The University of Michigan Office of Research Administration Ann Arbor, Michigan INTERIM PROGRESS REPORT to Materials Central Wright Air Development Division NOTCH SENSITIVITY IN STRUCTURAL AND ENGINE ALLOYS (Analysis of Planned Experimental Program) by H. R Voorhees J. W. Freeman Project 03728 Contract AF 33(616)-7416 March 1961

INTRODUCTION Past attempts to explain creep-rupture behavior of notched specimens under axial load were handicapped by uncertainties as to: 1) the exact stress-strain history at each location in a notched specimen under the localized plastic deformation when the load is applied, and under the subsequent non-uniform creep, and 2) the manner in which the changing stress levels and their multiaxiality influence the fracture process. The present program seeks to experimentally establish the changes in stress and strain distribution during creep-rupture testing for the particular case of plate specimens with edge notches. Observation of the location in these specimens where cracks initiate, the period of the test at which these occur, and the manner, rate and direction of their progression toward failure are to be correlated with the measured history of stresses and strains in the regions involved. Supplementary experiments on unnotched plate specimens with edge loading will verify behavior under biaxial conditions. Such a specimen permits evaluations under conditions of uniform biaxiality, free from the point-to-point strain gradients of a notched specimen. The combined test results are expected to serve as a guide to refine and check analytical procedures for predicting notch sensitivity under creep conditions. REQUIREMENTS FOR TEST MATERIALS AND CONDITIONS Since an ultimate goal of this research is a general solution to notchedspecimen behavior under creep-rupture conditions, alloys and test methods have been chosen with a view toward positive separation of pertinent variables and exact evaluation of parameters, rather than to provide design data for specific materials. Prime consideration was given to alloys and conditions expected to permit the most ready interpretation in terms of past

experience, but limitations of currently-obtainable instrumentation restrict test temperatures and specimen dimensions. The following paragraphs cover these various considerations which led to the final selection of test materials and methods. General Observations from Prior Studies: Yielding during load application and later creep relaxation with time both act to redistribute the stress concentration present near the notch of a loaded specimen. To separate effects from these two factors, at least some test conditions should allow a notched specimen to be taken to rupture at a nominal stress below that at which substantial yielding at the notch takes place at loading. In order to generalize the findings for the opposite case when short-time yielding is of importance in stress leveling, at least two quite-different values of Young's elastic modulus (E) should be represented in the test materials and these materials should preferably exhibit dissimilar stress-strain characteristics in the yield range. Past studies suggest that progressive aging reactions and alteration of subsequent creep-rupture strengths by a momentary plastic prestrain can make interpretation of rupture data very difficult for conditions of changing stress level such as exist at any point in a notched specimen under test. At least one of the alloys to be studied should possess a high degree of freedom from such metallurgical alterations for test times and temperatures to be investigated so as to eliminate the need to assign different strength properties to the material at different locations in a notched specimen at the same test stage, or to use changing creep-rupture strengths as the test progresses. Any deviation from isotropy also makes more difficult the calculation of stress components from measured strains. Special care should, therefore, be exercised to procure test materials processed to give like properties in all directions of strain measurement. Choice of alloys without excessive ductility can be expected to help to limit the development of anisotropy from the unequal plastic strains expected in different directions, and, at the same time, reduce experimental difficulties of strain measurement during late stages of the test when localized "necking" can occur.

A critical review of available data bearing on notch sensitivity of heatresistant alloys (Ref. 1) pointed out areas where further study should especially contribute to a basic understanding of notched-specimen behavior. The most-universal observation from the assembled data was that for every alloy at every test temperature, without exception, notch strengthening was obtained for intermediate values of notch acuity when the study covered a wide range. The most-detailed investigation (cylindrical notched specimens of A-286 alloy tested at 1200~F) displayed peak notch strengthening for a theoretical stress concentration factor (Kt) between 1.5 and 2. 4 for all levels of nominal stress employed, but specimens with Kt = 4. 1 or 5. 7 showed a transition from notch strengthening at short times (high stresses) to notch weakening for nominal stresses below 50, 000 psi. The extensive data accumulated for this alloy in a prior research (Ref. 2) and its apparent variation in behavior for different ranges of notch acuity and level of nominal stress suggest that A-286 should make an excellent material against which to check any hypothesis which can be developed to explain notch effects. The material is readily available in most commercial forms and presents no particular problems of specimen machining. At its most-usual test temperature of 1200~F, elongation at rupture is moderate -- about 5-10% -- and plastic prestrains of the order of one per cent exert but little influence on subsequent rupture life. Moreover, the 1000-hour rupture strength of typical notched specimens at 1200~F is half or less of the material's yield strength, so that tests of an acceptable duration can be run on notched specimens without the introduction of large amounts of initial plastic strain in the vicinity of the notches. Any major drawback to use of A-286 would seem to derive from possible difficulties with instrumentation. Current Commercially-Available Instrumentation: Any method to determine localized stresses involves experimental measurement of the corresponding strains at or near the specimen surface by any of several means, including: 1) Small resistance strain gages 3

2) Measurement of changes in the spacing of a fine grid ruled onto the surface or otherwise applied to the specimen 3) Photoelastic coatings 4) X-ray diffraction. Each of these methods has definite limitations for the problem in hand. Resistance Strain Gages. Two primary factors limit existing resistance strain gages for static measurements in long-time tests at elevated temperatures. Particularly at 1000~F or above, strain gage materials tried to date lack stability (i. e., their zero point drifts and the gage sensitivity changes with time and strain) unless they are pre-treated at conditions which limit their subsequent ductility to unacceptable low values. Even at short times, where the gage metals have predictable behavior, the ceramic cements needed to attach the gages to the test piece may be the limiting factor in the strains that can be measured, while at the higher temperatures the electrical conductivity of these cements becomes a problem. A lesser limitation in the application of strain gages to the present problem is their finite dimensions. To determine localized strains at discrete positions across a notched plate specimen requires that the active portion of the gage employed must be small relative to the specimen dimensions. Moreover, a specimen width of more than about eight inches is difficult to grind to uniform thickness with equipment to be found in the usual job shop, and larger specimens also make a uniform distribution of test temperature across the test section more difficult to achieve. Table 1 lists some dimensions for the smallest sizes of strain gages currently available from the two major suppliers of commercial gages (Baldwin-Lima-Hamilton and The Budd Company). Up to their limiting temperature of 200~F, the smallest of these gages will measure longitudinal strains over a 1/32-inch length of the specimen and transverse strains across 1/64 inch of specimen width, and these gages could be placed at 0. 1-inch or closer intervals across the width of the specimen. Determination of the pattern of longitudinal strains should be quite satisfactory with a Budd type 4

lX1-32A or Baldwin type FA-03-12 gage cemented at the base of the notch to determine the axial strain at the very edge of the notched cross section and with similar gages spaced at intervals across the flat surface of the specimen between the notches. Six or eight gage locations should suffice to establish the monotonic curve of longitudinal strain versus distance in from the notch, and their exact location should not be critical. The curve of transverse strain components across the specimen width is more difficult to define by a small number of gages. Starting from zero at the notch, this component rises to a maximum which may be located at a distance in from the notch of only of the order of 10% of the half width for a specimen with relatively-high stress concentration factor. At positions closer to the center of the specimen, the transverse strains fall off in value. Results cited by Mirkin and Trunin (3) and by Garofalo (4) suggest that stress conditions in the region of the peak transverse strain are those of particular interest to notched-bar rupture behavior. For a specimen width between notches of the order of six inches, a sufficient number of transverse-strain gage locations in 10% of the half width should be obtainable at ordinary temperatures by using the tiny Budd Company gage type 1X1-64 trimmed to a "length" of 1/16. inch or less. However, the smallest stock gage for hightemperature service (Baldwin type FNH-06 - 1 2 - B) can hardly be placed closer together than about 1/8 inch, so that these gages may provide only an approximate location and an approximate peak value for the transverse strain. The finite dimensions of any strain gage introduce an added uncertainty when one desires6 to convert strain measurements to stress components. Except along planes of specimen symmetry, the principal strain directions will vary from point to point. Consequently, the strains indicated by a gage represent a summation of components resolved in the direction of sensitivity of the gage grid from the various strain orientations. The result so indicated by the gage is not truly applicable to any particular point. In fact, the apparent longitudinal and transverse strain indications for superimposed gages oriented lengthwise and crosswise to a specimen over the same spot might well not apply to conditions at a common point. Such difficulties should 5

