ae ~ THES BS REVERSE TORSION TES . GORTON a) Hn mae S a) aeey ASG Wel A ok R. O. KNUDSON m= UN | KX og - ewe 19 (25 PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES retum on or before date due. DATE DUE DATEDUE DATE DUE ae —{— === == SS Is An Affirmative Action/E qual Opportunity Institution Design and Construction of a Reverse Torsion Testing Machine A Thesis Submitted to the Faculty of MICHIGAN AGRICULTURAL COLLEGE by ae oe et . Jo W. T. Gorton 7 R. 0. Knudson Candidates for the Degree of ‘Bachelor of Science June 1916. THESIS ---- Preface.---- aeees Historical. The following extract is taken from the eleventh edition of Merriman's "Mechanics of Materiale®. "The first experiments on the strength of materials were made on the rupture of beams of timber. A picture in Galil- eo's Discorsi (Leiden, 1638), shows a cantilever beam pro- jecting from a wall and loaded with a weight at the free end, and it was probably from experiments of this kind that Galileo was led to the conclusion that the strength of rectangular beams varies as the squares of their depths. During the ecighteenth century experiments were made in France on tim- ber in flexure and tension, only questions of ultimate strength being considered, while the elastic limit was unrecognized. Hooke's experiments on springs, from which he deduced the law of proportionality between stress and elong- ation had, indeed, been announced in 1678, but it was not until 1798 that Girard made the first series of experiments on the elastic properties of beams. Nearly a quarter of a century later Barlow, Tredgold, and Hodgkinson experimented on timber and cast iron, both in the form of beame and col- umne; their methods although now seemingly crude and defect- ive, are deserving of praise as the first of real practical value. "In 1849 was published in London the'Report of the Comm- ission on the application of Iron to Railway Structures’, 36433 2 which may be regarded as the landmark of the beginning of the modern methods of testing. The immediate result of this report was the decision of the English board of trade that the factor of safety for cast iron should be twice as great for rolling loads as for steady ones, while throughout Europe and the United States it aroused marked impetus in the sub- ject of testing materials. "The first testing machines in the United States were those built by Wade and Rodman in the period of 1850 to 1860 for testing gun metal. About this time the rapid introduction of iron bridges led to experiments by Plympton and Roebling. Prior to 1865 apparatus was built for his special work by each experimenter, but in that year Fairbanke put upon the market the first testing machines for commercial work. A little later the machines of Olsen and Riehle for tensile, compressive, and flexural teste were introduced, and have since been widely used. The machine devised by Emery, soon after 1875, is a very precise apparatus which is used in large laboratories. Large machines for testing eye bars have been built by bridge companies, and numerous testing laboratories now contain apparatus for every kind of work. eee eees "Tensile tests are the most common, *****. Nearly all tensile machines may be also used for compressive tests, and also for the flexural testing of short beams. **** "Commercial teets of materials are rarely made under shear- ing and torsional stresses. Thurston in 1870 devised a torsion 3 machine for emall specimens, and the torsion machines of Oleen and Riehle, which are found in the laboratories of most engineering colleges, prove very serviceable for illus- trating the phenomena of twisting. Impact machines have been built for special investigaticns, but the only one on the market is that of Keep, which is designed for test bars of cast iron. Fatigue or endurance tests, which subject the specimens to alternating stresses for long periods of time, are made on special machines.*® It is for the investigation of these alternating or fatigue teste that the machine considered in this theses is designed. Since the publication of Merriman's text in 1914, or rather since the preparation of the material for this publication, more has been done in these directions than the extremely meager degree of progress cited above. It is becoming more and more recognized that, while the usual tensile and compressive tests are undoubtedly of great value in showing the behavior of materials under steadily applied loads, still, this does not establish an infallible criterion for the determination of relative merits. More should be known of the behavior of materiales when subjected to intermittent, repeated, or reverse stresses, especially when these stresses are similar to those ocourring in materials under actual working conditions. Since in many phases of practice stresses of this nature are the rule rather than the exception, it is very wet 4 desirable that data be secured bearing on the effect of such etresses on the materials used in constructicn. Following are extracts taken from the American Machinist, and written by G.B.Upton, Assistant professor of experimental engineering, Cornell University, and G.W.Lewis, Assistant professor of experimental engineering, Swarthmore college. "The Fatigue Failure of