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By E. R. Buchanan, R. E. Reed-Hill

Cylindrical magnesium single crystals were deformed in torsion. The axis of torsion was the basal pole. Five crystals were deformed to different strains between 0.08 and 1.03 and then sectioned in order to determine their dislocation densities using the transmission electron microscope. The work hardening rate of all specimens was at least an order of magnitude higher than that normally associated with easy glide in a tension test and comparable to that obserzed in stage B of a tension test. The correspondence between stage B in a tension test and the initial stages of a torsion test is believed to result from the fact that in both cases deformation occurs in a structure containing roughly equivalent densities of the dislocations associated with the three basal slip vectors. THERE are three basic ways of changing the shape of a crystal using slip dislocations. The crystal can be sheared along a slip direction in a slip plane; it can be bent about an axis in the slip plane normal to the slip direction; and, if the slip plane contains multiple slip directions, it can be twisted or rotated about the slip plane normal. Of the three processes, generally known as translational, flexural, and rotational slip, only rotational slip has not been extensively investigated. The object of the present research was to obtain basic information about this phase of crystalline plasticity. This paper is concerned with some aspects of the stress-strain curves obtained by twisting magnesium crystals about their basal poles. Magnesium was selected for four reasons. One, its recovery rate at room temperature is relatively low. Two, single crystals may be easily grown. Three, at room temperature the critical resolved shear stress for basal slip is about two orders of magnitude lower than that for nonbasal slip, so that rotational slip might be expected to occur primarily by basal slip. Finally, relationships between flow stress, shear strain, and dislocation density have been determined for tensile deformation of magnesium crystals,' thereby providing a basis of comparison for the torsional results. EXPERIMENTAL PROCEDURES Crystals were grown from 0.5 in. diam extruded sublimed magnesium rod furnished by the Dow Chemical Co. who reported that it contained in weight percent less than 0.0003 Al, 0.01 Ca, 0.01 Cu, 0.0012 Fe, 0.001 Mn, 0.0005 Ni, 0.003 Pb, 0.001 Si, 0.01 Sn, and 0.02 Zn, with the balance magnesium. All crystals were grown in a dried argon atmosphere using Jill-son's2 modified Bridgman technique. Two different methods were used to obtain crystals with the basal plane normal to the specimen axis. These included direct growth from seeds of the proper orientation, and spark machining (trepanning) of 0.5 in. diam cylinders from larger (1.5 in. diam) randomly grown crystals. The crystals thus produced were polished in a 20 pct HC1 water solution and then etched in a 1 pct HC1 water solution to develop etch pits lying in rows parallel to the basal plane trace. The crystals were then revolved about their axes on the stage of a low-powered microscope. Torsion specimens were prepared only from those crystals whose axes were normal to the rows of etch pits. It is estimated that this simple orientation method was accurate to about 51 deg. 1.625 in. long cylinders were next cut from these selected crystals and then acid machined in a 20 pct HC1 water solution into torsion specimens with a 1 in. long by 0.30 in. diam reduced gage section. Following this, they were annealed in air at 400°C and furnace cooled to room temperature. The specimens were given a final polish in a 10 pct HC1 water solution, rinsed in ethanol, dried, and cemented into brass grips with an epoxy resin. In addition to the torsion specimens, several tensile specimens with their basal planes at 45 deg to the stress axis were also prepared with similar dimensions except that the gage sections were increased to 4 in. in length. The torsion specimens were tested in the apparatus

Jan 1, 1970

By J. Stringer, I. W. Edington, C. R. Rarey

THE geometrical interpretation of transmission electron micrographs of hcp metals is more complicated than the equivalent interpretation of cubic metal for two reasons: firstly, prominent zone axes are not in general normal to prominent planes, so that a simple diffraction pattern often corresponds to a nonra-tional foil plane; and secondly, the Miller-Bravais sys-tem of indexing directions is not easy to visualize. In this, the indexing is referred to the Bravais four-axis system, and the direction is labeled [hkil], chosen so that and I are shown in Fig. 1. Some geometrical relationships useful for the interpretation of transmission micrographs have been calculated and are tabulated below: 6) Direction of the intersection of two planes; this is easily calculated by applying Condition 4 to both planes: a direction that lies in both planes is clearly their direction of intersection. Some of the above expressions have also recently been given by Otte and Crocker;' Expression 5 is of course in most standard crystallographic texts. It is generally considered easier and quicker to use graphical methods for the interpretation of electron micrographs than analytical methods. For this purpose, it is most convenient to use a "double stereo-gram" in which both the poles alzd the rational directions are plotted. It is, of course, necessary to orient

Jan 1, 1967

By N. J. Olson, G. W. Toop

A series of equations previously derived for calculating ternary thermodynamic properties using binary data has been applied to the problem of predicting ternary phase diagrams and quaternary excess free energy. The methods are considered to be rigorous for regular ternary and quaternary systerns and empirical for nonregular systems. The equations have been used to predict ternary phase boundaries in the Pb-Sn-Zn system at 926°K and the Ag-Pd-Cu system at 1000ºK. Calculated quaternary excess free-energy values are presented for the Pb-Sn-Cd-Bi system at 773°K. A method for predicting the location of ternary phase boundaries would be a useful supplement to experimental measurements in ternary systems. This has been recognized with the considerable work that has been done to find models to predict or extend thermodynamic properties and phase diagrams in binary and ternary systems1-18 for which direct experimental measurements are limited. With the access to highspeed digital computers and mechanical plotting devices, it is currently rather easy to compare mathematical models with experimental data. The regular-solution model is consistent with systems which exhibit negative heats of mixing, positive heats of mixing, and miscibility gaps, and therefore it is applicable to simple phase diagrams. The purpose of this paper is to illustrate the use of regular-solution equations to predict, empirically, phase equilibria in some types of nonregular ternary systems. Corresponding equations for regular quaternary systems are given and used to calculate empirical quaternary excess free-energy data. METHOD FOR PREDICTING THE LOCATION OF TERNARY PHASE BOUNDARIES USING BINARY DATA Meijerin1,6 has used the regular-solution model to calculate common tangent points to ternary free energy of mixing surfaces and hence to determine phase boundaries in ternary systems involving miscibility gaps. He used the following equation to calculate ternary excess free energy of mixing values: stants characteristic of the binary solutions, and Ni is the mole fraction of component i. An alternate expression which gives for regular solutions as a function of binary values of along composition paths with constant N1/N2, N2lN3, and N1/N3 may also be derived:15 ternary r xs 1 ?c-*n.Ti*.U*. This expression for is more useful for the empirical calculation of ternary excess free-energy values for nonregular systems because actual binary AFXS data may be used in the expression rather than attempting to find suitable constants for Eq. [I]. The results of this feature of Eq. [2] are illustrated in Table I where calculated excess free-energy values for the Ni-Mn-Fe system at 1232°K are compared with experimental data of Smith, Paxton, and McCabe.19 Although regular-solution equations have been shown to give calculated thermodynamic quantities which agree quite well with experiment for single-phase nonregular ternary systems,14,15 care should be exercised in the use of the equations to predict thermo-dynamic properties of multiphase ternary systems in which strong compound formation is suspected. This precaution is consistent with the simple regular-solution model which for negative values of ai_j will indicate a tendency toward compound formation but even for very large negative values of ai-jwill not give multiphase binary or ternary systems involving a distinct stable compound. Hence, calculated ternary free-energy data using Eq. [2] might be expected to vary between being rigorous and poor, in the following order, for ternary systems which are: a) regular solutions, b) nonregular single-phase liquids in which random mixing is nearly realized, c) nonregular single-phase solids, d) nonregular multiphase systems exhibiting miscibility gaps, e) nonregular multiphase systems with binary compounds but no ternary compounds, f) nonregular multiphase systems with highly stable binary and ternary compounds. The calculated data will be expected to be least accurate for the last two cases. The general method adopted in this paper involves two-dimensional plots of ternary activity curves. The principle used is that tie lines indicating two-phase equilibria join conjugate phases a and B for example, for which a1(a) = a1(B), a2(a) = a2(B), and a3(a) = a3(B). Tie lines may be determined by plotting the ternary activities of two components along an isoactivity line for the third component and the unique points where the above equalities hold may be found graphically.