not be of significance for the tiny gages available for room-temperature measurements, but could be troublesome at higher temperatures for locations removed from the specimen's lines of symmetry. As presently envisioned, the planned research requires the continuous short-time determination of strains during the original loading of a notched plate, as well as periodic measurement of elastic unloading strains after prior extensive localized creep near the notch. Any gage material and the cement used to affix the gage to the specimen surface should preferably be able to withstand up to several per cent of initial strain and the subsequent creep strain associated with relaxation of the starting stress gradients. At 500~F or below, strains above 2% are obtainable using heat-curing epoxy cements with a rather long cure time at the 500~F temperature. Most heat-curing ceramic cements for higher temperatures are claimed to be usable only to about 1/2% of strain, but the consultant Mr. William To Bean, Jr. of Detroit, Michigan has expressed the opinion that his type "H" cement with the addition of special'plasticizers" should maintain a bond for any strain to which present high-temperature gage materials will continue to give accurate results. The actual usable strain limits remain to be determined. The Norton Company has developed a method for applying a protective coating of fused oxides as a molten spray. Tests made by them in conjunction with Arthur C. Ruge Associates, Inc. indicated that this "Rokide" coating could maintain a useful bond between a standard-size foil gage and a metal specimen for strains exceeding two per cent. However, tests run at the University of Michigan on small gages (Baldwin FNH-06-12-B) mounted by the Ruge organization onto two strip specimens of A-286 were disappointing. The specimens were brought to 1200~F and then loaded to 60, 000 and 55, 000 psi, respectively. When the tests were interruptedthe next day at about 0. 95% and 0. 55% creep strain, respectively, nearly the entire Rokide deposit and the imbedded strain gages had separated from the specimens. Even a gage mounted onto the shank of one specimen where strains were negligible had fallen offo Adhesion of the Rokide was maintained 6

only a few spots at the edge of the coated areas where the coating thickness tapered down from the 0. 010 inch or more total thickness over the gages as mounted. No further tests are planned unless "soft" ceramic cements give equally poor results. Where strain gradients are moderate and maximum strains are within the limits of the gage materials and cements, resistance strain gages offer a convenient and precise measuring method. Probable zero-point drift at elevated temperatures should not affect determination of loading strains or of short-time dynamic strains during periodic momentary load reduction. But, supplementary methods appear to be required to measure the gross strains of time-dependent creep during the test. Strain Measurement by Grids. A finely-spaced grid with clear-cut lines of uniform width permits determination of strains at any desired location within the grid but suffers from the handicap that precise readings cannot normally be obtained without interruption of the test in elevated-temperature studie s In room-temperature measurements with a 100 line/inch grid applied by a photographic method, the limiting accuracy attained by Brown and Jones (Ref. 5) under their most ideal conditions was stated to be + 0. 1 per cent of strain for a 0.6 inch gage length. To get this accuracy required measurement of each grid interval both before and after straining. Where a gage length of 0. 01 inch was required, the limiting accuracy was stated to have jumped to + 2 per cent. A 50-power metallurgical microscope provided with a Filar micrometer eyepiece was found suitable to measure changes in the gage length of from 0. 01 to 0. 08 inch adopted for the different problems considered. A recent Russian research determined strains and stresses in an aluminum-alloy plate 3 cm wide with a central hole, tested in creep at 200 C. A precision of 0. 3 micron was claimed for a grid of superficial scratches ruled onto the surface of the plate with a diamond pyramid indenter, which grid was stated to guarantee an accuracy to about 0. 05% of strain over a 0.4 mm length. This particular study related stresses to the measured 7

total plastic strains by analytical means in contrast to our proposed direct measurement of elastic strains of periodic momentary load removal. Still, the Russian paper was considered of sufficient potential interest that a complete translation has been included as Appendix A to the present report. For specimens as large -as those required for instrumentation with resistance strain gages, the application of scratched grid lines would seem to be impractical. Modern photoengraving techniques permit the preparation of metal masks with parallel slits of very uniform width and highly-accurate spacing. Grid lines can then be formed on the specimen by evaporating the vapor of a suitable metal through the mask. Care must be exercised to insure that the mask and specimen surface are in good contact during the metal evaporation step in order to prevent "leakage" under the masked-off portions. Even with good technique, the lines will be substantially wider than the finest line that could be scratched onto a smooth surface. For a typical evaporated grid with fifth lines per inch, the line width will be about 8% of the 0. 020-inch spacing. Considering that the center of a given grid line can probably be determined only to an accuracy of about one-tenth the line width, the smallest permanent deformation that can be detected with certainty in a 0. 02-inch length is of the order of 1% of strain. To get measurements even that precise requires sharply-defined grid lines that will remain visible under the test conditions. An unnotched A-286 alloy strip and a strip specimen of 2024-T4 aluminum alloy with edge notches, both available from an earlier research, were used to test the feasibility of vapor-plated grids to measure gross plastic strains after a period of creep. Grid lines on one face of the A-286 strip were of gold and on the other were of titanium metal. For the aluminum specimen, the grids were of copper and titanium, respectively. Some lines were not so uniform as would be desired, apparently as a result of metal vapor leaking under the etched mask. In other respects, the grids seemed satisfactory. When the A-286 specimen failed after 76 hours at 1200~F under 55, 000 psi stress, the axial deformation was still less than 0. 5%, but an overall 8

strain of nearly 4% was introduced into the aluminum specimen during the first 210 hours at 500~F under an average nominal stress of about 5000 psi. Casual examination of the grid deformation in the latter specimen at that time indicated strains of over 10% but no exact measurement were triedo Both specimens were returned to temperature without load to evaluate effects of long test times on the grids. After a total time of 700 hours at 500 F, both the copper and the titanium grids on the aluminum strip were still rather sharply defined and they resisted removal with a soft rubber eraser. Any preference for grid metal was probably in favor of the copper which showed the more-uniform coloration of grid lines after prolonged exposure to temperature. By the end of 500 hours at 1200~F, the A-286 strip showed general discoloration, but both the gold grid on the one face and the titanium grid on the other were visible over most of the area when the proper illumination was obtained. Little further change in appearance had taken place by the 1174 hours time when the test was discontinued. Even then, measurements of gross deformation by these grids should still have been possible over most of the grid area. Both grid metals remained adherent and still resisted ready removal with an eraser. Either grid metal appears to be satisfactory, with possible slight preference in favor of gold. On the whole, the grid method seems very useful for determining large strains in the vicinity of a notch in a specimen taken all or most of the way to fracture. The grid should also permit one to assign coordinates and dimensions to any cracks or other features detectable by radiography of a specimen after successive interruptions of a test, thus to follow the fracture progression in a single specimen. Photoelastic Coatings. This relatively-new technique employs a birefringent plastic coating applied either by brushing a liquid plastic metal onto the metal surface and polymerizing the coating by heating the part, or by prefabricating a sheet of the plastic and bonding it to the part at room temperature. The major advantage of photoelastic coatings is that readings can be determined in a continuous distribution over the entire surface and that principal-strain differences indicated for any given point are for virtually 9

zero gage length. To determine the individual principal strains, a photoelastic analysis must be made with polarized light under oblique illumination. Sensitivity for this determination has been stated (Ref. 7) to be + 10 or + 20 microinches per inch, depending on the instruments used, for a coating of type "S" plastic 0. 120 inch thick. Present photoelastic coatings are not usable for prolonged tests at temperatures above about 300~F. In the present study, their use to measure the elastic strains part way through a test would require the specimen to be cooled with the load maintained, the coating to be applied, and strains associated with load reduction to then be measured at ambient temperature. The available cements to apply sheets of photoelastic materials require the inconveniently-long drying time of 24 hours. The alternate liquid coating requires application of several successive layers with intermediate heating to 150-230~F to harden each layer, and subsequent determination of the final coating thickness at each point where a strain measurement is to be made. For comparable conditions, a number of small resistance strain gages could be mounted with Eastman 910 cement, ready for use in but a fraction of an hour, and would permit direct measurement of individual strain components to as close as + 1 microinch/inch at discrete locations where the principal directions are known from symmetry considerations. Under these circumstances, photoelastic coatings appear to hold insufficient advantage over resistance strain gages, even at room temperature, to warrant the estimated $3000. cost of the necessary polariscope and accessories. Stress Determination by X-ray Diffraction. The X-ray diffraction method depends on changes in inter-atomic spacings which result from elastic strains. Since these same elastic strains cause the existing stresses in the material, X-ray diffraction permits one to measure the momentary stress condition without need to know the prior stress-strain history. The X-ray beam usually employed determines stresses in an area roughly 1/8 inch in diameter for layers very near the surface of the specimen. With annealed steel of fine-grain structure, accuracies of + 2000-3000 10