Metals*- "Kxamination under the microscope of the internal structure of any of the engineering metals shows that the metal is an aggregate of an immense number of minute crystals. The separate crystals in a steel, for example, Vary from a maximum diameter of 0.01 in. or 0.08 in. down to around 0.0001 in. and even smaller, sometimes being too small for even the highest powered microscope to make them visible. The external shapes of these crystals are irr- egular, being determined simply by their interference with their neighbors. At their bounding surfaces the crystals are firmly and strongly interlocked with each other; not between them along the boundaries, merely pulling the crystals apart. "The break of the metal, then whether it occurs at the end of a single loading, or at the end of many repeated loadings is a break through the crystals. The study of the nature of the break of the metal resolves itself into the study of the Way in which the separate crystals may be broken. ******* "The way in which a crystal breakes is determined by the 5 nature of its component particles and the pattern in which they are put together. ‘***** No other breaks than these two (tension and shear) are possible. There is one essen- tial difference between them. The tension break is a complete break from its beginning; the parts are separated. The shear may make one layer slip over the next a little way, and then cease. The crystal is not yet broken, but merely permanently distorted. The particles along one side of the shear slip plane still have hold of the particles on the other side of this plane, though not the same particles as before. The crystalline structure would not be hurt in the least by such @ slip, were it not that in that in slipping past each other the layers interfere slightly, and a little debris or dust of particles torn out is left between the layers that have slipped. This amorphous material, formed in the slip planes, is peculiarly related to the chemically identical material from which it has been torn. In the engineering metale the amorphous material is somewhat (sometimes even decidedly) harder and stronger than the crystalline. This results in a complicated reaction of the shear crystals to shear loading. "The crystalline structure starts to slip or yield along some plane of weakness lying near to the direction of the maximum intensity of shear stress. As the yield progresses, the formation of amorphous material makes it increasingly difficult for the slip to continue. It is easier to start a new slip along an adjacent parallel plane. This in turn 6 increases its resistance; a third slip starts, and so on, until the orystal has yielded to the stress by slipping an infinitesimal amount on each of a great number of slip planes. "These little slips are all permanent, persisting after the removal of the load which caused them. We say the crystal shows plastic yield to loading, and comment on the harden- ing and strengthening of the material by cold working. ***** "We may now study the loading of the metal as a whole, remembering that it is an aggregate of a great number of crystals. In the cast metals the crystals have about the same dimensions in all directions through the piece, save that at or near the surfaces of the casting they are longer and per- pendicular to the piece. Away from the surface there has been no tendency for the crystals to grow in one direction more than another, or to arrange the alignment of their in- ternal patterns in one direction more than another. ®In the worked metals the rolling or forging has tended to make the crystals somewhat longer parallel to the length and surface of the piece, giving a semi- fibrous structure; but again there is little else but chance in the alignment of the crystal patterns with regard to the dimensions of the metal as a whole. "Consider now the ordinary tension test, where the loading process progresses till the rupture occurs in a single applica- tion. All the crystals are pulled out simultaneously and fairly equally. 7 Each crystal so yields as to become much longer in the direc- tion of the pull, and thinner, perpendicular to the pull. With a material already semi- fibrous this results in the familiar "fibrous" or "silky" fracture. "In the cast metals the stretching rarely goes so far as to give the ‘fibrous appearance to the fracture, for it has to overcome too much of a handicap in the initial arrange- ment of the crystal dimensions. ******! "What are the laws governing the number of applications of @ given kind of loading and stress intensity required to produce failure? Frankly, we do not know. No one has been able as yet to tell us the relation between the results of the conventional tension test and the fatigue tests. There is no accepted and standard method of fatigue testing. Wohler's tests, over a generation old, are not yet explained. In this field of experimental engineering we are but on the threshold of knowledge. "Something of the probable form of the laws of fatigue failure we may perhaps derive from the study more in detail of the way in which repeated loading breaks down, one after another, the crystals which compose the metal. We may best study the steels, both because of their importance, and be- cause they are the most complex in structure of engineering metals; hence the study will be of the most general form.