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By H. M. Otte, A. G. Crocker

SLIP, twinning, stacking faults, and precipitates on well-defined planes in a crystal produce traces that are visible on either a polished or an etched surface. The purpose of this note is to establish the usefulness and limitations of the information obtained from such traces when determining the orientation of single crystals or grains in a polycrystal. Attention will be confined specifically to traces produced by octahedral planes in cubic crystals, though most of the remarks can be taken as more generally valid. The problem of determining the crystal orientation is completely solved in principle' and in particular for the special case under consideration.1'2 Tables are available3 in which the orientations can simply be looked up when given the two or three angles between the traces. Thus a quick and simple method is available for obtaining the orientation of a crystal from surface traces. In this note two examples will be given from recently published papers and will show the use of the method with the aid of the Tables, as well as some of the precautions that should be taken in the procedure. As part of an analysis of X-ray Kossel lines, Peters and Ogilvie 4 determined from them the crystallographic orientation of the specimen. They chose a Cu-5.10 wt pct Si alloy that had been partly transformed from the a (fee) phase to the k (hcp) phase. The latter formed as very straight platelets along the octahedral planes of the a phase, and a photograph (Fig. 7 of Ref. 4) was reproduced in the paper4 of the region for which the orientation had been determined from the Kossel lines. Apart from a very small area (about 0.15 mm diam) near the top center of the photograph, the region shown was clearly all of one orientation. Traces in four different directions were readily identified. Starting with the smallest angle and proceeding counterclockwise, the angles between the traces were measured to be 27° 43', 55° 16', 64 3 43 1, and32"26'. These add up to 1802 08 1, indicating a cumulative error of 8'. The correct values should, of course, be taken from the original glass plates, or at least from prints on distortion-free paper, so the precision of the quoted values is actually greater than their accuracy. The solutions can be looked up in the Tables3 in four ways, depending on how the angles are paired, tion for the minutes of arc is required and the solution obtained will be identical for all the four pairs if the values of the angles are not in error. In a practical situation, such as this one, there are several sources of error, so that the four solutions obtained will all be slightly different. An arithmetic average of the four solutions is mathematically incorrect, but may, in special cases, give an answer close to the correct one. A rigorous procedure for refining the orientation has been described by Mackenzie;5 he gives a least-squares method that can be applied, if necessary, to this type of problem. The orientation thus determined can be compared with the one from the Kosel lines and discrepancies larger than the experimental error assigned to nonor thogonality of the X-ray or electron beam to the specimen. Here the example will only be used to illustrate the general procedure for making a very rapid rough check. From measurements on the stereographic projection, Fig. 9 of the paper,4 we can determine that the surface normal is approximately (0.434, 0.704, 0.562). From the Tables3 we find, using 28°, 55" as a good approximation to the first pair (27°43', 55°16'), that the surface normal is (0.453, 0.678, 0.579).* These two values are within 2 deg of each