Jan 1, 1970

By V. Leroy, A. G. Guy

Serious disagreements are often found between experimentally determined intrinsic diffusion coefficients and those calculated employing the usual form of the vacancy theory. In the new theory it is proposed that the total intrinsic flux, Ji, of component i, is the sum of a part, f, due to the usual random exclzanges of component i with the vacancies, and a second part, Ji, due to exchanges with the uacancies composing the net vacancy flux. The present treatment, while less powerful than that of Manning, has the advantage of easy uisualization and of facilitating the application of the vacancy-flux effect to complex systems. IT is becoming increasingly evident that there are serious deficiencies in the version of the vacancy theory of diffusion that has been widely used for the past 20 years. One type of evidence is the frequent lack of agreement between intrinsic diffusion coefficients and tracer diffusion coefficients, even taking account of the thermodynamic factor. A second kind of evidence is the observation of a Kirkendall shift larger than theoretically possible, that is, larger than can be accounted for without assigning a negative value to one of the two intrinsic diffusion coefficient.'- The thermodynamic factor could conceivably make both coefficients negative, but not just one. It is clear that a cause of these anomalies, apart from any inadequacy of the usual vacancy theory, might lie in an oversimplified treatment of the data. Adequate experimental techniques, including the use of moderate pressure during the diffusion anneal, are now available to insure that porosity, lateral expansion, and so forth, can be kept negligibly small in most cases. The effect of differences in atomic volume can be of major importance, and it is essential that one of the available methods4 be used to account for this factor. In the present treatment this is accomplished by the consistent use of moles per cubic centimeter as the unit of concentration. Of the various possible inadequacies of the vacancy theory, attention will be given here only to effects of the net vacancy flux. annin' has previously considered this question, beginning with an analysis of atomic jumping of tracer atoms. When he added the effect of a concentration gradient, new terms arose that could be associated with the flow of vacancies. The present treatment uses quite a different approach. The usual vacancy flux, J,, is introduced explicitly, and a simple analysis predicts major changes in the intrinsic diffusion coefficients from this cause. The usual assumptions are made that only a vacancy mechanism is operative, that the formation of voids can be neglected, and that changes in the partial molal volumes, vl and v2, are negligible. The significant diffusion coefficients for the present topic are Dl and D,, the intrinsic coefficients, which enter in the equations, where the flux Ji, moles per sq cm per sec, is that crossing the Kirkendall interface. The concentration, ci, is in units of moles per cu cm, and the concentration gradient, aci/ax, is evaluated at the Kirkendall interface. It will be recalled' that the calculation of Dl and D2 involves the measurement of areas on the diffusion curve with respect to the positions of the Kirkendall and Matano interfaces. In the case of the anomalies mentioned earlier, the Kirkendall shift is too large to be accounted for by the diiferetzce in fluxes (J2 -J1), given by Eqs. [I] and [2]. The logical inference is that the flux of the solvent atoms, J1, is actually in the same direction as the flux of the solute atoms, Jz. In terms of Eq. [I] this requires that Dl have a negative value. However, it would be somewhat misleading to state that the solvent atoms are diffusing up their own concentration gradient. The explanation that will be advanced here pictures competing processes producing the net flux of solvent atoms: 1) diffusion of the solvent atoms down their own gradient by random exchanges with vacancies; and 2) diffusion of solvent atoms in the opposite direction by exchanges with the net vacancy flux. ACTION OF THE NET VACANCY FLUX Theories of vacancy diffusion can be formulated with varying degrees of refinement, and the present theory has purposely been kept as simple as appeared adequate to explain the phenomenon in question. In particular the following aspects have been neglected: 1) the gradient of vacancy concentration in comparison to the gradient of the atomic species; 2) departure of vacancy concentration from the local equilibrium value; 3) variation of the jump frequency, LO, with the specific surroundings of the atom-vacancy pair being considered; 4) correlation effects. These and other refinements can be considered once the essential mechanism has been established. The essential idea of the present analysis is to calculate the total intrinsic flux, Ji, of component i as the sum, JlJ?±j{ [3] where J; is attributable to the usual random atomic jumping, and J{ is a contribution arising from the net vacancy flux, J,. The latter quantity, of course,

Jan 1, 1967

By Y. C. Liu, G. A. Alers, S. S. Choi

In searching for an explanation for the obvious difference between the copper and the brass type of rolling texture, it is common practice to look for correlations with other properties. For example, there are obvious differences between copper and brass in the critical resolved shear stress, the extent of easy glide or stage I, and the amount of "overshooting)) during single-crystal deformation.' Also, the slip lines in copper are fine and wavy while those in brass are more coarse and better described as slip bands.' Since neutron irradiation is known to make these properties in copper change in such a way as to resemble brass,2'3 an excellent test for these possible correlations is to see whether neutron irradiation produces a corresponding change in the texture, i.e., whether irradiated copper develops a brass-type rolling texture. The experiment would also answer the more important question of whether or not lattice defects like those introduced by neutron irradiation have any effect on the development of rolling textures in fcc metals. Experimental studies using conventional X-ray pole figure techniques are inconvenient because the X-ray detection system must be modified to discriminate against the radioactivity which is induced in the specimen by the necessarily long exposure to neutrons. Nevertheless, some texture determinations have been

Jan 1, 1968

By J. D. Hunt, D. T. J. Hurle

A uariety of eutectic structures are formed in faceted/nonfaceted eutectics. The various structures are explained in terms of the absence or presence of small facets in the liquid groove. Regular structures are produced when, for purely geometric reasons facels cannot form. The presence of a facet in the liquid groove leads to the formation of an irregular or a cell-like complex regular structure, due to the relative immobility of the groove. A classification of eutectics was proposed by Hunt and jackson, based on the presence or absence of facets on the primary phases (the absence of facets may be predicted from the dimensionless entropy of melting2). Eutectics were divided into three groups: 1) eutectics in which both phases grow in a nonfaceted manner; 2) eutectics in which one phase grows faceted, the other nonfaceted; 3) eutectics in which both phases grow faceted. It was suggested that regular1 rodlike or lamellar structures1 should be formed in the first group, that irregular or complex regular structures1 should be formed in the' second, and that irregular structures1 should be formed in the third. Recently it has been shown that the structural classification is incomplete. Regular rodlike structures (InSb-NiSb eutectic3), or broken lamellar structure (Bi-Zn eutectic, Fig. 8), are formed in alloys of the second group when the faceted phase has a large volume fraction. Hunt and jackson' argued that regular structures could form in faceted/nonfaceted systems, but that such structures would be unstable in the presence of microfacets on the lamella of the faceting phase, because the growth rate at a point on such a facet would depend on the kinetic undercooling at the point of nu-cleation on the facet, and not on the local kinetic undercooling. In these circumstances it would not be possible to consistently balance the compositional and kinetic undercooling over a lamellar structure and thus obtain a stable isothermal interface. In this paper we discuss in detail the origin of the various structures formed in faceted/nonfaceted systems, pointing out that the most important factor promoting the formation of a regular structure is the absence of a facet in the liquid groove. 1) FACET FORMATION IN SINGLE-PHASE MATERIALS Facets form when there is an energy barrier for the addition of a new solid layer on an existing solid. When a barrier is present,2 growth proceeds by the lateral movement of steps across a crystallographic plane. The rate-controlling stage of the process occurs when the step is first formed. Hulme and Mullin6 have shown that faceting in single-phase materials can only occur when both interface curvatures are convex with respect to the solid and when the surface is tangential to the facet plane. When even one of the curvatures is concave a facet does not form because new layers of solid from adjacent regions can always feed the facet plane, Fig. 1. Growth under these conditions is then as easy as elsewhere. Similar considerations will apply to eutectic growth; consequently the shape of the faceted phase is extremely important. 2) LAMELLAR SPACING CHANGES IN EUTECTICS Jackson and Hunt7 have shown that the interface undercooling AT of a growing lamellar interface (neglecting kinetic undercooling) is related to the lamellar spacing, A, and growth velocity, v, by an expression of the form: where m, Ql, and nL are constants of the system given in Ref. 7. Eq. [I] is plotted for fixed v in Fig. 2. Jackson and Hunt postulate that a regular eutectic grows near, but to the right of the minimum in the AT vs A curve. They argue that the spacing cannot be to the left of the minimum because the interface is then unstable to fluctuations in A. It cannot grow too far to the right, because when the spacing becomes too wide an isothermal interface can no longer be maintained over the large-volume-fraction phase.7 It is argued that during any change in growth rate the lamellar spacing remains in the permitted range by the movement of lamellar faults. When the spacing is too wide, the fault, shown in Fig. 3, moves to the left; when the spacing is too narrow it moves to the right. The faults, however, have to be formed. heir formation has been shown to occur when local regions deviate considerably from the spacing defined by the lamellar When the spacing is locally too narrow (it passes to the left of the minimum, Fig. 2), pinching off of the narrow phase occurs. When the spacing is locally too wide, the interface on the large volume-fraction phase can no longer be maintained as an iso-

