TIRE REINFORCEMENT AND TIRE PERFORMANCE A symposium sponsored by ASTM Committees D13 on Textiles and F09 on Tires AIVIERICAN SOCIETY FOR TESTING AND MATERIALS Montrose, Ohio, 23-25 Oct 1978 ASTM SPECIAL TECHNICAL PUBLICATION 694 R A Fleming and D I, Livingston, Goodyear Tire and Rubber Company, editors List price $34.50 04-694000-37 # ^AMERICAN SOCIETY FOR TESTING AND MATERIALS 1916 Race Street, Philadelphia, Pa 19103 Copyright © by American Society for Testing and Materials 1979 Library of Congress Catalog Card Number 79-53318 NOTE The Society is not responsible, as a body, for the statements and opinions advanced in this publication Printed in Baltimore, Md Dec 1979 Foreword The Symposium on Tire Reinforcement and Tire Performance was held 23-25 Oct 1978, in Montrose, Ohio ASTM Committees D13 on TextUes and F09 on Tires jointly sponsored the symposium R A Fleming and D I Livingston, Goodyear Tire and Rubber Company, presided as chairmen on the symposium and served as editors of this pubUcation The Program Committee consisted of C F Brenner, National Highway Traffic Safety Administration, J W Hannell, E I duPont de Nemours and Co., Inc., and C C McCabe, E I duPont de Nemours and Co., Inc Related ASTM Publications Surface Texture Versus Skidding, STP 583 (1975), $12.00,04-583000-37 An Analysis of the Literature on Tire-Road Skid Resistance, STP 541 (1973), $5.50,04-541000-37 Skid Resistance of Highway Pavements, STP 530 (1973), $12.25,04-530000-37 Annual Book of ASTM Standards, Part 15, Road and Paving Materials; Bituminous Materials for Highway Construction, Waterproofing and Roofing, and Pipe; Skid Resistance (1979), $38.00,01-015079-08 Annual Book of ASTM Standards, Part 38, Rubber Products, Industrial—Specifications and Related Test Methods; Gaskets; Tires (1979), $29.00, 01-038079-20 A Note of Appreciation to Reviewers This publication is made possible by the authors and, also, the unheralded efforts of the reviewers This body of technical experts whose dedication, sacrifice of time and effort, and collective wisdom in reviewing the papers must be acknowledged The quality level of ASTM publications is a direct function of their respected opinions On behalf of ASTM we acknowledge their contribution with appreciation ASTM Committee on Publications Editorial Staff Jane B Wheeler, Managing Editor Helen M Hoersch, Associate Editor Ellen J McGlinchey, Senior Assistant Editor Helen Mahy, Assistant Editor Contents Introduction Challenges Facing Tire Cord Engineers Today—c z DRAVES, JR AND LEONARD SKOLNIK Survey of Mechanical Properties of Steel Cord and Related Test Methods— L BOURGOIS 19 Steel Tire Cord—Low Load Elongation—A C LOWELL AND LEONARD SKOLNIK A Shorter Route to Steel Tire Cord—F R COWLISHAW Steel Cord: Analysis of Used Truck Tires and Simulation of the Found Phenomena in Laboratory Experiments—c c J DE JONG Adhesion of Steel Tire Cord to Rubber Compounds Mutual Influence of Brass and Rubber Compounds on the Adhesion—M P BOURRAIN Belt Test for the Evaluation of the Fretting Fatigue and Adhesion Behavior of Steel Cord in Rubber—L BOURGOIS 47 57 69 87 103 Laboratory Machine to Evaluate the Resistance of Tire Cords (Textile or Steel) to Tensile Fatigue or Compressive Fatigue or Both—CESARE CANEVARI AND A G LALA 110 Adhesive and Processing Concepts for Tire Reinforcing Materials— R S BHAKUNI, G W RYE, AND S J DOMCHICK 122 Degradation of Adhesion of Coated Tire Cords to Rubber by Atmospheric Pollutants—R E HARTZ AND H T ADAMS 139 Physical Factors in Cord-to-Rubber Adhesion by a New Tire Cord Adhesion Test—G S FIELDING-RUSSELL, D W NICHOLSON, AND D L LIVINGSTON 153 Dynamic Moduli of Continuous Filament Yams Subjected to Low Frequency Excitation Superimposed on High Initial Longitudinal Strain— C F ZOROWSKI AND Z P SMITH 163 Role of Tire Reinforcements on Composite Static and Dynamic Characteristics—J J voRACHEK 180 Study of Fiber Fracture and Interfacial Chemistry Using the Scanning Electron Microscope—A G CAUSA 200 Viscoelastic Properties of Tire Cords Under Conditions of Rolling Tires— Y D KWON, R K SHARMA, AND D C PREVORSEK 239 Relative Importance of Cords and Rubber in Tire Rolling Resistance— R K SHARMA, Y D KWON, AND D C PREVORSEK Design of Radial Passenger Tires with Aramid Cord Belts—D F RYDER 263 284 Bias Passenger Tires: Effect of Construction on the Cord Deformation and Temperature Rise During Rolling—D C PREVORSEK, C