Jan 1, 1967

By G. Sandoz, D. A. Meyn

The fracture surfaces of specimens of titanium a1loys which exhibited susceptibility to subcritical crack growth in a wide variety of environments, including aqueous solutions, alcohols, hydrocarbon gases, carbm tetrachloride, and dry air, were examined. The dominant and characteristic fracture mode was cleavage. which became mixed with an increasing porportion of ductile fracture modes (dimples. and so forth) as the applied KI was increased. The cleavage plane in all the alloys was oriented at 15 deg from (0001) of the a phase. No indices could be assigned to the 15 deg cleavage Plane because of uncertainty as to which zone it belonged to. SLOW crack growth and delayed fracture take place in certain titanium alloys at stress intensity (KI) lower than the critical values for complete fracture (KIc) found in short-time tests for plane strain fracture toughness.' Such crack growth may take place in very dry air on sustained loading if the alloy contains a sufficient amount of hydrogen and if the stress intensity factor is higher than a threshold value designated KIH.2 Similarly, a number of environments such as water, alcohols, and hydrocarbons may cause slow crack growth provided the stress intensity factor exceeds the threshold value KISCC. In this paper it is intended to examine some fracto-graphic and crystallographic details of this subcritical crack propagation process as related to alloy composition, environment, and stress intensity. It has been previously reported that subcritical crack growth takes place in titanium alloys in aqueous environments by cleavage.2"6 The observations to be described here indicate that in the alloys investigated the mode of subcritical crack propagation is more dependent on the stress intensity during cracking than on the environment. The fracture mode is illustrated with photographs of the fracture surfaces at a wide range of magnifications. The crystallographic character of the cleavage mode is also presented and the results discussed. EXPERIMENTAL APPROACH The studies were made on four titanium alloys— Ti-8A1-1Mo-lV, Ti-5A1-2.5Sn, Ti-7Al-1Mo-lV, and Ti-0.350. Of these four alloys the first two were mill annealed and fine grained. The latter two were noncommercial and coarse grained, having been prepared for other experimental purposes. The crystallographic studies required a large-grain size. Consequently the fine-grained alloys were an- nealed in a vacuum at 1950°F and furnace cooled to produce samples for these studies. This treatment did not alter the microstructure significantly except for grain size. All the aluminum-containing alloys showed primary a with a network of ß-phase particles within the a grains; Figs. 1 and 2 show this microstructure for the specific case of fine-grained Ti-8A1-1Mo-1V. The cracks in the figures will be discussed later. Fractographic studies were made on all the alloys, but the electron fractographs displayed herein are from the Ti-8A1-1Mo-1V alloy in the fine-grained condition. Emphasis was placed on this commercial alloy because considerable information was available on the stress-corrosion cracking characteristics in a variety of environments. Sufficient supplementary studies of the alloy after the anneal to produce large grains were conducted to establish that the stress-corrosion cracking susceptibility and fractographic characteristics were not changed significantly. Thus it could be inferred that the crystallographic data obtained exclusively on large-grained specimens would apply also to fine-grained specimens. Fracture surfaces for study were obtained using precracked cantilever beam specimens loaded as described by Brown. The precracked section of a specimen was immersed in the environment of interest. Values of initial stress intensity factor Kli were chosen slightly higher than KISCC in order to obtain a fairly extensive region of slow crack growth. Fracture surfaces representative of a variety of stress intensity levels could then be examined because in the cantilever beam test KI increases as the crack propagates.

Jan 1, 1970

By M. A. Grossman

The harden ability of most steels can be predicted within 10 to I5 per cent provided the complete chemical composition is known, including "incidental" elements; and provided the as-quenched grain size is known; and provided, finally, that the composition and heating temperatures for hardening are such as to result in austenite free from carbide particles. In the method proposed herein, the steel is considered as having a base hardenability due to its carbon content alone (the hardenability of a "pure steel" of the given carbon content, without any other elements), and this base hardenability is multiplied by a multiplying factor for each chemical element present. After multiplying all these together, the final product is the hardenability. Grain size may be taken into account either in the base hardenability or after the multiplication. Hardenability is stated in terms of "ideal critical diameter", namely, the diameter of bar, in inches, that will just harden all the way through (absence of un-hardened core) in an "ideal" quench, and the calculation may also be related to the Jominy test The data bring out certain features rather clearly. For example: i. It is quite useless to attempt to predict hardenability unless all elements, including "incidentals,,) are known; thus an "incidental,, chromium content of 0.20 per cent increases the hardenability by about 50 per cent. 2. The relative effectiveness of different alloys is sometimes unexpected; thus molybdenum when calculated in this way appears to be of the same order of effectiveness as manganese, rather than much more powerful, as would appear to be common experience; observe that an increase from no manaanese to 0.20 per cent Mn provides a multiplying factor of 1.67, and an increase from no molybdenum to 0.20 per cent Mo provides a factor of 1.63, an increase of over 60 per cent in each case. However, if to a steel containing 0.50 per cent Mn there is added "20 points of manganese," the factor is raised from 2.65 (for 0.50 per cent Mn) to 3.35 (for 0.70 per cent Mn), or an increase of only 26 per cent. Thus the fist small addition of an element has a much more powerful percentage effect than an equal further addition when some is already present, and in most cases the effect of molybdenum is considered in relation to a steel in which molybdenum is absent. 3. If two elements are equally effective, a greater hardenability will be obtained by using, for example, 0.5 per cent of each than by using I.o per cent of either of them alone. 4. A knowledge of the as-quenched grain size is essential for precise work, since a difference of only one grain size number (say No. 7 instead of No. 6) makes a difference of almost 10 per cent in hardenability (in these units); this, however, does not apply to certain It should be emphasized that in chromium steels (over 0.30 per cent Cr) and chrome-molybdenum and chrome-vanadium steels, un-dissolved carbides are likely to be present in the steel as quenched, and that in such cases the charts can indicate only a maximum Passible hardenability, whereas the extent of hardening actually obtained may be much less. Thus tests on a number of chrome-molybdenum steels have indicated a degree of hardening amounting to only 50 to 65 per cent of the maximum possible, and in chromium steels from full hardening (100 per cent) down to as low as 70 per cent. On the other hand, when the amount of such elements is small (Cr under 0.30 per cent, Mo up to 0.25 per cent in the