Jan 1, 1969

By C. D. Williams, C. E. Ells

The susceptibility of quenched and aged Zr-2.5 wt pct Nb alloy to embritt2ement during irradiation has been examined for a number of solution temperatures and aging times. Material quenched from temperatures approximately 40°C below the transus has high tensile ductility, and this ductility is insensitive to aging at 500°C or to irradiation. If, however, the material is quenched from temperatures above the transus it becomes highly susceptible to loss of ductility either from aging at 500 or from irradiation. Inter granular failure is characteristic of the materials having low ductility. The distribution of the equilibrium phase is found to control the susceptibility to embrittlement by restricting 6 grain growth during heat treatment and thus influencing crack propagation. IN zirconium, as in titanium, -stabilizing alloy additions are used to obtain high strengths via quench and age heat treatments, and the Zr-2.5 pct Nb alloy has been developed1 because of its strength advantage over the Zircaloys. Early in the development of the Zr-2.5 pct Nb alloy the problem of 13 embrittlement was appreciated, and for this reason the solution temperature was chosen below the p transus.' In the course of irradiation studies on quenched and aged Zr-2.5 wt pct Nb alloy it was found' that irradiation introduced an important aspect of p embrittlement, riz., material quenched from the phase and aged 24 hr at 500°C was severely embrittled by moderate doses of neutron irradiation. This effect had not been studied in titanium alloys. In titanium the metallurgical features leading to 0 ernbrittlement were found to be structures with: a) coarse a platelets at the grain bondaries, b) finely dispersed a uniformly distributed throughout the (0) matrix,6 c) Widmanstatten a-13 with more than 50 pct P, d) the presence of some metastable p transformation products,3 and e) large prior -phase grain size.5 Alternatively, the presence of a uniform distribution of coarse a was conducive to high ductility and a structure largely of equiaxed a was very dctile. The detailed mechanisms of the embrittlement have not been worked out for all of these conditions, although weakness at either a-matrix boundaries or prior p grain boundaries have been prominent in the eculation. It was proposed that acicular a might act as a mild notch, and low ductility has been associated with easy fracture along its boundary.' There have been two opposing suggestions for the source of the high ductility associated with equiaxed a phase. JaffeeB proposed that this a would accept a large por- tion of the oxygen, thus increasing the ductility of the matrix, whereas after study of a Zr-Nb-Cu alloy Weinstein and oltz proposed that the a phase, softer than the martensitic matrix, acted to blunt cracks formed in the matrix. In the present work we have studied the effect of neutron irradiation on the ductility, particularly the P embrittlement, of the Zr-2.5 wt pct Nb alloy. By a variation of solution temperature and aging time a variety of metallurgical conditions have been examined, and a range of resultant ductilities obtained. The ductility has been related to the material microstructure and mode of fracture. EXPERIMENTAL The alloy used in the present work came from two separate ingots fabricated into rod of 3/8 or i in. diam, Table I. For both batches the P transus temperature was approximately 890° C. Most of the heat treatments were done directly on lengths of the j} in. diam rod, after which the tensile test specimens were machined. Quenching was achieved by dropping rods from a dynamic vacuum into water, the cooling rate estimated to be 2 100°C per sec. For aging the rods were encapsulated in evacuated silica tubes. Round tensile test specimens, with gage diam and length 0.160 and 1.0 in., respectively, were used throughout and pulled at room temperature or 300°C on Instron tensile machines, at a crosshead speed of 0.05 ipm. Specimens were irradiated in the NRX and NRU reactors, in facilities described in previous publications.'0 The metallurgical conditions examined have been: All tensile test specimens were machined with axes in the axial direction of the swaged rod. Although the specimen had a degree of preferred crystallo-graphic orientation with basal plane normals both parallel with and perpendicular to the tensile axis, the material was comparatively isotropic." The techniques of thin foil examination in the electron micro-

Jan 1, 1970

By W. L. Phillips

Stress-train curves were obtained for single crystals of silver, Ag-5 pct Zn, Ag-10 pct Zn, and Ag-20 pct Zn tested in tension and shear at 78°, 195°, and 297°K. At room temperature the critical resolced shear stress gC increased, the length of' the easy-glide region increased, and the rate of' work hardening dwving easy glide decreased with increasixg zinc concentration. The change in the ratio of uc at room temperature to that at lower temperatures was significantly greater for the alloys than for pure silver. It was found that an increment in stress was necessary to continue slip when the slip direction was rotated 60 deg. The magnitude of this increment increased with strain for all alloys, increased with zinc concentration for a given strain, and for a given strain increased with decreasing -temperature. DESPITE its practical importance in improving the mechanical properties, alloying is not fully understood. Except for copper alloys few sets of systematic data are available. Von Goler and Sachs' studied the deformation of Cu-Zn alloys of increasing zinc content and found that, for dilute alloys, the critical resolved shear stress increases linearly with concentration. The range of easy glide was found to increase with increasing zinc content. Schmid and seliger,2 Sachs and Weerts,3 and Osswald4 have shown that with Mg-A1, Au-Ag, and Cu-Ni crystals, respectively, the critical resolved shear stress also varies linearly with concentration. More recently, Linde and his coworkers have investigated the variation of the critical shear stress of copper alloyed with tin , antimony, indium, germanium, silicon, nickel, and gold. They found that the slope of the critical resolved shear stress is related to the change of lattice parameter with composition, and also to the difference in Goldschmidt's atomic diameter between solvent and solute atoms. Garstone, Honey-combe, and creetham6 have shown that similar relationships can be found for small additions of silver, gold, and germanium to pure copper. They found that, with increasing silver or gold concentration, the critical shear stress for glide is increased by alloying, and so is the range of easy glide, which reaches as much as 60 pct for 0.50 pct Ag alloy and 0.62 pct Au alloy, as compared to 6 pct for pure copper of similar initial orientation. They also found that the alloying additions had little effect on the rate of hardening during easy glide, the slope scarcely changing with increasing alloy content. General secondary slip was detected only when the crystals began to harden rapidly. Although the slip appeared to be very fine in the early stages of deformation, coarser slip bands were formed towards the end of the extensive easy-glide range. The present investigation describes the deformation characteristics of single crystals of Ag-Zn containing different concentrations of zinc. Tension and shear testing were used for this study. EXPERIMENTAL PROCEDURE The method of growing the single crystals, sample preparation, and method of testing have been described in detail previously.' EXPERIMENTAL RESULTS A) Tension-Room Temperature. The initial orientations and stress-strain curves of single crystals of silver, Ag-10.0 pct Zn, and Ag-20.0 pct Zn are shown in Fig. 1. It is evident that there is considerable change in the stress-strain characteristics as a function of zinc concentration. The effects of zinc concentration on the critical resolved shear stress for both CU-zn8 and Ag-Zn alloys are summarized in Fig. 2. At all concentrations the resolved shear stress of the Cu-Zn alloys is higher than that of the Ag-Zn alloys. The resolved shear stress increases parabolically as a function of composition for both alloy systems. The length of easy-glide region increased with increasing zinc concentration, Fig. 3b). As the length increased the slope (do/de) decreased slightly, Fig. 3(b). Metallographic investigations demonstrated two significant effects of increasing zinc concentration. First, the amount of clustering increased, compare Figs. 4(a) and (b). The slip lines changed from uniform in pure silver to clustered in the Ag-20 pct Zn and Ag-30 pct Zn alloys. Second, the amount of cross slip decreased as the amount of clustering decreased.