psi can be expected, but cold working or other metallurgical factors producing diffuse diffraction lines can cause errors several times this large. Since the X-rays used in stress analysis penetrate the metal specimen to a depth of only a few thousandths of an inch at most, surface condition is critical. Of more concern, several workers have noted abnormally-low stress indications by the X-ray diffraction method for materials strained beyond the elastic region. In its current state of development, X-ray diffraction seems unsuited for the present research. PROPOSED STRAIN-MEASURING PROCEDURES Preceding paragraphs suggest that a combination of resistance strain gages and vapor-deposited grids should permit the desired data to be obtainedo Even so, these strain-measuring methods place definite limitations on permissible test conditions and dictate different procedures to measure strains in short-time versus long-time tests. Stress Patterns Upon Tensile Loading of Notched Plates: At test temperatures in the creep range of an alloy, a unique stressstrain relationship no longer exists. However, at low load levels, the timedependent strains of creep should be negligibly small compared to strains from short-time load changes. The higher the applied load becomes, the more critical is the need to provide for rapid scanning and reading of the strains to prevent time-dependent creep strains from being troublesome. A single short-time tension test for each combination of test material and notch configuration is currently envisioned. During early stages of the test, readings from any reasonable number of strain gages could be taken each time the load was increased in steps. But the only known strain-gage scanning recorder which combines the desired high precision with a cost within the budget for the research (The Budd/Datran digital strain indicator with coordinated switching, balancing, control and print-out accessories) requires up to four seconds to reach a balance and an additional 0. 8 second 11

to switch and print. Consequently, when loading reaches the stage of localized yielding near the notches, readings would best be taken only for a few selected strain gages so as to minimize delays in the loading process and to prevent significant creep strains from confusing the observations. As soon as erratic output indicates that any given gage has exceeded its limit of useful strain, no further readings with it would be taken. According to published results of Vinckier and Dechaene for room-temperature experiments (Ref. 8), strain gages in areas near the specimen mid-section should still remain within their strain limits when the material closer to the notch has already reached incipient fracture. If loading is finally stopped just before the last of the gages approach their maximum useful strain and the load then removed promptly, a cross check can be made between strain measurements by the grid and those by strain gages for at least one area of the specimen, and the grid will also permit evaluation of the gross strains to be found in other areas at or close to the start of fracture. Biaxial Stress-Strain Evaluations. The planned combination of continuous measurements with resistance strain gages and a final measurement with a grid should suffice to provide patterns of total strain for a wide range of loads, plus the final elastic unloading strains in one small region. But, additional information is needed before one can use the data to find the stress pattern for loads between that at which localized yielding begins near the notch and that from which the final unloading is done. For a notched specimen loaded monotonically, i. e., without reduction of the load at any stage of the process, the most direct approach is to empirically establish the stresses corresponding to any plastic strain in an unnotched specimen of suitable design subjected to biaxial loading. An absolutely rigorous treatment would require that the entire.history of each location of interest in the notched specimen be duplicated exactly on a separate unnotched biaxial specimen and note taken of the biaxial-stress history needed to produce this duplication However, for most locations in a notched specimen, the ratio of principal strains will probably be sufficiently constant during any portion of the test to permit satisfactory stress evaluations 12

by interpolation of data from a limited number of experiments on unnotched plate specimens loaded at their four edges to maintain fixed ratios of increasing principal strains. Four such tests with principal-strain ratios of e /e = 0, 1/4, 1/2, and 1. 0 are suggested for each specimen material at its test temperature. Stress Redistribution in Notched Specimens Under Creep Conditions: Present knowledge leaves unanswered the question of relative pertinence of stress level and of degree of plastic strain on the expenditure of rupture life under creep conditions. The present study seeks to measure changes with time in both of these parameters at a number of locations in notched plate specimens creeping at elevated temperature under steady axial load. When a long gage section of uniform strain rate is available, timedependent strain can be measured continuously by any of several forms of extensometer, but such a device is of limited utility when creep at widelydiffering rates must be determined at many localized spots of a notched plate. A grid on the specimen surface seems the most feasible method for measuring localized creep strains over the entire area of interest. Even so, continuous precise readings from a grid would be costly and difficult to obtain, especially at high test temperatures. A practical procedure appears to require interruption of the experiment at each stage of the test at which a strain survey is desired. Present-day commercial resistance strain gages do not appear satisfactory to measure creep strains, particularly at the 1200~F needed for tests on A-286 alloy. But, gages made from some of the current materials should remain intact throughout loading and a subsequent extended creep period during which the total deformation remains within the strain limits claimed for the best existing cements. Zero-point drift of the gages can be expected to be so extensive as to make static measurements quite useless, but dynamic strains of loading and unloading should be usable. Auxiliary tests with strip specimens instrumented with both the strain gages and precise optical extensometers would ascertain changes in strain-gage characteristics as a function 13

of time and strain at temperature, as well as to establish the maximum allowable strain for various combinations of gage material and cement to bond the gages to the specimen. As was true for strain evaluations with a grid, determination of the stress pattern at any stage in a test will require the test to be interrupted, in this case by momentary removal of the load at constant uniform temperature. Provided the residual stresses are all low enough to preclude plastic strains upon load removal, conversion of measured unloading strains to absolute levels of elastic strain (and in turn to stress levels) requires simply that the integrated longitudinal elastic strain across the specimen midsection be set equal to its required equilibrium value of zero in the unloaded state. Were the specimen permitted to remain at the elevated temperature with the load removed, relaxation of residual strains could occur. Therefore the load must be re-applied immediately. If a strain survey with the grid is to be performed at this same stage of the test, the load should be put back in place while the temperature is dropped to below the creep range. Prior experience in creep testing of bar specimens in tension has shown that such cooling under load effectively prevents significant strain recovery for most test conditions. If the specimen is later reloaded and then brought back to temperature without undue delay, the creep rate soon re-establishes itself at its former value and rupture properties will usually remain the same as though no interruption in the test had occurred. Since the localized plastic strain in a typical notched specimen during loading to the stress for a rupture time of 100 hours is commonly of the order of 1% or below, and since a like amount of creep strain should permit extensive leveling of the initial stress concentration, a total usable strain of two per cent in a strain gage should allow quite useful data. But care must be exercised to insure that strain gages across the entire specimen width -- from notch root to the centerline -- remain within their allowable strains. Otherwise,* the equilibrium condition of zero average longitudinal stress at zero axial load cannot be employed with the accuracy needed to convert 14

relative strains from point to point into actual values of elastic strain, and then into stresses. This does not say that the original set of gages must last throughout the entire test. All that is required to be known is the differential elastic strains when the load is applied or removed at each interruption of the test, plus the elastic properties of the specimen material and the characteristics of the strain gages in their existing state. Prior history is of no direct concern to determination of the present stresses following plastic strains. Consequently, a new set of gages may be applied to the specimen during any interruption of the test and then used until they approach their limits of allowable accumulated strain. Meanwhile, the grid on the opposite face of the specimen can furnish a continuous picture of the plastic strains from the time the test was first started. At each stage in the test when the specimen is cooled for measurement of the changes in grid spacing, x-ray examination could be rrade to ascertain the start of cracking and later growth of these cracks. Since the stress-redistribution process in a notched specimen should depend on the extent of yielding at initial load application, two quite different levels of nominal stress are proposed to be investigated at each notch acuity for each test material. In supplementary studies of the factors controlling crack initiation and growth, strain gages will permit one to confirm whether the biaxial stress state obtained in the central portion of unnotched plate specimens is uniform and in agreement with the levels predicted from load and area values Once these conditions have been shown, conventional extensometers should provide stable and precise readings of deformation at minimum expense. For stress determinations, orientation of strain gages in the principalstress directions lessens the number of gages required while also simplifying calculations. Only at free edges or along the transverse and longitudinal center lines of specimen symmetry can the principal-stress directions be stated a' priori. At other locations, the principal axes of the existing stresses 15