Jan 1, 1942

By M. A. Grossman

The harden ability of most steels can be predicted within 10 to I5 per cent provided the complete chemical composition is known, including "incidental" elements; and provided the as-quenched grain size is known; and provided, finally, that the composition and heating temperatures for hardening are such as to result in austenite free from carbide particles. In the method proposed herein, the steel is considered as having a base hardenability due to its carbon content alone (the hardenability of a "pure steel" of the given carbon content, without any other elements), and this base hardenability is multiplied by a multiplying factor for each chemical element present. After multiplying all these together, the final product is the hardenability. Grain size may be taken into account either in the base hardenability or after the multiplication. Hardenability is stated in terms of "ideal critical diameter", namely, the diameter of bar, in inches, that will just harden all the way through (absence of un-hardened core) in an "ideal" quench, and the calculation may also be related to the Jominy test The data bring out certain features rather clearly. For example: i. It is quite useless to attempt to predict hardenability unless all elements, including "incidentals,,) are known; thus an "incidental,, chromium content of 0.20 per cent increases the hardenability by about 50 per cent. 2. The relative effectiveness of different alloys is sometimes unexpected; thus molybdenum when calculated in this way appears to be of the same order of effectiveness as manganese, rather than much more powerful, as would appear to be common experience; observe that an increase from no manaanese to 0.20 per cent Mn provides a multiplying factor of 1.67, and an increase from no molybdenum to 0.20 per cent Mo provides a factor of 1.63, an increase of over 60 per cent in each case. However, if to a steel containing 0.50 per cent Mn there is added "20 points of manganese," the factor is raised from 2.65 (for 0.50 per cent Mn) to 3.35 (for 0.70 per cent Mn), or an increase of only 26 per cent. Thus the fist small addition of an element has a much more powerful percentage effect than an equal further addition when some is already present, and in most cases the effect of molybdenum is considered in relation to a steel in which molybdenum is absent. 3. If two elements are equally effective, a greater hardenability will be obtained by using, for example, 0.5 per cent of each than by using I.o per cent of either of them alone. 4. A knowledge of the as-quenched grain size is essential for precise work, since a difference of only one grain size number (say No. 7 instead of No. 6) makes a difference of almost 10 per cent in hardenability (in these units); this, however, does not apply to certain It should be emphasized that in chromium steels (over 0.30 per cent Cr) and chrome-molybdenum and chrome-vanadium steels, un-dissolved carbides are likely to be present in the steel as quenched, and that in such cases the charts can indicate only a maximum Passible hardenability, whereas the extent of hardening actually obtained may be much less. Thus tests on a number of chrome-molybdenum steels have indicated a degree of hardening amounting to only 50 to 65 per cent of the maximum possible, and in chromium steels from full hardening (100 per cent) down to as low as 70 per cent. On the other hand, when the amount of such elements is small (Cr under 0.30 per cent, Mo up to 0.25 per cent in the

Jan 1, 1942

By Strathmore R. B. Cooke

On the basis of experiments con- ducted on quartz using a bubble pick-up method, it was shown in an earlier paper1 that this mineral will preferentially adsorb hydrogen, calcium, or sodium ions, depending on the relative concentrations of those ions in the solution in which the quartz is immersed. For quartz particles ranging in size from 0.2 to 1 mm, it was demonstrated that the concentration of calcium in solution (assumed present as ions) necessary to completely activate quartz for flotation is given by the expression: In this expression, ionic concentrations are in mols per liter. It was further shown that the pick-up method is apparently more sensitive to changes in reagent concentration than the standard captive-bubble method, and that induction times are apparently much reduced. Since completing these earlier tests, a new type of cell has been constructed; this is shown in Fig 1 and 2. In Fig 1, A is a ground joint, B is a ceutral tube reaching to within a few millimeters of the bottom of the cell, and C is a stopper which may be removed for re- agent addition, and serves the further purpose of excluding carbon dioxide from the air during the test. The entire cell is constructed of Pyrex glass, and does not give the trouble experienced with the earlier cell, in which activating ions were released from the glass at high pH values. The only critical factor in the construction of the cell is the clearance between the central tube and

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