December 1. lf>iy. 



THE INDIA RUBBER WORLD 



149 



What the Rubber Chemists Are Doing. 



By P. Schidrnwitz and H. A. Goldsborough. 



STUDIES IN VULCANIZATION. 



THE RUBBER STRESS-STRAIN CURVE. 



THE .\UTii(iRs have iiulilislud the first ut a scries of papers* in 

 which they purpose to carry out their deferred plan to dis- 

 cuss their studies in vulcanization. The leading features 

 of their paper on the rubber stress-strain curve and determina- 

 tion of "correct cure" are given below, necessarily somewhat 

 condensed. 



NATURE OF STRESS-STRAIN CURVE. 



E. Hatschek and II. .\. Goldsborough examined the practica- 

 bility of obtaining a single expression for the stress-strain curves 

 of a series of cures of the same mixing. (The mixing employed 

 in the fundamental experiments consisted of 100 parts of rubber 

 to eight of sulphur, cured for periods varying from 15 to 405 

 minutes at 286 degrees F. in molds in live, steam"). 



As bearing on the mathematical nature of "type," it is desirable 

 to restate, briefly, the following characteristics of progressive 

 cures of the same rubber-sulphur mixing, as first set forth by 

 Schidrowitz : , ,,, 



1. The process of vulcanization is physically and mechanically 

 of a definitely progressive character, and its progress can be ac- 

 curately and graphically represented by a series of stress-strain 

 curves. 



2. The state of cure of a given mixing of any rubber at any 

 given time (assuming standard conditions) is graphically ex- 

 pressed by the form and position of the corresponding stress- 

 strain curves representing progressive cures which bear a certain 

 mathematical relationship to each other for any one rubber, and 

 a relationship exists between the series of curves representing 

 progressive cures of any one rubber and the series of cures 

 representing progressive cures of any other rubber. 



3. As curing proceeds the curves come farther down the paper 

 in regular fashion and do not intersect at any point. 



4. At a part of the curve not far from the point of inflection 

 the curves become parallel to each other. That is to say, the 

 rate of stretch decreases with increasing loads, and is independent 

 of the state of cure. The above characteristics for a single set of 

 cures may be readily gathered from Figure 1. 



Examination of the curves showed that they belong to the con- 

 choid family, and it was found that a conchoid corresponding 

 closely to the rubber curve could be expressed, referred to Car- 

 tesian coordinates as follows : 



The rubber curve is derived from the parent conchoid by plot- 

 ting the ordinates against a constant fraction (>i) of the corre- 

 sponding abscissa, as expressed in the above equations. 



The interpretation of the terms in the above expressions may be 

 obtained from the following considerations: 



(1.) a represents the distance between the pole of the curve 

 and the asymptote. 



(2.) n is a constant in the expression x — (nx') in which 

 .*■ is the load at any point on the stress-strain curve and .v' is a 

 corresponding point on the parent conchoid. 



(3.) a.n is a constant for any given set of curves. 



H represents the increase of stretch per increment of 

 - in other words slope or "type." 

 Hence a/n or J/n is the degree of stretch or disten- 



^4.) 

 load, o: 



(5.) 

 sibility. 



(6.) 



(7.) b represents the limits of extension. 



In every set of curves (progressive cures of the same mixing) 

 there must be a specific curve in which a = b. It follows that this 

 specific curve represents a theoretically ideal balance of proper- 

 ties. The curve in question is the one we term the correct or 

 perfect cure. 



It is remarkable that a.n (i. c, slope or type), wmch obviously 

 represents a fundamentally important quality of a rubber, is a 

 constant for any rubber, theoretically from the point of in- 

 flection upwards and actually, as found experimentally, from a 

 point not far removed from the latter. 



Expressed in other terms, this means that after the initial 

 stage of stretching, equal increments of load produce equal 

 elongations, whatever the state of cure. 



I... 



Load tGRA 



Sqc 



Cross Sect 



It follows that a represents a quality which is the inverse 



of stretch capacity, namely, toughness or tenacity. 



•".Toiirnal of the Society nf Chemical Industry," September 15. 



Stress-Strain Curves Representing Successive Ci'Res of One 

 .G AT 15-MiNUTE Intervals (e. g., V = 75 Mi-vutes, VI =; 90. 

 Minutes, etc.) in Steam at 286 Degrees F. 

 Part of a Series from 15 Minutes to 6H Hours. 



It has been found by solving the correct cure curves by the 

 method of trial and error that all correct cure curves are 

 derived from the parent conchoid in which b (and therefore 

 also o) = 10.5. Since the curve meets the asymptote at infinity, 

 it follows that we are justified in concluding that all correct 

 cures of a standard- mixing consisting of 100 parts of rubber to 

 eight parts of sulphur (whatever the nature of the rubber, pro- 

 vided it is Hcvca) meet at a point for which the coordinates 

 are y = lO.S, .i- = oc; that is, an extension of ll.S times the orig. 

 inal length is the limit of distensibility. 



METHOD or DETEHMINING "COHRECT CURE.' 



From the above it will readily be inferred that to obtain the 

 correct cure it is necessary to determine a, b and A. In other 

 words, it is essential to determine (1) type and (2) the par- 

 ticular curve in any set in which = 6. 

 TYFE. 



In practice the determination of a.n ("type") by means of 

 the expressions corresponding to the coordinates is obviously 

 inconvenient. Taking advantage of the fact that "type" repre- 

 sents increase of stretch per increment of load, we determine the 



