All solids deviate more or less from the theoretical perfectly elastic body and though many experiments have been undertaken in order to explain these deviations, we can hardly claim that any of the numerous theories proposed by the different investigators has yet cleared up the intricate relations involved

Guthe, K. E.

English

University of Northern Iowa

Proceedings of the Iowa Academy of Science Volume 15 Annual Issue Article 24 1908 Some Peculiarities in the Elastic Properties of Certain Substances K. E. Guthe Copyright ©1908 Iowa Academy of Science, Inc. Follow this and additional works at: https://scholarworks.uni.edu/pias Recommended Citation Guthe, K. E. (1908) "Some Peculiarities in the Elastic Properties of Certain Substances," Proceedings of the Iowa Academy of Science, 15(1), 147-156. Available at: https://scholarworks.uni.edu/pias/vol15/iss1/24 This Research is brought to you for free and open access by the Iowa Academy of Science at UNI ScholarWorks. It has been accepted for inclusion in Proceedings of the Iowa Academy of Science by an authorized editor of UNI ScholarWorks. For more information, please contact scholarworks@uni.edu. .• SOME PECULIARITIES IN THE ELASTIC PROPERTIES OF CERTAIN SUB­STANCES.  B Y  K .  E. GUTHE. All solid"s deviate more or less from the theoretical perfectly elastic body and though many experiments have been undertaken in order to explain these deviations, w e  can hardly claim that any of the numerous theories proposed by the different investigato rs has yet cleared up the intricate relations involved. The best known of these deviations is the so-called elastic after effect. It was first discovered in silk fibers in 1 8 3 5  by W. Weber and consists in a lagging of the establishment or disappearance of a strain behind a distorting force. Thus if  we twist a wire at one end while the other end is kept fixed, then upon re­leasing the wire there will be at first a rapid return towards the original shape, followed by a slower change in the same sense, extending sometimes over con­siderable time. The longer the original deformation has l asted the stronger will be the after effect. Of course the deformation is supposed to remain always below the value at which a permanent set occurs, so that after a sufficiently long time the return to the original condition is complete. M any experimental and theoretical investigations have led scientists to believe that elastic after effect may be considered as a kind of viscosity. It  must, however, be remem­bered that it differs in its nature from the viscosity of fluids because in the latter case there is no tendency to return to the original shape after the stress is re­moved. The elastic after effect is especially apparent in soft m etal wires, while the same wires hardened show it to a much smaller degree .  Quartz fibres, car­bon filaments and wires of hardened steel, phosphor bronze and platinum-irid­ium have very small elastic after effects. Another deviation from the demands of the theory has received the name "el astic fatigue." Lord Kelvin1 observed that a wire which had been kept under torsional vibrations for some time has a l arger period of vibration and a larger logarithmic decrement than a wire which has been at rest. J. 0. Thompson• has later demonstrated that as long as the amplitude and temperature remain constant there is  no such change, · even if the wire is  kept vibrating for days. It is,  however, a well known fact that when the amplitudes decrease from larger values to smaller the period, as well as the logarithmic decrement, decrease somewhat. So far only cases were known in which the variations of these quantities are quite small ; in the course of some experiments with platinum­iridium wires which show almost no elastic after effect I found such remarkable 1 .  