum were prepared by chill casting into a heated graphite mold, followed by annealing at 635° ± 5°C for 24 hr with an 8-hr fur- nace cool, and finally either etching7 or electropol-ishing.&apos; The samples, with a 7 to 10 cm length between grips and 4.4 by 6.6 mm in cross section, were deformed at a strain rate of about 3 10 -3 . per min in a tensile device which has been described elsewhere.5 The composition was reported by Alcoa as 99.992 pct Al, 0.004 pct Zn, 0.002 pct Cu, 0.001 pct Fe, and 0.001 pct Si; nine samples were deformed while immersed in liquid helium and three in air at room temperature. The stress-strain curve for one of the samples (P-1) deformed at 4.2 "K has been reported previ~usl~.~ This sample was selected for determination of active slip systems. Eighteen of the crystals were examined by optical microscopy to determine the angles of slip line traces and by X-ray back reflection to determine orientation. By this means the slip planes were determined and the resolved shear stress factors for possible slip systems could be computed. Finally each sample was sectioned so that after etching, the number of crystals could be counted for each of ten newly exposed surfaces. The average of these ten values will be termed n, the number of crystals per cross section. Values of 11, varied from 1.9 (nearly bamboo structure) to 12.7. Sketches of typical cross sections appear in Fig. 1. RESULTS AND DISCUSSION: SLIP SYSTEMS 1) Determination of Acting Slip Planes—The stress axis orientation and operative slip planes in eighteen crystals of sample P-1, as determined by slip line traces and crystal orientation, are summarized in Fig. 2. For one of the crystals two planes had a common trace. so that the traces alone did not distinguish which plane or planes were slipping. However it was found that the stress resolving factor for the primary system was 0.386, .while that for the most stressed system in the other plane (indicated bv the dotted arrow) is 0.138. It will be assumed tgerefore that only the primary plane acted. Since the orientations were determined after extending the samples 4 pct, the stress axes may be rotated from their original value by as much as 2 deg in some cases. It is interesting to note that in five crystals only one slip plane acted, in eight two acted, and in five three planes were observed—an average of two slip

Jan 1, 1962

By R. A. Vandermeer, P. Gordon

The study of recrystallization in cold-worked metals is complicated by the impossibility of making direct three-dimensional optical measurements. Metallo-graphically, theinternal three-dimensional features of samples must be inferred from their intersections with the two-dimensional plane of polish. The inherent difficulties involved in this procedure have led— particularly during the last few years—to some instances of rather doubtful interpretations of experimental data in terms of nucleation and growth rates in recrystallization. In the present paper an analysis ; is given of the recrystallization characteristics in a polycrystalline alloy containing 0.008 wt pct copper in ZONE-refined aluminum *and an effort is madf to reemphasize the necessity in such studies for attention to the proper statistical relationships between one- two- and three-dimensional features of opaque samples. It is shown that, in common with several recently described cases for other types of transformations,1-5 recrystallization in this alloy can best be rationalized on the basis that all nucleation took place essentially at time zero—i.e., there is no significant time-dependent nucleation during annealing—and that the kinetics are controlled exclusively by the growth-rate parameters. This is true despite the fact that the number of