W BERINGER, Y D KWON, AND R K SHARMA 298 Summary 327 Index 329 STP694-EB/Dec 1979 Introduction This special technical publication comprises the proceedings of the Symposium on Tire Reinforcement and Tire Performance jointly sponsored by ASTM Committees D13 on Textiles and F09 on Tires The symposium was so titled to stress the important technical relationship between the two aspects of the subject matter and to stimulate contributions in each area, emphasizing the connection between them This theme successfully generated the technological and scientific papers collected here The goal of the symposium to bring together contributions on the many aspects of the subject has been well reahzed by these proceedings which have covered the spectrum of tire cord reinforcements and their adhesion to the viscoelastic rubber compounds, two highly dissimilar materials which unite in the composite tire structure to produce its final, unique performance The history of the development and improvement of tire cords to their present sophistication in materials and configuration, testing their strength and dynamic properties relevant to performance in the tire, and a novel method of evaluating their adhesion to the rubber matrix are examples of the content of these proceedings which have served to further illuminate the subject The editors acknowledge the assistance of many individuals in ASTM who managed the symposium and ensured the production of this work in its final critically reviewed form We especially thank the Program Conmiittee of the symposium who were primarily responsible for its quality The committee members were F C Brenner, National Highway Traffic Safety Administration of the U.S Department of Transportation, C C McCabe, Du Pont Company, and John Hannel, Du Pont Company, who were instrumental in securing many of the papers presented, who ensured a smoothly running symposium, and who participated prominently in the review process We are grateful to all these people for their expert help R A Fleming Goodyear Rubber Company, Akron, Ohio 44316, editor D I Livingston Goodyear Rubber Company, Akron, Ohio 44316, editor Copyright® 1979 b y A S I M International www.astm.org 318 TIRE REINFORCEMENT AND TIRE PERFORMANCE FIG 22—Indication of compressive mode of failure in bias tires PREVORSEK E T A L O N BIAS PASSENGER TIRES 319 APPENDIX I Obtaining Unique Solution to the Heat Transfer Equations Heat Transfer Equations The generalized heat transfer equation (Eq 3) is pCp ^ 6f = K^^T + Gc^c + GR^R (4) where p = density, k = thermal conductivity, Cp = heat capacity, t = time, _ r = temperature, g( and G R = heat generation rates of cord and rubber, respectively, V( and VR = volume fractions of cord and rubber, and V^ = Laplacian operator Equation expresses the rate of temperature change in an infinitesimaUy small volume element as the function of material properties (p, Cp, and k)^ the local temperature gradient (7^T), and the heat generation rates (^^ and Q R ) under the assumption of constant thermal conductivity When the system is at a steady state, the right hand side of Eq is zero To obtain the solution to Eq relating to the pneumatic tires under consideration, it is necessary to have a specific form of Eq which is simple enough for the numerical solution but rigorous enough to result in a meaningful solution For the sidewaU region, we take the one-dimensional approach [see Fig 23, (a)] and Eq is written as pCp^^-K~ + ^,V, + Q^Vj, (5) 8T ^!?=^ci„a-7'a:JatX=0 ^in ^ "in 8X (6) ~K^^=h.{T-T,)atX ^O ^ 8X (7) with the boundary conditions and '^O =L T^ are heat transfer coefficient and air temperature, respectively, and the subscripts "in" and " o " refer to the inside and outside, respectively In taking this one dimensional approach, we are assuming that the temperature profile at the sidewall does not change with position in the meridional direction and circumferential direction This assumption is applicable to the portion of sidewaU where the wall thickness is fairly uniform 320 TIRE REINFORCEMENT AND TIRE PERFORMANCE outside surface inside surface thermocouple outside air inside air composite rubber x=0 (a) Sidewall Region crown zone outside air e=o composite inside air (b) Shoulder-Crown Region FIG 23—Geometry of the tire cross section For the shoulder-crown region, we take the two dimensional approach Referring to Fig 23 (6) we divide the region