*** "When the load applied to a piece of metal is very small, the internal condition of the metal approximates most closely 8 to equality of deformation from crystal to crystal. Whether the stresses are similarly equal depends upon the stiffness of the different crystals. In the steels the stiffnesses are nearly equal for all orystals at firet, and we have fair equality of stress as well as of deformation from orystal to crystal. In metals other than steels the stiffnesses frequent- ly vary from crystal to crystal, so that with emall loads the condition ia one of equality of deformation with stresses varying from crystal to crystal in proportion to their stiff- Ness. "As the load increases, these conditions change radically. If no crystal broke before the rest and ceased to be useful in carrying the load we should approach at high loads a con- dition of equality of stress from crystal to crystal, with variable deformation. For at some stage of the loading the elastic limit of the ductile type of crystals in the struct- ure is past, and they begin to give plastic yield, and subse- Quently must yield largely to increase their stresses. The soft ductile crystals cannot transmit to the hard crystals bedded among them any greater stresses than the soft crystals carry. "Certain other factors must not be forgotten. To some ex- tent the shape and size of the crystals and the way they come together at their boundaries influences the stress in- tensities that they can transmit to each other. The smaller the separate crystals in average size the more uniform are 9 the stresses from orystal to crystal, and therefore the stronger the material in the engineering sense of the strength of the piece as a whole. It is perhaps true that surface ten- sion effects make a very small orystal intrinsically stronger than a large crystal of the same material. "There are residual stresses, from one crystal to another, or between different parts of the piece, coming over from the previous history of the piece. Such residual stresses come from cold working, heat treatment, etc. Cold working tends to elongate the outer parts of the cross—- section of the bar more than the inner parts: consequently it leaves the outer parts with compression stresses, and the inner parts with tension stresses. ******* "There is a time factor between shear stress and shear def- ormation, or slip. This time factor depends partly on the fact that the slip itself is not quite instantaneous, and still more on the fact that after slip ocours in one crystal the distribution of stresses from that crystal to others is al- tered, which may cause slip somewhere else, and so on through an appreciable time interval of internal adjustment under load. | "Load suddenly applied, as by a blow, tends to equality of deformation from crystal to crystal, with stresses determined by the common deformation and the individual stiffness. Load slowly applied tends to equality of stresses, with adjust- 10 ment of deformations to an equilibrium depending on the load, but rarely attained with light loads. "The above paragraphs on the distribution of stress and deformation from crystal to crystal, make it apparent that we do not mean what we say when we make the statement that the stress intensity is so many pounds per square inch. What we mean is that, if the material, instead of being a conglom- erate of crystals, were a perfectly homogeneous substance; if our assumptions as to the elastic actions following a straight line law were true; if the'load were applied as we assume it is, etc., the stress intensity would be what we say it is. "When we calculate from our formulas for loading the result is at best only an average value of stress or deformation for the crystals of a given region of the piece, or perhaps for the whole section; at its worst a merely nominal quantity that is convenient to our calculations for design, because on reversing the calculation, perhaps with changed dimensions, we may come out again somewhere near to the external loading the piece will carry. Even in a case so simple as that of pure tension loading we calculate for engineering purposes "load per square inch of original area" beyond the yield point, forgetting that the original area ceased to exist when the yield point was passed. "As for our "moduli of rupture® of the torsion and transe- verse loadings, we have recognized in the names used that 11 they are only nominal stress values. Yet how many engineers know just how far these "moduli of rupture" may be from the average real stress in the outer fiber at break, or the diff- erence between ‘maximum etress per square inch of original area' and the real value of (breaking load/area at break) of the same test? "Keeping in mind the variation of stress and deformation from one crystal to another through the piece; the residual internal stresses; the effect of shape and size of the crys- tals; the variable orientation of crystal patterns, even if the crystals are all of one kind; and the inadequacy of the assumptions on which we calculate stresses, can we say that when the nominal stress from