Jan 1, 1960

By M. J. Marcinkowski, A. Szirmae, R. M. Fisher

Room -temperature hardness measurements obtained from single and polycrystalline samples of a 47.8 at, pet Cr-Fe alloy which were aged for various times al 500°C show a two-fold increase over that of the unaged alloy after annealing for 1000 hr. A detailed examination of the deformation markings in the neighborhood of the hardness imbressions reveals that twinning becomes an increasingly more important mode of deformation as aging proceeds. this observation is shown to be inconsistent with the Proposals that the transformation is eve of order-disorder On the other hand, the results are in agreement with previous observations of Fisher et al. of a coherent chromium-rich precipitate which forms in an iron-rich matrix as a result of a miscibility gap in this alloy system as proposed by Williams . Using the coherent precipitate hypotlzesis as a model, a detailed analysis of the various possible strengthening contributions to both the slip mid twinning stresses is made. In the case of&apos; slip, lattice friction within the chromium-rich phase and the chemical energy associated with the interface between the two phases contribute about 60pet to the total strength. The contributions from coherency strains and modulus differences are thought to contribute the remaining 40 pet of the strength but are difficult to evaluate because of uncertainties regarding the flexibility of the dislocation line. All of the factors have nearly the same or else a smaller effect on the twinning stress in the aged alloy. Twinning is never observed in the unaged alloy because the twinning stress is much higher- than that for slip. With increased aging times, the various contributions to the total stress for both twinning and slip increase, but most of those for slip increase much more rapidly, so that, in the fully aged alloy, it surpasses the stress for twin propagation. When a twin is nucleated by the chance occurrence of an internal stress concentration during a test, the subsequent twin burst results in a low hardness reading. FeRNTIC Fe-Cr alloys from about 15 to 80 at. pet Cr content show considerable change in properties such as hardness, electrical resistivity, saturation magnetization, and so forth, after aging in the vicinity of 500°C.* The most marked change is a large increase in hardness accompanied by a sharp decrease in ductility, so the phenomenon has often been referred to as the 475°C (885°F) em-brittlement problem. Changes in microstructure are rather subtle and most investigators have not been able to observe any X-ray diffraction or metal-lographic changes during aging. There is little doubt that the phenomenon is inherent to the Fe-Cr binary system and is not directly related to the formation of a phase. Two distinct schools of thought have developed during the past decade concerning this problem. Masumoto, Saito, and sugiharal have concluded, from their own specific-heat measurements, that atomic ordering occurs in this temperature range. Pomey and Bastien2 have also attributed the changes in physical properties with aging in the neighborhood of 500°C to atomic ordering. In addition, Takeda and Nagai3 claimed to have found X-ray verification for superlattices corresponding to the compositions FesCr, FeCr, and FeCr3. However, all known attempts to observe superlattices in Fe-Cr alloys using neutron diffraction, which should be much more sensitive, have been unsuccessful. These have been reported by Shull et al.4 for 25 at. pet Cr, williams5 for 75 at. pet Cr, and Tisinai and samans6 for a 28.5 at. pet Cr. steel. The second and more prevalent opinion ascribes the 475°C embrittlement phenomenon to the formation of a coherent precipitate due to the occurrence of a miscibility gap in the Fe-Cr system below about 550°C. This latter concept was first indicated by the results of Fisher, Dulis, and Carroll,7 who were able to extract fine particles about 200Å in diameter from samples of 28.5 at. pet Cr steels aged from 1 to 3 years at 475°C. The extracted material was found to be nonmagnetic, to have a bee structure with a lattice parameter between that of iron and chromium, and to contain about 80 at. pet Cr. Williams and paxton8 and williams5 confirmed these results and first explicitly proposed the existence of a miscibility gap below the a region in the equilibrium diagram. Alloys aged within this gap

Jan 1, 1964

By L. J. Dijkstra, R. J. Sladek

IN earlier work the effect of manganese on the general behavior of nitrogen in iron was the subject of a careful examination by Fast.&apos; Part of the investigation was made, in collaboration with one of the present authors (L.J.D.), by using the internal friction method. This technique, which has been described elsewhere,&apos; showed some significant changes in the properties of Fe-N alloys by the addition of a small amount of manganese namely: 1—Under standard conditions the maximum of the nitrogen peak in pure iron appears around 20 °C and the half width is about 27 °C. By addition of 0.5 atomic pct Mn a general broadening of the internal friction peak occurs. The half width is increased by about 9°C. Moreover, a shift of the maximum of about 5°C toward a higher temperature takes place, Fig. 2. 2—The precipitation of nitrogen from the supersaturated solution, measured, e.g., at 200 °C, was inhibited by the addition of the amount of manganese given in effect 1. The broadening of the nitrogen peak was confirmed in more recent work3 on samples which were prepared from Westinghouse Puron iron. The effect of manganese on the rate of precipitation, however, was much less striking than in the earlier work&apos; based on Philips high purity iron. Theory To explain the first change in properties just referred to, effect 1, the following two assumptions were made:&apos; First, every manganese atom in sub-stitutional solid solution creates around it six interstices located between an iron and a manganese atom, as is evident from Fig. 1. These interstices, conveniently called Fe-Mn interstices, have for nitrogen a free energy level which is AG* lower than the normal Fe-Fe interstices between two iron atoms. For such low concentrations of manganese as 0.5 atomic pct, the possibility that two manganese atoms will be nearest neighbors can be disregarded. Second, it is assumed that in addition to the normal relaxation time TFe at least one new relaxation time, Mn, Fe, enters in the phenomena which is associated with the elementary diffusion jumps between a Fe-Mn interstice and an adjacent Fe-Fe interstice. Fig. 1 gives schematically the free energy for a nitrogen atom as a function of its position along the line ABC. A tentative analysis of the nitrogen peak in a 0.5 pct Fe-Mn alloy based on these assumptions has been made in Fig. 2. The dotted curve with a maximum at 22°C is caused by jumps between Fe-Fe interstices, the dotted curve with maximum at 32°C by jumps between an Fe-Mn and an Fe-Fe interstice. The two effects added together give the dash-dot internal friction curve for the alloy. In the following these two components will be referred to as the normal peak at 22°C and the abnormal one. (The small secondary peak at