may be expected to change under the continuing biaxial yielding, with the axes of principal stress at each stage of the test coincident with the principal axes of the final increment of strain just preceding. (See Ref. 9, p. 38 ff, or other text on plasticity theory. ) The practical answer seems to be to locate.the majority of strain gages along the lines of symmetry of the notched specimens, orienting the gages parallel to the transverse and longitudinal axes. At a few other locations away from these axes, sets of gages would be mounted to obtain strain readings in a third direction as well as along the length and width directions of the notched specimens. TEST MATERIALS AND SPECIMEN DESIGNS Inquiries have shown that available epoxy cements should allow strains in excess of two per cent in long-time tests at 400-500~F. Certain of the aluminum-base alloys possess favorable properties for study in this temperature range, but the alloy chosen must permit the multiple-step cure of the cement which includes several hours at 500~F. In addition, a suitable specimen material must meet the following requirements: 1) It should be available in plate form in dimensions suitable for making large specimens. 2) Strength properties should be uniform between specimens and should not vary with direction or location for any given specimen, so as to minimize scatter between tests. 3) The alloy should exhibit sufficient stability of properties after shorttime plastic strains and under creep exposures to minimize the need for assigning different strengths to material at different locations in the same specimen or for successive periods of the same test. Selection of a Particular Aluminum Alloy: Many aluminum alloys can be eliminated from consideration by the last of these criteria; their residual rupture strengths fall drastically with time of exposure to elevated temperature, even in the absence of an applied load. A 16

notable exception is a series of alloys produced from aluminum powder as a starting material and containing a fine dispersion of A1203. Private communications from G. W. Stickley of the Aluminum Company of America verify the good stability of materials of this type. Results from experimental extrusions of the "APM" alloys show no effect on tensile properties from prior exposures between 1/2 and 1000 hours at temperatures up to 600~F or higher. Limited data for the new standard wrought alloy 2219, likewise, show no influence of exposure time at 500~F on tensile properties at that temperature, although measurable change in properties at 400~ and 6000F have been found for this alloy after exposure to temperature for times as short as 10 hours. Data supplied by Mr. Stickley on both types of material are analyzed and compared in Table 2 in terms of the following criteria: 1) Elongation. A low value of elongation is desired to minimize instrumentation difficulties and to limit build-up of anisotropy from large biaxial plastic strains before the end of the test. The values listed in the Table are from tensile tests on bar material. They should be at least as high as the creep-rupture elongation of specimens made from plate. 2) The ratio of the short-time yield strength to the 100-hour rupture strength, both at the same elevated temperature. Data for 400~, 500~, and 600~F are given when available. This ratio is of interest to see whether the alloy promises to permit rupture tests on a notched specimen without a large amount of localized yielding at the notch while the load is being applied. 3) The ratio of the rupture strengths (at 400~, 500~, and 600~F) for rupture times of 10 and of 1000 hours. These numbers furnish a measure of the slope of the curve of stress versus rupture time. Should this slope be too low, the trend of the curve cannot be established with precision from a small number of test points. The -T6 temper of 2219 alloy can be dropped from consideration by its high elongation compared with other materials listed. APM alloy M257 17

has almost as much ductility and has added disadvantages of low relative yield strength to rupture strength and a flat curve of stress versus rupture time. Alloy M430 would seem to be superior on all counts at 500 F, but past attempts to produce plate from that material were rated unsatisfactory. The similar alloy M470 has been successfully rolled into sheet and plate, but only on a limited basis. In contrast, 2219-T81 is obtainable from regular commercial production. No data were available for M470 material at 500~F, nor were creeprupture properties of 2219-T81 alloy at that temperature found. However, by interpolation and extension of the data provided, the tabulated strength ratios seemr to be about the same for the two materials. Its lower elongation is a definite advantage of the powder-metal product in the present instance and its better stability and better isotropy are also in its favor. Mr. Stickley cited unpublished data for M470 sheet showing less than 1000 psi difference in tensile strength at room temperature for the longitudinal versus transverse' I directions. Roughly comparable data for 2-inch plate of an early lot of 2219-T6 material showed an average of about 2000 psi difference in tensile strength with direction in tests at room temperature, 300~, and 400~F. The M470 alloy was finally selected for the present research on the basis of its superiority in meeting the difficult technical requirements discussed above. The material is to be supplied by Alcoa as flat hot-rolled pieces. A-286 Sheet Material: This alloy is being tentatively retained in the program with the hope that existing types of electrical-resistance strain gages and cements will enable measurement of enough strain data in creep-rupture tests on notched plates to permit a reasonably-acceptable analysis. A-286 melted by the vacuum-arc process was obtained in the expectation that such material should be of uniform high quality with a minimum of inclusions which might impart directionality. The hot-rolled A-286 sheet was produced by Allegheny-Ludlum Steel Corporation in a continuous coil 36 inches wide by about 0. 2 inch thick. The finishing temperature of about 18

1700~F at the end of the rolling procedure should introduce sufficient cold work to insure recrystallization during a subsequent conventional solution treatment at 1800~F. In this recrystallized form, A-286 is reported by Allegheny-Ludlum's Brackenridge Quality Control Department to show as little directionality of properties as any of the alloys the company has rolled. Selection of Specimen Thickness: In a long sheet tension specimen with edge notches at the mid-length, use of multiple rows of pins at each end to distribute the pull allows the specimen to be made of uniform thickness over its entire length. But, in an unnotched plate specimen with loads applied through pins at many points along all four edges, such an arrangement is not suitable. To prevent premature failure through loading-pin holes in the latter case, some form of reinforcement rhust be provided around the holes. If raised beads or "bosses" are formed by machining away material from all the rest of the specimen surface, the initial stock must be of the order of twice the final desired thickness of the central test section. With the 0. 2-inch thick A-286 stock readily available from Allegheny Ludlum, this would mean a 0. 1-inch thickness of the test section for unnotched biaxial specimens. Any notched-specimen thickness from 0. 2 inch down is theoretically possible if one can provide sufficient loading capacity for tests on plates of the width envisioned, especially if supplemental tests at room temperature are performed. A specimen thinner than about 1/8 inch would be difficult to machine and might result in "corrugation" of the specimen under load. Design of Notched Sheet Specimens: Adopting the 1/8-inch thickness, and allowing for a limiting pull corresponding to a room-temperature tensile strength of 160, 000 psi for heat-treated A-286 sheet, the specimen cross section at the notch cannot exceed six inches and still stay within the 120, 000-pound capacity of the usual tensile machine. One theoretical stress concentration factor (Kt) between 1. 5 and 2, 0, and one sharper notch (say, Kt between 3 and 4) are to be studied. For this 19

range of stress concentrations in notched flat plates under tension, the least scatter from unavoidable tolerances in notch dimensions should obtain for a ratio of width at the notch to overall width (d/D of Fig. 18 of Ref. 10) ranging from about 0. 7 to about 0. 8. A ratio of d/D = 0. 75 has been adopted for this investigation, with a nominal notch-root radius of 1 6 inches to provide a Kt of 1.8, and a nominal-root radius of 1/4 inch to give a Kt just below 3. 6. Special bolts with a standard taper of 1/4 inch per foot of length and corresponding to a No. 5"taper pin in size are planned to be used to assure equal proportionment of the end pull from cover plates to each loading hole in the ends of the specimen. For the average pin diameter of 0. 283 inch, twelve tapered bolts in double shear would have a total area in shear of 1. 51 sq. in. Neglecting any help from the added shear force due to friction between the cover plates and the specimen surfaces, the shear strength of the pins need be only (0. 75)/(1. 51) = 0. 5 of the strength in tension of the specimen material over its 0. 75 sq. in. minimum section. For a variety of materials studied under creep conditions by Yerkovich (Ref. 11), the shear strength was uniformly 0. 6 or more of the strength in tension. Therefore, little concern need be felt for possible shear failures of the taper bolts, provided the bolts are made of material at least as strong as the specimen alloy. Moreover, stress conditions are not especially critical in the specimen cross section along any line of pin holes except the one nearest the specimen mid-section since the portion of the specimen outside the innermost row of pins is subjected to only part of the total end pull. But, except for whatever support is provided by the cover plates where they extend toward the specimen center beyond the pin connections, the entire pull on the specimen must be borne by the specimen material along the innermost row of pin holes. Mordfin, Halsey, and Greene (Ref. 12) have cited experimental data of others comparing rupture strengths at 400~F of 2024-0 aluminum alloy sheet in tension and in combined tension and bearing from a single pin at the midwidth. The same minimum cross section was subjected to the tensile force in each case and the pin-hole diameter was made 1/3 of the width of the un20