into three, mutually overlapping zones: inner zone, crown zone, and shoulder zone We use a polar coordinate system for the inner zone and write Eq in the form of ot r or \ or I r 6e PREVORSEK ETALON BIAS PASSENGER TIRES 321 with the boundary conditions of K^=K- (T- T^ )a.tr=o (9) — = o at = o and = d„ 00 For the crown and shoulder zones, we write Eq in the form of '^57"'^ll^'^l7*&"-e.v (.0) with the boundary conditions of —- = at x = in crown zone, and oX at X = Xmax ^ shoulder zone '^^j and C 'T' -^ — = ^co (^ ~ ^ao) at X = JCmax in crown zone (13) For the overlapping region, the boundary conditions are of the Dirichlet type (that is, temperature at the boundary point is given) and the temperature values are taken from the neighboring region The division of shoulder-crown region into three overlapping zones is for eliminating the irregular boundary lines to which the Neumann type boundary conditions (that is the heat flux at the boundary point is given) applies General Aspects of Numerical Solution of Eq Through the use of the finite approximation technique, one can obtain a unique solution to Eq if the following information is given: (a) geometrical parameters of the system, {b) thermal properties of the material, (c) values of the heat generation rates and volume fractions of cord and rubber, (d) initial conditions, (e) time, t, at which the solution is required; the steady state solution can be obtained by setting f to a reasonably large value, (J) heat transfer coefficients, and (g) inside and outside air temperature Among the above listed, (c) and (/) require additional comments In considering the composite section, a question arises as to whether it should be handled as a continuum of homogeneous composition or as a heterogeneous sys- 322 TIRE REINFORCEMENT AND TIRE PERFORMANCE tem involving distinct boundary surfaces between cord and rubber In view of the relatively fine distribution of the cords in the rubber matrix and of the complexity of numerical procedure, we took the continuum approximation The amount of cord in the composite section was measured and converted to the volume fraction data As for the heat transfer coefficient data, h^ and h^ , the values were experimentally determined by use of measured tire temperature and by trying various values of h^ and finding the ones which fit the observations consistently Determination of Temperature Profiles in the Tire Cross Section Under Rolling Conditions from the Temperature Measurements With regard to the tire failure and energy loss from tires, the tire temperature is the key variable and it is desirable to obtain the temperature profile in the tire cross section while the tire is roUing In the wheel test which simulates the tire rolling on road, one can embed thermocouples into the tire to measure the temperature But, because the insertion of thermocouples alters the heat transfer environment, it is difficult to embed many thermocouples Using the data of temperature obtained by measurements at limited number of points, we can establish the temperature profile in tire by finding the solution to Eq which matches the measured temperature This is done by the following procedure Cord and rubber specimens are subjected to the mechanical loss measurement under cyclic tension using the high strain viscoelastometer The data are collected as the function of specimen temperature and strain amplitude and are put into a polynomial expression for retrieval purpose These data provide the heat generation terms Q^ and R of Eq We consider the case in which only one thermocouple reading is used in the sidewall region or shoulder-crown region (see Fig 23) First we choose a pair of cord strain amplitude and rubber strain amplitude and Eq is numerically solved for the steady state temperature profile If the temperature obtained from this profile for the thermocouple point does not match the measured temperature, the rubber strain amplitude is varied and a new solution is obtained By this trial and error procedure one comes up with a pair of cord strain amplitude and rubber strain amplitude which make the calculated and measured temperatures match Using this procedure we obtain several pairs of the cord and rubber strain amplitudes, each of which gives the temperature at the thermocouple point which matches the observed temperature for one speed (for example, 48 km/h) under a given load