Jan 1, 1954

By A. T. Robinson, J. E. Dorn

The electrical resistivities of aluminum alloys containing CU, Ge, Zn, Ag, Cd, and Mg were found to increase linearly with the atomic percentage of the solute atoms. Application of Linde&apos;s rule to these data suggests that each aluminum atom contributes 2.5 electrons to the metallic bond. ALTHOUGH aluminum invariably exhibits a Jt\. valence of three in ionic solids, it does not follow necessarily that its valence in the metallic state is also three. As a matter of record, many properties suggest that the number of bonding electrons in metallic aluminum is less than three. For example, as shown in Fig. 1, the atomic radii1 of the metallic elements in the solid state decrease with increasing atomic number at the beginning of any one period. The atomic radius of aluminum, however, is greater than that which would result from a regular decrease in atomic radius with increasing atomic number, suggesting that the number of bonding electrons in aluminum is somewhat less than three. Correlated with the anomalously large atomic radius of aluminum is its abnormally low melting temperature. As the atomic numbers increase in any one period, the melting temperatures of the metallic elements increase.&apos; As shown in Fig. 2, however, the melting temperature of aluminum (13) is only slightly greater than that of magnesium (12). Again the number of bonding electrons in metallic aluminum appears to be nearer two than the expected value of three. In addition Ageev and Ageeva3 alculated the electron density distribution in the aluminum lattice. A comparison of such electron density curves for various assumed valence states of aluminum with experimentally determined curves suggests that the actual number of bonding electrons in metallic aluminum is between two and three. Hume-Rothery and Raynor&apos;, " have suggested that the above-mentioned abnormalities are associated with the overlapping of the Brillouin zones of metallic aluminum when it is in the usual face-centered cubic structure. The importance of the number of bonding electrons in metals has been extended recently into the field of mechanical properties. While formerly it was thought that the plastic properties of alpha solid solutions were primarily dependent upon the lattice strain induced in the solvent by the solute, it is now known that the difference in the number of bonding electrons of the solute and solvent also has its influence on the plastic properties."1&apos; In order to achieve a satisfactory correlation of the effect of alloying elements on the plastic properties of aluminum alloys,"&apos;T however, it was necessary to assume that the number of bonding electrons contributed by aluminum was about two rather than the expected value of three. It appeared to be desirable, therefore, to seek other criteria for evaluating the number of bonding electrons contributed by aluminum to its alpha solid solutions, especially in view of the practical as well as the theoretical importance of the effect of valency on the plastic properties. Norbury&apos; was perhaps the first to illustrate that the increase in resistance of alpha solid solutions is associated with the differences in valence of the solute and solvent metals. In a series of illuminating investigations Linden-&apos;&apos; has shown that the electrical

Jan 1, 1952

By R. A. Anderson, O. D. Sherby, J. E. Dorn

Solid solution alloying increases the plastic properties of aluminum at elevated temperatures by solid solution strengthening, by restraining recovery and recrystallization, and by a Cottrell effect. When binary aluminum alloys are strained and aged at 1940° to 300°K they develop a yield point. This is attributed to a migration of dislocations to solute atoms during aging. IN view of the ever expanding interest in applications of metals and alloys to high temperature service conditions, it becomes increasingly important to be cognizant of the effect of various metallurgical factors on the strength of alloys at elevated temperatures. One problem of wide interest, not only because of its engineering significance but also due to its fundamental scientific importance, is the elucidation of the effect of alloying elements on the plastic properties of homogeneous a solid solutions at elevated temperatures. It is indeed astonishing to note that in spite of its importance, and in spite of extensive random testing of alloys at elevated temperatures, no systematic investigation has been reported yet on the effect of alloying additions on the plastic properties of a solid solutions at elevated temperatures. This deficiency in our knowledge prompted the investigation described in this report. Rather extensive data are currently available on the effect of alloying elements on the plastic properties of a solid solutions at atmospheric and sub-atmospheric temperatures. Such data might be ex- trapolated to higher temperatures and reasonable guesses might be made regarding the influence of such factors as recovery and recrystallization in order to hazard a qualitative estimate of the effect of alloying elements on the plastic properties of a solid solutions at elevated temperatures. Such