Jan 1, 1968

By B. H. Kear, S. M. Copley

Stress-stvain curves are presented for Ni3Al (y') cvystals in several ovientations, deformed in tension and compression at constant displacement rate, at temperatures from 70° to 2000°F. Both the yield stress and wovk havdening increase with temperature, with the magnilude of the effect dependent on ovientation. The yield stress maximum occurs at 1500°F in [001], at 1400°F in [011], and at 1200°F in [111]. The suppression of the yield stress peak in [011] and [111] orientatiorzs is due to the onset of cube slip, rather than octahedval slip, a1 elerated temperatures. The temperature and orientalion dependence of work hardening in nominal single slip orientations corvelates with changes in the CRSS ratio for octahedral slip and cube slip, in agreement with a model for work hardening based on pinning of screw dislocalions by cross slip from an octahedral plane into a cube plane. It is concluded that the unique plastic properties of y' have a decisive influence on both ductility and strength characleristics of y +y' nickel-base superalloys. It has long been recognized that the strength of y + y' nickel-base superalloys depends on the precipitation of the y' phase [basically Ni3(Al,Ti)]. This paper presents new data on the strength characteristics of single crystals of simple y' (Ni3Al), and forms the first step in a systematic program aimed at elucidating the mechanisms of hardening in the complex commercial alloys. 1) EXPERIMENTAL PROCEDURE Single crystals of off-stoichiometric NiA1 were grown from the melt under vacuum by a modified Bridgman method. The melt was poured into a preheated alumina mold and crystal growth was promoted from one end by gradient cooling. The crystals were homogenized by annealing in hydrogen at 2400° F for 72 hr followed by furnace cooling. Chemical analysis of samples taken from several crystals gave an average composition of 88.2 wt pct Ni. Spectrographic analysis gave as the principal impurities in weight percent— Si (0.02), Mg (0.01), Fe (0.02), Ti (0.002), Cu (0.008), and Co (0.03). Tensile specimens with specifications as in Fig. 1 were prepared by a series of operations involving electrical discharge machining, precision grinding, and electropolishing. Compression specimens with dimensions 1/4 by 1/4 by -3/4 in. were prepared in a similar manner, except for the initial shaping operation using a precision cut-off wheel/two-circle goniometer unit to give selected crystal orientations. Specimens were deformed in a Baldwin-Wiedemann testing machine with furnace attachment, using a strain rate of 5 x 10-4 sec-1. The strain measuring device consisted of extension arms attached to the tensile grips (or compression plattens) at one end and leading out of the furnace to an LVDT at the other. Temperature was controlled by a thermocouple placed in contact with the specimen. According to the known phase diagram for the Ni/A1 system,' when an alloy of the specified composition is cooled from the melt, primary y (nickel solid solution) dendrites grow at the expense of the liquid phase, which becomes enriched in aluminum. At the eutectic composition the remaining liquid freezes as a two-phase mixture of y + y' (Ni3Al). Upon further cooling, a solid state transformation occurs, involving the precipitation of y' in the primary dendrites, and the complete transformation of the eutectic mixture to massive y'. The as-cast structure consists, therefore, of y + y' dendrites with interdendritic regions of massive y', i.e., transformed eutectic, Fig. 2. 2) DISCUSSION OF RESULTS 2.1) Stress-Strain Curves. Fig. 3 shows tensile stress-strain curves for crystals in orientations close to [001] deformed at temperatures from 70° to 2000°F. Both the yield stress and total elongation are strongly temperature-dependent. At 70°F, easy glide is absent, and the work hardening coefficient BIT - G/300. At T > 1500°F, the negative slope of the stress-strain curves is due to pronounced necking in the crystals. The yield stress maximum at 1500° F corresponds with a minimum in the ductility, Fig. 4. The extensive duc-

Jan 1, 1968

By V. B. Kurfman

The temperature, strain rate, and orientation deDendence of defbrnzation of single-crystal MgAg has been examined. The crystals exhibit a tendency to single glide and little or no hardening at 25°C for many orientations. A much higher hardening rate is observed when multiple glide occurs, such as can be initiated by surface defects. The tendency for easy glide becomes less dependent on surface preparation and orientation as T — 100°C and bars so tested often fail after one-dimensional necking-. At T > 200°C (transition temperature for single-crystal notch sensitivity and poly crystalline ductility) single glide diminishes and two-dirnensionul necking begins. The crystals do not strictly obey a critical resolved shear stress law, but show the influence of {loo) cracks in determining the slip mode. The results are correlated with the difficulty of sciperdzslocation intersection and semibrittle behavior of this compound in single-crystal and poly crystalline form. Comparisons are made with the slip selection mode observed in tungsten, with the reported observations of easy glide in bee metals. and with the mechanical behavior of poly crystalline MgAg. PREVIOUS work on tensile deformation of polycrys-talline MgAgl and bending deformation of single-crystal MgAg2 has shown that the compound is semi-brittle (i.e., notch and grain boundary brittle). If this semibrittleness is supposed to result from the difficulty of multiple glide (associated with the problems of superdislocation intersection) one might expect single crystals deformed in tension to show pronounced single glide and strong orientation dependence of hardening rate. These experiments were done to examine this supposition and to study the tensile deformation of a highly ordered system which may be considered bcc if the difference between the two kinds of atoms is ignored (actual structure: CsC1). EXPERIMENTAL Single-crystal ingots were grown by directional freezing as previously described.' These ingots were sliced into a by a by 2 in, rectangular bars by electric discharge machining, then round tensile bars were conventionally machined to 1/8-in.-diam by 1-in.-long reduced section. The bars were typically tested without an anneal because of the problem of magnesium vapor loss and they were typically tested as mechanically polished. The analyses are within the same limits as those reported earlier; i.e., the average composition for each specimen is within 0.5 at. pct of stoichiometry, while the total range from end to end in a given specimen varies from 0.7 to 1.4 at, pct. There has been no indication in the results of any variation in slip or fracture mode attributable to the composition fluctuations. The slip systems were determined by two-surface analysis of the bars after testing to failure at room temperature. Single glide was so dominant that there was little difficulty in identification of the dominant slip system even though the tensile elongation to failure often approached 7 to 8 pct in room-tempera- ture tests. Elevated-temperature testing was done in a silicone oil bath and low-temperature testing was done in liquid Np or a dry-ice bath. All stress measurements are reported as engineering stress unless otherwise specified, and crosshead travel is used as the strain measurement. RESULTS The tendency toward single glide is best seen in the pictures, Figs. 1, 2, and 3, which depict deformation at fracture as a function of test temperature. While it is possible to find regions of secondary slip by careful microscopy, such regions are very small. The development of a ribbon-shaped configuration from an initially round section bar pulled at 100°C is typical, occurred by single glide, and illustrates the degree to which such glide continues. At temperatures =100°C the bars typically show elongation of 20 to 50 pct by predominently single glide. Despite the large elongation, fracture even at 150°C occurs in a brittle mode, Fig. 2, in the sense that it is an abrupt failure which shows no discernible necking in the second dimension of the bar's cross section (i.e., there is no appreciable action of any slip modes which would decrease the broad dimension of the cross section). Near 200°C the fracture mode changes slightly. Although most of the sample extension is by single glide, after the bar develops the characteristic ribbon shape it begins to neck in the second (i.e., broad) cross-sectional dimension. The bar becomes very thin in the "necked down" region, Fig. 3, and the reduction in area approaches 100 pct. Often there oc-

Jan 1, 1967

By D. McLean

For many pu@oses uniform strength is desired over a long temperature range, coupled to a band of softness at the hot end for easy shaping. Various types of material fulfill such a requirement to different degrees, depending on the regularity of their atomic structure. In long-chain polymers and vitreous glasses the irregular structure leads to a steep temperature dependence of deformation resistance and the temperature band between the hard and brittle condition and the soft condition is only about 100 C. In crystals and especially metals the atomically regular structure leads to a much smaller sensitivity over a wide temperature band, thus approaching the ideal behavim. The reason for this insensitivity is that the regular crystalline structure deforms by the movement of dislocations and the elastic interactions of dislocations in- PLASTICS, GLASSES, AND CRYSTALS The ease or otherwise of deformation varies with temperature much more in some substances than in others. This is an important matter when service over a wide temperature range is needed, especially volve energies of several hundred electron volts compared with which the energy of thermal agitation is insignificant. However, temperature affects a metal's defmmation resistance through its influence on the annealing, m coarsening, of the three-dimensional dislocation network. This coarsening is a phenomenon very similar to grain growth and ideas about grain growth can be applied to it. Taking into account also the temperature dependence of the glide resistance from alloying additions, a reasonable account can be given of the overall effect of temperature on deformation strength and of stress and grain size on deformation rake. Special structures me described. some arising from these ideas and as yet untried, which may benefit metals and polymers but not ni-treous glasses. when in addition a degree of softness suitable for shaping is required at some stage. It would be nice if one could write on this subject in as much detail about plastics, glasses, and so forth, as about metals, but there has been far more study of this matter in metals than in other substances, which is one reason why most of this paper concerns metals. However, in Fig. 1 there are shown the deformation strengths of several nonmetallic substances as a function of temperature. In many tests the attempt at deformation caused breakage and the graph lines are then drawn dashed. Long-chain plastics, a glass, and a crystalline substance are included in Fig. 1. The notable feature of all of them is the sensitivity of the