Kelvi n ,  Math . and Phys . Papers , III , p. 22 . 2. J .  0 .  Thompso n ,  Phy s .  Rev . VIII , p .  lU � ( 147) 1Guthe: Some Peculiarities in the Elastic Properties of Certain SubstancePublished by UNI ScholarWorks, 1908148 IOWA ACADE MY OF SCIENC E  deviations from t h e  behaviour of ordinary wires that I decided t o  investigate the matter further. The wires which carried at their lower end cylinders of Tobin bronze were su spended from the top and inside of a large hollow brass cylinder having a glass window at its lower end. The whole brass case coul d be rotated around a ,. central pivot and thus the suspended cylinders set in vibrations.  The glass window allowed the observation of a small mi rror attached to the lower end of the vibrating system. The period was determined by chronographic records and the amplitudes by a telescope and scale placed at a distance of  100 centi-m eters from the m irror. A platinum-iridium wire containing 2 5  per cent of  iridium, when hardened by drawing a period of  6 .7766 sec. with an amplitude of 5°, which decreased to 6.7745 sec. with an amplitude of 0.05, while its logarithmic decrement decreased between the same amplitudes from 0 .0012 to 0 .00091 .  A still more surprising behaviour was found in a 40 per cent platinium-iridium wire whose period o f  vibration changed through the same range o f  amplitude from 1 2 . 0 6 0  sec. t o  1 1 . 8 9 0  sec. , while its decrement decreased from the enormous value of 0 .012  t o  0.0030.  The period,  as well as the logarithmic decrement, are very nearly proportional .to the amplitude, though the increase i s  sl ightly smaller than that of the ampli­tude. The decrease o f  amplitude between successive swings is very nearly pro­portional to the square of the preceding ampl itude. Since such enormous varia­tions h ave never before been observed in other wires, a great m any observations were made, but in every case the same effect was found. In the following tables I have picked out at random a few of them and the values are plotted in figures 1 to 3 . 2Proceedings of the Iowa Academy of Science, Vol. 15 [1908], No. 1, Art. 24https://scholarworks.uni.edu/pias/vol15/iss1/24IOWA ACADEMY OF SCIENCE ---·-----TABLE I .  Forty per cent Platinum-Iridum Moment of Inertia :  372 . 4 .  - -- ------ - - --- - -Amplitudes , 1st,  5th , 9th , etc . 6 A 4K 7 42 . 5 :l7 . 9  3 L O  30 . 7  2 8 . 0  :2 5 . G  23 . 6;) 2 1 . �J 20 . 45 rn . 10 17 . 85 lG . 88 lo . 88 10 . 02 1 1 . 22 13 . 55 1 2 .  o :>  12 . 30 11 . 76 11 . 27 10 . 82 10 . 38 1 0 . 00  9 . 62 9 . 26 8 . 22 8 . 6% 8 . 33 8 . 09 7 . 82  7 . 58 7 . 34 7 . 11 6 . 90 6 . 70 6 . 50  6 . 32 6 . 16 5 . 99  5 . 84 5 . 67 5 . 54 5 . 40 5 . 26 5 . 13 - - - -�:r- - - · 1 :L O I 3 . :;  2 . 7 2 . 4  1 . 9.) l .  7 1 . 5  l , ;J;) 1 . 2 ) l . 02 O . H.5 0 . 86 0 . 80  0 . 67 0 . 62 0 . 6.S  O . •l l  0 . 49 OA5 0 . 4 1  O . :lll 0 . 38 0 . 36  O . :H 0. 30 0 . 29 0 . 2-1  0 . :.:7  0 . 24  0 . 24 0 . 2.3  0 . 21  0 . 20  0 . 20  () . 18 0 . 16 0 . 17 0.15 0. 17 0 . 1 3  0 . 1 4  0 . 14 0 . 1 3  Wire . ------- - - --A "  " 2372 1806 0 . 013.1 1430 0 . 0121 1156 0 . 01 1 1  842 0 . 010;) 78! 0 . 009� ()..:);') o . om2 55() O . OOR·l 482 0 . 0070 418 0 . 0076 305 0 . 0072 :na 0 . 0068 2S:l 0 . 006') 2:52 0 . 0062 226 0 . 00•)!) 202 o . �J'i6 184 0 . 00):l 167 O.OO'i:l 151 0 . 00.51 l:JS 0 . 0048 127 0 . 0045 117 0 . 00'5 108 0 . 004:> 100 o . oon 93 0 . 00·42 86 0 . 0041 80 o . oo:w 74 0 . 0038 OU O . OO:l5 65 0 . 0034 61 0 . 0035 57 0 . 0034 54 0 . 0035 51 0 . 0034 48 0 . 0032 45 0.0032 42 0 . 0032 40 0.0029 38 0 . 0029  36 0 . 0029  3i 0. 0000 32 0 . 0028  31 0 . 0028  29 0 . 0026  28 0 . 0028 26 0 . 0028  14fl Double Period 1 4 . 700 sec . H . 620 1 4 . 'i65 1 4 , 515 U . ii25 1Ui08 14 , 4!17 1 ± . 