perforated sheet specimen. The plot of average net tensile stress versus time to rupture obtained for the plain sheet was essentially identical to that for perforated specimens in which the bearing load was either 1/2 or 1/3 of the total tensile load. In the notched specimen design of Fig. 1, the portion of width removed by the three holes is considerably less than the two inches reduction of width at the notched cross section so that failure through the line of pin holes should not even be anticipated to occur in a specimen of material which is prone to significant weakening from a stress concentration. As was stated earlier, the grid dimensions of the smallest available strippable foil strain gage for use at elevated temperature are only 0. 07 inch wide by 0. 15 inch long. However, when these gages are to be mounted with ceramic cement, an area of 0. 15 x 0. 25 inch is estimated to be the least that can be allowed for each gage. The planned layout of gages for the first tests (Fig. 1) assumes this limiting spacing along the transverse specimen center line. Duplicate gages, one at each edge of the specimen, will measure longitudinal strains at the very notch root. Readings of longitudinal strains are also provided for from single strain gages at six additional locations across the specimen mid-section. Transverse strains are proposed to be measured at a total of nine positions, of which five will be located less than 20% of the half width in from the notch root. Aside from cost considerations, the need for rapid scanning precludes the use of a large number of gages to survey conditions away from the specimen mid-section. Two sets of gages have been shown in Fig. 1 at a longitudinal distance of one-half inch from the transverse mid-plane. For each set, one gage would be oriented longitudinally, one in the transverse direction, and one each along the 45~ angles from these. The redundant reading of the fourth gage in each group, in combinations with the 45~ configuration, permits use of least-square theory for a best determination of the principal strains from the separate readings. Without trimming their epoxy backing, even the available miniature gages with 1/32 or 1/64 inch gage length for use below 250~F still have roughly the overall dimensions of the area required to mount an elevated21

temperature gage. But by careful trimming of the backing or by permitting the backing from one gage to overlap another gage already cemented in place on the specimen, either transverse or longitudinal strains at room temperature should be capable of measurement at intervals of 0. 1 inch or, perhaps, even as low as 0. 05 inch. Thus, a means of determining elastic strains on a very localized basis still seems possible with a specimen of the size proposed, provided one accepts the need for cooling the specimen under load and applying a new set of epoxy-backed gages at each stage in the test for which the corresponding pattern of residual stresses is desired. (Such a change from one uniform temperature to another will result in no permanent thermal stresses provided all deformations which arise during the temperature change remain within the elastic strength of the specimen material. ) With Eastman 910 adhesive (Tatnall Type GA-1 Contact Cement), a gage can usually be installed, cured, and wired ready for use in less than ten minutes. When a long-time notched-specimen test has progressed to the stage where the most-highly strained gages have ceased to function, a reading of the grid strain will probably be desired in any case. The specimen would be cooled with the load maintained constant, miniature gages applied to the specimen in place, and the elastic strains measured for these gages plus all other good gages as the load was reduced to zero or some other known low value. After use, the room-temperature gages would be stripped off before the specimen was again heated for another portion of the test. (A 5-10 minute soaking in dimethyl formamide permits Eastman 910 cement to be wiped off easily, according to limited investigation reported by the Budd Company. ) Design of Unnotched Biaxial-Stress Specimens: The desire in this portion of the research is for a simple plate specimen with uniform biaxial stressing over as much of the center region as possible and with the principal stresses parallel to the plate's length and width directions. Independent loads all of the same magnitude and direction, applied at many locations along an edge of the specimen, will result in many localized stress concentrations, but these should die out at a relatively22

short distance in from the edge of the specimen. A compound whippletree (shown schematically in Figs. 2 and 3) seems a practical way to achieve equal division of a tensile pull among several n loading points. By its very nature, this arrangement requires 2 loading points, where n is an integer. With only 22 = 4 such locations in each direction, adequate uniforming of the stress pattern would hardly be obtained in 4 the central portion of the specimen. Use of 2 = 16 loading points for each direction would be excellent from the standpoint of stress pattern near the center, but the specimen size would tend to be excessive. The intermediate 3 case of 2 =8 loading locations per side provides an acceptable compromise. The 0. 2-inch thickness of A-286 sheet procured for this study lends itself to the machining of integral reinforcements at the loading points, so that simple pin connections are feasible. However, the most-readily available M470 sheet (donated by the Alcoa Research Laboratories) was just under 1/8 inch thick. For that material and thickness, the multiple loads can more conveniently be applied through pairs of tabs fastened to the M470 sheet by ultrasonic welding. Specimens with Reinforced Pin Holes. The diameter of pins connecting a whippletree to a specimen must be large enough and the pins close enough together to prevent their failure by shear, while the height and diameter of the raised bosses must reinforce the holes sufficiently to prevent failure along a line through them. Eight pins of 5/16 inch diameter (0. 0767 sq. in. cross section) provide (8)(2)(0. 0767 sq. in.) = 1.227 sq, in. of total area in double shear. For a sheet specimen 6 inches wide by 0. 1 inch thick in the mid-section, the shear strength of the pins need be only (0. 6 sq. in. )/(1. 227 sq. in. ) = 0. 489 times the maximum tensile stress to be applied by the lengthwise pull on the transverse specimen section. The corresponding shear strength needed for the crosswise pull on the 7. 5-inch specimen length is (0. 75 sq. in. )/(1. 227 sq. in.) = 0. 612 of the secondary stress level. These numbers predict no difficulty in obtaining suitable pins to supply the largest (longitudinal) principal load, but suggest that eigher the pin material must be stronger than that of the specimen or else the secondary (transverse) stress 23

must be kept slightly below the uniaxial strength of the specimen for the dimensions illustrated. The fillet design of the raised reinforcements around the pin holes (Fig. 2) was selected to use the smallest (1/8 inch diameter) stock size ball end mill. With this fillet, the amount of reinforcing metal adjacent to the pin hole almost exactly compensates for the amount of metal lost as a result of the hole. The groove around each reinforcement has the form of a segment of height h = 0. 050 inch from a circle of diameter D = 0. 125 inch. A table of areas of segments shows that for h/D = 0. 4, A = 0. 29337 D = 0. 004585 sq. in. Consider the section through the line of eight pin holes along the 6-inch end of the specimen. Its area equals the section of a uniform plate 0. 2 inch thick, less the combined cross section of sixteen of the above segments and of eight holes 5/16 inch wide: Net Area = (6")(0. 2") - (16)(0. 0045851) + (8)(5/16")(2") = 1. 20 - 0. 57 = 0.63 sq. in. For the section through the centers of the ten holes total along the side of the specimen, the net area is 1.50 - 0. 72 = 0. 78 sq. in. According to the findings of Ref. 12, the small (0. 03 sq. in) surplus of cross section through the pin holes compared with the section through the specimen center line should prevent preferred failure through the line of holes. Should this expectancy fail to materialize, the uniform thickness of the central portion of the specimen can be reduced as needed without other change in the specimen or the loading fixtures. Biaxial Specimens with Welded Tabs. After negotiations had been opened with the Aluminum Company of America for them to use their research facilities to roll some M470 alloy to our desired special thickness of 1/4 inch, the Company offered to make immediately available without charge some 0. 120-inch thick sheet they had on hand for evaluation in their laboratories. The material was sufficient to meet the needs of the present study and was almost exactly the thickness desired for the notched specimens. 24

Therefore, consideration was given to ways of using the thin sheet for the unnotched biaxial-stress specimens. The most apparent answer was to apply the loads through extension tabs of a stronger material, with the tabs to be brazed or welded to the M470 sheet. Of the possible welding methods, the ultrasonic technique used by Aeroprojects, Inc. seemed most suited to aluminum-alloy sheet. Mr. H. L. McKaig of that company stated that dissimilar metals are readily joined by the ultrasonic method provided the hardness levels of the two materials are not too different and provided the pieces to be joined are not too thick. He suggested a maximum thickness of about 0. 025 inch for the welded portion of tabs to be made from steel or nickel-base alloy. Some available 0. 065-inch thick sheet of 17-7PH stainless alloy in the soft "A" condition was selected for tabs in a series of trial welds because its strength at 500~F is several times that of the M470, although the two materials differ but little in hardness. Five strip specimens of the M470 aluminum sheet were welded without charge by Aeroprojects, each with a pair of 17-7PH tabs joined to the strip at one end by four overlapping spot-type ultrasonic welds in an area about 3/8 x 3/8 inch. They reported shear strengths of 1750 and 1420 pounds at room temperature for individual tabs on another specimen of the M470 material. Tests at the University of Michigan provided the additional data: SHORT-TIME TENSILE TESTS Temperature Load at Failure Mode of Failure Stress in M470 (~F) (lb.) of Weld Joint at Failure, psi Room 1840 One tab sheared off. 30, 750 500 1660 M470 strip ruptured. 28, 100 500 1580 One tab sheared off. 26, 650 500 1150 Weld failed in tab, but the 19,250 adhesion was sufficient to lift base metal out of the M470 strip. 25