the external loading is 1000 # per eq. in., there is not at least one crystal in a million which has been pushed beyond 50000 # per eq. in., and perhaps ten crystals more in the million between 1000 and 50000, and hundreds between 1000 and 10000, and thousands that do not reach 1000; again others that have still, from residual internal stresses, even large stresses of the opposite sign from that which we impute? Remember that there are from 1,000,000 to more than 1,000,000,000 crystals per cubic inch of steel. "We believe that the more careful the study given to this Question, the more sure will be the conviction that a piece of metal, as a whole, has no "primitive elastic limit", because any loading, even no loading, finds some crystals 12 carrying high stresses and deformations, that the law of stress and deformation from crystal to crystal throughout the material ia one of those "probability" lawe rendered so familiar to mathematicians by the kinetic theory of gases. "The exact form of these distribution laws for stress and deformation will vary with the material and with the history of the piece - whether it has been cold worked, heat treated, etc. It would follow from this that any stress, however emall, if repeatedly applied, would finally cause failure. But it will be evident that from a study of the tests that have been made, a comfortably large stress from external loading may be applied so many times that the piece, and the machine of which it is a part, will surely wear out long before fatigue failure need be anticipated. "The number of applications of a load to produce failure depends upon; (a), the number of shear slips caused at each application; (b), the number of crystals affected by these slips; (c) the ratio of the number of these crystals to the total number; (d) the percentage of orystals that must be put out of commission before the break occurs. The factors (a) and (b) depend on the stress intensity, or deformation applied, the nature and size of the crystals, and the past history of the piece; (c) depends on the nature of the material; (d) depends on the kind of loading, being probably least for torsion, slightly larger ffor transverse, 13 and still larger for tensile loads. "For any given material and method of loading, from the fact that we are dealing with probability functions, there is as the simplest possibility, a chance that the relation between stress intensity and number of applications required to break the so called endurance curve, is a logarithmic one- such a relation as that stress versus log (number) is a stra- ight line, or log (stress) versus log (number) is a straight line. The real function between number and stress is probably &@ complicated exponential relation." In a following article by the same authors there is a discussion of the design and operation of a reverse flex- ure fatigue machine. So far as the authors of this theses have been able to ascertain, this machine and the Landgraf- turner machine, handled by Queen & Company, Philadelphia, are the only ones of the kind that have been developed in a com- mercial way? Below is a synopsis of the article mentioned, with ex- tracts from it, together with editorial comment:- "The design of a new machine for the fatigue testa of materiale. From its use a number of important results have been obtained. A piece of ductile material broken with from one to ten applications of load has a fracture of the cup and cone type as in tensile tests. With applicatios greater than one hundred the breaks are square. 14 "The logarithmic curve giving the relation between maximum strese and number of cycles is found to be nearly a straight line. Further for similar materials the curves are found to be parallel. This foreshadows a radical change in fatigue testing, for the "figure of merit" can be obtained with a few cycles, say from 500 to 10,000. This would permit of the completion of a test in from five minutes to one hour, compared to half & day or several days as at present.* "For practical testing the same kind of materials for their comparative values, the paralleliem of the curves opens the way to some radical changes from present methods. ***** "The testing time may be immensely shortened. On the Upton- Lewis machine runs ar 1, - 3/4, - and 1/3 inch crank radius would give from 500 to 10,000 cycles, and would be sufficient to place the material. A run of 500 cycles would take, com- plete, about five minutes; at 10,000 cycles, about one hour. This is a very pleasant contrast to the half day or days hitherto used for fatigue testing. ******* The real use of this straight line approximation to the curve, however, is that it enables the finding of a figure of merit for the material by which it may be compared with other materials of similar character. The equation of the straight line is:- log n ~- K=m. log p, where n is the number of cycles to break, p, the stress, and k and m are constants. With p in pounds per square inch, m has the value 8.5 2 for steels and wrought irons. 