Jan 1, 1952

By R. Raring, W. J. Harris, J. A. Rinebolt

The effects of additions of alloying elements on the true-stress, true-strain characteristics of 0.30 pct C, 1.00 pct Mn, 0.30 pct Si pearlitic steel were studied. The alloying elements investigated were C, Mn, Si, P, The alloys are compared on the basis of fracture stress, fracture strain, energy to fracture, rate of strain hardening, strain hardening exponent, height of the flow curve, and lower yield point. IN the past, nearly all studies of the effects of alloying elements on the tensile properties of metals have compared the conventional engineering parameters, namely, tensile strength, yield strength, elongation, and reduction of area. Recently, however, the true-stress, true-strain method of recording results from the tension test has been used; Lacy and Gensamer,&apos; Hollomon," and French and Hibbard- are used this method to study the effects of composition on strength and ductility of metals. In this paper, the effects of certain alloying elements on true-stress, true-strain curves of steels with nearly constant grain size and pearlite spacing are presented. The notation employed in this paper is given in Table I. Since the definitions of stress and strain and the analytical geometry of the stress-strain curve have been explained previously, for example by Gensamer,&apos; they will not be reviewed here. However, the method used for the determination of energy to fracture, E,, requires mention. These energy values were calculated on the assumption that the flow curve followed the idealized equation:&apos; corresponds to the specific energy absorption to that strain value. There is justification for preferring the use of eq 1 for the determination of the energy to a particular strain rather than the area under the experimental stress-strain curve, since Gensamer showed that the use of the Bridgman correctione for stress at the neck of a tensile specimen brought the corrected experimental curve nearer to the idealized power-law curve than to the uncorrected experimental curve. However, it should be noted that the difference between the areas under the idealized curve and the experimental curve is not great for strain of less than 1.0, as can be seen from Fig. 1. In this figure, the true-stress, true-strain curve for a 0.01 pct C, 1.00 pct Mn steel is plotted through the experimental data points. From the value of a,, from this curve and the value of n as determined by the Inm-

Jan 1, 1952

By R. Raring, W. J. Harris, J. A. Rinebolt

G. W. Geil (National Bureau of Standards, Washington, D. C.)—The authors state that the degree of accuracy realized in the experimental determination of a, is likely rather low. This inaccuracy is attributed to the difficulty in reading the load of the tension machine at the instant of fracture of the test bars. I believe there is another factor which may have added considerably to the inaccuracy in the determination of a,, namely, the determination of 8,. Fracture of a cylindrical tensile specimen of a ductile metal tested in tension at room temperature is generally initiated at the axis and rapidly propagates radially to the periphery of the necked section. During the propagation of the fracture, the metal at the rim of the minimum cross-section extends longitudinally and contracts radially. Thus values of 81, based on diameter measurements made after complete fracture of the specimens do not necessarily represent the strain at the initial fracture." Data obtained at the National Bureau of Standards with a 0.3 pct C steel in the condition as-quenched from 1575°F and tempered at 1000°F for 1 hr and tested in tension at room temperature indicated a considerable "rim effect" and as shown in Fig. 13, resulted in an apparent increase in Sf from 0.90 to 0.98. As the fracture strain of this steel is approximately equal to those of the steels reported by the authors, it seems probable that a similar "rim effect" may have added to the inaccuracies in the reported values of Si and accompanying values of El. R. Raring (authors&apos; reply)—The authors are grateful to Mr. Geil for having called attention to a possible source of uncertainty in the determination of fracture stress, and they are in agreement with the principles upon which his discussion is based.