485 14 . 475 1 4 . 46.5 H . 455 1 4 . 446 1 4 . 439 1 4 . 432 14. 426 1 4 . 420 1 4 . 415 l + . H2 1 4 . 408 1 4 . 405 14.-102 H . 399 H . 396 1 4 . 393 1 4 . 390 1 4 . 388 1 4 . 386  1 4 , 38! 1 4 . 383 1 4 . 381 14 . 380 14 . 378 14. 377 14. 376 1 4 . 375 1 4 . 373 14 .372 14 . 370 1 4 . 368  14 . 366 14 . 364 14 . 363  1 4 . 361 14 , 359 14 . 358  3Guthe: Some Peculiarities in the Elastic Properties of Certain SubstancePublished by UNI ScholarWorks, 19081 50 I OWA ACADE MY OF SCIENCE TABLE I I .  Forty p e r  cent Platinum-Iridium Wire , Moment of Inertia :  987 . 7 .  --------- -- --- - -==---- ----- ·-----Amplitudes , 1st,  5th , 9th , etc . __ J----= A _l A 2 -----I I �t� 1 - ---32.-.. -96_____ i�rf 0.0104 28. 9 835 0.0097 26 . 6  ' 2 . 3  708 0 . 0091 24 . 45 2 .1-5 &.JS 0.0086 22 . 7  1 . 75 49·3 0 . 0080  21 . 1  1 . 6  445 0 . 0077 19 . 7  1 . 4  388 0.0074 18. 4 1 . 3  339 0.0070 17 . 35 1 . 0;) 301 0 . 0066 16 . 3  1 . 05 266 0 . 0063 15 . 45 0.85 239 0 . 0058 14 . 65 0 . 80 215 0 . 0056 13 . 94 0. 71 194 0.0054 13 . 27 0 . 67 176 0 . 005.� 12 . 65 0 . 62 160 0.0050 12 . 10 0 . 55 146 0 . 0018 1 1 . 58  0 . 52 134 0. 0046 11 . 12 0 . 46 124 0.0045 10. 67 0. 45 114 0 . 00!3 10 . 27 0 . 40 115 0 . 00!2 9 . 88  0 . 39  98 0. 0042 9 . 49 0 . 39  00 0. 0040 9 . 17 0 . 32 84 0 . 0038 8 . 86 1 _ 0 . 31  78 0 . 0037 8 . fi6 0.30 73 0 . 0036 8 .  29 o. 27 69 0 . 0033 8 . 04 0 . 25  65 0 . 0033 ________ 7._8 __________ 0.:..c2l ____ 6_l __ ___ O_.OOG3 Double Period 24 .120 24.060 24 . 020 23 . 980 23 . 965 23 . 940 23 .925 23. 910 23 , 898 23.886 23 . 874 23 . 868 23 . 856 23. 8l8 2.3 . 840 23, 832 23 . 826 23.818 23.812 23.806 23 . 800 23 . 7\l6 23 . 793 23 . 790 23 . 787 23 . 784 23 .782 23.780 4Proceedings of the Iowa Academy of Science, Vol. 15 [1908], No. 1, Art. 24https://scholarworks.uni.edu/pias/vol15/iss1/24IOWA ACADE 1\1Y OF SCIENCE ( ; I H . .J 11 -. .... d..C: I r CJ I I c , I I i I I .. ' le k , • , • ,. . � . , ,. . 1 . ,,. � • IL ,. • j,r. ,. -r v � � c  . la..,• - � - """ -F I G . 1 .  Period and Amplitude . . , _  . � 1µ � 'l. '< �  lr l 0 ..... 5Guthe: Some Peculiarities in the Elastic Properties of Certain SubstancePublished by UNI ScholarWorks, 1908152 I OWA ACADE MY OF SCIENCE IC I( • . -� 1 1  .._ '1 ,...... : t-.IU , ._� " M ! _ ,__ I_,_ I r ,_  • �"Ii . -F: ! I -.. • ')( ... �-• I'. • � .,. . � L  • • :::r • •  . - -..: . FIG . Z. Decrease in Amplitude and Square of Amplitude. 6Proceedings of the Iowa Academy of Science, Vol. 15 [1908], No. 1, Art. 24https://scholarworks.uni.edu/pias/vol15/iss1/24I OWA ACAD E M Y  OF SCIENCE 153 -� I . t-H � -� I I-'" •L\ '"' I . • .I -" . -..... " t: " :r-" . .. . l 11 . !IC . t · .. lt . .. Jl I( . , '>t 'II -... . " . ,. ii � .,.... 0 15 FIG . 8 Logarithmic Decrement and Amplitude. 7Guthe: Some Peculiarities in the Elastic Properties of Certain SubstancePublished by UNI ScholarWorks, 1908154 IOWA ACADEMY OF SCIENC E  Having thought a t  first that the property of. iridium t o  absorb oxygen m ight be the reason for the observed anomalies, I experimented with the same wire under different pressures. The changes in the period and decrement were as large as before, even when the pressure was only 2 . 5  cm. A further decrease in pressure could not be obtained because the l arge brass case was not perfectly airtight. The observations were repeated with a different moment of inertia suspended from the wire.  