Procedure is repeated for various speeds under the given load The cord strain amplitudes are then cross-plotted against the corresponding rubber strain amplitudes (see Fig 24) for the various speeds The point where these plots converge uniquely defines the point of cord and rubber strain amplitude which match the observed temperatures The temperature profile obtained with this pair of strain amplitudes is the unique solution to the Eq at each of the speeds In this procedure, we have assumed that the cord and rubber strain amplitudes are uniform in the region under consideration Effect of Radiative Heat Transfer on the Solution of the Equations In Eq 4, the radiative heat transfer term was omitted In the following, we first PREVORSEK ET AL ON BIAS PASSENGER TIRES cord strain amplitude 323 *• 30 MPH e 50 MPH • 65 MPH converging point rubber strain amplitude FIG 24—Cross plot of the temperature-matching cord and rubber strain amplitudes at various speeds to determine the unique pair of cord and rubber strain amplitudes examine the magnitude of heat transfer by radiation relative to the total (convective and radiative) heat transfer from the tire surface When the tire surface temperature is T^ and the environment temperature (air and surrounding walls) is T^, v/e determine the heat transfer coefficient h^ such that q = h^A(T,- Ta) (14) represents the total rate of heat transfer from the surface Rate of the radiative heat transfer is Qr = h,AiT,^*-T^^'') (15) with 72r = a Fy (16) where h^ = radiative heat transfer coefficient, a = Steffan-Boltzmann constant, = emissivity, Fy = view factor, and k = the Kelvin scale of temperature For a conservative consideration, we assign a value of 1.0 to E and Fy a has a value of 1.37 X 10'^^ cal/s'cm^'K* The value of ftp at the crown zone has been experimentally determined to be 1.5 X 10^ cal/s*cm^ C at 80 km/h speed Talcing the case of T^ = 80°C and Tg = 25°C for ^ = cm^, for example 324 TIRE REINFORCEMENT AND TIRE PERFORMANCE = 1.5X 10'^ ( - 25) = 8.25 X 10"^cal/s = 1.37 X 10"'^ ( " - 298")= 1.05 X lO'^cal/s Thus, the rate of radiative heat transfer is about one eighth of the total under the condition Now, we examine the magnitude of error which is incurred because of lumping the radiative transfer into the convective term If we handled the convective term and radiative term separately, value of h^ would have been 1.5 X 10 ' X 7/8 = 1.31 X 10"^ Suppose the tire surface temperature is 100°C which is 20°C higher than the temperature at which the lumped heat transfer coefficient was fixed The total heat transfer rate by the lumped calculation would be q = 1.5X 10"^ ( ) = 11.3 X 10"^ whereas the separate calculations would give = 1.31 X 10"^ ( ) + 1.37 X 10*^(373"- 298")= 11.38 X 10'^ and the error is about - 0.8 percent APPENDIX II Heat Generation by Cord under Compression Under sinusoidal straining with percent strain amplitude at room temperature, the PET cord specimen which was used in the comparative examination generated heat at a rate of 1.3 X 10* erg/cm' cycle while the rubber specimen which was tested generated heat at a rate of 2.6 X l O ' erg/cm' cycle Thus, under cyclic tension, the cord generates approximately 500 times more heat than rubber In order to determine the heat generated by rubber and cord in the rubber matrix under cyclic compression, we prepared the cylindrical blocks as shown in Fig 25 The specimen was held between two holding plates and subjected to a sinusoidal compression with an amplitude of 0.5 mm and a precompression of 0.5 mm (thus, during the cyclic compression, maximum length of the specimen was 31 mm and minimum length of the specimen was 30 mm) At room temperature, the rate of heat generation from the rubber and rubbercord composite specimens under this cyclic compression were found to be 0.713 X lO" erg/cm' cycle and 2.925 X lO" erg/cm' cycle, respectively Volume fraction of the cord in the composite was 10 percent Therefore, the ratio of heat generation rates between cord and rubber under cyclic compression is A 2.925-0.9(0.713) ^i = = 32 (5R 0.1(0.713) Comparing this ratio with the previously mentioned ratio 500 for the case of cyclic tension, it is seen that the cord contribution to heat generation relative to rubber is about 1/16 of that in the cyclic tension PREVORSEK ET AL ON BIAS PASSENGER TIRES I- »H 325 k» H direction of cyclic compression ^cy rubber D = 31 mm