CREEP-RUPTURE RESULT Temperature Stress in 1/2-in. wide Rupture Time Mode of (~F) M470 strip, psi (hr) Failure 500 16, 000 1.9 M470 ruptured These measured strengths were probably low due to unequal loading of the two tabs. For final tests under biaxial loading, suitable fixtures would insure more-exact alignment during welding and load application. With these precautions and/or use of two rows of three or more weld spots in a line along the axis of pull of the tabs, failure should always occur in the base metal. Fig. 3 shows the specimen as tentatively planned to include the modified tabs. 26

BIBLIOGRAPHY 1. Howard R. Voorhees and James W. Freeman, "Notch Sensitivity of High-Temperature Alloys", Wright Air Development Division, WADC Technical Report 59-470, March 1960. 2. Howard R. Voorhees and James W. Freeman, "Notch Sensitivity of Aircraft Structural and Engine Alloys, Part II. Further Studies with A-286 Alloy", Wright Air Development Center, WADC Technical Report 57-58, Part II. January 1959. (ASTIA Document No. 207, 850). 3. I. L. Mirkin and I. I. Trunin, (An Investigation of Creep and Failure of Steel in the Zone of Stress Concentration), Trudy Tsentral'nyy Nauchno-Issledovatel'skiy Institut Tekhnologii i Mashinostroenii, 79, pp. 24-35, (1957). See Translation No. W-8321 of Wright Air Development Center, DCS/ Plans and Operations, Technical Information and Intelligence Division, Intelligence Branch (WCOSN). 4. F. Garofalo, "Creep-Rupture Behavior of Notched and Unnotched Specimens of Type 304, 316, and 321 Austenitic Stainless Steels", Proceedings, American Society for Testing Materials, 59, ppi 957-982, (1959). 5. W. F. Brown, Jro and M. H. Jones,'."Strain Analysis by Photogrid Method", Iron Age, 158, No. 1, pp. 50-55, (Sept. 12, 1946). 6. N. A. Borodin and S. V. Serensen, (On Long-Time Static Rupture in a Zone of Stress Concentration), Izvestiya Akado Nauk SSSR, OTN, Mekhanika i Mashinostroenia, 1960, No. 4, pp. 65-72. See translation, Appendix A of this report. 7. F. Zandman, "Photoelastic-Coating Technique for Determining Stress Distribution in Welded Structures", Welding Journal, 39, No. 5, pp. 191S-198S, (May 1960). 8. A. Vinckier and R. Dechaene, "Use of the Moire' Effect to Measure Plastic Strains", Transactions, American Society of Mechanical Engineers, Vol. 82, Series D, Journal of Basic Engineering, No. 2, pp. 426-434, (June 1960). 9. R. Hill, "The Mathematical Theory of Plasticity", Oxford University Press, London, (1950). 27

10. Ro Eo Peterson, "Stress Concentration Design Factors", John Wiley and Sons, Inc. New York, 1953. 11. Luke A. Yerkovich, "Investigation of the Compressive, Bearing, and Shear Creep-Rupture Properties of Aircraft Structural Metals and Joints at Elevated Temperatures", Wright Air Development Center, WADC Technical Report 54-270, Part IV. (ASTIA Document No. 155570), May 1958. 12. Leonard Mordfin, Nixon Halsey and Gary E. Greene, "Investigation of Creep Behavior of Structural Joints Under Cyclic Loads and Temperatures", NASA, Technical Note D-181, October 1959. 28

Table 1 COMMERCIALLY-AVAILABLE STRAIN GAGES TO MEASURE LOCALIZED STRAINS Manufacturer: Budd Budd BLH Budd BLH Type No.: 1X1-32A 1X1-64 FA-03-12 S-710 FNH-06-12-B Alloy Designation: Advance Advance Constantan "700 Alloy" Nichrome V Max. Temp. (~F) Static Tests: 200 200 250 1200 1000 Dynamic Tests: 250 250 250 1700 (5)1400 Gage Length, in.: 0.031 0.015 0.04 0.0625 0.06 Grid Width, in.: 0.035 0.031 0.06 0.125 0.07 Overall Dimensions Without Backing Length: 0.160 0.022 0.09 0.218 0.15 Width: 0.035 0.127 0.06 0.07 With Untrimmed Backing Length: 0.260 0.122 1/4 Width: 0. 135 0.227 3/32 min. Nominal Resistance, Ohms: 60 65 120 140 120 Nominal Gage Factor: 2.0 1.9 2.1 2.6 2.2 List Price: $5. $10. $10. $9. $6. Comments: (1) (1,2) (1) (3,4) (3) 1) Epoxy-backed gages - can be installed in 15 min. or less with Eastman 910 cement. Available with self temperature compensation or for high elongation. 2) The stated "width" will be in the direction of the specimen length when this gage is used to measure transverse strains in the notched specimens. 3) Strippable foil gages. 4) Could be obtained on special order with a grid width of 0. 0625 inch, for an extra charge of $350. 00 for the lot. 5) With AL-P1 or AL-PBX cement.

Table 2 COMPARISON OF SOME PROPERTIES OF CERTAIN ALUMINUM ALLOYS Tensile Test Alloy Nominal Al 0 Temp. Elongation Ratio: Ratio: Designation Content, % (~F) %/4 Diam. Y.S./lO/100 hr. R.S. 10 hr. R.S./lOOOhr. R.S. Comments M430 APM 14 400 7 1.30 1.19 a, b 500 7 1.50 1.47 600 6 1.44 1.21 M470 APM 10 400 - - 1.15 a,b 600 8 1.36 1.33 M257 APM 5 400 16 1.06 1.12 b, c 500 17 1.14 1.15 600 13 1.25 1.30 2219-T6 0 400 23 1.12 1.22 d 500 25 1.29 1.43 600 26-38 1.78 1.85 ZZ219-T81 0 400 15-18 - - e,f 500 17 (1.41) (1.43) 600 18-28 a) Made from imported aluminum powder produced in Switzerland. b) Data from experimental extrusions. c) Made from powders produced in the U. S. by Alcoa. d) 2219-T6 tensile properties for forgings. e) 2219-T81 tensile properties for sheet and plate, transverse to the rolling direction. f) Creep-rupture properties of 2219-T81 at 500~F assumed to be the same as for 2219-T6.

~ L ------------— 8" 0.7 NO. 5 STD. X 6-^q~ ~~~~) Q~~ ~ ~~ O~ O~ ( TAPER 0 -0.5 1.75 1.0 0 0 1.0 — ------ 2.0 1.0 1.75 - 2.259.0 18" — 10.50 0.50 -75 0'.325 NI - Ki3.6 80p.C.9 0.075 0.175 0:32 ED.(9 0.50k r 0.725 1.0 1.0 2.0 2.0 1 1.0 2.85 3.0 Fig. 1 - Design of Notched Sheet0 - Fig. 1 - Design of Notched Sheet Specimen, Showing Strain-Gage Layout.

REAM HOLES TO FIT 5/16" DOWEL PINS. 3/8 + + (ID Q - - F — J43/4 7.5 38 - ^~~~~~~~~~~~~~~~1/16 R_________ ___ ___ _ 0. 100 0.2 ______ r^\ I 1 i^\ t t Fig. 2 - Unnotched Biaxial-Stress Plate Specimen with Reinforced Pin Holes, with Schematic Representation of a Whippletree Arrangement to Apply Primary and Secondary Tensions P| and P2.