The time o f  vibration was now only 7.274 sec . for the larger am plitude and decreased to 7 .10:3  with the sm aller amplitude. But most sur­prising of all was the Iact that values of the logarithmic decrement when plottetl as a function of the amplitude fell closely upon the same curve which was obtained with t_he larger perio d, and seems,  therefore, to b e  intl ependent of the velo city with which the system moves. I t  made no difference whatever with how large an amplitude I started, whether or not the wire had been kept swinging fo r some time, and if it was swinging under atmosph eric or decreased prpssure ; for the same ampl itude al­ways the same large logarithmic decrement was found. The phenomenon wh ich this wire exhibits in such an exceptional degree has usually been considered as closely connected with elastic after effect, but the fact that the wire shows almost no after effect when tested by the usual method seems to indicate that there is l ittle or no connection between the two. My first thought was that the wire did not follow Hooke's law and I therefore connected one of its ends rigidly to a steel wire of equal length and at the con­necting point a small mirror was sealed to the wires. The lower end of the steel wire was securely fastened and the upper end of the platinum-iridium wire clamped in a torsion head. It was found that equal deflections of the mirror were produced by equal angular displacements of the torsion head. This shows that the wire followed Hooke's law within the limits of  the experiment. I am unable to explain at the present time the results obtained with the pla tinum-iridium wire, but hope to continue the investigation with wires of different length and diameter and possibly also with alloys of platinum with other rare metals. While the elastic after effect may have some influence upon the rate of dis­sipation of energy in a wire in torsional vibrations, there can be no simple re­lation between the after effect and the logarithmic decrement, even in the case o f  ordinary wires, because frequently wires with smallest after effect show very large values for the decrement. I have shown this to be true in all cases. D rawn wires have a considerably l arger logarithmic decrement than softer wires. I have made a large number of experiments on this point, using first hard drawn wires and repeating the experiments after the wires had been an­nealed by drawing them through the flame of a Bunsen burner. I n  every case the soft wires show the smaller decrement and the larger moment of torsion.  Thus copper wire, hard drawn, had a period of 5 .78 0  sec .  and a logarithmic decrement of 0.0057. After annealing its time of vibration with the same mo­ment of inertia and at the same temperature was 5.702, decrea·sing with ampli­tude to 5 .692 ,  and the decrement had decreased to 0.0022 , more than one-half. New light has recently been thrown upon the physical process taking place during the drawing of a wire. Beilby" arrives by very interesting m icroscopi c  3 .  B eil b y ,  N ature , 76 , p .  572 , 1907 . • 8Proceedings of the Iowa Academy of Science, Vol. 15 [1908], No. 1, Art. 24https://scholarworks.uni.edu/pias/vol15/iss1/24I OWA ACADEMY OF SCIENCE 155 investigations at the result that all crystalline substances can also exist · in a noncrystalline or amorphous form and that these two forms are so distinct from each other that they must be regarded as definite allotropic modifications. Further he showed that in the pure ductile metals the crystalline state is actually the soft state, while the hardened metal is  a complex structure built up of crystalline and noncrystalline substance. During the drawing some o f  the crystals pass into the amorphous state and during the sudden congealing after the removal of the p ressure the crystals are bound into a rigid mass irrespective of any orientation. When this mass is heated to a temperature far below the melting point of the metal recrystallization of the amorphou s  part takes place and the wire becomes soft. This theory explains many peculiarities of hard drawn wire. Gray and Mees and more recently Wassmuth have shown that the density of  wires drawn under great pressure is smaller than before drawing. Applying thi s  theory to the re­sults discussed in this paper, we have to assume that the amorphous state has a smaller rigidity than the crystalline state and we must expect a larger logarith­mic decrement in amorphou s  sol ids. If  the elastic after effect is  due to a slipping of crystals w ith respect to each other the after effect should become smaller when the crystals are closely surrounded by the amorphous m ass.  