Jan 1, 1952

By R. I. Jaffee, F. C. Holden, H. R. Ogden

Alpha solutes increase the strengths of Ti-Mn alloys through solid-solution strengthening. The substitutional a addition, aluminum, decreases, and the interstitial solutes, carbon and nitrogen, increase the rate of nucleation and growth of a from ß. The best combinations of properties of a-ß alloys are obtained when there is a sufficient quantity of a phase in the structure to dissolve the a solutes. OF the many different titanium-base alloy systems, the predominant alloy type is the a-ß alloy. The properties of the a-ß alloys are dependent on solid-solution strengthening and heat-treatment effects involving the a-ß ratio and transformation reactions. Another variable which influences the mechanical properties of a-ß alloys is the a-stabilizer content of the alloy. An a solute may be present as an intentional addition, such as aluminum, or as an impurity element, such as carbon, oxygen, or nitrogen. It is known that these a stabilizers, when added to titanium, form single-phase alloys which are not heat treatable but which obtain their strength from solid-solution strengthening. Thus, it would be expected that a additions to a-ß alloys would increase the strength of the alloys by solid-solution strengthening of the a phase. In addition, they would affect the transformation kinetics of the ß-to-a reactions and other processes based on the instability of the ß phase. The effects of heat treatment and structure on the mechanical properties of Ti-Mn alloys have been shown in a previous paper.6 This system offers a good base to demonstrate the effects of typical a solutes on the properties of a-ß alloys. The three a solutes described in this work are aluminum, representative of a substitutional a solute, nitrogen, representative of an interstitial a solute, and carbon, representative of an interstitial compound-forming element. The effects of heat treatment and microstructure on the properties of a alloys containing these three elements are described in concurrent publications. Some of these data are used for base-line points in several of the curves used for illustration herein. Experimental Procedures Iodide titanium was used as the base for all of the alloys studied in this work. The alloys were prepared as ½ lb ingots by double arc melting in an argon atmosphere. The ingots were forged to ¾ in. rounds, vacuum annealed for 6 hr at 900°C at a pressure of 10 &apos; to 10-5 mm of Hg to remove hydrogen, and hot swaged to 1/4 in. diam rod. After me- chanical descaling, test specimens were prepared for heat treatment. The alloys used in this study together with the fabrication temperatures are given in Table I. Heat treatments were done in argon. For the most part, the specimens were sealed in Vyeor capsules under a partial pressure of argon. Quenching was accomplished by breaking the capsule under water. Other cooling methods used included oil quench, argon cool (simulated air cool in an argon atmosphere), and furnace cool. The times for the various heat-treating temperatures are given in Table 11. The tests performed on the alloys consisted of tensile tests on ? in. diam specimens, hardness tests, and microimpact tests. Specimen sizes have been adequately described in a previous publication.&apos; The micrographs presented in this paper were taken from specimens cut from the shoulders of broken tensile specimens. Final polishing was done with Linde B on a slow-speed wheel, and the specimens were etched with a 1½ HF — 3½ HNO, solution. Ti-N-Mn Alloys The transformation diagram and microstructures of the Ti-0.1 pct N-Mn alloys used in this investigation are given in Fig. 1. The effect of small nitrogen additions on the binary Ti-Mn diagram is to raise the ß-transus temperature with little effect on the a solubility of manganese. Also, as has been noted previously,&apos; high manganese-content alloys containing nitrogen, when quenched from temperatures high in the ß field, contain a subgrain boundary phase which appears to be nitrogen-rich a. Marten-site is formed when alloys containing less than about