Jan 1, 1969

By W. D. Forgeng, R. E. Grace

The rate of copper corrosion in liquid lead was studied as a function of flow rate and temperature in a closed isothermal loop system between 350" and 500°C. Kinetic data were interpreted with the Nernst-Brunner equation and the Chilton-Colbum mass transfer analogy to heat transfer. Over the range of temperatures and flow rates employed the solution rate constant varied from 2 x 10-3 to 20 x 10-3 cm per sec. The rate constant was found to vary with the 0.76 power of the Reynolds number in the range 7500 < Re < 40,000. The results of this investigation indicate that the Cu-Pb corrosion process is controlled largely by diffusion across a boundary layer. particularly at the higher temperatures. The effective boundary layer for diffusion is found to be approximately three to four times smaller than the momentum boundary layer. CORROSION by liquid metals has long been a problem during melting, static containment, and casting. Recently, considerable emphasis has been placed on the understanding of liquid metal corrosion mechanisms in an effort to prevent mass transfer and eventual failure in liquid metal heat exchangers and in liquid-metal-fueled nuclear reactors. The present investigation was conducted to determine the relationships which exist between corrosion kinetics and hydrodynamic conditions in an isothermal loop containing a simple liquid metal-solid metal corrosion system. The Cu-Pb system was chosen for its simplicity and ease in handling. Previous isothermal Cu-Pb corrosion studies1-3 have been conducted in both static and dynamic systems but not under conditions which allow easy "scale-up" to engineering systems, such as liquid metal heat exchangers. On the other hand, most liquid metal loops which have been used to evaluate mass transfer rates4 have been driven with temperature gradients under conditions of natural convection and unknown flow rates. The primary contributions of this research are twofold: 1) to evaluate the design of a simple isothermal loop corrosion system and 2) to investigate liquid metal corrosion behavior under well-defined hydrodynamic conditions. MATERIALS AND EXPERIMENTAL WORK The apparatus used to measure the Cu-Pb corrosion rates is shown schematically in Fig. 1. The loop system consisted of 1) a reservoir made of Type 316 stainless steel containing a centrifugal pump and 2) stainless-steel tubing containing a removable copper test section. The copper test section was OFHC hard-drawn tubing, 11.0 0.05 cm in length and 0.775 ±0.005 cm ID. A Type 316 stainless-steel venturi meter* was inserted in place of the copper test sec- tion in order to determine the lead velocity as a function of pump speed at each temperature. The Cu-Pb system was chosen for this study because the solubility of copper in liquid lead is large enough to measure accurately but small enough that the diameter of the copper tubing was not changed significantly by corrosion. There are no intermediate phases formed in the system, and the solid solubility of lead in copper is vanishingly small so that back-diffusion cannot occur. Molten lead (corroding grade; 99.94+ pct Pb, 0.0015 max pct Cu) was charged from an auxiliary melting furnace into the system under an argon cover to minimize oxidation. The lead was then maintained at constant temperature by a stirred molten salt bath in which the loop was immersed to a depth just above the lead level in the reservoir, Fig. 1. The total volume of lead in the system was 320 2 cu cm.

Jan 1, 1969

By H. I. Aaronson, C. Laird

The kinetics of thickening and of lengthening of ?&apos; plates in an Al-3.93 pct Cu alloy in the temperature range 203" to 300" C were determined by means of transmission electron microscopy. The rate of thickening was found to be less than that allowed by volume diffusion control at all temperatures, by amounts which increased with decreasing temperature, in agreement with the predictions of a general theory of precipitate morphology.1 Thickening was treated on the basis of the ledge mechanism. Ledges were deduced to spread across the broad faces of ?&apos; plates at volume dzjrfusion-controlled rates, as anticipated from the disordered structure of their edges. Lengthening of 8&apos; plates, on the other hand, took Place more rapidly than allowed by volume dzjrfusion. This occurred despite clear morPhological evidence of a bmrier to growth at the edges of these plates. It was concluded that the misfit dislocation structure comprising the barrier requires that lengthening take place by a jog mechanism. The tnisfit dislocations, however, also serve as diffusion short circuits, and allow high overall lengthening rates to be achieved. In Part I&apos; it was shown that, within the range of aging temperatures and times studied, the broad faces of 8&apos; plates formed in Al-4 pct Cu are fully coherent with the a, matrix. Virtually .all of the dislocations present in these faces were found to have developed as a result of plastic deformation in the a phase. Such dislocations are thus "intruders", rather than the more usual misfit-compensating variety. The edges of 8&apos; plates were confirmed, by extension of the earlier studies of Mat-suura and Koda,3 to be made up of edge-type misfit dislocations, in sessile orientation with respect to lengthening of the plates. These interfacial structures should cause 8&apos; plates to thicken and to lengthen at rates less than those allowed under the condition of volume diffusion control, such as would be expected if the interphase boundaries had disordered structures.&apos; The narrow width of 8&apos; plates, the reproducible crystallography of their broad faces, and the appearance of these plates in cross section as octagons rather than as circular discs2 provide qualitative support for these deductions. The present study of the rate of thickening and the rate of lengthening of 8&apos; plates was undertaken in order to examine them on a quantitative basis. I) THICKENING KINETICS OF THE BROAD FACES OF?&apos; PLATES A) Literature Review. The measurements now available on the thickening kinetics of single-phase precipitate plates consist of one plot of the thickening of a proeutectoid ferrite plate in an Fe-C alloy,&apos; showing (as predicted) thickening rates less than those allowed by volume diffusion control. B) Experimental Procedure. Details of the preparation of the 4-3.93 pct Cu alloy used in this study have been previously reported.4 As in Part 1,&apos; transmission electron microscopy was the observational tool employed. A general description of the apparatus and procedures of the electron microscopy studies is given in Section I of Part I. In thin foils, 0&apos; plates tend to form at and parallel to the foil surface.&apos; A direct investigation of the thickening process by means of hot-stage transmission electron microscopy was therefore not feasible. It was thus necessary to use the conventional method of aging individual bulk specimens for a wide range of different times at the various temperatures studied. In each specimen, the thicknesses of a number of plates were measured. Since thin foils prepared from "bulk-aged" material contain a large proportion of grains with orientations near (001) , it was relatively easy to find, near the edges of the foils, the characteristic multifold patterns of intersecting extinction contours which indicate regions where the foil is exactly at an (001) orientation. The thicknesses of large numbers of plates were measured along the (200) branches of the "stars" so that the 8&apos; plates were precisely parallel to the optical axis of the microscope. Wherever possible, intersecting extinction contours were adjusted with the parameter s > 0 to improve the visibility of the plates in bright-field illumination. These precautions, in combination with taking the measurements at the thinnest parts of the foils, minimized the errors in the measurement of the thickness of the plates resulting from inexact parallelism to the electron beam. Since the plates were very thin, it was not easy to measure their thickness on the photographs. The techniques of enlargement and of microdensitometry were employed to minimize errors from this part of the measurement. A further source of possible error, that the plates can appear thicker because of contrast associated with mismatch normal to the plane of the plate, was also considered. The images of the plates were usually thinner than those of dislocations, however, and no anomalous changes in apparent plate thickness were observed when regions of foil containing plates were tilted through various diffracting conditions. Any error from this cause must therefore be small. Other sources contributing errors were: a) the microdensitometer traces per se and the subjective estimates of their peak limits, and b) slight fluctuations in magnification associated with small changes in the current of the objective lens of the electron microscope. The overall error probably amounted to no more than 5 to 10 pct. In order to obtain readily interpretable data on thickening kinetics, it is essential that the diffusion fields of adjacent ?&apos; plates not be allowed to overlap. Calculations&apos;-&apos; showed that this condition is definitely not ful-

