I N D U S T R I A L A N D ENGINEERING CHEMISTRY
June, 1925
623
The Resilient Energy Criterion’ As Applied to the Shape of the Rubber Stress-Strain Curve By William B. Wiegand AMES HOLDE\TIRE& RUBBERC o , LTD , KITCHEKER, Our
T
H E criteria that have a t various times been used or proposed for assessing and comparing the physical properties of rubber specimens are numerous. Tensile strength, elongation a t rupture or a t a given impressed stress, set-whether permanent or subpermanent-hardness, etc., are representative of what may be termed “single” measures. A popular and useful criterion of dual character is “tensile product,” variously defined as the product of final strength and final length, or of final strength and percentage of elongation a t rupture. The former expression for tensile product is equivalent to the strength a t rupture referred to the actual cross section a t rupture (volume increases being neglected). The criterion which perhaps embodies the most important group of physical properties is the “energy of resilience,” defined2 as the total mechanical work done on the sample in stressing same to rupture, referred to unit original volume -as, for example, foot pounds per cubic inch. The energy criterion, it will be seen, differs from those formerly employed in that it evaluates the entire stress-strain history of the sample, from zero to ultimate deformation. Recent work has confirmed the theory that this criterion is perhaps the best single index of resistance to abrasive wear. It is now proposed to apply the same general method to the evaluation of certain properties associated with the shape of the rubber stress-strain curve. The reader should first be reminded that the tensile product may be rightly regarded as an energy index. Defined as the product of final tensile into final elongation, it exactly represents twice the energy of resilience of the sample, had it followed Hooke’s law-i. e., had its stress-strain curve been linear (Diagram 1).
EDiagram l
It is well known that, in the main, the stress-strain curves of soft rubber mixings are concave to the load axis, differing in this respect from those of other structural materials which are linear to the yield point, thereafter in general becoming convex. The degree to which any given curve approaches or departs from linear or Hooke’s law conditions cannot be completely assessed by a statement of the stress at 100 per cent elongation (Young’s modulus) nor by the more commonly em* Received January 17, 1925. 8
Wiegand, Can. Chem. J . , 4, 160 (1920).
ployed stress a t 300 per cent elongation. These are of necessity isolated values. For several years the degree of concavity of the curves has been measured in this laboratory by recording, as a percentage, the ratio between the energy of resilience a t rupture and the energy of the “ideal” (or Hooke’s law) curve, to the same end point. This index to the hollowness or concavity of the curve has been called the “concavity factor” or, for short, “C.” It should a t this point be emphasized that a concavity factor of 100 per cent indicating a sample the stress-strain curve of which follows Hooke’s law is not always meant to imply technically superior conditions. (Strictly speaking, a sinuous curve could show “C” = 100 per cent and still not be in accord with Hooke’s law. In actual practice, however, this condition is, in this laboratory, rarely if ever met with.) Certain classes of shock-absorption apparatus require, in fact, stress-strain relationships corresponding to a very low concavity factor. Even in such cases the information conveyed by this ratio may be found not entirely valueless. In general, however, the more closely the rubber stressstrain curve approaches that of the rigid structural materials the more readily will the engineer be enabled to calculate and control the properties and behavior of rubber members when, as so frequently happens, they are employed in positions where they are stressed to points falling far short of rupture and where the capacity for resilience a t such intermediate strains is of prime importance. From the point of view of abrasive wear, a property which is of importance to rubber technologists in practically every branch of the industry, it is believed that approximation to linear or Hooke’s law behavior is likely to coincide with superior performance, provided, of course, that the other properties remain unimpaired. Why, it may be asked, is 100 per cent set as the “ideal” ratio? There are two reasons. First and foremost, this laboratory has never observed any mixings or cures resulting in a concavity factor of over 100 per cent which had not become most seriously reduced in quality. Again, from the engineering point of view, a rubber mixing developing a convex stressstrain curve (“C” greater than 100 per cent) would offer the same disadvantages as a rigid structural material stressed beyond its yield point. In other words, given fixed breaking strength and elongation, that rubber sample will provide maximum resistance to impressed stresses of any intermediate magnitude which shows a concavity factor of 100 per cent. I n general, therefore, such a sample will, it is believed, offer maximal resistance to general wear and tear. Effect of Crude, Cure, and Compounding Ingredients upon “c”
CRUDB Fine para Smoked sheets Pale crepe
“C” factor at optimum Per cent 76 75 75
Crude CRUDE Clean thin brown Coarse para Caucho ball
“C” factor at optimum Per cent 76 88 96
It will be noted the variation in “C” due to the change from hard to soft rubber is not more than 20 per cent; also that “C” is higher for the latter.
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INDUSTRIAL AND ENGINEERING CHEMISTRY
624
I
I
VOLUME LOADING
-
VOLUME
Clue Stock A
B
C
Time of cure Minutes 180 240
300
65 63 64
300
60 65 67
Opt. not reached 90 180 opt.
90 180 opt.
300
D
E F G 4 ‘
15 180 opt. 300 6 15 opt. 60 6 15 opt. 90 5 opt. 30 60 240 opt. 300
I
30 60 opt. 240
J
60 240 opt
K
I5 60 opt. 120 30 60 opt. 120 10 15 opt. 90 5 opt. 90
L M A’
‘C” factor Per cent
58.5 65 64 62 67.5 67 66 64.5 67 69.5 71.5 76 73 75 62 70.5 72.5 58 64 75 69 72.5 64 75 84 6 -5 69 71 70 78 84 66 GS
Variation Per cent 2
7.6 5.5
2.5
6.5 2 10.5 17
3.5
LOADING
14
2
1
I
VOLUME
LOADING
-
Over very wide curing ranges “C” shows maximum variation of 20 to 25 per cent, with mean of 8 per cent.