PI 4-|5/6"6 AM l _____ ____ ultrasonic-weld spots _ O0 _ 0.375 0.025 in. thick Pairs of 17-7PH tabs A ~ ~-. from 0.065 i n sheet P - - / o -0.758-0.80o — —'-P2 M-470 sheet specimen - 1.55 -.25 Section A-A I I J L 4 4~~~~~~~~5/16 DIAM. Six overlapping II ultrasonic-weld spots 0Q375 0.025 in. thick Pairs of 17n-TenPH tabs offrom 0.065 in. seet approx. 0.12 in. thick 7.5" Section A-A

APPENDIX A ON LONG-TIME STRESS RUPTURE IN A ZONE OF (STRESS) CONCENTRATION By N. A. Borodin and S. V. Serensen (Moscow) Izvestiia Akademii Nauk SSSR, Otdelenie Tekhnicheskikh Nauk, Mekhanika i Mashinostroenia, 1960, No. 4, pp. 65-72. A Translation from the Russian. Translated by H. R. Voorhees The University of Michigan Ann Arbor, Michigan

ON LONG-TIME STRESS RUPTURE IN A ZONE OF (STRESS) CONCENTRATION To analyze the condition of long-time static rupture in a zone of (stress) concentration, it is necessary to obtain data on the distributipn of deformation and stress during the loading process. Within elastic limits, the analytical solution of H. Neuber (1) for stresses in the vicinity of a notch characterizes only the initial stress condition for a specimen in long-time service at elevated temperature. With the appearance of plastic deformation, redistribution of stress occurs. At present, to obtain a set of analytical results for a problem on stress conditions in an area of concentration under creep (2, 3), experimental verification of the derived solution can still cause trouble in the absence of a method to analyze deformation patterns during the creep process. Development of experimental methods to investigate stresses, in this case, permits one to study the quantitative aspect of stress concentrations and, in particular, to evaluate the notions of sensitivity to concentrated stresses commonly used in practice to evaluate materials. In the work under consideration, an analysis is derived for deformation and stress conditions originating in the zone of concentrated stresses around a hole in a thin sheet undergoing creep. The investigation of deformation conditions in the plastic region employed the widely-used method in which grids are applied on the specimen surface in one way or another. This grid method has been used in a number of investigations (4, 5) A-1

of deformed states in the concentration zone of plates pulled beyond the elastic limit. To analyze deformation and stress changes with time by the grid method, it is necessary to measure creep deformations over short time intervals during which the accumulation of deformation will be small. Therefore, in the case of the grid method, one must insure sufficiently-accurate measurement of relatively-small deformations. For this reason, the grid applied to the surface of a specimen must possess temperature stability. To analyze deformation at the stage of specimen fracture, the grid must maintain satisfactory legibility to the end of the test. Existing methods (4, 6) are for the most part applicable to determination of large plastic deformations and do not satisfy the demands of the problem now before us. The present work uses the method of microgrids suggested by G. I. Gudkova, N. E. Karskii, and G. I. Sobolev (7) for study of microplasticity of alloys. A net is applied by scratching with a diamond pyramid indenter used for measuring microhardness. The main disadvantage of their method appears to be that a series of sharp scratches is built up on the surface of the specimen, creating localized stresses in a shallow surface layer of metal. It is necessary to note that the depth of the scratches is only of the order of a micron. For plastic studies of metals, particularly at elevated temperatures with relaxation of stresses, the local stress level for each scratch has no real significance. The method of microgrids answers the requirements of the present problem for exceptional accuracy in grid application. The precision of a grid may be significantly increased, as is shown in the present work, if one lays it out with a PMT-3 comparator instrument for which the precision is 0. 3 micron. The comparator instrument PMT-3 used allows one to obtain precise grids with a base from a few microns to 1. 5 mm, maintained with an accuracy to 0. 3 micron. The experimental part of this research was carried out on flat specimens with a (central) hole and made of the aluminum structural alloy V-95. A-2

The plate dimensions adopted (30 mm width, 1 mm thickness, and 6 mm hole diameter) allowed the specimens to be considered infinitely-wide plates in a state of plane stress. Experiments were conducted on a DST-5 machine at a temperature of 200~C. Measurements of deformation with the same PMT-3 instrument used to draw the grid guaranteed an accuracy for the 0. 4 mm base up to 0. 05% in deformation units. An essential factor for accuracy in a test is the choice of the base for measuring deformations. Since stress conditions vary in passing from the edge of an opening to an adjacent zone, measurement of deformations necessarily is conducted on as small a base as possible (yet not less than the grain size)o However, realization of this condition requires very accurate measurements. In available studies (5, 8) on this problem, it is demonstrated that for a base value of 20% of the radius of the opening, the relative error in comparison with a zero base is about 1. 1%. In the work cited, for a 3 mm hole radius and a base of 0. 4 mm, the error introduced by the base size was negligibly small. Periodic measurements of specimen deformations were taken with the equipment during equal time intervals of 20 hours. (At the start of the experiment, the specimens were also measured at 3 hr.) The initial maximum stress slightly exceeded the yield point, but the stress during unloading of the specimen never caused permanent deformation. For the alloy investigated, interruption of the tests was not reflected in the character of the deformation. In Fig. 1 are shown curves of creep with stress Co (Kg/mm ) as a parameter, obtained from experiments on plate specimens of alloy V-95 at t=200 ~C. In particular, curves for or = 8, 9 and 11 Kg/mm were obtained in experiments interrupted each 20 hours. It is evident that, for this method of testing, only plastic deformation of creep was measured. The elastic portion of deformation is relatively small and must be studied by determining stresses. Measurements were made in the range of uniformly-distributed deformation (i. e., up to the appearance of local reduced thickness and holes in the vicinity of the opening). A-3

Distribution of principal strains for the minimum section of the plate is presented with time as a parameter in Fig. 2, showing appreciable concentration of deformation in the vicinity of the hole. The rate of accumulation of creep strains is considerable in the early hours of the test, and decreases with time. Thus, if in the first 20 hours deformation 81 at the edge of the hole is 0. 6%, then between 80 and 100 hours its increase was found to equal only 0. 2%. In Fig. 3 is shown the measured concentration of creep deformation /rfi in the most-highly stressed point at the edge of the hole. The creep deformation corresponding to the nominal stress in a uniform-stress condition is taken as the nominal deformation. The high degree of initial concentration of deformation falls off in the first stage of the test in connection with relaxation of the stress, then remains nearly constant for a long time. With onset of third-stage creep in the specimen, local thinning of the cross section develops, which gives rise to a stress rise and a renewed increase in the rate of deformation for conditions of constant load on the specimen. As is known (based on proposals of N. M. Belyayeva (9) ), the relationship between stress and deformation in calculations of creep for plane-stress conditions may be expressed in the form: = x- (-.- l:) + - (ax-am) V - (ay- Max) + 2- (yV- am) (1) 2 (1+ -t) ^TX E (l+P) t, Here Om = 1/3 (x +- ay) is the average nominal stress and ~ is a function characterizing creep (the creep modulus). The shape of creep curves in the stage of steady creep rate gives rise to a relationship between A-4

creep rate and stress: v = COP For solution of the stated problem, let us consider a small interval of test time At during which with a certain approximation one may assume the shear-stress intensity and, therefore, also the creep function. Such an approach to solution of the problem, even though it introduces a negligible error, still permits convenient application for practical development of an expression when the given problem is considered only for steady-state creep: 3P ~ 2 — )1 -CG-iP- At (ti= -f aX2+ ay2- axay + 3rx2) (z) where Ti is the shear-stress intensity. Accuracy of the solution by stages depends essentially on the choice of size of the time interval At. Diminution of the length of the stages is associated with reduced accumulation of creep deformation in that time and with increased errors in its measurement, which leads to errors in stress determinations. For determination of the optimum duration of time interval, tests were conducted in a series of experiments with deformations measured during 10, 15, 20, and 40-hour increments for a common test time of 120180 hours. The most acceptable of the given cases proved to be the 20-hour time. To determine stresses corresponding to the measured deformations, let us examine some transformations of expressions (1) and (2), taking account of characteristics of the present problem. For an infinitely-wide thin plate (Fig. 4) in a state of plane stress, the initial elastic stress for cross section AB establishes itself according to A-5

known expressions: S I a'2 \ S( 3aU a2 = (1- - r 2 ( + 4 2 Or 2 r4 r2 - Oo 2 r2 )+ 2 (1 + 3- (3) bH, /,, a2 \, ~y /., 3a*\(3) Tr0 = 0 Stresses Or0 and Q00 are principal values. The intensity of shear stress may be written in the form: 3i -Q- V /l2 + 022 7- 102 and the function characterizing creep assumes the simpler form: p-1 (4) 4 = 3CG (a12 + oa2 - 01a2) 2 At ( The relationship between stress and creep deformation may be presented as 81 =6% (2a1- 02), = S (202 -- ) (5) Substituting into equations (5) the known creep function from (4), we get: =- -1 CAt (a12 - 1a + oa2) 2 (2a, - a2) 1 P-21 82 -- c\t (oi2 -C 1 + o2)"2 (22 - oa) where 81 and 82 are the increments of creep deformation in time At. Solving this system of equations with respect to stress, we obtain the formulas for our calculations. For the maximum principal stress, the derived expression will assume the following form: 1-p 2 (2 i+ -2) [ - 22 + gi (2s+ 81\2l 2 l -- -bC/t L1 2sl — 2 \ eA- 82/) (6) A-6