Jan 1, 1969

By K. P. Gupta, P. C. Panigrahy

The stabilization of the R, a-Mn, and 0-Mn phases have been studied in the Mn-Ti-Fe and Mn-Ti-Co systems. Iron and cobalt both appear to stabilize the (Mn-Ti) R phase to almost the sarne extent. The R-phase region was found to extend from the lowest e/a to slightly beyond the maximunz e/a limit known for this phase. But, while iron appears to stabilize the a-Mn phase, cobalt tends to stabilize the p-Mn phase. In the two systems manganese appears to get replaced by iron and cobalt in each of the mentioned phases. The instability of the a-Mn phase in the Mn-Ti-Co system and the /3 -Mn phase in the Mn-Ti-Fe system cannot be explained on the basis of adverse size effects because atomic diameters for both iron and cobalt (C.N. 12 at. diam) are ziery similnr and not much different from manganese which they replace. Qualitatively, the reason for the stability of the a-Mn and the p-Mn phases can be traced to the more favorable e/a ratio prevailing in the respective systems and to a competing tendency between the two phases. In transition metal alloy systems the o, p,P, R, a- Mn,&apos; and p-Mn2 phases have been claimed as electron compounds. A large volume of work has been done to establish the criterion for the formation of the o phase but until very recently practically no systematic work was done on the a-Mn and the /3-Mn phases. A recent investigation on the P-Mn phase3 indicates the e/a criterion for p-Mn phase stabilization. Since the R phase was first known to appear only in certain ternary systems1 no detailed work was then possible for this phase. The R phase has been recently discovered as a binary intermetallic compound in the Mn-Ti~ and Mn-si~-&apos; binary systems. The existence of binary R phases opens up the possibilities of studying the effect of alloying elements on the stabilization of the R phase. Of the two binary systems possessing an R phase, the Mn-Ti system appears to be more interesting because at a suitable high temperature it is possible to find the three electron compounds, the a-Mn, p-Mn, and R phases, side by side and it is possible to study the effect of a third transition element on these three electron compounds. For the present investigation iron and cobalt, so called B elements for the formation of electron compounds, have been used as the third element to study the stabilization of the a-Mn, P-Mn, and R phases. EXPERIMENTAL PROCEDURE The alloys were prepared by using 99.9 pct pure electrolytic Fe and Mn, 99.5 pct Co, and crystal bar titanium, supplied by Semi Elements Inc., New York and Gallard Schelsinger Mfg. Co., New York. Weighed amounts of the components were melted in recrystal-lized alumina crucibles in an inert atmosphere (argon) high-frequency induction melting unit. Titanium was made into fine chips for easy dissolution and a special charging procedure was adopted to avoid contacts of titanium chips with the alumina crucibles. Up to 20 at. pct Ti, the maximum titanium content in the investigated alloys, there was no visible sign of reaction of titanium with the alumina crucibles. With a careful control of melting time and temperature the losses were minimized and were always found to be below 0.1 pct. Because of such small and almost constant weight losses, the alloys were not finally analyzed. The alloys were wrapped in molybdenum foil and annealed in evacuated and sealed silica capsules at 1000" * 2°C for 72 hr and subsequently quenched in cold tap water. Annealed samples were examined metallographically and by X-ray diffraction. For all high manganese alloys oxalic acid solutions of various concentrations and 1.0 pct HN03 solution were found suitable as etching reagents. Best contrast between the a-Mn and the R phases could be obtained by using freshly prepared 60 pct glycerine + 20 pct HN03 + 20 pct HF solution. For high iron and cobalt containing alloys, especially for alloys containing the a-Fe, y-Fe, and P-Co phases, 15 cc HNOJ + 60 cc HC1 + 15 cc acetic acid + 15 cc water solution was found to be the best etching reagent. All X-ray diffraction work was carried out (using specimens prepared from annealed powders) with a 114.6 mm diam Debye-Scherrer camera using unfiltered FeK radiation at 25 kv and 10 ma. All calculations for X-ray diffraction work were carried out using an IBM 7044 digital computer RESULTS AND DISCUSSION The two ternary systems, MnTiFe and MnTiCo, were investigated near the manganese rich end, Figs. 1 and 2, and show some common features. In both alloy systems large extensions of narrow R phase regions occur at almost constant titanium contents. At titanium contents higher than that of the single phase R-phase alloys, the same unidentified X phase was found in both ternary systems. The extensions of the X phase close to the Mn-Ti binary indicate that this phase could be the TiMns phase. Too few X phase diffraction lines were present in the diffraction patterns to make positive identification of the X phase. In contrast to this similarity the two systems show opposite behavior in the extensions of the a-Mn and 8-Mn phase regions; while iron tends to stabilize the a-Mn phase, cobalt

Jan 1, 1970

By Pedro Bolsaitis, Paul M. Sullivan

The activities of zinc in liquid Zn-A1 alloys in the temperature range of 1000&apos; to 1160°K were determined by means of the isopiestic technique. The results are in reasonable agreement with the previous values determined by the radioactive tracer dew point method. Slightly negative excess entropies of mixing were found. The measured activities suggest that the a function for these alloys is not a constant, as has frequently been assumed, but is better represented by two straight line segments of different slopes. THE thermodynamic data of Al-Z alloys have been the subject of investigation by many authors. However, in the recent compilation of such data by Hult-gren et al.,5 the conclusion is reached that none of the previous measurements are reliable or consistent with each other. Since then two new sets of measurements have been reported,2, 8 both laying claim to good accuracies, yet showing very significant disagreement in the measured activity coefficients of zinc in Zn-A1 alloys and in the magnitude and sign of the excess entropies of mixing. Information on the thermodynamics of the system is of particular interest for interpreting results of the Bureau of Mines research on refining of zinc by distillation of die cast scrap. The present study was undertaken as an independent check on the recent values obtained from dew point measurements 8 and electromotive force measurements.&apos; The isopiestic method, first introduced by Herasy-menko,&apos; was chosen because it is one of the few thermodynamic techniques which, in principle at least, is carried out under perfect equilibrium conditions. The disadvantage of the method is that data are obtained at various random compositions and temperatures, which makes the interpretation somewhat cumbersome. The random errors arising from temperature gradients and fluctuations appear to be comparable to those of other techniques, as evidenced by the magnitude of the estimated uncertainties in the calculated integral thermodynamic quantities. An advantage of the method is that each run provides a relatively large amount of data; thus, it is less time consuming than those methods where samples of each composition must be measured individually. EXPERIMENTAL PROCEDURE The activities of zinc in liquid Zn-A1 alloys were measured by the isopiestic method which uses the principle of the tendency toward equilibrium of a series of samples at various temperatures under an imposed vapor pressure of the more volatile component (i.e., zinc, in this case). The basic apparatus is shown in Fig. 1. The small graphite crucibles that contained the metal samples were 15 mm ID and 13 mm deep with approximately 3 mm wall thickness. Each crucible was notched at the top and bottom to allow easy passage of vapor from one to another. At the beginning of an experiment each crucible was weighed on an analytical balance. Zinc and aluminum of spectrographic purity (99.999 pct) were then weighed into the crucibles. The amounts of each metal added were such that initial compositions varied above and below equilibrium values. One crucible contained only pure zinc. After weighing, the crucibles were stacked with the pure zinc on the bottom (corresponding to the lowest temperature in the furnace) and richest aluminum alloys at the top. The entire stack of crucibles was then placed in the silica glass container "E" which was then sealed under vacuum. Sixteen to twenty calibrated Chromel-Alumel thermocouples were attached by wire along the length of the silica tube, one or more adjacent to each sample.

Jan 1, 1970

By J. R. Cahoon, H. W. Paxton

The possibility of using unidirectionally solidified, two-phase alloys as an approximation to fiber composite materials is investigated. The short-term me.chanical properties and failure modes of unidirectionully solidified A1 (rich)-Cu alloys containing ap -Proximately 0, 17.5, and 27.7 vol pct of 0 phase &apos;fibers" are determined at temperatures from 25" to 500" and compared with those obtained for conventionul SAP alloys. In a previous publication,&apos; hereafter referred to as I, the possibility of understanding some of the room-temperature mechanical properties of unidirectionally solidified castings was explored. For Al(rich)-Cu and Al(rich)-Mg two-phase alloys over a substantial range of compositions, the yield and ultimate strengths and common ductility measures were very adequately predicted from the principles of fiber strengthening4 and the analysis of ductility outlined by Gurland and Plateau." The results obtained in I suggest the possibility of using unidirectionally solidified, two-phase alloys to simulate fiber composite materials where the inter-dendritic second phase or constituent acts as the reinforcing material. Recent attempts concerning the fabrication of fiber conlposites have concentrated on producing composites with a good bond between fiber and matrix and with very long fibers so that their maximum contribution to the strength of the composite may be realized. However, these objectives are difficult to attain in practice and present fabrication processes are either extremely laborious or costly.13 The slow, unidirectional solidification of eutectics has received considerable attention as a method for producing composite materials. 5,6 This method can fulfill both of the above objectives but it is currently laborious, expensive, and has the additional disadvantage that the volume fraction of reinforcing phase cannot be easily varied. On the other hand, unidirectionally solidified, two-phase alloys, also with a good bond between the phases, are relatively easy to make and the volume fraction of reinforcing "fibers" can be easily varied by changing the average composition of the alloy. The disadvantage of the cast alloys is that the mechanical effectiveness of the "elongated interdendritic reinforcements" (EIR)* may be reduced due to their rela- tively short lengths, the w factor in Eq. [2] of I. However, if the EIR have a high strength their contribution can be considerable. For composite materials containing discontinuous cylindrical fibers of various lengths the ultimate strength is given by1 where it is assumed that the composite fractures when the fibers fail. In Eq. [I], a, is the stress in the matrix just prior to failure of the composite, Vf is the total volume fraction of fiber reinforcing constituent, Vf(l+) is the volume fraction of fibers whose lengths exceed the critical length, I,, which is defined as the shortest length of fiber in which the stress can build up sufficiently to break the fiber. af is the fracture strength of the fiber material, w is a factor accounting for the discontinuity of those fibers whose lengths exceed I,, 1-/d is the average aspect ratio of those fibers whose lengths are shorter than I,, and t is the shear stress in the matrix at the fiber-matrix interface. The factor w is dependent on the length of the fibers and also on whether deformation of the matrix occurs plastically or elastically. However, for a given length of fiber, w is smaller when elastic deformation of the matrix is assumed.&apos; It is of interest to consider the properties of simple unidirectionally solidified, two-phase alloys at elevated temperatures in view of the possibility of using suitable modifications for high temperature service. Knowledge of the creep behavior of these materials is still rudimentary (although under active investigation) and the present paper concerns itself with short time tensile properties of some alloys similar to those investigated in I (i.e., unidirectionally solidified Al(rich)-Cu alloys). Unidirectionally solidified alloys containing 5.6, 17, and 23 wt pct Cu were tested parallel to the direction of solidification at temperatures from 25" to 500°C. In the present investigation, the alloys were homogenized for 2 days at 535°C giving a matrix of homogeneous a phase (5.2 wt pct Cu) and an interdendritic constituent (EIR) which was completely Q phase (53 wt pct Cu). EXPERIMENTAL Alloys of nominal composition 5.6, 17, and 23 wt pct Cu (containing approximately 0, 17.5, and 27.7 vol pct 8 phase, respectively, after homogenization at 535°C) were prepared by melting 1200 g of A1 (99.99 pct) in a high purity graphite crucible and adding the appropriate amount of freshly cleaned copper chips (99.9 pct). The molten alloy (at 700°C) was poured into a preheated graphite mold (also at 700°C) and the ingot unidirectionally solidified by impinging water on the steel baseplate of the mold. The alloy was degassed immediately