Jan 1, 1956

By H. T. Green, R. M. Brick

True stress-strain data on alloys of pure iron with up to 2.4 pct Al were obtained in the temperature range +100° to —185°C. Alumi-num was found to reduce yield and flow stresses of iron at low temperatures but to have little or no effect on ductility. The effects of temperature and composition on strain hardening are discussed. SEVERAL independent studies of the behavior of high purity iron binary alloys at low temperatures are now in progress in attempts to evaluate systematically the variables affecting the low temperature brittleness of ferritic steels. This paper reports the results of one such investigation in which the tensile properties of aluminum and aluminum plus silicon ferrites were measured from 100" to —192°C. True stress-natural strain data have been obtained in order to evaluate as many as possible of the parameters which describe the behavior of the materials involved. In comparable studies at the National Physical Laboratory in England, iron and iron alloys of high purity have been produced&apos; and tested at subat-mospheric temperatures.&apos; True stress-natural strain curves were obtained there also. The purest iron contained 0.0025 pct C and 0.001 pct O and N. Even this, as normalized at 950°C following hot rolling, showed little ductility at -196°C. The grain size was ASTM No. 3, and the room-temperature yield strength was 17,800 psi (which seems too high for pure iron). Some of the NPL irons contained considerably more oxygen and demonstrated intergran-ular fracture at —196°C. The authors2 carefully differentiated between intergranular fractures associated with excessive oxygen content and transcrys-talline cleavage with little ductility encountered at —196°C in the purer material. The cleavage stress was half again as great as that associated with inter-granular fracture. Test Material, Preparation, and Procedures Of a number of Fe-A1 alloys produced, eight were considered to be sufficiently pure for testing. Partial chemical analyses (Table I), low observed yield points, and high ductilities indicate these alloys to be comparatively pure for vacuum-melted irons of sizable ingots, 5 Ib or more. To produce the binary Fe-A1 alloys, electrolytic iron was melted in air, cast into slabs, and rolled to strips 0.010 in. thick. These strips, joined into a continuous ribbon and wound into 2 1/2 in. diameter spools, were subjected for four weeks to a moving atmosphere of purified dry hydrogen in a stainless-steel tube at 1050" to 1150°C. Charges of these spools were melted in beryllia crucibles under good vacuums (1 micron), and aluminum (99.97 pct Al) was added to the melts. Compositions of these alloys are recorded in Table I. The ingots were hot forged and then cold rolled at least 65 pct to 3/8 in. rods which were vacuum annealed to the desired grain size, approximately ASTM No. 4, prior to machining into tensile test bars. All tensile specimens had gage sections 1 in. long, with a fillet of 1.5 in. radius to the shoulder. Gage diameters were 0.250 in, except for a few rods where additional cold work required use of a 0.200 in. gage section. After machining, 0.002 in. was removed from the gage diameter using 240, 400, and 600-grit metallo-graphic papers. The final polish with 600 grit left the fine scratches running in the longitudinal direction. By this means, surface metal strained during machining was removed. A few specimens heat treated after machining were similarly reduced 0.004 in. to remove any material affected chemically by the atmosphere during heat treatments, as is discussed in a later section. Tensile tests of the eight alloys at constant temperatures from +100° to —185°C were performed in apparatus which has been described." The essentials include a double-walled insulated metal vessel which contained the liquid heat-transfer medium surrounding the test specimen. A constant temperature was maintained by means of a pyrometer which regulated the pressure of dry air driving liquid air through a copper coil. Temperature variation was less than ±2°C during a specific test. For axial straining, two lengths of case-hardened chain, terminating in simple shackles, loaded the specimen through threaded grips. The lower grip bar passed through a hole in the bottom of the test vessel to which it was joined by a thin-walled

Jan 1, 1955

By R. J. Franklin, G. W. Beckman, D. Warren, E. Both, J. F. Libsch

BINARY and ternary alloys of iron, nickel and cobalt respond to annealing in a magnetic field by a characteristic change in the shape of their hysteresis 100p.l,2 An increase in retentivity and a decrease in coercive force produced by the magnetic treatment cause the hysteresis loop to approach the appearance of a rectangle. Materials with a rectangular hysteresis loop have made possible the contact-rectifier³ and have greatly improved the performance of pulse transformers4 and magnetic amplifiers." In the best material presently available for these applications, a 50 pct nickel-iron alloy," the desired characteristics are achieved by aligning the preferred crystallographic directions of magnetization along the rolling direction of the tape. The objective of the present study has been to produce rectangular hysteresis characteristics in materials with inherently high saturation. Iron-cobalt alloys, exhibiting saturation values up to 24,000 gausses&apos; appeared to offer promise for the magnetic annealing technique, because they remain magnetic to very high temperatures,8 exhibit favorable magnetostriction properties: and show zero crystal energy at 42 pct cobalt.10 Among the ternary iron-cobalt-nickel alloys,7,11 response to heat treatment in a magnetic field is unfortunately limited to alloys having rather low saturation values.&apos; It appeared interesting nevertheless, to study a series of compositions connecting the optimum composition (50/50) of the binary iron-cobalt system with the "Perminvar" composition (30 pct Fe, 25 pct Co, and 45 pct Ni). Very recently, R. Smoluchowski and R. W. Turner," have shown that under certain circumstances magnetic annealing can produce oriented recrystallization. A combination of this technique with the domain orientation utilized in the present study might well result in further improvements. The advantages of the powder metallurgy technique in preparing magnetic alloys for study have