Creep constants C and p needed for the solution are determined experimentally from creep tests in uniaxial tension (Fig. 1) in the range of small elastic-plastic deformations for which it may be established that a functional relationship between intensity of shear stress and intensity of shear strain does not depend on the type of stress state. After determining the rate of steady-state creep from the curves (Fig. 1) for a pair of stresses, the values of the creep constants were found to be C=3. 2xl 31 and p=8. 55. By the stated test methods and treatment of the data, a series of curves results for the distribution of stress across the specimen section (Fig. 5). These curves are plotted with a time parameter to permit analysis of the stresses during the creep process. In Fig. 6 are shown a curve for relaxation of the principal stress for a point toward the edge of the hole and a curve of variation of stress at the edge of the plate. As is seen from the figures, the fastest stress relaxation is in the first part of the test, which is explained by the high initial stress gradient and the consequent significant inequality in creep rates in neighboring areas. Conforming to the relaxation of stresses, differences in creep rates diminish and, consequently, the rate of stress redistribution decreases. The results presented show that complete leveling of the stresses does not occur; the concentration of stress lessens somewhat, but remains detectable during the entire test. The curves of stress distribution (Fig. 5) are plotted in the range of comparatively-uniform deformation -- up to the start of local thinning at the edge of the hole. In this range, the third principal strain E is small and barely enters into the results (the nominal stress may be considered practically constant. ) In the period of development of thinning around the contour (of the hole) the influence of c becomes substantial; at the edge of the hole, there is a uniaxial stress condition, but biaxial tension exists in an adjacent area of the plate. With relaxation ofor 1, the stress gradient significantly lessens (Fig. 5) and the rate of decrease of cross section thickness in an area situated at A-7

some distance from the (hole) periphery rises more than in the area immediately adjoining the periphery. All this brings about a minimum section thickness that is found somewhat removed from the edge of the holeo In Fig. 7 is shown, at a magnification of 40X, the transverse cross section of a specimen after formation of a hole near the (original) opening. Significant decrease in section thickness of the specimen in regions adjacent to the periphery of the opening naturally leads to additional redistribution of deformations and stresses. In Fig. 8(a) is shown the surface of a specimen with a deformed grid at the start of appreciable local deformation. With the development of local thinning, the creep rate noticeably increases in a band situated at a short distance from the edge of the opening and this band's deformation increases more than in the band at the periphery, which is readily visible in the distortion of the grid lines (Fig. 8(b) ). Such redistribution of deformation permits one to suppose that fracture initiates not at the periphery of the opening but at some distance from it in the zone of maximum deformation. To verify this proposal, the specimen rupture process was investigated. Specimens were tested in a specially-designed furnace permitting them to be photographed during the test. Observation and photography of the specimen was done with the aid of a microscope with 40X magnification and a microphotograph head MFN-1 under illumination from the -opposite side of the furnace (through an opening for the thermocouple) permitting observation of the start of formation of a through crack (Fig. 9(a) )o In Figures 9(b) and 9(c) are shown the passage of the crack to the edge of the hole, its opening up and further growth in the specimen interior. It is knrown that creep strengths for short-time tests on a perforated plate specimen of alloy V-95 at elevated temperature are higher than for smooth specimens. This raises the question whether the insensitivity is retained for long-time tests in the presence of a hole. To clarify this question, experiments were conducted on plate specimens with holes and without holes for several levels of nominal stress. A-8

In Fig. 10, curve 1 correlates the start of fracture in specimens with a hole, curve 2 (solid line) correlates complete fracture of specimens with a hole, curve 3 smooth specimens, and curve 4 the maximum stress, Uo, in Kg/mm at the start of fracture of specimens with a hole. These test results show that creep-rupture of specimens with or without a hole displayed nearly identical criteria for complete failure. Consequently, it should be possible to reach a conclusion about insensitivity of an alloy with a stress concentration under elevated-temperature service or about capabilities for evaluating strength in terms of nominal stresses of plane structural elements with perforations without allowing for (stress) concentrations. Analysis of the results obtained shows that this conclusion is of provisional character. In specimens with a perforation, the development of localized deformation and abrupt reduction in cross-section thickness in the area of the hole set in considerably earlier than complete fracture. The test time until start of specimen thinning is about 50% of the time until complete fracture. Earlier start of local deformation is explainable if we turn to the diagrams showing deformations and stresses (Figs. 5 and 2)o The metal in the stressconcentration region deforms at faster rate than the remainder of the cross section. Appreciable plastic deformation of this zone soon develops. But, since this zone is comparatively small, its increase of deformation does not determine fracture of the specimen as a whole. Development of localized thinning in the vicinity of an opening is inadmissible in many structures in that besides disturbing the nature of the assembly it facilitates chances for rupture from fatigue, repeated static loads, etco The test results indicate that as a criterion of limiting conditions for equally suitable designs one can use the start of localized deformation in zones of stress concentration. From the rupture-strength curves of Fig. 10 can be seen that strength corresponding to a criterion of initiation of localized deformation in a specimen with a hole proves to be lower than for a smooth specimen. Thus, for a base of 100 hours, the nominal stress leading to formation of local deformation in a specimen with a hole (curve 1) is 12Z0 A-9

less than the stress giving rise to rupture of a smooth specimen (curve 3). At the same time, the curve for complete fracture of a specimen with a hole (curve 2) passes through on a level with the rupture curve 3 for smooth specimens o CONCLUSIONS 1o Concentration of creep deformation in the area of a hole in a plate decreases somewhat at early times, but remains high during the course of the testo The maximum level of deformation is attained in a zone situated at some distance (0, Z - 0. 3 mm) from the edge of the hole Z2 In the concentration zone, considerable stress relaxation is observed but a stress concentration persists substantially up to fracture of the specimen. The fastest rate of stress relaxation is in the early hours of the test and the rate of stress redistribution dies out with reduction of the stress gradient. 3. Rupture under plane stress conditions of a plate with a hole begins at some distance from the edge of the hole in a section with reduced section thickness. 4. Formation of local deformation in the area of the hole starts noticeably before complete rupture of the specimen, which indicates existence of conditions for a method to allow for stress concentrations in respect to load-carrying capacity. Nominal stress for the start of localized deformation in specimens with a hole is lower than rupture strength in smooth specimens for the ductile aluminum alloy studied. Received April 22, 1960, A-10

BIBLIOGRAPHY 1. Ho Neuber, (Stress Concentrations), Gostekhizdat, 1947. 2. L. M. Kachanov, (Some Questions on Creep Theory), GITTL, 1949. 3. A, P. Filinnov, (Influence of Creep on Stress Concentrations in Plates with a Circular Hole. Investigation into Questions of Stability and Strength), Izdo AN USSR, Kiev, 1956. 4. T. Ko Zilova and Ya. B. Fridman, (Investigation of Deformation Conditions by Means of Rolled-on Grids), ZhTF, 1949, Vol. XIX, No. 3. 5. V. S. Zhukovskii, (Stress Distribution in Notched Bars Under ElasticPlastic Deformations), Izv. AN SSSR, OTN, 1957, No. 7. 6. W. F. Brown, Jr. and M. H. Jones,'Strain Analysis by Photogrid Method", Iron Age, Vol. 158, No. 11, (Sept. 12, 1946)o 7. G. I. Gudkova, N. E. Karskii, and G, I. Sobolev, (Investigation of Microplasticity in Commercial Alloys with the Aid of Microgrids), Zavodskaya Laboratoriya, 1949, Volo XV, No. 7. 8. E. Siebel and A. Hosang, (Investigation of the Plastic Reinforcing Effect in Notched Bars), VDI Zeitschrift, 1954, No. 4.. (In German). 9. N. M. Belyaev, (Application of Plastic-Deformation Theory for Calculations in Design for Creep at Elevated Temperatures), Izv. AN SSSR, OTN, 1943, No. 7. A-1i

!% I 1 I i {y l 1 111l l i 17 15 14 15 Ot13 12.5 12 11.5 /1 20 40 60 80 r. hours Fig. 1 C/5 5O SO 40 80 Z, hours 0.8 Fig. 3 so 20 25 3 Time hr.! V//f I''' s-6. 4 0.4/ -x-rX- 40I S -.. —- 0 ---- 0= 80 I 0=0o0' II.. _ -j Q8~Eo - ~-Z —I20,:, Fig. 2 Fig. 4 Fig. 4

_/'Z/-H2 Time, hr. S64. Kz/MM2 * t=3 f t 0 r=2 /^tl A rz g /n'\ I Tr! i Nominal Stress 4 - 0 10 IS 20 25 3 Fig. 5'5'0'Nominal Stress 0 40 r 1 hours 5 o 20 50 00, Fihoursg Fig. 10