Jan 1, 1970

By Ben-Zion Weiss, Melvin R. Meyerson

Chromium diffusion coatings on commercial Armco iron lead to carbide precipitation at the grain boundaries in and below the coatings. High compressive stresses are introduced into the coating and, as a result, tensile stresses are introduced into the base material below the coating. In coated samples, fatigue cracks form at the grain boundaries below the coating after only a limited portion of the total lifetime (5 to 10 pct). Residual tensile stresses and a stress concentration caused by precipitated carbides seems to be responsible for early crack nucleation. Stage I of Propagation may be divided into two substages: I-a in which the crack Propagates along grain boundaries, and I-b in which the crack propagates along slip boundaries according to a shear mode. In uncoated samples, the cracks form at slip bands after 40 to 50 pct of the total lifetime. In coated samples the Propagation process takes longer than in uncoated samples because of the moderate rate of crack extension until the crack breaks through the coating. The chromium-diffusion coating causes little if any increase in fatigue life. CHROMIUM diffusion is one of the most popular processes used to apply coatings to iron alloys. This popularity stems from the fact that the diffusion treatment is comparatively easy to carry out, and it improves certain surface properties such as corrosion and wear resistance as well as some other properties. Very little effort has been devoted to the investigation of the effect of chromium-diffusion coatings on mechanical properties and particularly on fatigue properties. Since the chromium coating usually represents a small fraction of the total volume of the base material it is generally assumed that the macro properties are dependent principally on the base material rather than the coating. Insofar as fatigue is concerned, there are indications that the fatigue life of the chromium coating is not less than that of the basic material and the fatigue properties are generally not reduced by it.&apos; But chromium diffusion causes drastic structural and chemical changes in the region of the material surface2-4 which introduce additional residual stresses. Such changes must affect fatigue crack nucleation and may sometimes affect the initial stages of propagation. Furthermore, it is conceivable that the secondary stages of the crack propagation could be influenced by some irreversible structural changes in the core of the material, which stem from the long-time heat treatment at high temperatures required to apply the coating. This paper analyses the structural and compositional changes produced in commercial Armco iron by a chromium-diffusion coating and the effect of the coating on fatigue crack initiation and propagation. EXPERIMENTAL PROCEDURES The investigations were carried out with commercial Armco iron. The chemical composition of the iron, the number of specimens tested, the grain size produced during chromizing and heat treating, and the thickness and microhardness of the chromized layers are shown in Table I. Samples were chromized by a gas diffusion process. The temperature and time of the diffusion coating process were chosen according to a previous grain growth study. It had been found that at a temperature of 970°C and a holding time of between 3 and 9 hr there are practically no changes in grain size. To describe the grain size more accurately the ASTM method5 was supplemented by a statistical analysis of the mean volume diameter as outlined by Fullman6 and The The mean volume diameter was deter- mined from D = p/2m where D is the mean volume diameter, and m is the mean reciprocal value of grain diameters as seen on the micrograph. The shape and the size of the asymmetrical sample, see Fig. 1, were chosen so as to facilitate the study of fatigue crack initiation. Before coating, the samples were machined and the surface of the groove was polished. After chromizing, the two side surfaces were machined and polished so as to retain the coating only on the top surface of the groove. Residual stress in the chromized layer was measured on the top of the grooved section of the specimen after the diffusion process. The inclined incident X-ray beam procedure was used.9&apos;10 The computations were performed with the initial assumption of a zero surface normal stress component. An electron microprobe analyzer was used to obtain the relative amounts of chromium and iron con-

Jan 1, 1970

By George S. Ansell, John B. Hudson, Stephen A. Koffler

The permeability of hydrogen through the a phase of palladium has been measured by a low pressure permeation technique under conditions such that bulk diffusion was the rate-controlling process. The observed permeability is described by the equation: J = 1.80 x 1O-3 P½exp(-3745)/RT) cc(stp)/sec/cm2/en over a range of hydrogen pressure, P, from 2.9 x 10-5 m Hg to 5.0 x 10-3 cm Hg, and over a temperature range, T, from 300" to 709°K. The fact that the permeability shows a square root dependence on pressure and a reciprocal dependence on thickness was taken as evidence that bulk diffusion, rather than surface reactions, was the rate-controlling process. The permeability data were used in conjunction with the solubility data of Salmon et al., to determine the diffusivity of hydrogen through palludium as: D = 4.94 x 10-3 exp(-5745/RT) cm2/sec There was no influence of sub structural defects observed over the temperature range employed. From the permeability data obtained, coupled with grain size measurements, it was concluded that the ratio of grain boundary diffusivity to bulk diffusivity was less than 105 over the range of temperature investigated. THE diffusive mass transport of hydrogen in the a phase of palladium has been studied previously by numerous investigators.&apos; In spite of the large amount of attention this system has received, there is not good agreement between the results obtained in different investigations.&apos; This is due in part to the fact that the mass transport was surface-limited during some of these studies, rather than being diffusion-controlled3-5 The reason for the disagreement in other cases is not clear. These studies made use of such techniques as rate of absorption from solutions6 and gases,&apos; electrochemical potential,8 time lag,&apos; and permeation10,11 to determine the mass transport behavior. Of these, the gas permeability technique is the only method which allows an easy test to determine if diffusion is the rate-controlling mechanism, thus eliminating the uncertainty regarding the limiting transport processes inherent in the other techniques. The two most recent permeability studies are those of Toda10 and Davis." Toda determined the permeability of hydrogen in the a phase of palladium over the temperature range from 170" to 290°C, and over the pressure range from 36 to 630 mm Hg utilizing a steady-state gas-permeability technique. Toda&apos;s result was: J = 1.41 x 10-3 P½ exp(-3220/RT) where J = specific permeability in cc(stp)/sec/cm2/cm, P½ = square root of the inlet pressure in (cm Hg)½, R = Universal gas constant, and T = temperature in deg Kelvin. Davis11 also employed a steady-state gas-permeability technique over the temperature range from 200" to 700°C and over the pressure range from 0.02 to 760 mm Hg. His result for the permeability of hydrogen in the a phase of palladium was: J = 3.15 x 10-3 P½ exp(-A440/RT) In the range of overlapping temperature for these two investigations, the values of the specific permeability calculated from the above two equations differ by a factor of about 1.8. In the present investigation, the permeation of hydrogen in the a phase of palladium was determined over a wide temperature range, 27" to 436oC, and over the pressure range from 2.9 x 10-5 to 5.0 x 10-3 cm Hg. This temperature range overlaps that of the previous investigations of Toda and Davis, but also covers the lower temperature range which has never before been investigated. The lower pressure range used here avoided the interaction between the dissolved hydrogen atoms observed at higher hydrogen concentrations.&apos; MATERIALS The as-received palladium specimens were cold rolled from a casting and were supplied as 5.08 cm discs of 0.508 and 0.762 mm thickness. According to J. Bishop and Company specifications, the composition of the discs was 99.95 pct Pd, the balance being Cu, Ag, Au, and Ir. In order to obtain samples of varying grain size, the as-received discs were then heat treated. Sample 1 was treated for eight minutes in a nitrogen atmosphere at 810°C and then air-cooled. Sample D was heated first to 550°C in helium. The helium atmosphere was then immediately replaced by hydrogen and the temperature was slowly raised to 1220°C and held for 22 hr. The sample was then cooled to 550°C where the hydrogen was replaced by helium and the disc was further furnace-cooled to room temperature. Sample H was given the same heat treatment, only with hydrogen substituted for helium below 550°C. The reason that hydrogen was not used throughout the entire annealing cycle for samples D and H was to prevent the distortion encountered by low-temperature cycling in hydrogen observed by Darling." After these heat treatments were completed, the