To test these conclusions experiments were made with fused quartz and car­bon filaments, both amorphous substances. The quartz fibre was very thin and 4 8 0  mm. long. The elastic after effect was very small, the time of vibration very constant and n o  decrease of the de crement with amplitud e  could be ob­served. The decrement was 0 .000572 , a value twice as large as was obtained with much thicker metall ic  wires. The thin c arbon fil ament, 2 0  cm. long, had the very large decrement of 0 . 00548 ,  the amplitude decreasing in 176  swings to one-tenth of its original value.  But the decrement remained perfe ctly constant. A similar effect to that of hardening by drawing can be produced in a palladium wire if hydrogen is deposited upon it by electrolysis.  With a palla­dium wire this treatment produced an increase of the decrement from 0 .0006 to 0.003,  while the period was decreased from 7 .954  sec. to 7 .778  sec. The absorp­tion of hydrogen is considered as a solution of hydrogen in the metal and it is quite reasonable to suppose that the crystalline structure o f  the wire is greatly impaired by such a treatment. With the 25 per cent platinum-iridium wire men­tioned above, annealing reduced the logarithmic decrement from 0.00124 to 0.000327 without showing any other notewo rthy effects. The same treatment failed, however, completely with the 40 per cent plat­inum-iridium wire. Thinking that perhaps the temperature of the Bunsen burner was too low to raise the wire to the point of recrystallizatio n, I sent through the wire, not under tension, an electric current sufficiently large to heat it to bright yellow heat. The point of recrystallization was undoubtedly reached and the crystals must have arranged themselves in any imaginable w ay ; for placing the wire again in the torsion apparatus I was unable to get any zero point at all, though the wire was kept in continuous vibration for two days in the hope to have the crystals fall in line. They absolutely refused to do so and during each attempt of making a measurement the zero point shifted at least 10 cm. over the scale in the direction in which the torsion had first been applied. 9Guthe: Some Peculiarities in the Elastic Properties of Certain SubstancePublished by UNI ScholarWorks, 1908156 IOWA ACADE MY OF SCIENC E  Then t h e  w i r e  was heated again b y  a/l elect r i c  c u r r e n t  to r e d  heat, b u t  this time under a load which it  was to carry in the torsional experiments. No higher temperature was attempted for fear that the wire might permanently stretch under the load. The zero point after this treatm ent was again quite steady, but at the same time all i ts  forme r vecu l i ar i t i es reappeared .  Apparently the conditions under which the anneal ing of the wire takes place has a great influence upon the l'i astic properties of  the wire, and in future ex­periments this point shall rece ive  special attention .  1 .. 10Proceedings of the Iowa Academy of Science, Vol. 15 [1908], No. 1, Art. 24https://scholarworks.uni.edu/pias/vol15/iss1/24

Some Peculiarities in the Elastic Properties of Certain Substances

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Some Peculiarities in the Elastic Properties of Certain Substances

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