Jan 1, 1951

By B. L. Averbach, Morris Cohen, S. A. Kulin

The martensitic transformation can be initiated by elastic stresses at temperatures above M. in a steel containing 20 pct Ni and 0.5 pct C. Shear strains and normal tensile strains acting on a potential habit plane promote the transformation but compressive strains oppose it. THE strain sensitivity of the martensitic transformation has long been recognized. It is now well known that martensite formation can be induced by plastic deformation at temperatures below, and not too far above, the M, point.&apos; However, the exact role of elastic vs. plastic strains and of the concomitant stresses has proved to be a very elusive matter. Many investigators2-&apos; of the steel hardening reaction have made use of the stresses resulting from volume changes to account for such observations as the existence of retained austenite and its variation across the section of a bar, the change in the amount of retained austenite with quenching rate, and the self-stopping nature of the transformation when the cooling is stopped. The effect of applied strain as an independent variable has been studied in 70 pct Fe-30 pct Ni alloys by Scheil7 and McReynolds.8 Some data are also available for lithium and Li-Mg alloys,9 Cu-Zn,10 Cu-Sn and Cu-A1 alloys," and aus-tenitic stainless steels."-" It has been found that martensite formation can be induced isothermally, even at temperatures above M,, by mechanical deformation of the parent phase. The competitive nature of plastic yielding by slip and by the martensitic reaction has been depicted by Scheil.7 Basically, Scheil postulated that: 1—at temperatures not too far above M, (where austenite is less stable than martensite), a critical resolved shear stress (within the elastic range) is required to promote the transformation to martensite; 2—at and below M,, the austenite lattice becomes mechanically, as well as thermodynamically, unstable and shears over spontaneously into martensite without the application of external stress; and 3—at temperatures sufficiently far above M8, the critical resolved shear stress for martensite formation increases to a level above that required for slip, and plastic flow then supersedes the transformation when external stress is applied. Scheil&apos;s concepts were tested by McReyno1ds8 ho found no change in the elastic moduli (measured both statically and dynamically) of 71 pct Fe-29 pct Ni alloys in the vicinity of the M, temperature. Since the moduli did not approach zero or become negative on cooling to M,, it was concluded that the austenite lattice does not become mechanically unstable at M2, as postulated by Scheil. McReynolds also reported that M, is not raised by elastic stresses. Accordingly, plastic deformation was considered to stimulate the transformation by generating martensite nuclei in the distorted regions of the parent phase. The above issues with regard to the role of applied stress require clarification, if a basic understanding of the martensitic transformation is to be obtained. For example, in the reaction-path theory,&apos;"," it is postulated that strain embryos exist in the austenite that provide part of the activation energy for the nucleation process. These embryos are visualized to be regions of localized strain in which the atoms in the austenite lattice are displaced part way along the path to their ultimate positions in the martensite. Consequently, it would

Jan 1, 1953

By W. H. Chang

The phase identification results on several Mg-base alloys are presented. These results have been correlated with strength data and microstructural studies to indicate that carbide dispersion may contribute significantly to raising the recrystallization temperature and strength of Mo alloys. Evidence is presented to show that the degree of carbide dispersion, and hence the extent of strengthening, is governed by the "metal/carbon" ratio which, in turn, depends on both the carbon content and the presence of stable -carbide-forming alloying elements. IN recent years, Mo-base alloys containing small additions of C, Ti, and/or Zr have been developed, which exhibit much higher recrystallization temperature and strength than those of unalloyed Mo. The superiority of these alloys undoubtedly results from simultaneous operation of more than one strengthening mechanism. In the present paper, the strengthening effect of carbide dispersion will be discussed. Although the role of carbide dispersion is being increasingly recognized, the nature of the carbides has, to the author&apos;s knowledge, not been well es- tablished. In Table I are presented some of the phase identification results on representative Mo alloys. These results have been obtained by X-ray diffraction of residues electrolytically extracted from an ethyl alcohol solution containing 7 pct HC1.

