Hysteresis, Elastic Modulus, and Growth of Tire Cords under Comparable Loads EDITH HONOLD AND HELMUT WAKEHAM Southern Regional Research Laboratory, U.S . Depar t mnt of Agriculture, New Orleans, La. the energy converted into heat during the stress cycle. The slope ( S Y )of the loop was converted into an elastic modulus by taking into account the cross-sectional area of the cord. The displacement of the loop along the strain axis permitted the evaluation of total growth as percentage of the length of the original cord with a 4-ounce tension. The growth rate, or increme in elongation per tenfold increase in cycle number, waa determined by plotting the per cent growth a t 100, 300, 1000, 3000, and 10,000cycles against the logarithm of time and taking the slope of the best straight line through these points. The individual slogks per tenfold increase in cycle number are more or less uniform. Typical hysteresis loops for cotton, rayon, and nylon tire corde after 1000 stress cycles are shown in Figure 2. I n these experimenta the load range was the same for all cords in terms of grams per grex, the low point of each cyc!e being 0.1 gram per grex, and the maximum, 0.4 gram per grex.
The method of determining hysteresis, elastic modulus, total growth, and growth rate of tire cords under conditions of rapid cyclic loading is reviewed. Measurements of these properties are reported for cotton, mercerized cotton, rayon, and nylon tire cords at three conditions of moisture content and temperature. Some possible significances of these factors are discussed.
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N A previous publication (9) the authors described a method for evaluating certain elastic properties of tire cords, such as mechanical hysteresis, elastic modulus, and growth rate, under conditions of rapid cyclic loading. It was shown that these mechanical properties of the cord are affected variously by changes in moisture content, temperature, cycle number, or load range. The present work is concerned with a comparison of these properties for typical tire cords of native cotton, mercerised cotton, rayon, and nylon under conditions simulating the actual service conditions that might be expected for such cords in the modern tire. Measurement of these elastic properties involves the simultaneous determination of stre= and strain while the cord is subjected to a complete stress cycle a t a rate of 1-cycle per second. This was accomplished as follows: The length of the cord to be tested wm tied at each end to the stirrup of a wire leader and placed in the tubular oven previously described (6). The wire a t one end was connected to a calibrated screw arrangement which was used to take up any growth of the cord during cyclic loading. The wire a t the other end was connected to a spring, which in turn was connected to a motor-driven adjuatable eccentric. The position, a t any instrint, of each end of the spring was recorded by means of kymograph pens on a moving paper strip. From the sinusoidlike tracings (CFK and BEH, Figure 1) made by these pens, simultaneous stress and strain values were calculated for both the loading and unloading portions of the stress cycle. The plot of these values gave directly the mechanical hysteresis loop from which the other elastic properties were calculated. The area of the entire loop (Figure 1)represents
TABLE I.
TIRE CORD SAMPLES
Fourteen cotton, rayon, and aylon tire cords were tested. The usual physical properties of them cords as determined at standard A.S.T.M. test conditions (1)are shown in Table I. Description of these cord samples follows: Cords C1 and C2 were samples of commercial cotton tire cord used in tire manufacture. Cords-C3 and M4 were of Wilds-13 (1943) cotton and were spun, twisted, and stretched in a commercial mill They differed in that the sin les yarn used for manufacture of the M4 cord waa first mercerize8 and then twisted into a cord of the zsz type instead of the conventional zzs form. Samples C5 and C6 were cords of Wilds-13 (1942) cotton prepared as experimental cords, and differed only in that the C5 cord was unstretched whereas the C6 cord had been stretched to reduce its elongation and increase its strength. Cord M7 was of the same cotton and construction as C5 and C6, and like the M4 had been mercerized and twisted into a zsz pattern. The M8 and M9 cords were of Wilds-13 (1943) cotton and were of identical construction and mercerizing treatment but differed in the twist pattern,*theformer being zzs and the latter zsz.