Jan 1, 1970

By Robert E. Green, Wolfgang Sachse

Simullaneous ultrasonic attenuation measurements of both quasishear waves propagating in single cryslals of aluminum indicate that, in the undeformed annealed state, the dislocation density is generally not uniform on all slip systems. Change oof attenuation measurements made during plastic defortnation of crystals , which possessed specific orientations ideal for studying the orientation dependence of dislocation damping, indicate that, for low strain levels, dislocation motion occurs on additional slip systems besides the primary one, even for crystals oriented for plastic deformation by single slip. THE sensitivity of internal friction measurements permits such measurements to be used successfully in studying the deformation characteristics of metal crystals. On the basis of experimental observations, T. A. Read1 was the first to associate internal friction losses with various dislocation mechanisms. Since that time further work2-&apos; has been performed and a dislocation damping theory has been formulated by Granato and Lucke.6 In the amplitude independent region, this theory predicts the attenuation a to be dependent on an orientation factor O, a dislocation density A, and an average loop length L. if is a constant, independent of crystallographic orientation. For a given crystallographic orientation, changes in dislocation density and loop length give rise to the observed attenuation changes accompanying plastic deformation. The Granato-Liicke theory suggests the investigation of the orientation dependence of attenuation measurements in hopes of obtaining information to separate dislocation motion losses from other losses.7 An experimental study of the orientation dependence of attenuation in undeformed annealed single crystals should yield an insight into the uniformity of dislocation distribution throughout the entire specimen. A similar study on crystals plastically deformed in a prescribed fashion should give information about the alterations in the dislocation distribution on the slip systems activated during plastic deformation. The possible modes of elastic waves which can be propagated in aluminum,8 copper,9 zinc,10 and other hexagonal metals" have been calculated. Associated with each mode of wave propagation are dislocation damping orientation factors, which are based on the resolution of the stress field of that particular elastic wave onto the various operative slip systems in the material. These orientation factors have also been calculated as a function of crystallographic orientation in the papers cited above. Einspruch12 obtained agreement between predicted and observed attenuation values of longitudinal and shear waves in (100) and (110) directions of two undeformed aluminum crystal cubes. He ascribed the slight deviations between predicted and observed values to a nonuniform dislocation distribution, or to other loss mechanisms. In shear deformation of zinc crystals, Alers2 found that the attenuation of shear waves having their particle displacements in the slip plane was very sensitive to the deformation, while the longitudinal wave attenuation was affected only when the wave propagation direction was not normal to the slip plane. Using aluminum single crystals oriented for single slip, Hikata3 et al. found that during tensile deformation the change of attenuation of the shear wave (actually quasishear) having particle displacements nearly perpendicular to the primary slip direction exhibited the easy-glide phenomena, while longitudinal waves did not. Similar results were reported by Swanson and Green5 during compressive deformation of aluminum crystals. These results are in qualitative agreement with the calculated orientation factors for specimens of this orientation. In well-annealed, undeformed aluminum crystals, the damping is expected to be due to dislocations vibrating on all twelve slip systems. The orientation factors associated with this initial damping will be designated by O2 and O3, where a, represents the average orientation factor for the slow shear (or quasishear) wave and O3 represents the average orientation factor for the fast shear (or quasishear) wave. The calculation of these values for aluminum crystals by Hinton and Green8 shows that they vary very little as a function of crystallographic orientation—at most, by a factor of 2.47. If the dislocation density and loop length are uniform, then in the initial undeformed state, Here the subscript zero refers to the initial value of the attenuation. Also for aluminum, the calculations8 show that the orientation factors for primary slip only, associated with each shear wave, exhibit a sharp minimum for particular crystallographic orientations. A composite plot of the two shear wave orientation factors for primary slip only is shown in Fig. 1. Since these orientation factors are associated with dislocation motion occurring on the primary slip system only, the proper condition to check these factors might be attained by slightly deforming a single crystal oriented for primary slip. For dislocation motion on the primary slip system only,

Jan 1, 1969

By W. C. T. Yeh, T. G. Oakwood, A. A. Hendrickson, R. H. Hammar

The objective of the research is to determine whether solid-solution strengthening effects observed in dilute solutions of silver can be accounted for by the influence of the solute addition on the dislocation structure oj- the crystals. The additions of both tin and indium produced only small changes in the dislocation densities and arrangements in silver crystals. However, as found previously, small solute additions have large effects on the tensile properties; the inj-luence of the tin and indium additions on the temperature dependence of the flow stress and the easy-glide range is especially strong; It is concluded that the indirect strengthening effect of the solute due to variations in the dislocation density as proposed by Seeger is of minor importance and that solute atom-dislocation interactions are responsible for the observed strengthenirzg effects. The experimental results were combined with those of Rogausch to test the concenlvatiorz dependence of solute strengthening. Both the first and one-half power dependences of the critical resoleed shear stress on concentratiorz fail in very dilute solutions. THE objective of the research is to determine whether solid-solution strengthening effects observed in dilute solutions of silver can be accounted for, at least in part, by the influence of the solute addition on the dislocation structure of the crystals. It is recognized that the addition of solute atoms may influence the strength properties of a metal through both "direct" and "indirect" effects. The former refer to the strengthening mechanisms that result from the interaction of solute atoms with dislocations; in the latter case, the strengthening effects arise as a result of solute&apos;s influence on quantities such as dislocation density, dislocation arrangement, stacking-fault energy, diffusivities, the elastic constants, and so forth. It is clear that the correct interpretation of solid-solution strengthening phenomena cannot be given until the importance of indirect strengthening effects is properly evaluated. In the particular case of close-packed metal crystals, Seeger showed that solute strengthening effects in dilute solutions of copper and silver might be accounted for by an increase in dislocation density due to the addition of the solute. Seeger&apos;s argument was that the strengthening effects extrapolated from more concentrated solutions indicate that small concentrations of impurities raise the critical resolved shear stress much more than is predicted by a concentration-independent dislocation density. The above idea was a very reasonable one. The dislocation theories of work hardening of Taylor,2 Cot-trell, 3 Mott, 4 and seeger5 had already associated the increased flow stresses with increased dislocation densities in deformed metals; investigations of the dislocation structure of metal crystals had provided a logical basis for expecting an increased dislocation density in crystals containing impurities (see for example, Ref. 6). The numbers involved seem reasonable, too. It can be expected that the flow stress of the crystal would increase as the one-half power of the dislocation density.&apos; Solute additions of 1 at. pct to metal crystals result in strength increases by factors in the range of three to ten. If one assumes that the strengths of the pure metal crystals are determined by their dislocation densities, then dislocation-density increases of one to two orders of magnitude as a result of solute addition would be required to account for the observed strengthening—not an unreasonable expectation. In addition to the effect of the solute addition on dislocation density, one might also anticipate important strengthening contributions to result from the solute&apos;s influence on the dislocation arrangement. Parker and washburns have reviewed a number of experimental evidences which show important strengthening effects due to the presence of subboundaries. Further, lattice strains due to impurity segregation would be expected to influence the distribution as well as the dislocation density of the as-grown crystal. As pointed out in the reviews of Chalmers,6 Elbaum,9 and winegard,lo micro segregation of impurities occurs at all interfaces of crystals in cellular growth; the impurity gradient results in lattice strains which can be reduced with the presence of dislocation arrays in the region of the impurity gradient. Hence, one would expect the presence of a solute to favor the formation of dislocation subgrain structures and that the subgrains would have an important influence on the strength of the crystal. The experimental observations that concern the possibility of an important strengthening contribution through the influence of the solute on the dislocation density or arrangement are not in agreement. Haasen has reviewed the observations of Meakin and Wils-dorf,12 Howie,13 and Bocek 36 and concluded that the solute&apos;s influence on dislocation density is not sufficient to account for strengthening effects in concentrated solutions but might, as seegerl suggested, make an important contribution in very dilute solutions. On the other hand, Hendrickson and Fine 14 concluded that changes in the dislocation density and dislocation width accounted for the solid-solution strengthening effects observed in silver-based aluminum solid solutions. Goss et a 1.I5 observed dislocation arrays in Ge-6 at. pct Si, Ge-0.2 at. pct Sn, and Ge-0.2 at. pct B crystals that were not observed in germanium crystals of

Jan 1, 1968