15 Aseuming this, K becomes the figure of merit for the steel. Reeve & The practical testing schedule for the test of steels on the Upton-Lewis machine would consist of runs of two or more pieces each, with 1, - 3/4, - and 1/2 inch crank throws. From the section dimensions of the piece, the value of pencil travel ( indicating the stress ), and the constants of the machine, the values of the nominal stress intensity for each run would then be found. Substituting in log n * K = 8.5 log p will give half a dozen or more values of K; the average of these is the figure of merit of the steel. The time for these tests would be about half a day. Different steels would be compared by comparing their figures of merit. fhis procedure breaks down when the materials to be compared are unlike; then the only way is to determine the endurance curve from n ® 100 to 1000 up to n @ 10,000,000 or more; plot the curves, and compare the plots. Editorial comment on the Upton- Lewis articles and testing machine. From American Machinist. weeee* Testing by applying repeated alternating stresses has not yet gained for itself a place in shop laboratories for two major reasons: There ig some question as to its value in pointing out the property of endurance under load and vibration; and more important than thie, a machine which oa 4. 16 will permit of accomplishing such tests quickly has not been available. "The types of apparatus used generally have been such that &@ long period of time was necessary to test a single specimen. This period may be from half a day to several days. This con- diticn in itself has been sufficient to make this test prac- tically unusable in commercial testing. The article in this issue is of importance in showing that a machine from which results can be obtained in a short time, say in from five minutes to half an hour, depending on the number of stress cycles required, has been made commercially practicable. "Furthermore a connection between the tensile stress and the number of cycles to break is, we believe, for the firet time pointed out. The stress- cycle curves, for metals with different tensile strengths, apparently belong to the same family, but occupy different positions with respect to the axis, these relative positions indicating their tensile strengths. "Another worthy feature is the corroborative evidence that the older theory of crystallization under vibration is erroneous. This theory has been attacked many times, and is generally discredited. But in spite of that condition it is well to bring forward such evidence as the authors discovered, showing that the appearance of the fracture is dependant on the original crystallized condition of the material and the 17 manner of breaking. The tests illustrated from wrought iron specimens are particularly interesting in this particular; as this metal is usually looked upon as the best example of a fibrous metal. The tests show that under proper conditions of breaking, a fracture could be obtained from wrought iron equal in fineness to that of the highest grade, most care- fully treated tool steel.* An article in the "Proceedings of the American Society for Testing Materials", volume fourteen, 1914, discusses a new vibratory testing machine designed to perform "oscillating and rotative vibratory tests," as well as tension tests. This is a stay bolt testing machine, and performs tests in flexure. No torsional stresses are developed in the specimen. The material outlined above, with catalogs of the standard types of testing machines, constitutes all that we find avail- able bearing on the subject of this work. On account of the scantiness of the supply of information along thie line, the foregoing extracts and comments have beem presented somewhat in detail, in order to give something of an idea of the field for the application of this kind of testing of materials, particular- ly metals; to show the extent of what hase been done in this di- rection; and to make clear that this work ia one in which the investigators must proceed almost entirely on their own resour- CesS. ar 18 There is undoubtedly other material, but the idea in presenting this quite completely from are joint of view, rather than as a comparison of many theories is not to subscribe en- tirely to just the statements outlined, but were to show that the subject of fatigue testing is one in which little has been done, and that much of value may be accomplished along this line. Nor do we claim for this study anything more than a step, tho truly hoping it to be a step forward, in the almost un- touched field of fatigue testing. beginnings must be made slowly, especially along the lines of research, and this field is so broad and varied that only one small phase of it can be logically.studied at a time. The design, then of this ma- Chine, leading eventually to its construction, and operation in the testing laboratories of the Michigan Agricultural College, is submitted as the authors’ mite toward the gain- ing of a more complete and detailed understanding of the phenomena of the fatigue failure of metals. Degign of the machine. The machine, which we have designated a "Reverse Torsion Testing Machine" is intend- ed to investigate torsional fatigue failure of metals in form of test bars by subjecting them to repeated or rever- sed torsional stresses, these stresses not to exceed the nom- inal elastic limit of the material. 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