Compounding Ingredients The accompanying graphs show the effects of several of the common pigments-viz., carbon black,a zinc, oxide, magnesium a basic carbonate, china clay, whiting, and barytes-using mix2 of Fine Para 100, sulfur 5, and litharge 30.
From these data the following general conclusions can be drawn; of course, these should be regarded as suggestive rather than conclusive: 1-The concavity factor, “C,” is enormoudy more sensitive to pigmentation, ranging from 45 to 140 per cent, than to cure or crude. 2-The relation between “C” and pigment concentration is approximately linear, the inclination being in general a function of particle size. (The anomalous behavior of clay and magnesium carbonate may be ascribed to particle shape as distinguished from particle size.) 3-The pigment concentration necessary to make “C” = 100 per cent is in every case one which exceeds the value corresponding to optimum reinforcement (as measured by maximum energy of resilience). 4-The pigment showing finest subdivision-viz., carbon black-displays the highest resilient energy a t a concavity factor of 100 per cent.
20 G
-
I
Vol. 17, No. 6
The Ideal Wear-Resisting Pigment
I n view of the foregoing data one is tempted to offer the suggestion that the pigment which will bring maximum reinforcement may be the one which will endow the mixing 3
The grade used was “Micronex” as furnished by Binney and Smith,
N e w Y ork.
I-VD CSTRIAL A S D Eh’GIATEERI,VG CHEMISTR I’
June, 1925
with a concavity factor of 100 per cent a t the same concentration which produces maximum energy of resilience at rupture. At present, carbon black offers the closest approximation to this ideal. Such a combination of properties would provide the engineer with rubber structural members the behavior of which could be calculated as readily as those of steel, wood, and concrete, although, of course, offering a much wider range of elastic properties. Summary
An energy criterion for the degree of concavity of the rubber stress-strain curve is proposed in the form of the ratio between the area subtended by the curve on the strain axis and half the tensile product, expressed in energy units. This ratio-as a percentage-is called the concavity factor “C.” I t is calculated as follows: “C”
=
24 E>f X 700 per cent -
625
where E y = energy of resilience in foot-pounds per cubic inch T P = tensile strength in pounds per square inch multiplied by per cent elongation divided by 10,000 i. e., T
P
=
T X E 10,000
“C” is slightly responsive to changes in crude and cure, but very highly sensitive to pigmentation. The finer the pigment the greater its power to increase the value of “C”. Maximum reenforcement may ultimately be attained through the coincidence of 100 per cent concavity factor with high energy of resilience, a t rupture. Carbon black shows the nearest approximation to this ideal, the complete realization of which may greatly expand the application of rubber in the arts. Acknowledgment
The writer gratefully acknowledges the aid received from H. A. Braendle in the preparation and calculation of these data.
Measurement of Susceptibility of Fats to Oxidation’ By G. R. Greenbank and G. E. Holm RESEARCH LABORATORIES. BUREAUOF
HE presence of exceedingly small traces of oxidation products in fats may be shown by the application of various chemical tests. Although delicate enough to be of value in detecting the first oxidation products, these tests are hardly delicate enough to follow oxidation susceptibility changes quantitatively. The method described herein employs directly the principle of oxygen absorption, and is therefore a direct comparative measure of susceptibility. The figure illustrates the type of apparatus that has been used in these laboratories for some time. The samples of fat or materials containing fat are placed in small filtration flasks (175 cc.); the flasks are evacuated, filled with oxygen, placed in a constant-temperature oven a t 70” C., and connected to the tubes leading to the manometers. During the temperature adjustment, the pressures in the systems are adjusted by means of the 3-way stopcocks inserted in the tubes. When the systems have become stable the electrical connections are made, the platinum-tipped copper wire leading into the manometer being fixed a t a point where it is immersed to the extent of 1 to 2 mm. In the apparatus used the clock closes the circuit a t minute intervals, thereby actuating the four relays, to each of which is fastened an arm holding a marking device. Every minute, therefore, there is made upon a record sheet held upon the drum a dot for each 1
Received April 10, 1925
DAIRYING, WASHINGTON, D .
C.
circuit, so long as the pressures in the manometers remain normal. As soon as oxygen absorption begins in any one flask the circuit is broken and the relay in this circuit will not be actuated when contact is again made in the clock, though the other ,relays will function until the respective circuits are broken in the manometers. The record sheet is ruled to 10-minute intervals to facilitate the time readings. For confirmation of results, the contacts in the manometers may be reset and a second reading obtained. If the first break is due to true absorption a second break will follow within a short time. Where the experiment extends over a period longer than a working day there is danger of flow of mercury into the flasks with continued oxygen absorption. To avoid this care should be taken that the manometers do not contain too much mercury. Where a small amount is used in each manometer the air will be allowed to enter the system as soon as the mercury is depressed to the bend in the tube, thus forming a by-pass and preventing a backflow of mercury into the tubes. It is realized that every laboratory engaged in work upon fat oxidation does not possess a recording device of the type illustrated here, but numerous other devices (bells, lights, etc.) may be employed; however, these need more or less constant attention.
A M e t h o d for M e a s u r i n g t h e Susceptibility of F a t s to Oxidation