Jan 1, 1961

By W. Rostoker, D. W. Levinson, A. Yamamoto

The influence of carbon on tensile strength, tensile ductility, transformation kinetics, and grain growth characteristics of selected Ti-Mo base alloys was studied. No systematic influence of carbon in tensile strength or significant deleterious effect on tensile ductility was observed. There was a marked increase in transformation rate due to carbon. Dispersed carbides exert a marked inhibiting effect on grain boundary migration, and thus effectively prevent grain coarsening during solution treatment in the ß phase field. AS part of a research program directed toward the illumination of factors governing modes of transformation, transformation kinetics, and mechanical properties obtainable through these transformations by heat treatment, Ti-Mo base alloys were selected for study. The binary system is a characteristic phase diagram type which has been studied in some detail&apos;, &apos; in relation to transformation kinetics and mechanical properties. Although carbon bearing alloys have acquired a bad reputation, the possibilities of melting titanium under conditions which occasion some carbon pickup are very attractive. It is therefore of considerable importance to know whether carbon, present as a dispersed carbide phase, is actually deleterious when all other detrimental factors are minimized. Basic alloy compositions containing nominally 3, 5, 7, and 11 pet Mo were prepared with systematic carbon addition up to 1 pet by weight. Various of these alloys were subjected to a series of critical and definitive experiments to delineate the effect of carbon on the transformation behavior and associated mechanical properties. Experimental Procedure Alloys were prepared from 115 Bhn magnesium-reduced sponge titanium. This sponge analyzed ap- proximately 0.05 pet C. Ti-Mo and Ti-C master alloys were made by arc-melting the sponge with high purity (99.9 + pet) molybdenum and spectro-scopic grade graphite, respectively. Alloys were then prepared from the master alloys and sponge by double are-melting. One kg ingots were prepared by melting in a nonconsumable electrode furnace. These ingots were forged at 1000°C to &apos;/z in. rods, and cleaned and processed into electrodes for the second melting operation. The final ingots were ground to remove surface defects, then forged again to 1/2 in. or 3/8 in. diam rods for processing to test samples. It is significant that all of the alloys at all carbon levels forged satisfactorily. For convenience, the alloys will be referred to throughout the text by their nominal analyses. Samples for the study of transformation rates were prepared from 1/2 in. diam round stock. They were then solution treated in a helium filled tube furnace at 1000°C for 30 min prior to the isothermal transformation treatments in lead bath furnaces. Temperature control in both cases was within ±3oC. Following the isothermal transformation treatments the samples were water quenched. These experiments were carried out before the general adoption of the resistometric procedure for kinetic studies. The data were therefore obtained entirely by metal-lographic analysis. M, temperature was also determined by the metallographic method. Shoulder-type tensile test pieces were machined from heat treated, 1/2 in. diam slugs to provide a 0.252 in. test diam and a 1 in. gage length. The isothermal-type heat treatments were chosen from previous data&apos; to provide three levels of strength and ductility.

Jan 1, 1957

By H. Conrad

The strain hardening associated with the creep of magnesium single crystals at room temperatu.Je was investigated by shear tests in which the direction of stressing was reversed a number of times after creep in a <100> direction. The strain hardening was strongly anisotropic; the largest amount occurring in the direction of flow and the least 180 deg to this. The time law for creep changed from a parabolic type to logarithmic for the first and subsequent reversals of stress. For a given stress the creep strain decreased significantly for the first and second reversals and then only slightly for subsequent reversals. The logarithmic creep constant a changed in a similar manner. A linear relationship was observed between the creep strain for a given reversal and the stress. The slope for the third reversal yielded a strain hardening coefficient 12 to 16 times greater than that observed for unidirectional flow. Al-though no recovery was observed upon resting at room temperature, the hardening resulting from stress reversals could be completely removed by heating to 450" C. PREVIOUS work1.&apos; indicated that the creep rate of magnesium single crystals tested in the temperature range of 78" to 364°K decreased with time. This was attributed to an increase in internal stress resulting from an accumulation of dislocations at internal obstacles. The object of the present investigation was to further evaluate the nature of this hardening by conducting tests in which the direction of stressing is changed after previous creep in shear in a given slip direction. Previous to 1950 three investigations indicated that a Bauschinger effect3 occurred for single crystals as well as polycrystals brass in tension compression,

Jan 1, 1960