SOME PHYSICAL PROPERTIES OF
TIRECORDS
:rex At 10 lb. At break: g./grex At 10 Ib A t break 4342 18/4/3 18.7(z) lO.O(s) 2.09 12.3% Commercial cotton 1.85 6.0 7 .o% 8.7 5064 2.39 16/4/3 16 l ( s 11.2 5.0 2.22 c 2 Commerioal cotton 5.2 9.1 4638 17/4/3 20:3(2{ 9.7 4.8 2.49 2.38 c3 Cotton qtretched 4.2 7.8 4457 2.30 18.1(s) 9 . 7 ( s ) 9.7 4.1 2.39 5.2 M4 MerceriLed, stretched 17, 5/4/3 8.0 4716 2.25 20.6(z) 10,4(s) 21.8 14.7 1.78 c 5 Cotton, unstretched 17/4/3 10.4 15.4 4446 17/4/3 20.1(2) 10.2(s) 2.52 11.8 6.2 2.24 C6 Cotton, stretched 0.0 9.1 4648 11.3 4.8 lQ .4(s) 9 . 3 b ) 2.40 2.38 M7 Mercerized. stretched 17/4/3 6.1 11.4 4648 20.2(2) l O , l ( s ) 2.04 10.3 4.7 2.24 M8 Mercerized, stretched 17.5/4/3 5.3 9.6 4570 9.6 20.4(s) 10.0(z) 2.07 4.6 2.06 M9 Mercerized, stretched 17.5/4/3 5.6 9.2 2398 1100/2 16.6 10.6(s) 2.64 9 8 3.40 R1 Commercial rayon 4.5 10.8 2455 1100/2 15.4 ll.l(s) 2.49 11.1 3.34 R2 Commercial rayon 4.6 11.4 5366 2200/2 2.39 17.5 10.9(s) 6.1 2.90 R3 Commerci61 rayon 3.3 12.2 2200/2 0080 17.2 9.4(s) 7.2 2: 36 3.21 Rd Commercial rayon 2.6 11.2 210/4/2 1 . o ( 4 12.8(2) 10 .'4($ 22.0 12.4 5.76 1986 5.80 Commercial nylon N 22.0 11.8 The first figure represents size of single yarns (denier for nylon and rayon, and yarn number for ootton); the second figure represents number yarns per ply' the third figure represents number of plies in the cord. b As meas&d in the finished cord. c (;rex is a measure of the weight of cord or yarn per unit length and is defined as the number of grams per 10,000 metera.
c1
131
1.32 1.66 1.64 1.90 1.32 1.60 1.94 1.76 1.78 2.51 2.60 2:44
..
of single
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Figure 1. Method of Calculating Hysteresis Lobp at Right from Kymograph Tracings a t Left The rayons R1 and R 2 were 1100/2-ply viscose rayons of types used extensively in tire manufacture. Rayon R 3 was an early type 2200/2 viscose rayon; R4 was also a 2200/2 now being used in tire production. The nylon cord N, was a 210/4/2 construction of considerable elongation and tyiieal of some of the early nylon tire cords. TEST CONDITIONS
The test conditions a t which the comparison of elastic properties was made are shown in Table 11. Since the cords varied in gage and count (grex number) the load range of the stress cycle was maintained at 0.1 to.0.4 gram per grex for al1,cords. This range was near the low end of the stress-strain curvesfor these cords and thus approximated the loads believed to be applied to the cords in the tire during operation. The cycle frequency of 1 cycle per second was slow when compared with the frequencies with which cords are stressed in tires on rapidly moving vehicles. A 7.00-20 tire a t 50 miles per hour, for example, rotates a t a speed of about 10 revolutions per second. The present test apparatus, however, would not permit accurate measurement of the elastic properties a t higher cycle rates without radical changes in design; the comparison was therefore made a t the frequency indicated. I n the earlier investigation of the variation with cycle number it was shown that elastic properties change continuously throughout the fatigue life of the cord.' Elastic modulus and growth rate show more or less uniform increases with each tenfold increase in cycle number. The hysteresis values, on the other hand, decrease rapidly during the first 500 cycles but after that settle down to a fairly constant value under most conditions and with most cords. For this reason the properties of the cords n-ere compared a t the end of the first 1000 cycles.
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The optimum conditions of temperature and moisture content for testing tire cords have not been satisfactorily established. Most testing laboratories measure properties of the dry cord, because this condition lends itself easily to routine control Jvork. Unfortunately, however, the dry condition does not exist in the tire, nor does the moist condition specified in the A.S.T.M. standard testing conditions ( 1 ) . The actual moisture contents of tire cords during service have been shown to be Letween those of the dry and standard conditioned states ( 6 ) . Furthermore, in actual service the tire cords frequently get hot, reaching temperatures as high as 130' C. in some heavy-duty trucking service and retaining a t the same time much of the moisture which they possess a t lower temperatures. A strictly fair comparison should therefore include measurements a t a fairly high temperature and a moderate moisture content. I t was with these considerations in mind that the following three test conditions were chosen:
I. Temperature, 25' C., vacuum-dried cords with less than 1% ' moisture, dry basis. 11. Temperature, 25" C., equilibrium moisture a t a relative humidity of 40%. At this condition the cotton cords ranged between 4.0-4.5% moisture, the mercerized cottons 5.4-6.0Yc, the raypns about S.O%, and the nylon 2.1y0 moisture, and all dry basis. 111. Temperature, 90' C., moisture values approximately the same as those for condition 11. These moistures were maintained during the test by passing into the oven air a t approximately 4001, relative humidity a t 90' C. Moisture values were determined on the cords which were actually tested immediately upon completion of the test. The standard procedure for obtaining moisture and oven dry weight was followed throughout ( 2 ) . RESULTS AND DISCUSSION
Hysteresis data, elastic moduli, total growth values, and growth rates for the fourteen cords studied a t three conditions are shown in Tables 111, IV, and V, and are graphed in Figures 3 and 4.
TABLE 11. TESTCONDITIONS Load range, g./grex Cycle rate, cycle/second Cycle number Condition Temperature, C. Moisture (valuea baaed on dry weight), 7 0 Cottons Mercerized Rayons Nylon
0.1-0.4 1
1000
I
I1
I11
26
25
90
